Finite Group Databasebeta

← C2×#20257418 #27124271

Subgroups — C2×#20257418 #27124271

Order 12032.

8774 conjugacy classes of subgroups.

The subgroup lattice has 1420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257418C2132yesmaximal, direct product factor
2C2×#15689837C211yesmaximal, characteristic, complemented
3C2×#15689829C211yesmaximal, characteristic, complemented
4C2×#15689826C211yesmaximal, characteristic, complemented
5C2×#15689820C211yesmaximal, characteristic, complemented
6C2×#15689818C212yesmaximal, complemented
7C2×#15689793C211yesmaximal, characteristic, complemented
8C2×#15689770C212yesmaximal, complemented
9C2×#15689765C212yesmaximal, complemented
10C2×#15689762C212yesmaximal, complemented
11C2×#15689758C211yesmaximal, characteristic, complemented
12C2×#15689757C211yesmaximal, characteristic, complemented
13C2×#15689757C211yesmaximal, characteristic, complemented
14C2×#15689724C211yesmaximal, characteristic, complemented
15C2×#15689709C212yesmaximal, complemented
16C2×#15689705C212yesmaximal, complemented
17C2×#15689670C211yesmaximal, characteristic, complemented
18C2×#15689651C211yesmaximal, characteristic, complemented
19C2×#15689631C212yesmaximal, complemented
20C2×#121×D47C212yesmaximal, complemented
21C2×#15689597C211yesmaximal, characteristic, complemented
22C2×#15689595C211yesmaximal, characteristic, complemented
23C2×C4×D4×D47C211yesmaximal, characteristic, complemented
24C2×C47×#540C211yesmaximal, characteristic, complemented
25C22×#10625350C2212yescomplemented
26C22×#10625352C2212yescomplemented
27C23×D188C2211yescharacteristic
28C22×D4×D47C2211yescharacteristic
29C22×D4×D47C2211yescharacteristic
30C22×D4×D47C2212yescomplemented
31C22×D4×D47C2212yescomplemented
32C22×D4×D47C2212yescomplemented
33C23×C4×D47C2212yescomplemented
34#15689837C22116yescomplemented
35#15689829C22116yescomplemented
36#15689826C22116yescomplemented
37#15689820C22116yescomplemented
38#15689818C22132yescomplemented
39#15689793C22116yescomplemented
40#15689770C22132yescomplemented
41#15689765C22132yescomplemented
42#15689762C22132yescomplemented
43#15689758C22116yescomplemented
44#15689757C22116yescomplemented
45#15689757C22116yescomplemented
46#15689724C22116yescomplemented
47#15689709C22132yescomplemented
48#15689705C22132yescomplemented
49#15689670C22116yescomplemented
50C2×#13094023C2211yescharacteristic, complemented
51C2×#13094020C2211yescharacteristic, complemented
52C2×#13094020C2211yescharacteristic, complemented
53#15689651C22116yescomplemented
54C2×#13094019C2211yescharacteristic, complemented
55C2×#13094019C2212yescomplemented
56C2×#13094017C2211yescharacteristic, complemented
57C2×#13094017C2212yescomplemented
58C2×#13094015C2211yescharacteristic, complemented
59C2×#13094014C2211yescharacteristic, complemented
60C2×#13094011C2212yescomplemented
61C2×#13094010C2211yescharacteristic, complemented
62C2×#13094010C2212yescomplemented
63C2×#13094010C2212yescomplemented
64#15689631C22132yescomplemented
65C2×#13094009C2212yescomplemented
66C2×#13094009C2211yescharacteristic, complemented
67C2×#13094007C2212yescomplemented
68C2×#13094006C2211yescharacteristic, complemented
69C2×#13094006C2212yescomplemented
70C2×#13094005C2212yescomplemented
71C2×#13094004C2212yescomplemented
72C2×#13094002C2212yescomplemented
73C2×#13094002C2212yescomplemented
74C2×#13094002C2211yescharacteristic, complemented
75C2×#13093999C2211yescharacteristic, complemented
76C2×#13093999C2211yescharacteristic, complemented
77C2×#13093999C2212yescomplemented
78C2×#13093998C2212yescomplemented
79C2×#13093997C2211yescharacteristic
80C2×#13093997C2212yescomplemented
81C2×#13093997C2212yescomplemented
82C2×#13093997C2212yescomplemented
83C2×#13093997C2212yescomplemented
84C2×#13093996C2212yescomplemented
85C2×#13093996C2212yescomplemented
86C2×#13093996C2212yescomplemented
87C2×#13093995C2212yescomplemented
88C2×#13093995C2211yescharacteristic, complemented
89C2×#13093995C2211yescharacteristic, complemented
90C2×#13093995C2212yescomplemented
91C2×#13093995C2212yescomplemented
92#121×D47C22132yescomplemented
93C2×#13093994C2212yescomplemented
94C2×#13093994C2212yescomplemented
95C2×#13093992C2212yescomplemented
96C2×#13093992C2212yescomplemented
97C2×#13093992C2212yescomplemented
98C2×#13093992C2212yescomplemented
99#15689597C22116yescomplemented
100#15689595C22116yescomplemented
101C2×C4×Dic94C2211yescharacteristic, complemented
102C2×C4×D188C2211yescharacteristic
103C2×C4×D188C2211yescharacteristic
104C2×C4×D188C2211yescharacteristic, complemented
105C2×C4×D188C2211yescharacteristic, complemented
106C2×C4×D188C2211yescharacteristic, complemented
107C2×D4×Dic47C2211yescharacteristic, complemented
108C2×D4×Dic47C2211yescharacteristic, complemented
109C2×#13093986C2211yescharacteristic
110C2×#13093986C2211yescharacteristic
111C2×#13093986C2212yescomplemented
112C2×#13093986C2212yescomplemented
113C2×#13093986C2212yescomplemented
114C2×C4×C22⋊D47C2212yescomplemented
115C2×C4×C22⋊D47C2211yescharacteristic, complemented
116C2×C4×C22⋊D47C2211yescharacteristic, complemented
117C2×C4×C22⋊D47C2212yescomplemented
118C2×C4×C22⋊D47C2212yescomplemented
119C2×(C22⋊D47)⋊C4C2212yescomplemented
120C2×(C22⋊D47)⋊C4C2212yescomplemented
121C2×(C22⋊D47)⋊C4C2212yescomplemented
122C4×D4×D47C22116yescomplemented
123C2×#13093983C2211yescharacteristic, complemented
124C2×#13093982C2211yescharacteristic, complemented
125C2×#13093981C2211yescharacteristic, complemented
126C2×#13093980C2212yescomplemented
127C2×C4⋊C4×D47C2211yescharacteristic, complemented
128C2×C4⋊C4×D47C2212yescomplemented
129C22×(C2×D47)⋊C4C2212yescomplemented
130C2×C22⋊C4×D47C2212yescomplemented
131C2×C22⋊C4×D47C2212yescomplemented
132C2×C22⋊C4×D47C2212yescomplemented
133C2×C22⋊C4×D47C2212yescomplemented
134C2×C42×D47C2211yescharacteristic, complemented
135C47×#540C22116yescomplemented
136C2×#127×C47C2211yescharacteristic, complemented
137C2×#125×C47C2211yescharacteristic, complemented
138C2×#123×C47C2212yescomplemented
139C2×#123×C47C2212yescomplemented
140C2×#121×C47C2211yescharacteristic, complemented
141C2×#121×C47C2211yescharacteristic, complemented
142C2×#121×C47C2212yescomplemented
143C2×#121×C47C2212yescomplemented
144C2×C4×D4×C47C2211yescharacteristic, complemented
145C2×C4×D4×C47C2211yescharacteristic, complemented
146C2×#117×C47C2211yescharacteristic, complemented
147C24×D47C2312yes—
148C24×D47C2312yes—
149C24×D47C2312yes—
150C2×#10625350—48no—
151C2×#10625350C23116yescomplemented
152C2×#10625352—48no—
153C2×#10625352C23116yescomplemented
154C22×Dic94C2311yescharacteristic
155C22×Dic94C2312yes—
156C22×D188—28no—
157C22×D188C2318yes—
158C22×D188C2312yes—
159C22×D188C2312yes—
160C22×D188C2311yescharacteristic
161C22×D188C2311yescharacteristic
162C22×D188C2312yes—
163C22×D188C2311yescharacteristic
164C22×C22⋊D47C2312yes—
165C22×C22⋊D47C2312yes—
166C22×C22⋊D47C2312yes—
167C22×C22⋊D47C2311yescharacteristic
168C22×C22⋊D47C2311yescharacteristic
169C22×C22⋊D47C2312yes—
170C22×C22⋊D47C2312yes—
171C22×C22⋊D47C2312yes—
172C22×C22⋊D47C2312yes—
173C22×C22⋊D47C2312yes—
174C2×D4×D47—28no—
175C2×D4×D47—28no—
176C2×D4×D47—48no—
177C2×D4×D47—48no—
178C2×D4×D47—48no—
179C2×D4×D47C2318yes—
180C2×D4×D47C2318yes—
181C2×D4×D47C23116yescomplemented
182C2×D4×D47C23116yescomplemented
183C2×D4×D47C23116yescomplemented
184C23×Dic47C2312yes—
185C23×Dic47C2312yes—
186C22×C4×D47—48no—
187C22×C4×D47C2311yescharacteristic
188C22×C4×D47C2311yescharacteristic
189C22×C4×D47C2311yescharacteristic
190C22×C4×D47C2312yes—
191C22×C4×D47C2311yescharacteristic
192C22×C4×D47C2312yes—
193C22×C4×D47C2312yes—
194C22×C4×D47C2312yes—
195C22×C4×D47C2312yes—
196C22×C4×D47C2312yes—
197C22×C4×D47C2312yes—
198C22×C4×D47C23116yescomplemented
199#13094023C2318yescomplemented
200#13094020C2318yescomplemented
201#13094020C2318yescomplemented
202#13094019C23116yescomplemented
203#13094019C2318yescomplemented
204#13094017C23116yescomplemented
205#13094017C2318yescomplemented
206#13094015C2318yescomplemented
207#13094014C2318yescomplemented
208#13094011C23116yescomplemented
209#13094010C2318yescomplemented
210#13094010C23116yescomplemented
211#13094010C23116yescomplemented
212#13094009C23116yescomplemented
213#13094009C2318yescomplemented
214#13094007C23116yescomplemented
215#13094006C2318yescomplemented
216#13094006C23116yescomplemented
217#13094005C23116yescomplemented
218#13094004C23116yescomplemented
219#13094002C23116yescomplemented
220#13094002C23116yescomplemented
221#13094002C2318yescomplemented
222#13093999C2318yescomplemented
223#13093999C2318yescomplemented
224#13093999C23116yescomplemented
225#13093998C23116yescomplemented
226#13093997C2318yes—
227#13093997C23116yescomplemented
228#13093997C23116yescomplemented
229#13093997C23116yescomplemented
230#13093997C23116yescomplemented
231#13093996C23116yescomplemented
232#13093996C23116yescomplemented
233#13093996C23116yescomplemented
234#13093995C23116yescomplemented
235#13093995C2318yescomplemented
236#13093995C2318yescomplemented
237#13093995C23116yescomplemented
238#13093995C23116yescomplemented
239#13093994C23116yescomplemented
240#13093994C23116yescomplemented
241#13093992C23116yescomplemented
242#13093992C23116yescomplemented
243#13093992C23116yescomplemented
244#13093992C23116yescomplemented
245C4×Dic94C2318yescomplemented
246C4×D188C2318yes—
247C4×D188C2318yes—
248C4×D188C2318yescomplemented
249C4×D188C2318yescomplemented
250C4×D188C2318yescomplemented
251D4×Dic47C2318yescomplemented
252D4×Dic47C2318yescomplemented
253#13093986C2318yes—
254#13093986C2318yes—
255#13093986C23116yescomplemented
256#13093986C23116yescomplemented
257#13093986C23116yescomplemented
258C4×C22⋊D47C2318yescomplemented
259C4×C22⋊D47C2318yescomplemented
260C4×C22⋊D47C23116yescomplemented
261C4×C22⋊D47C23116yescomplemented
262C4×C22⋊D47C23116yescomplemented
263(C22⋊D47)⋊C4C23116yescomplemented
264(C22⋊D47)⋊C4C23116yescomplemented
265(C22⋊D47)⋊C4C23116yescomplemented
266#13093983C2318yescomplemented
267#13093982C2318yescomplemented
268#13093981C2318yescomplemented
269#13093980C23116yescomplemented
270C2×C4⋊Dic47C2311yescharacteristic
271C2×C4⋊Dic47C2312yes—
272C2×C4⋊Dic47C2311yescharacteristic
273C2×C4⋊Dic47C2311yescharacteristic
274C2×C4⋊Dic47C2311yescharacteristic
275C2×Dic47⋊C4C2311yescharacteristic
276C2×Dic47⋊C4C2312yes—
277C2×Dic47⋊C4C2312yes—
278C2×Dic47⋊C4C2311yescharacteristic
279C2×Dic47⋊C4C2311yescharacteristic
280C2×Dic47⋊C4C2311yescharacteristic
281C2×Dic47⋊C4C2312yes—
282C2×Dic47⋊C4C2311yescharacteristic
283C2×Dic47⋊C4C2311yescharacteristic
284C4⋊C4×D47C23116yescomplemented
285C4⋊C4×D47C2318yescomplemented
286C2×C22⋊Dic47C2312yes—
287C2×C22⋊Dic47C2312yes—
288C2×C22⋊Dic47C2312yes—
289C2×C22⋊Dic47C2312yes—
290C2×C22⋊Dic47C2311yescharacteristic
291C2×C22⋊Dic47C2311yescharacteristic
292C2×C22⋊Dic47C2312yes—
293C2×(C2×D47)⋊C4C2312yes—
294C2×(C2×D47)⋊C4C2311yescharacteristic
295C2×(C2×D47)⋊C4C2312yes—
296C2×(C2×D47)⋊C4C2312yes—
297C2×(C2×D47)⋊C4C2312yes—
298C2×(C2×D47)⋊C4C2312yes—
299C2×(C2×D47)⋊C4C2312yes—
300C2×(C2×D47)⋊C4C2311yescharacteristic
301C2×(C2×D47)⋊C4C2312yes—
302C2×(C2×D47)⋊C4C2311yescharacteristic
303C2×(C2×D47)⋊C4C2312yes—
304C2×(C2×D47)⋊C4C2311yescharacteristic
305C2×(C2×D47)⋊C4C2311yescharacteristic
306C2×(C2×D47)⋊C4C2312yes—
307C2×(C2×D47)⋊C4C2311yescharacteristic
308C2×(C2×D47)⋊C4C23116yescomplemented
309C22⋊C4×D47C23116yescomplemented
310C22⋊C4×D47C23116yescomplemented
311C22⋊C4×D47C23116yescomplemented
312C22⋊C4×D47C23116yescomplemented
313C2×C4×Dic47C2311yescharacteristic
314C2×C4×Dic47C2311yescharacteristic
315C2×C4×Dic47C2311yescharacteristic
316C2×C4×Dic47C2312yes—
317C2×C4×Dic47C2312yes—
318C2×C4×Dic47C2311yescharacteristic
319C42×D47C2318yescomplemented
320C22×D4×C47C2311yescharacteristic
321C22×D4×C47C2311yescharacteristic
322C22×D4×C47C2312yes—
323C22×D4×C47C2312yes—
324C22×D4×C47C2312yes—
325C22×D4×C47C2312yes—
326C23×C4×C47C2311yescharacteristic
327C23×C4×C47C2312yes—
328C23×C4×C47C2312yes—
329#127×C47C2318yescomplemented
330#125×C47C2318yescomplemented
331#123×C47C23116yescomplemented
332#123×C47C23116yescomplemented
333#121×C47C2318yescomplemented
334#121×C47C2318yescomplemented
335#121×C47C23116yescomplemented
336#121×C47C23116yescomplemented
337C4×D4×C47C2318yescomplemented
338C4×D4×C47C2318yescomplemented
339#117×C47C2318yescomplemented
340C2×C4⋊C4×C47C2311yescharacteristic
341C2×C4⋊C4×C47C2311yescharacteristic
342C2×C4⋊C4×C47C2311yescharacteristic
343C2×C4⋊C4×C47C2311yescharacteristic
344C2×C4⋊C4×C47C2312yes—
345C2×C4⋊C4×C47C2312yes—
346C2×C22⋊C4×C47C2311yescharacteristic
347C2×C22⋊C4×C47C2311yescharacteristic
348C2×C22⋊C4×C47C2312yes—
349C2×C22⋊C4×C47C2312yes—
350C2×C22⋊C4×C47C2312yes—
351C2×C22⋊C4×C47C2312yes—
352C2×C42×C47C2311yescharacteristic
353C2×C42×C47C2311yescharacteristic
354C24×C47C2411yescharacteristic
355C24×C47C2412yes—
356C24×C47C2412yes—
357C23×D47—28no—
358C23×D47—28no—
359C23×D47—28no—
360C23×D47—28no—
361C23×D47—44no—
362C23×D47—44no—
363C23×D47—44no—
364C23×D47—44no—
365C23×D47—44no—
366C23×D47C2411yescharacteristic
367C23×D47C2412yes—
368C23×D47C2418yes—
369C23×D47C2412yes—
370C23×D47C2411yescharacteristic
371C23×D47C2418yes—
372C23×D47C2418yes—
373C2×D4×C47—24no—
374C2×D4×C47—24no—
375C2×D4×C47—44no—
376C2×D4×C47—44no—
377C2×D4×C47—44no—
378C2×D4×C47—44no—
379C2×D4×C47C2414yes—
380C2×D4×C47C2414yes—
381C2×D4×C47C2418yes—
382C2×D4×C47C2418yes—
383C2×D4×C47C2418yes—
384C2×D4×C47C2418yes—
385C22×C4×C47—24no—
386C22×C4×C47—44no—
387C22×C4×C47—44no—
388C22×C4×C47C2411yescharacteristic
389C22×C4×C47C2411yescharacteristic
390C22×C4×C47C2411yescharacteristic
391C22×C4×C47C2411yescharacteristic
392C22×C4×C47C2411yescharacteristic
393C22×C4×C47C2412yes—
394C22×C4×C47C2412yes—
395C22×C4×C47C2414yes—
396C22×C4×C47C2418yes—
397C22×C4×C47C2418yes—
398C22×C4×C47C2411yescharacteristic
399C2×C22⋊D47—28no—
400C2×C22⋊D47—28no—
401C2×C22⋊D47—24no—
402C2×C22⋊D47—28no—
403C2×C22⋊D47—24no—
404C2×C22⋊D47—28no—
405C2×C22⋊D47—44no—
406C2×C22⋊D47—44no—
407C2×C22⋊D47—44no—
408C2×C22⋊D47—44no—
409C2×C22⋊D47C2418yes—
410C2×C22⋊D47C2418yes—
411C2×C22⋊D47C2418yes—
412C2×C22⋊D47C2414yes—
413C2×C22⋊D47C2414yes—
414C2×C22⋊D47C2418yes—
415C2×C22⋊D47C2418yes—
416C2×C22⋊D47C2418yes—
417C2×C22⋊D47C2418yes—
418C2×C22⋊D47C2418yes—
419C22×Dic47—28no—
420C22×Dic47—44no—
421C22×Dic47C2411yescharacteristic
422C22×Dic47C2411yescharacteristic
423C22×Dic47C2412yes—
424C22×Dic47C2411yescharacteristic
425C22×Dic47C2411yescharacteristic
426C22×Dic47C2412yes—
427C22×Dic47C2411yescharacteristic
428C22×Dic47C2418yes—
429C22×Dic47C2418yes—
430C22×Dic47C2411yescharacteristic
431#10625352—432no—
432D4×D47—232no—
433D4×D47—232no—
434D4×D47—432no—
435D4×D47—432no—
436D4×D47—432no—
437#10625350—432no—
438C2×D188—28no—
439C2×D188—24no—
440C2×D188—28no—
441C2×D188—24no—
442C2×D188—232no—
443C2×D188—44no—
444C2×D188#4118yescomplemented
445C2×D188C2418yes—
446C2×D188C2418yes—
447C2×D188C2414yes—
448C2×D188C2414yes—
449C2×D188C2418yes—
450C2×D188C2414yes—
451C2×C4×D47—24no—
452C2×C4×D47—24no—
453C2×C4×D47—24no—
454C2×C4×D47—24no—
455C2×C4×D47—28no—
456C2×C4×D47—432no—
457C2×C4×D47—44no—
458C2×C4×D47—44no—
459C2×C4×D47—44no—
460C2×C4×D47—44no—
461C2×C4×D47—44no—
462C2×C4×D47—44no—
463C2×C4×D47C2414yes—
464C2×C4×D47C2414yes—
465C2×C4×D47C2414yes—
466C2×C4×D47C2418yes—
467C2×C4×D47C2414yes—
468C2×C4×D47C2418yes—
469C2×C4×D47C2418yes—
470C2×C4×D47C2418yes—
471C2×C4×D47C2418yes—
472C2×C4×D47C2418yes—
473C2×C4×D47C2418yes—
474C2×Dic94—24no—
475C2×Dic94—44no—
476C2×Dic94C2414yes—
477C2×Dic94C2418yes—
478C4⋊C4×C47C2414yes—
479C4⋊C4×C47C2414yes—
480C4⋊C4×C47C2414yes—
481C4⋊C4×C47C2414yes—
482C4⋊C4×C47C2418yes—
483C4⋊C4×C47C2418yes—
484C22⋊C4×C47C2414yes—
485C22⋊C4×C47C2414yes—
486C22⋊C4×C47C2418yes—
487C22⋊C4×C47C2418yes—
488C22⋊C4×C47C2418yes—
489C22⋊C4×C47C2418yes—
490C42×C47C2414yes—
491C42×C47C2414yes—
492C22⋊Dic47C2418yes—
493C22⋊Dic47C2418yes—
494C22⋊Dic47C2418yes—
495C22⋊Dic47C2418yes—
496C22⋊Dic47C2414yes—
497C22⋊Dic47C2414yes—
498C22⋊Dic47C2418yes—
499(C2×D47)⋊C4C2418yes—
500(C2×D47)⋊C4C2414yes—
501(C2×D47)⋊C4C2418yes—
502(C2×D47)⋊C4C2418yes—
503(C2×D47)⋊C4C2418yes—
504(C2×D47)⋊C4C2418yes—
505(C2×D47)⋊C4C2418yes—
506(C2×D47)⋊C4C2414yes—
507(C2×D47)⋊C4C2418yes—
508(C2×D47)⋊C4C2414yes—
509(C2×D47)⋊C4C2418yes—
510(C2×D47)⋊C4C2414yes—
511(C2×D47)⋊C4C2414yes—
512(C2×D47)⋊C4C2418yes—
513(C2×D47)⋊C4C2414yes—
514C4⋊Dic47C2414yes—
515C4⋊Dic47C2418yes—
516C4⋊Dic47C2414yes—
517C4⋊Dic47C2414yes—
518C4⋊Dic47C2414yes—
519Dic47⋊C4C2414yes—
520Dic47⋊C4C2418yes—
521Dic47⋊C4C2418yes—
522Dic47⋊C4C2414yes—
523Dic47⋊C4C2414yes—
524Dic47⋊C4C2414yes—
525Dic47⋊C4C2418yes—
526Dic47⋊C4C2414yes—
527Dic47⋊C4C2414yes—
528C4×Dic47C2414yes—
529C4×Dic47C2414yes—
530C4×Dic47C2414yes—
531C4×Dic47C2418yes—
532C4×Dic47C2418yes—
533C4×Dic47C2414yes—
534C23×C47—24no—
535C23×C47—24no—
536C23×C47—22no—
537C23×C47—24no—
538C23×C47—24no—
539C23×C47—24no—
540C23×C47—22no—
541C23×C47—22no—
542C23×C47—24no—
543C23×C47C2512yes—
544C23×C47C2514yes—
545C23×C47C2514yes—
546C23×C47C2511yescharacteristic
547C22×D47—22no—
548C22×D47—22no—
549C22×D47—24no—
550C22×D47—24no—
551C22×D47—22no—
552C22×D47—24no—
553C22×D47—24no—
554C22×D47—24no—
555C22×D47—22no—
556C22×D47—22no—
557C22×D47—216no—
558C22×D47—216no—
559C22×D47—216no—
560C22×D47—216no—
561C22×D47—48no—
562C22×D47—432no—
563C22×D47—48no—
564C22×D47—48no—
565C22×D47—48no—
566C22×D47—48no—
567C22×D47—816no—
568C22×D47—816no—
569C22×D47C2×#4118yes—
570C22×D47H(5,𝔽2)14yes—
571C22×D47C2512yes—
572C22×D47C2514yes—
573C22×D47C2514yes—
574C22×D47C2512yes—
575D4×C47—28no—
576D4×C47—28no—
577D4×C47—48no—
578D4×C47—48no—
579D4×C47—48no—
580D4×C47—48no—
581C2×C4×C47—22no—
582C2×C4×C47—22no—
583C2×C4×C47—24no—
584C2×C4×C47—22no—
585C2×C4×C47—22no—
586C2×C4×C47—24no—
587C2×C4×C47—22no—
588C2×C4×C47—28no—
589C2×C4×C47—48no—
590C2×C4×C47—48no—
591C2×C4×C47C2×#4114yes—
592C2×C4×C47C2512yes—
593C2×C4×C47C2512yes—
594C2×C4×C47C2512yes—
595C2×C4×C47C2514yes—
596C2×C4×C47C2512yes—
597C2×C4×C47C2514yes—
598C2×C4×C47C2512yes—
599C2×C4×C47C2512yes—
600C22⋊D47—216no—
601C22⋊D47—216no—
602C22⋊D47—216no—
603C22⋊D47—28no—
604C22⋊D47—28no—
605C22⋊D47—216no—
606C22⋊D47—48no—
607C22⋊D47—48no—
608C22⋊D47—48no—
609C22⋊D47—48no—
610C2×Dic47—22no—
611C2×Dic47—22no—
612C2×Dic47—22no—
613C2×Dic47—22no—
614C2×Dic47—24no—
615C2×Dic47—24no—
616C2×Dic47—22no—
617C2×Dic47—216no—
618C2×Dic47—48no—
619C2×Dic47H(5,𝔽2)14yes—
620C2×Dic47C2512yes—
621C2×Dic47C2512yes—
622C2×Dic47C2512yes—
623C2×Dic47C2514yes—
624C2×Dic47C2512yes—
625C2×Dic47C2512yes—
626C2×Dic47C2514yes—
627C2×Dic47C2512yes—
628D188—216no—
629D188—216no—
630D188—28no—
631D188—28no—
632D188—48no—
633D188C2×#41116yescomplemented
634C4×D47—28no—
635C4×D47—28no—
636C4×D47—28no—
637C4×D47—28no—
638C4×D47—216no—
639C4×D47—48no—
640C4×D47—48no—
641C4×D47—48no—
642C4×D47—48no—
643C4×D47—48no—
644C4×D47—48no—
645Dic94—28no—
646Dic94—48no—
647C2×#3519—471nomaximal, Sylow
648C22×C47—24no—
649C22×C47—24no—
650C22×C47—22no—
651C22×C47—24no—
652C22×C47—24no—
653C22×C47—24no—
654C22×C47—22no—
655C22×C47—22no—
656C22×C47—24no—
657C22×C47—48no—
658C22×C47—44no—
659C22×C47—48no—
660C22×C47C22×#4112yes—
661C22×C47C2×H(5,𝔽2)12yes—
662C22×C47C2×H(5,𝔽2)12yes—
663C22×C47C2611yescharacteristic
664C2×D47—22no—
665C2×D47—22no—
666C2×D47—24no—
667C2×D47—24no—
668C2×D47—28no—
669C2×D47—216no—
670C2×D47—22no—
671C2×D47—24no—
672C2×D47—24no—
673C2×D47—24no—
674C2×D47—22no—
675C2×D47—22no—
676C2×D47—432no—
677C2×D47—48no—
678C2×D47—44no—
679C2×D47—816no—
680C2×D47—816no—
681C2×D47C22×#4118yes—
682C2×D47C2×H(5,𝔽2)14yes—
683C4×C47—22no—
684C4×C47—22no—
685C4×C47—24no—
686C4×C47—22no—
687C4×C47—22no—
688C4×C47—24no—
689C4×C47—22no—
690C4×C47C22×#4114yes—
691Dic47—22no—
692Dic47—22no—
693Dic47—22no—
694Dic47—22no—
695Dic47—24no—
696Dic47—24no—
697Dic47—22no—
698Dic47C2×H(5,𝔽2)14yes—
699#3519—4732no—
700C2×#555—471no—
701C2×#554—471no—
702C2×#553—471no—
703C2×#553—472no—
704C2×#553—471no—
705C2×#550—471no—
706C2×#546—472no—
707C2×#546—472no—
708C2×#546—472no—
709C2×D42—471no—
710C2×D42—471no—
711C2×D42—471no—
712C2×#540—471no—
713C2×#540D4711yescharacteristic, complemented
714C2×#538—472no—
715C2×#538—472no—
716C2×#532—471no—
717C2×#529—471no—
718C2×#525—472no—
719C22×#121—472no—
720C2×#518—471no—
721C2×#518—471no—
722C22×C4×D4—471no—
723C2×C47—44no—
724C2×C47—42no—
725C2×C47—44no—
726C2×C47#351914yescomplemented
727C2×C47C23×#4111yescharacteristic
728C2×C47C22×H(5,𝔽2)11yescharacteristic
729C2×C47C22×H(5,𝔽2)11yescharacteristic
730D47—24no—
731D47—28no—
732D47—44no—
733D47—42no—
734C22×#41—472no—
735C22×#41—472no—
736C23×D4—471no—
737C23×D4—471no—
738C23×D4—472no—
739C23×D4—472no—
740C23×D4—472no—
741C23×D4—471no—
742C24×C4—472no—
743#555—4716no—
744#554—4716no—
745#553—4716no—
746#553—4732no—
747#553—4716no—
748#550—4716no—
749#546—4732no—
750#546—4732no—
751#546—4732no—
752D42—4716no—
753D42—4716no—
754D42—4716no—
755#540—4716no—
756#540C2×D47116yescomplemented
757#538—4732no—
758#538—4732no—
759#532—4716no—
760C2×C4⋊Q8—471no—
761C2×#127—471no—
762C2×#127—471no—
763C2×#127C2×D4711yescharacteristic, complemented
764#529—4716no—
765C2×#126—471no—
766C2×#126—472no—
767C2×#126—471no—
768C2×#126—472no—
769C2×#125—471no—
770C2×#125—471no—
771C2×#125C2×D4711yescharacteristic, complemented
772C2×#124—472no—
773C2×#124—471no—
774C2×#124—472no—
775C2×#124—472no—
776#525—4732no—
777C2×#123—472no—
778C2×#123—472no—
779C2×#123—471no—
780C2×#123—472no—
781C2×#123—471no—
782C2×#123—472no—
783C2×#123C2×D4712yescomplemented
784C2×#123C2×D4712yescomplemented
785C2×C22⋊Q8—471no—
786C2×C22⋊Q8—472no—
787C2×C22⋊Q8—472no—
788C2×C22⋊Q8—472no—
789C2×#121—472no—
790C2×#121—472no—
791C2×#121—472no—
792C2×#121—471no—
793C2×#121—472no—
794C2×#121—472no—
795C2×#121—472no—
796C2×#121—471no—
797C2×#121—472no—
798C2×#121—4732no—
799C2×#121—472no—
800C2×#121—471no—
801C2×#121—471no—
802C2×#121—471no—
803C2×#121—472no—
804C2×#121—472no—
805C2×#121—472no—
806C2×#121—472no—
807C2×#121C2×D4712yescomplemented
808C2×#121C2×D4711yescharacteristic, complemented
809C2×#121C2×D4711yescharacteristic, complemented
810C2×#121C2×D4712yescomplemented
811C2×#120—472no—
812C2×#120—472no—
813C2×#120—472no—
814C2×#120—472no—
815C2×#120—472no—
816C2×#120—472no—
817#518—4716no—
818#518—4716no—
819C2×C4×Q8—471no—
820C2×C4×D4—471no—
821C2×C4×D4—471no—
822C2×C4×D4—472no—
823C2×C4×D4—472no—
824C2×C4×D4—471no—
825C2×C4×D4—471no—
826C2×C4×D4—472no—
827C2×C4×D4—4716no—
828C2×C4×D4—471no—
829C2×C4×D4—472no—
830C2×C4×D4—471no—
831C2×C4×D4—472no—
832C2×C4×D4—472no—
833C2×C4×D4—472no—
834C2×C4×D4—472no—
835C2×C4×D4—472no—
836C2×C4×D4—471no—
837C2×C4×D4—471no—
838C2×C4×D4—471no—
839C2×C4×D4—471no—
840C2×C4×D4—471no—
841C2×C4×D4C2×D4711yescharacteristic, complemented
842C2×C4×D4C2×D4711yescharacteristic, complemented
843C2×#117—471no—
844C2×#117—471no—
845C2×#117—472no—
846C2×#117—471no—
847C2×#117C2×D4711yescharacteristic, complemented
848C22×C4⋊C4—471no—
849C22×C4⋊C4—472no—
850C22×C22⋊C4—472no—
851C22×C22⋊C4—472no—
852C22×C22⋊C4—472no—
853C22×C22⋊C4—472no—
854C22×C22⋊C4—472no—
855C22×C42—471no—
856C47C2×#351911yescharacteristic, complemented, Sylow
857C25—472no—
858C25—472no—
859C25—472no—
860C2×#41—4716no—
861C2×#41—4716no—
862C2×#41—1888no—
863C2×#41—1888no—
864C22×Q8—471no—
865C22×Q8—472no—
866C22×D4—472no—
867C22×D4—472no—
868C22×D4—472no—
869C22×D4—471no—
870C22×D4—471no—
871C22×D4—472no—
872C22×D4—472no—
873C22×D4—472no—
874C22×D4—472no—
875C22×D4—472no—
876C22×D4—478no—
877C22×D4—478no—
878C22×D4—4716no—
879C22×D4—4716no—
880C22×D4—4716no—
881C22×D4—471no—
882C22×D4—472no—
883C22×D4—471no—
884C22×D4—472no—
885C22×D4—471no—
886C22×D4—478no—
887C22×D4—472no—
888C22×D4—948no—
889C22×D4—948no—
890C22×D4—948no—
891C22×D4—1888no—
892C22×D4—1888no—
893C22×D4—1888no—
894C22×D4C22×D4711yescharacteristic
895C22×D4C22×D4711yescharacteristic
896C22×D4C22×D4712yes—
897C22×D4C22×D4712yes—
898C22×D4C22×D4712yes—
899C22×D4C22×D4712yes—
900C23×C4—472no—
901C23×C4—472no—
902C23×C4—471no—
903C23×C4—471no—
904C23×C4—472no—
905C23×C4—471no—
906C23×C4—471no—
907C23×C4—472no—
908C23×C4—472no—
909C23×C4—472no—
910C23×C4—472no—
911C23×C4—472no—
912C23×C4—472no—
913C23×C4—4716no—
914C23×C4—1888no—
915C23×C4C22×D4711yescharacteristic
916C23×C4C22×D4712yes—
917C23×C4C22×D4712yes—
918C4⋊Q8—478no—
919#127—478no—
920#127—478no—
921#127C22×D4718yescomplemented
922#126—478no—
923#126—4716no—
924#126—478no—
925#126—4716no—
926#125—478no—
927#125—478no—
928#125C22×D4718yescomplemented
929#124—4716no—
930#124—478no—
931#124—4716no—
932#124—4716no—
933#123—4716no—
934#123—4716no—
935#123—478no—
936#123—4716no—
937#123—478no—
938#123—4716no—
939#123C22×D47116yescomplemented
940#123C22×D47116yescomplemented
941C22⋊Q8—478no—
942C22⋊Q8—4716no—
943C22⋊Q8—4716no—
944C22⋊Q8—4716no—
945#121—4716no—
946#121—4716no—
947#121—4716no—
948#121—478no—
949#121—4716no—
950#121—4716no—
951#121—4716no—
952#121—478no—
953#121—4716no—
954#121—4716no—
955#121—478no—
956#121—478no—
957#121—478no—
958#121—4716no—
959#121—4716no—
960#121—4716no—
961#121—4716no—
962#121C22×D47116yescomplemented
963#121C22×D4718yescomplemented
964#121C22×D4718yescomplemented
965#121C22×D47116yescomplemented
966#120—4716no—
967#120—4716no—
968#120—4716no—
969#120—4716no—
970#120—4716no—
971#120—4716no—
972C4×Q8—478no—
973C4×D4—478no—
974C4×D4—478no—
975C4×D4—4716no—
976C4×D4—4716no—
977C4×D4—478no—
978C4×D4—478no—
979C4×D4—4716no—
980C4×D4—478no—
981C4×D4—4716no—
982C4×D4—478no—
983C4×D4—4716no—
984C4×D4—4716no—
985C4×D4—4716no—
986C4×D4—4716no—
987C4×D4—4716no—
988C4×D4—478no—
989C4×D4—478no—
990C4×D4—478no—
991C4×D4—478no—
992C4×D4—478no—
993C4×D4C22×D4718yescomplemented
994C4×D4C22×D4718yescomplemented
995#117—478no—
996#117—478no—
997#117—4716no—
998#117—478no—
999#117C22×D4718yescomplemented
1000C2×C4⋊C4—471no—
1001C2×C4⋊C4—471no—
1002C2×C4⋊C4—472no—
1003C2×C4⋊C4—472no—
1004C2×C4⋊C4—472no—
1005C2×C4⋊C4—471no—
1006C2×C4⋊C4—471no—
1007C2×C4⋊C4—471no—
1008C2×C4⋊C4—471no—
1009C2×C4⋊C4—471no—
1010C2×C4⋊C4—471no—
1011C2×C4⋊C4—472no—
1012C2×C4⋊C4—471no—
1013C2×C4⋊C4—471no—
1014C2×C4⋊C4—478no—
1015C2×C4⋊C4—4716no—
1016C2×C4⋊C4C22×D4711yescharacteristic
1017C2×C4⋊C4C22×D4712yes—
1018C2×C4⋊C4C22×D4711yescharacteristic
1019C2×C4⋊C4C22×D4711yescharacteristic
1020C2×C4⋊C4C22×D4711yescharacteristic
1021C2×C4⋊C4C22×D4712yes—
1022C2×C22⋊C4—472no—
1023C2×C22⋊C4—472no—
1024C2×C22⋊C4—472no—
1025C2×C22⋊C4—472no—
1026C2×C22⋊C4—471no—
1027C2×C22⋊C4—471no—
1028C2×C22⋊C4—472no—
1029C2×C22⋊C4—472no—
1030C2×C22⋊C4—471no—
1031C2×C22⋊C4—472no—
1032C2×C22⋊C4—471no—
1033C2×C22⋊C4—472no—
1034C2×C22⋊C4—472no—
1035C2×C22⋊C4—472no—
1036C2×C22⋊C4—472no—
1037C2×C22⋊C4—472no—
1038C2×C22⋊C4—4716no—
1039C2×C22⋊C4—471no—
1040C2×C22⋊C4—471no—
1041C2×C22⋊C4—471no—
1042C2×C22⋊C4—471no—
1043C2×C22⋊C4—472no—
1044C2×C22⋊C4—472no—
1045C2×C22⋊C4—4716no—
1046C2×C22⋊C4—4716no—
1047C2×C22⋊C4—4716no—
1048C2×C22⋊C4—4716no—
1049C2×C22⋊C4C22×D4711yescharacteristic
1050C2×C22⋊C4C22×D4711yescharacteristic
1051C2×C22⋊C4C22×D4712yes—
1052C2×C22⋊C4C22×D4712yes—
1053C2×C22⋊C4C22×D4712yes—
1054C2×C22⋊C4C22×D4712yes—
1055C2×C42—472no—
1056C2×C42—472no—
1057C2×C42—471no—
1058C2×C42—471no—
1059C2×C42—471no—
1060C2×C42—471no—
1061C2×C42—478no—
1062C2×C42C22×D4711yescharacteristic
1063C2×C42C22×D4711yescharacteristic
1064C24—472no—
1065C24—471no—
1066C24—471no—
1067C24—472no—
1068C24—478no—
1069C24—478no—
1070C24—478no—
1071C24—948no—
1072C24—948no—
1073C24—948no—
1074C24—948no—
1075C24—1884no—
1076C24—1884no—
1077C24—1884no—
1078C24—1884no—
1079C24—1884no—
1080C24C23×D4711yescharacteristic
1081C24C23×D4712yes—
1082C24C23×D4712yes—
1083#41—18832no—
1084#41—18832no—
1085C2×Q8—474no—
1086C2×Q8—478no—
1087C2×Q8—944no—
1088C2×Q8—1884no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—44no—
1092C2×D4—44no—
1093C2×D4—44no—
1094C2×D4—44no—
1095C2×D4—478no—
1096C2×D4—478no—
1097C2×D4—478no—
1098C2×D4—474no—
1099C2×D4—474no—
1100C2×D4—478no—
1101C2×D4—478no—
1102C2×D4—478no—
1103C2×D4—478no—
1104C2×D4—478no—
1105C2×D4—478no—
1106C2×D4—474no—
1107C2×D4—478no—
1108C2×D4—474no—
1109C2×D4—478no—
1110C2×D4—474no—
1111C2×D4—478no—
1112C2×D4—9432no—
1113C2×D4—948no—
1114C2×D4—944no—
1115C2×D4—948no—
1116C2×D4—944no—
1117C2×D4—948no—
1118C2×D4—9432no—
1119C2×D4—9432no—
1120C2×D4—948no—
1121C2×D4—948no—
1122C2×D4—944no—
1123C2×D4—948no—
1124C2×D4—944no—
1125C2×D4—1884no—
1126C2×D4—18832no—
1127C2×D4—1884no—
1128C2×D4—1884no—
1129C2×D4—1884no—
1130C2×D4—1884no—
1131C2×D4—18832no—
1132C2×D4—18832no—
1133C2×D4C23×D4714yes—
1134C2×D4C23×D4714yes—
1135C2×D4C23×D4718yes—
1136C2×D4C23×D4718yes—
1137C2×D4C23×D4718yes—
1138C2×D4C23×D4718yes—
1139C22×C4—24no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—471no—
1143C22×C4—478no—
1144C22×C4—471no—
1145C22×C4—471no—
1146C22×C4—472no—
1147C22×C4—471no—
1148C22×C4—472no—
1149C22×C4—471no—
1150C22×C4—471no—
1151C22×C4—478no—
1152C22×C4—474no—
1153C22×C4—474no—
1154C22×C4—474no—
1155C22×C4—478no—
1156C22×C4—474no—
1157C22×C4—478no—
1158C22×C4—478no—
1159C22×C4—478no—
1160C22×C4—478no—
1161C22×C4—478no—
1162C22×C4—478no—
1163C22×C4—944no—
1164C22×C4—948no—
1165C22×C4—944no—
1166C22×C4—948no—
1167C22×C4—944no—
1168C22×C4—944no—
1169C22×C4—1884no—
1170C22×C4—1884no—
1171C22×C4—1884no—
1172C22×C4—1884no—
1173C22×C4—1884no—
1174C22×C4—1884no—
1175C22×C4—18832no—
1176C22×C4—1884no—
1177C22×C4C23×D4714yes—
1178C22×C4C23×D4711yescharacteristic
1179C22×C4C23×D4711yescharacteristic
1180C22×C4C23×D4711yescharacteristic
1181C22×C4C23×D4712yes—
1182C22×C4C23×D4711yescharacteristic
1183C22×C4C23×D4711yescharacteristic
1184C22×C4C23×D4712yes—
1185C22×C4C23×D4718yes—
1186C22×C4C23×D4718yes—
1187C22×C4C23×D4711yescharacteristic
1188C4⋊C4—474no—
1189C4⋊C4—478no—
1190C4⋊C4—478no—
1191C4⋊C4—474no—
1192C4⋊C4—474no—
1193C4⋊C4—474no—
1194C4⋊C4—474no—
1195C4⋊C4—478no—
1196C4⋊C4—474no—
1197C4⋊C4—474no—
1198C4⋊C4—478no—
1199C4⋊C4—474no—
1200C4⋊C4—474no—
1201C4⋊C4—474no—
1202C4⋊C4C23×D4714yes—
1203C4⋊C4C23×D4718yes—
1204C4⋊C4C23×D4714yes—
1205C4⋊C4C23×D4714yes—
1206C4⋊C4C23×D4714yes—
1207C4⋊C4C23×D4718yes—
1208C22⋊C4—478no—
1209C22⋊C4—478no—
1210C22⋊C4—478no—
1211C22⋊C4—478no—
1212C22⋊C4—474no—
1213C22⋊C4—474no—
1214C22⋊C4—478no—
1215C22⋊C4—478no—
1216C22⋊C4—474no—
1217C22⋊C4—478no—
1218C22⋊C4—474no—
1219C22⋊C4—478no—
1220C22⋊C4—478no—
1221C22⋊C4—478no—
1222C22⋊C4—478no—
1223C22⋊C4—478no—
1224C22⋊C4—474no—
1225C22⋊C4—474no—
1226C22⋊C4—474no—
1227C22⋊C4—474no—
1228C22⋊C4—478no—
1229C22⋊C4—478no—
1230C22⋊C4C23×D4714yes—
1231C22⋊C4C23×D4714yes—
1232C22⋊C4C23×D4718yes—
1233C22⋊C4C23×D4718yes—
1234C22⋊C4C23×D4718yes—
1235C22⋊C4C23×D4718yes—
1236C42—474no—
1237C42—474no—
1238C42—474no—
1239C42—478no—
1240C42—478no—
1241C42—474no—
1242C42C23×D4714yes—
1243C42C23×D4714yes—
1244C23—22no—
1245C23—24no—
1246C23—24no—
1247C23—24no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—22no—
1252C23—24no—
1253C23—478no—
1254C23—474no—
1255C23—474no—
1256C23—472no—
1257C23—472no—
1258C23—474no—
1259C23—9416no—
1260C23—9416no—
1261C23—9416no—
1262C23—9416no—
1263C23—942no—
1264C23—942no—
1265C23—944no—
1266C23—944no—
1267C23—942no—
1268C23—944no—
1269C23—944no—
1270C23—944no—
1271C23—942no—
1272C23—942no—
1273C23—37616no—
1274C23—37616no—
1275C23—1888no—
1276C23—1888no—
1277C23—1888no—
1278C23—1888no—
1279C23—1888no—
1280C23—18832no—
1281C23C24×D4712yes—
1282C23C24×D4714yes—
1283C23C24×D4714yes—
1284C23C24×D4711yescharacteristic
1285Q8—948no—
1286Q8—1888no—
1287D4—28no—
1288D4—28no—
1289D4—48no—
1290D4—48no—
1291D4—48no—
1292D4—48no—
1293D4—4716no—
1294D4—9416no—
1295D4—948no—
1296D4—9416no—
1297D4—948no—
1298D4—9416no—
1299D4—9416no—
1300D4—9416no—
1301D4—948no—
1302D4—9416no—
1303D4—948no—
1304D4—1888no—
1305D4—1888no—
1306D4—1888no—
1307D4—1888no—
1308D4—1888no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—28no—
1317C2×C4—48no—
1318C2×C4—48no—
1319C2×C4—474no—
1320C2×C4—472no—
1321C2×C4—472no—
1322C2×C4—472no—
1323C2×C4—474no—
1324C2×C4—472no—
1325C2×C4—474no—
1326C2×C4—472no—
1327C2×C4—472no—
1328C2×C4—948no—
1329C2×C4—9416no—
1330C2×C4—948no—
1331C2×C4—9416no—
1332C2×C4—942no—
1333C2×C4—942no—
1334C2×C4—944no—
1335C2×C4—942no—
1336C2×C4—942no—
1337C2×C4—944no—
1338C2×C4—942no—
1339C2×C4—948no—
1340C2×C4—948no—
1341C2×C4—1888no—
1342C2×C4—1888no—
1343C2×C4—1888no—
1344C2×C4—1888no—
1345C2×C4—1888no—
1346C2×C4—1888no—
1347C2×C4—1888no—
1348C2×C4#41×D4714yes—
1349C2×C4C24×D4712yes—
1350C2×C4C24×D4712yes—
1351C2×C4C24×D4712yes—
1352C2×C4C24×D4714yes—
1353C2×C4C24×D4712yes—
1354C2×C4C24×D4712yes—
1355C2×C4C24×D4714yes—
1356C2×C4C24×D4712yes—
1357C22—22no—
1358C22—24no—
1359C22—24no—
1360C22—24no—
1361C22—24no—
1362C22—24no—
1363C22—22no—
1364C22—22no—
1365C22—24no—
1366C22—44no—
1367C22—48no—
1368C22—48no—
1369C22—478no—
1370C22—474no—
1371C22—942no—
1372C22—9416no—
1373C22—948no—
1374C22—942no—
1375C22—944no—
1376C22—944no—
1377C22—942no—
1378C22—944no—
1379C22—944no—
1380C22—944no—
1381C22—942no—
1382C22—942no—
1383C22—37616no—
1384C22—37616no—
1385C22—18832no—
1386C22—1884no—
1387C22—1888no—
1388C22C2×#41×D4712yes—
1389C22H(5,𝔽2)×D4712yes—
1390C22H(5,𝔽2)×D4712yes—
1391C22C25×D4711yescharacteristic
1392C4—22no—
1393C4—22no—
1394C4—22no—
1395C4—24no—
1396C4—24no—
1397C4—22no—
1398C4—22no—
1399C4—474no—
1400C4—942no—
1401C4—942no—
1402C4—944no—
1403C4—942no—
1404C4—942no—
1405C4—944no—
1406C4—942no—
1407C4C2×#41×D4714yes—
1408C2—42no—
1409C2—44no—
1410C2—44no—
1411C2—948no—
1412C2—944no—
1413C2—1882no—
1414C2—1884no—
1415C2#2025741814yesdirect product factor
1416C2C22×#41×D4711yescharacteristic
1417C2C2×H(5,𝔽2)×D4711yescharacteristic
1418C2C2×H(5,𝔽2)×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#540C2
socleC23×C47C25
hypercenterC2×#540D47
hypocenterC47C2×#3519
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#540

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20257418C2direct (N × H)
2. C2×#15689837C2semidirect
3. C2×#15689829C2semidirect
4. C2×#15689826C2semidirect
5. C2×#15689820C2semidirect
6. C2×#15689818C2semidirect
7. C2×#15689793C2semidirect
8. C2×#15689770C2semidirect
9. C2×#15689765C2semidirect
10. C2×#15689762C2semidirect
11. C2×#15689758C2semidirect
12. C2×#15689757C2semidirect
13. C2×#15689757C2semidirect
14. C2×#15689724C2semidirect
15. C2×#15689709C2semidirect
16. C2×#15689705C2semidirect
17. C2×#15689670C2semidirect
18. C2×#15689651C2semidirect
19. C2×#15689631C2semidirect
20. C2×#121×D47C2semidirect
21. C2×#15689597C2semidirect
22. C2×#15689595C2semidirect
23. C2×C4×D4×D47C2semidirect
24. C2×C47×#540C2semidirect
25. C22×#10625350C22semidirect
26. C22×#10625352C22semidirect
30. C22×D4×D47C22semidirect
31. C22×D4×D47C22semidirect
32. C22×D4×D47C22semidirect
33. C23×C4×D47C22semidirect
34. #15689837C22semidirect
35. #15689829C22semidirect
36. #15689826C22semidirect
37. #15689820C22semidirect
38. #15689818C22semidirect
39. #15689793C22semidirect
40. #15689770C22semidirect
41. #15689765C22semidirect
42. #15689762C22semidirect
43. #15689758C22semidirect
44. #15689757C22semidirect
45. #15689757C22semidirect
46. #15689724C22semidirect
47. #15689709C22semidirect
48. #15689705C22semidirect
49. #15689670C22semidirect
50. C2×#13094023C22semidirect
51. C2×#13094020C22semidirect
52. C2×#13094020C22semidirect
53. #15689651C22semidirect
54. C2×#13094019C22semidirect
55. C2×#13094019C22semidirect
56. C2×#13094017C22semidirect
57. C2×#13094017C22semidirect
58. C2×#13094015C22semidirect
59. C2×#13094014C22semidirect
60. C2×#13094011C22semidirect
61. C2×#13094010C22semidirect
62. C2×#13094010C22semidirect
63. C2×#13094010C22semidirect
64. #15689631C22semidirect
65. C2×#13094009C22semidirect
66. C2×#13094009C22semidirect
67. C2×#13094007C22semidirect
68. C2×#13094006C22semidirect
69. C2×#13094006C22semidirect
70. C2×#13094005C22semidirect
71. C2×#13094004C22semidirect
72. C2×#13094002C22semidirect
73. C2×#13094002C22semidirect
74. C2×#13094002C22semidirect
75. C2×#13093999C22semidirect
76. C2×#13093999C22semidirect
77. C2×#13093999C22semidirect
78. C2×#13093998C22semidirect
80. C2×#13093997C22semidirect
81. C2×#13093997C22semidirect
82. C2×#13093997C22semidirect
83. C2×#13093997C22semidirect
84. C2×#13093996C22semidirect
85. C2×#13093996C22semidirect
86. C2×#13093996C22semidirect
87. C2×#13093995C22semidirect
88. C2×#13093995C22semidirect
89. C2×#13093995C22semidirect
90. C2×#13093995C22semidirect
91. C2×#13093995C22semidirect
92. #121×D47C22semidirect
93. C2×#13093994C22semidirect
94. C2×#13093994C22semidirect
95. C2×#13093992C22semidirect
96. C2×#13093992C22semidirect
97. C2×#13093992C22semidirect
98. C2×#13093992C22semidirect
99. #15689597C22semidirect
100. #15689595C22semidirect
101. C2×C4×Dic94C22semidirect
104. C2×C4×D188C22semidirect
105. C2×C4×D188C22semidirect
106. C2×C4×D188C22semidirect
107. C2×D4×Dic47C22semidirect
108. C2×D4×Dic47C22semidirect
111. C2×#13093986C22semidirect
112. C2×#13093986C22semidirect
113. C2×#13093986C22semidirect
114. C2×C4×C22⋊D47C22semidirect
115. C2×C4×C22⋊D47C22semidirect
116. C2×C4×C22⋊D47C22semidirect
117. C2×C4×C22⋊D47C22semidirect
118. C2×C4×C22⋊D47C22semidirect
119. C2×(C22⋊D47)⋊C4C22semidirect
120. C2×(C22⋊D47)⋊C4C22semidirect
121. C2×(C22⋊D47)⋊C4C22semidirect
122. C4×D4×D47C22semidirect
123. C2×#13093983C22semidirect
124. C2×#13093982C22semidirect
125. C2×#13093981C22semidirect
126. C2×#13093980C22semidirect
127. C2×C4⋊C4×D47C22semidirect
128. C2×C4⋊C4×D47C22semidirect
129. C22×(C2×D47)⋊C4C22semidirect
130. C2×C22⋊C4×D47C22semidirect
131. C2×C22⋊C4×D47C22semidirect
132. C2×C22⋊C4×D47C22semidirect
133. C2×C22⋊C4×D47C22semidirect
134. C2×C42×D47C22semidirect
135. C47×#540C22semidirect
136. C2×#127×C47C22semidirect
137. C2×#125×C47C22semidirect
138. C2×#123×C47C22semidirect
139. C2×#123×C47C22semidirect
140. C2×#121×C47C22semidirect
141. C2×#121×C47C22semidirect
142. C2×#121×C47C22semidirect
143. C2×#121×C47C22semidirect
144. C2×C4×D4×C47C22semidirect
145. C2×C4×D4×C47C22semidirect
146. C2×#117×C47C22semidirect
151. C2×#10625350C23semidirect
153. C2×#10625352C23semidirect
181. C2×D4×D47C23semidirect
182. C2×D4×D47C23semidirect
183. C2×D4×D47C23semidirect
198. C22×C4×D47C23semidirect
199. #13094023C23semidirect
200. #13094020C23semidirect
201. #13094020C23semidirect
202. #13094019C23semidirect
203. #13094019C23semidirect
204. #13094017C23semidirect
205. #13094017C23semidirect
206. #13094015C23semidirect
207. #13094014C23semidirect
208. #13094011C23semidirect
209. #13094010C23semidirect
210. #13094010C23semidirect
211. #13094010C23semidirect
212. #13094009C23semidirect
213. #13094009C23semidirect
214. #13094007C23semidirect
215. #13094006C23semidirect
216. #13094006C23semidirect
217. #13094005C23semidirect
218. #13094004C23semidirect
219. #13094002C23semidirect
220. #13094002C23semidirect
221. #13094002C23semidirect
222. #13093999C23semidirect
223. #13093999C23semidirect
224. #13093999C23semidirect
225. #13093998C23semidirect
227. #13093997C23semidirect
228. #13093997C23semidirect
229. #13093997C23semidirect
230. #13093997C23semidirect
231. #13093996C23semidirect
232. #13093996C23semidirect
233. #13093996C23semidirect
234. #13093995C23semidirect
235. #13093995C23semidirect
236. #13093995C23semidirect
237. #13093995C23semidirect
238. #13093995C23semidirect
239. #13093994C23semidirect
240. #13093994C23semidirect
241. #13093992C23semidirect
242. #13093992C23semidirect
243. #13093992C23semidirect
244. #13093992C23semidirect
245. C4×Dic94C23semidirect
248. C4×D188C23semidirect
249. C4×D188C23semidirect
250. C4×D188C23semidirect
251. D4×Dic47C23semidirect
252. D4×Dic47C23semidirect
255. #13093986C23semidirect
256. #13093986C23semidirect
257. #13093986C23semidirect
258. C4×C22⋊D47C23semidirect
259. C4×C22⋊D47C23semidirect
260. C4×C22⋊D47C23semidirect
261. C4×C22⋊D47C23semidirect
262. C4×C22⋊D47C23semidirect
263. (C22⋊D47)⋊C4C23semidirect
264. (C22⋊D47)⋊C4C23semidirect
265. (C22⋊D47)⋊C4C23semidirect
266. #13093983C23semidirect
267. #13093982C23semidirect
268. #13093981C23semidirect
269. #13093980C23semidirect
284. C4⋊C4×D47C23semidirect
285. C4⋊C4×D47C23semidirect
308. C2×(C2×D47)⋊C4C23semidirect
309. C22⋊C4×D47C23semidirect
310. C22⋊C4×D47C23semidirect
311. C22⋊C4×D47C23semidirect
312. C22⋊C4×D47C23semidirect
319. C42×D47C23semidirect
329. #127×C47C23semidirect
330. #125×C47C23semidirect
331. #123×C47C23semidirect
332. #123×C47C23semidirect
333. #121×C47C23semidirect
334. #121×C47C23semidirect
335. #121×C47C23semidirect
336. #121×C47C23semidirect
337. C4×D4×C47C23semidirect
338. C4×D4×C47C23semidirect
339. #117×C47C23semidirect
444. C2×D188#41semidirect
633. D188C2×#41semidirect
713. C2×#540D47semidirect
726. C2×C47#3519semidirect
756. #540C2×D47semidirect
763. C2×#127C2×D47semidirect
771. C2×#125C2×D47semidirect
783. C2×#123C2×D47semidirect
784. C2×#123C2×D47semidirect
807. C2×#121C2×D47semidirect
808. C2×#121C2×D47semidirect
809. C2×#121C2×D47semidirect
810. C2×#121C2×D47semidirect
841. C2×C4×D4C2×D47semidirect
842. C2×C4×D4C2×D47semidirect
847. C2×#117C2×D47semidirect
856. C47C2×#3519semidirect
921. #127C22×D47semidirect
928. #125C22×D47semidirect
939. #123C22×D47semidirect
940. #123C22×D47semidirect
962. #121C22×D47semidirect
963. #121C22×D47semidirect
964. #121C22×D47semidirect
965. #121C22×D47semidirect
993. C4×D4C22×D47semidirect
994. C4×D4C22×D47semidirect
999. #117C22×D47semidirect
1415. C2#20257418direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202574182
C2×#156898372
C2×#156898292
C2×#156898262
C2×#156898202
C2×#156898182
C2×#156897932
C2×#156897702
C2×#156897652
C2×#156897622
C2×#156897582
C2×#156897572
C2×#156897242
C2×#156897092
C2×#156897052
C2×#156896702
C2×#156896512
C2×#156896312
C2×#121×D472
C2×#156895972
C2×#156895952
C2×C4×D4×D472
C2×C47×#5402
C2×#351947