Finite Group Databasebeta

← C2×#20257256 #27124630

Subgroups — C2×#20257256 #27124630

Order 12032.

8622 conjugacy classes of subgroups.

The subgroup lattice has 1436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257256C2132yesmaximal, direct product factor
2C2×#15689857C212yesmaximal, complemented
3C2×#15689856C211yesmaximal, characteristic, complemented
4C2×#15689855C211yesmaximal, characteristic, complemented
5C2×#15689792C211yesmaximal, characteristic, complemented
6C2×#15689791C211yesmaximal, characteristic, complemented
7C2×#15689791C212yesmaximal, complemented
8C2×#15689769C211yesmaximal, characteristic, complemented
9C2×#15689767C211yesmaximal, characteristic, complemented
10C2×#15689764C211yesmaximal, characteristic, complemented
11C2×#15689763C212yesmaximal, complemented
12C2×#15689760C212yesmaximal, complemented
13C2×#15689725C212yesmaximal, complemented
14C2×#15689723C212yesmaximal, complemented
15C2×#15689688C212yesmaximal, complemented
16C2×#15689675C211yesmaximal, characteristic, complemented
17C2×#15689672C211yesmaximal, characteristic, complemented
18C2×#15689670C211yesmaximal, characteristic, complemented
19C2×#15689669C211yesmaximal, characteristic, complemented
20C2×#15689668C211yesmaximal, characteristic, complemented
21C22×#13094020C211yesmaximal, characteristic, complemented
22C2×#15689596C212yesmaximal, complemented
23C2×C4×#10625352C211yesmaximal, characteristic, complemented
24C2×C47×#546C211yesmaximal, characteristic, complemented
25C22×#10625354C2211yescharacteristic, complemented
26C22×#10625350C2212yescomplemented
27C22×#10625350C2211yescharacteristic, complemented
28C22×#10625352C2211yescharacteristic
29C22×#10625352C2212yescomplemented
30C22×#10625352C2211yescharacteristic, complemented
31C23×D188C2211yescharacteristic
32C23×C22⋊D47C2212yes—
33C23×C22⋊D47C2212yes—
34#15689857C22132yescomplemented
35#15689856C22116yescomplemented
36#15689855C22116yescomplemented
37#15689792C22116yescomplemented
38#15689791C22116yescomplemented
39#15689791C22132yescomplemented
40#15689769C22116yescomplemented
41#15689767C22116yescomplemented
42#15689764C22116yescomplemented
43#15689763C22132yescomplemented
44#15689760C22132yescomplemented
45#15689725C22132yescomplemented
46#15689723C22132yescomplemented
47#15689688C22132yescomplemented
48#15689675C22116yescomplemented
49#15689672C22116yescomplemented
50#15689670C22116yescomplemented
51#15689669C22116yescomplemented
52#15689668C22116yescomplemented
53C2×#13094023C2211yescharacteristic, complemented
54C2×#13094022C2211yescharacteristic, complemented
55C2×#13094020C2211yescharacteristic
56C2×#13094020C2212yes—
57C2×#13094020C2211yescharacteristic
58C2×#13094020C2211yescharacteristic
59C2×#13094020C2211yescharacteristic
60C2×#13094020C2212yes—
61C2×#13094020C22116yescomplemented
62C2×#13094020C2212yescomplemented
63C2×#13094020C2212yescomplemented
64C2×#13094014C2212yescomplemented
65C2×#13094013C2211yescharacteristic, complemented
66C2×#13094012C2211yescharacteristic, complemented
67C2×#13094011C2211yescharacteristic, complemented
68C2×#13094010C2212yescomplemented
69C2×#13094010C2212yescomplemented
70C2×#13094010C2212yescomplemented
71C2×#13094010C2212yescomplemented
72C2×#13094009C2212yescomplemented
73C2×#13094009C2212yescomplemented
74C2×#13094008C2212yescomplemented
75C2×#13094007C2212yescomplemented
76C2×#13094006C2212yescomplemented
77C2×#13094006C2212yescomplemented
78C2×#13094005C2212yescomplemented
79C2×#13094003C2211yescharacteristic
80C2×#13094001C2212yes—
81C2×#13093999C2211yescharacteristic, complemented
82C2×#13093999C2212yescomplemented
83C2×#13093998C2212yescomplemented
84C2×#13093998C2211yescharacteristic, complemented
85C2×#13093997C2212yescomplemented
86C2×#13093997C2212yescomplemented
87C2×#13093997C2212yescomplemented
88C2×#13093997C2212yescomplemented
89C2×#13093997C2212yescomplemented
90C2×#13093996C2212yescomplemented
91C2×#13093996C2212yescomplemented
92C2×#13093996C2212yescomplemented
93C2×#13093996C2212yescomplemented
94C2×#13093996C2212yescomplemented
95C2×#13093995C2212yescomplemented
96C2×#13093995C2211yescharacteristic, complemented
97C2×#13093994C2212yes—
98C2×#13093993C2212yes—
99C2×#13093992C2212yes—
100#15689596C22132yescomplemented
101C4×#10625352C22116yescomplemented
102C2×Q8×Dic47C2211yescharacteristic, complemented
103C2×C4×Dic94C2211yescharacteristic, complemented
104C2×#13093989C2211yescharacteristic, complemented
105C2×#13093989C2211yescharacteristic, complemented
106C2×#13093989C2212yescomplemented
107C2×C4×D188C2211yescharacteristic, complemented
108C2×D4×Dic47C2211yescharacteristic
109C2×D4×Dic47C2211yescharacteristic, complemented
110C2×#13093986C2211yescharacteristic, complemented
111C2×C4×C22⋊D47C2211yescharacteristic
112C2×C4×C22⋊D47C2211yescharacteristic, complemented
113C2×C4×C22⋊D47C2212yescomplemented
114C2×C4×C22⋊D47C2212yescomplemented
115C2×C4×C22⋊D47C2212yescomplemented
116C2×C4×C22⋊D47C2212yescomplemented
117C2×C4×C22⋊D47C2212yescomplemented
118C2×(C22⋊D47)⋊C4C2211yescharacteristic
119C2×(C22⋊D47)⋊C4C2211yescharacteristic, complemented
120C2×(C22⋊D47)⋊C4C2212yescomplemented
121C2×(C22⋊D47)⋊C4C2212yescomplemented
122C2×(C22⋊D47)⋊C4C2212yescomplemented
123C2×(C22⋊D47)⋊C4C2212yescomplemented
124C2×(C22⋊D47)⋊C4C2212yescomplemented
125C2×#13093982C2211yescharacteristic, complemented
126C2×#13093980C2211yescharacteristic
127C2×#13093980C2212yes—
128C2×#13093980C2211yescharacteristic, complemented
129C22×C22⋊Dic47C2212yes—
130C2×C22⋊C4×D47C2212yes—
131C2×C22⋊C4×D47C2212yes—
132C22×C4×Dic47C2211yescharacteristic
133C22×C4×Dic47C2211yescharacteristic, complemented
134C2×C42×D47C2211yescharacteristic, complemented
135C22×#41×C47C2211yescharacteristic, complemented
136C23×D4×C47C2211yescharacteristic
137C47×#546C22116yescomplemented
138C2×#124×C47C2211yescharacteristic, complemented
139C2×#123×C47C2212yescomplemented
140C2×C22⋊Q8×C47C2211yescharacteristic
141C2×#121×C47C2211yescharacteristic, complemented
142C2×#121×C47C2212yescomplemented
143C2×#120×C47C2212yes—
144C2×C4×D4×C47C2211yescharacteristic
145C2×C4×D4×C47C2211yescharacteristic, complemented
146C22×C22⋊C4×C47C2212yes—
147C24×D47C2312yes—
148C2×#10625354—44no—
149C2×#10625354C2318yescomplemented
150C2×#10625350—48no—
151C2×#10625350—44no—
152C2×#10625350C23116yescomplemented
153C2×#10625350C2318yescomplemented
154C2×#10625352—28no—
155C2×#10625352—44no—
156C2×#10625352—48no—
157C2×#10625352C2318yes—
158C2×#10625352C23116yescomplemented
159C2×#10625352C2318yescomplemented
160C22×Dic94C2311yescharacteristic
161C22×Dic94C2312yes—
162C22×Dic94C2311yescharacteristic
163C22×D188—44no—
164C22×D188C2311yescharacteristic
165C22×D188C2311yescharacteristic
166C22×D188C2318yes—
167C22×D188C2312yes—
168C22×D188C2312yes—
169C22×D188C2312yes—
170C22×C22⋊D47—216no—
171C22×C22⋊D47—48no—
172C22×C22⋊D47C2311yescharacteristic
173C22×C22⋊D47C2312yes—
174C22×C22⋊D47C2312yes—
175C22×C22⋊D47C2311yescharacteristic
176C22×C22⋊D47C2312yes—
177C22×C22⋊D47C2312yes—
178C22×C22⋊D47C2312yes—
179C22×C22⋊D47C2312yes—
180C22×C22⋊D47C23116yes—
181C22×C22⋊D47C23116yes—
182C22×C22⋊D47C2312yes—
183C22×C22⋊D47C2312yes—
184C22×C22⋊D47C2312yes—
185C22×C22⋊D47C2312yes—
186C22×C22⋊D47C2312yes—
187C22×C22⋊D47C2312yes—
188C23×Dic47C2311yescharacteristic
189C23×Dic47C2311yescharacteristic
190C23×Dic47C2311yescharacteristic
191C23×Dic47C2312yes—
192C23×Dic47C2312yes—
193C23×Dic47C2311yescharacteristic
194C22×C4×D47C2311yescharacteristic
195C22×C4×D47C2311yescharacteristic
196C22×C4×D47C2311yescharacteristic
197C22×C4×D47C2312yes—
198C22×C4×D47C2312yes—
199C22×C4×D47C2312yes—
200C22×C4×D47C2312yes—
201#13094023C2318yescomplemented
202#13094022C2318yescomplemented
203#13094020C2318yes—
204#13094020C23116yes—
205#13094020C2318yes—
206#13094020C2318yes—
207#13094020C2318yes—
208#13094020C23116yes—
209#13094020C23116yescomplemented
210#13094020C23116yescomplemented
211#13094014C23116yescomplemented
212#13094013C2318yescomplemented
213#13094012C2318yescomplemented
214#13094011C2318yescomplemented
215#13094010C23116yescomplemented
216#13094010C23116yescomplemented
217#13094010C23116yescomplemented
218#13094010C23116yescomplemented
219#13094009C23116yescomplemented
220#13094009C23116yescomplemented
221#13094008C23116yescomplemented
222#13094007C23116yescomplemented
223#13094006C23116yescomplemented
224#13094006C23116yescomplemented
225#13094005C23116yescomplemented
226#13094003C2318yes—
227#13094001C23116yes—
228#13093999C2318yescomplemented
229#13093999C23116yescomplemented
230#13093998C23116yescomplemented
231#13093998C2318yescomplemented
232#13093997C23116yescomplemented
233#13093997C23116yescomplemented
234#13093997C23116yescomplemented
235#13093997C23116yescomplemented
236#13093997C23116yescomplemented
237#13093996C23116yescomplemented
238#13093996C23116yescomplemented
239#13093996C23116yescomplemented
240#13093996C23116yescomplemented
241#13093996C23116yescomplemented
242#13093995C23116yescomplemented
243#13093995C2318yescomplemented
244#13093994C23116yes—
245#13093993C23116yes—
246#13093992C23116yes—
247Q8×Dic47C2318yescomplemented
248C4×Dic94C2318yescomplemented
249#13093989C2318yescomplemented
250#13093989C23116yescomplemented
251#13093989C2318yescomplemented
252C4×D188C2318yescomplemented
253D4×Dic47C2318yes—
254D4×Dic47C2318yescomplemented
255#13093986C2318yescomplemented
256C4×C22⋊D47C2318yes—
257C4×C22⋊D47C23116yescomplemented
258C4×C22⋊D47C2318yescomplemented
259C4×C22⋊D47C23116yescomplemented
260C4×C22⋊D47C23116yescomplemented
261C4×C22⋊D47C23116yescomplemented
262C4×C22⋊D47C23116yescomplemented
263(C22⋊D47)⋊C4C2318yes—
264(C22⋊D47)⋊C4C23116yescomplemented
265(C22⋊D47)⋊C4C2318yescomplemented
266(C22⋊D47)⋊C4C23116yescomplemented
267(C22⋊D47)⋊C4C23116yescomplemented
268(C22⋊D47)⋊C4C23116yescomplemented
269(C22⋊D47)⋊C4C23116yescomplemented
270#13093982C2318yescomplemented
271#13093980C2318yes—
272#13093980C23116yes—
273#13093980C2318yescomplemented
274C2×C4⋊Dic47C2311yescharacteristic
275C2×C4⋊Dic47C2311yescharacteristic
276C2×C4⋊Dic47C2312yes—
277C2×Dic47⋊C4C2311yescharacteristic
278C2×Dic47⋊C4C2311yescharacteristic
279C2×Dic47⋊C4C2312yes—
280C2×Dic47⋊C4C2312yes—
281C2×Dic47⋊C4C2311yescharacteristic
282C2×Dic47⋊C4C2311yescharacteristic
283C2×Dic47⋊C4C2312yes—
284C2×Dic47⋊C4C2312yes—
285C2×Dic47⋊C4C2312yes—
286C2×C22⋊Dic47C23116yes—
287C2×C22⋊Dic47C2311yescharacteristic
288C2×C22⋊Dic47C2312yes—
289C2×C22⋊Dic47C2312yes—
290C2×C22⋊Dic47C2312yes—
291C2×C22⋊Dic47C2311yescharacteristic
292C2×C22⋊Dic47C2312yes—
293C2×C22⋊Dic47C2312yes—
294C2×(C2×D47)⋊C4C2312yes—
295C2×(C2×D47)⋊C4C2312yes—
296C2×(C2×D47)⋊C4C2312yes—
297C2×(C2×D47)⋊C4C2312yes—
298C2×(C2×D47)⋊C4C2311yescharacteristic
299C2×(C2×D47)⋊C4C2311yescharacteristic
300C2×(C2×D47)⋊C4C2312yes—
301C2×(C2×D47)⋊C4C2312yes—
302C2×(C2×D47)⋊C4C2312yes—
303C2×(C2×D47)⋊C4C2312yes—
304C22⋊C4×D47C23116yes—
305C22⋊C4×D47C23116yes—
306C2×C4×Dic47C2311yescharacteristic
307C2×C4×Dic47C2311yescharacteristic
308C2×C4×Dic47C2311yescharacteristic
309C2×C4×Dic47C2311yescharacteristic
310C2×C4×Dic47C2311yescharacteristic
311C2×C4×Dic47C2311yescharacteristic
312C2×C4×Dic47C2318yes—
313C2×C4×Dic47C2311yescharacteristic
314C2×C4×Dic47C2311yescharacteristic
315C2×C4×Dic47C2311yescharacteristic
316C2×C4×Dic47C2312yes—
317C2×C4×Dic47C2312yes—
318C2×C4×Dic47C2318yescomplemented
319C42×D47C2318yescomplemented
320C25×C47C2312yes—
321C2×#41×C47—44no—
322C2×#41×C47C2318yescomplemented
323C22×Q8×C47C2311yescharacteristic
324C22×D4×C47—44no—
325C22×D4×C47C2311yescharacteristic
326C22×D4×C47C2311yescharacteristic
327C22×D4×C47C2311yescharacteristic
328C22×D4×C47C2318yes—
329C22×D4×C47C2312yes—
330C22×D4×C47C2312yes—
331C22×D4×C47C2312yes—
332C23×C4×C47C2311yescharacteristic
333C23×C4×C47C2311yescharacteristic
334C23×C4×C47C2312yes—
335C23×C4×C47C2312yes—
336#124×C47C2318yescomplemented
337#123×C47C23116yescomplemented
338C22⋊Q8×C47C2318yes—
339#121×C47C2318yescomplemented
340#121×C47C23116yescomplemented
341#120×C47C23116yes—
342C4×D4×C47C2318yes—
343C4×D4×C47C2318yescomplemented
344C2×C4⋊C4×C47C2311yescharacteristic
345C2×C4⋊C4×C47C2311yescharacteristic
346C2×C4⋊C4×C47C2312yes—
347C2×C22⋊C4×C47C23116yes—
348C2×C22⋊C4×C47C2311yescharacteristic
349C2×C22⋊C4×C47C2312yes—
350C2×C22⋊C4×C47C2312yes—
351C2×C22⋊C4×C47C2312yes—
352C2×C22⋊C4×C47C2311yescharacteristic
353C2×C22⋊C4×C47C2312yes—
354C2×C22⋊C4×C47C2312yes—
355C2×C42×C47C2311yescharacteristic
356C24×C47—28no—
357C24×C47—44no—
358C24×C47—44no—
359C24×C47C2412yes—
360C24×C47C2412yes—
361C24×C47C2411yescharacteristic
362C24×C47C2411yescharacteristic
363C24×C47C2418yes—
364C23×D47—28no—
365C23×D47—44no—
366C23×D47—44no—
367C23×D47C2412yes—
368C23×D47C2412yes—
369C23×D47C2411yescharacteristic
370C23×D47C2418yes—
371#41×C47—416no—
372C2×Q8×C47—24no—
373C2×Q8×C47C2414yes—
374C2×D4×C47—24no—
375C2×D4×C47—24no—
376C2×D4×C47—24no—
377C2×D4×C47—416no—
378C2×D4×C47—44no—
379C2×D4×C47—44no—
380C2×D4×C47—44no—
381C2×D4×C47C2414yes—
382C2×D4×C47C2414yes—
383C2×D4×C47C2414yes—
384C2×D4×C47C2418yes—
385C2×D4×C47C2418yes—
386C2×D4×C47C2418yes—
387C22×C4×C47—24no—
388C22×C4×C47—24no—
389C22×C4×C47—44no—
390C22×C4×C47—44no—
391C22×C4×C47C2411yescharacteristic
392C22×C4×C47C2411yescharacteristic
393C22×C4×C47C2412yes—
394C22×C4×C47C2411yescharacteristic
395C22×C4×C47C2412yes—
396C22×C4×C47C2411yescharacteristic
397C22×C4×C47C2414yes—
398C22×C4×C47C2414yes—
399C22×C4×C47C2418yes—
400C22×C4×C47C2418yes—
401C22×C4×C47C2411yescharacteristic
402C2×C22⋊D47—24no—
403C2×C22⋊D47—28no—
404C2×C22⋊D47—28no—
405C2×C22⋊D47—28no—
406C2×C22⋊D47—28no—
407C2×C22⋊D47—24no—
408C2×C22⋊D47—264no—
409C2×C22⋊D47—28no—
410C2×C22⋊D47—28no—
411C2×C22⋊D47—432no—
412C2×C22⋊D47—44no—
413C2×C22⋊D47—44no—
414C2×C22⋊D47—44no—
415C2×C22⋊D47—44no—
416C2×C22⋊D47—44no—
417C2×C22⋊D47—44no—
418C2×C22⋊D47C2414yes—
419C2×C22⋊D47C2418yes—
420C2×C22⋊D47C2418yes—
421C2×C22⋊D47C2414yes—
422C2×C22⋊D47C2418yes—
423C2×C22⋊D47C2418yes—
424C2×C22⋊D47C2418yes—
425C2×C22⋊D47C2418yes—
426C2×C22⋊D47C2418yes—
427C2×C22⋊D47C2418yes—
428C2×C22⋊D47C2418yes—
429C2×C22⋊D47C2418yes—
430C2×C22⋊D47C2418yes—
431C2×C22⋊D47C2418yes—
432C22×Dic47—24no—
433C22×Dic47—24no—
434C22×Dic47—24no—
435C22×Dic47—44no—
436C22×Dic47—44no—
437C22×Dic47#4118yescomplemented
438C22×Dic47C2411yescharacteristic
439C22×Dic47C2411yescharacteristic
440C22×Dic47C2411yescharacteristic
441C22×Dic47C2411yescharacteristic
442C22×Dic47C2414yes—
443C22×Dic47C2412yes—
444C22×Dic47C2412yes—
445C22×Dic47C2414yes—
446C22×Dic47C2414yes—
447C22×Dic47C2418yes—
448C22×Dic47C2418yes—
449C22×Dic47C2411yescharacteristic
450C22×Dic47C2411yescharacteristic
451C22×Dic47C2414yes—
452C22×Dic47C2411yescharacteristic
453#10625354—416no—
454#10625352—232no—
455#10625352—416no—
456#10625352—432no—
457#10625350—432no—
458#10625350—416no—
459C2×D188—24no—
460C2×D188—24no—
461C2×D188—416no—
462C2×D188—44no—
463C2×D188—44no—
464C2×D188—44no—
465C2×D188C2414yes—
466C2×D188C2414yes—
467C2×D188C2418yes—
468C2×D188C2418yes—
469C2×D188C2418yes—
470C2×C4×D47—24no—
471C2×C4×D47—24no—
472C2×C4×D47—24no—
473C2×C4×D47—44no—
474C2×C4×D47—44no—
475C2×C4×D47—44no—
476C2×C4×D47—44no—
477C2×C4×D47C2414yes—
478C2×C4×D47C2414yes—
479C2×C4×D47C2414yes—
480C2×C4×D47C2418yes—
481C2×C4×D47C2418yes—
482C2×C4×D47C2418yes—
483C2×C4×D47C2418yes—
484C2×Dic94—24no—
485C2×Dic94—24no—
486C2×Dic94—28no—
487C2×Dic94C2414yes—
488C2×Dic94C2418yes—
489C2×Dic94C2414yes—
490C4⋊C4×C47C2414yes—
491C4⋊C4×C47C2414yes—
492C4⋊C4×C47C2418yes—
493C22⋊C4×C47C2414yes—
494C22⋊C4×C47C2418yes—
495C22⋊C4×C47C2418yes—
496C22⋊C4×C47C2418yes—
497C22⋊C4×C47C2414yes—
498C22⋊C4×C47C2418yes—
499C22⋊C4×C47C2418yes—
500C42×C47C2414yes—
501C22⋊Dic47C2414yes—
502C22⋊Dic47C2418yes—
503C22⋊Dic47C2418yes—
504C22⋊Dic47C2418yes—
505C22⋊Dic47C2414yes—
506C22⋊Dic47C2418yes—
507C22⋊Dic47C2418yes—
508(C2×D47)⋊C4C2418yes—
509(C2×D47)⋊C4C2418yes—
510(C2×D47)⋊C4C2418yes—
511(C2×D47)⋊C4C2418yes—
512(C2×D47)⋊C4C2414yes—
513(C2×D47)⋊C4C2414yes—
514(C2×D47)⋊C4C2418yes—
515(C2×D47)⋊C4C2418yes—
516(C2×D47)⋊C4C2418yes—
517(C2×D47)⋊C4C2418yes—
518C4⋊Dic47C2414yes—
519C4⋊Dic47C2414yes—
520C4⋊Dic47C2418yes—
521Dic47⋊C4C2414yes—
522Dic47⋊C4C2414yes—
523Dic47⋊C4C2418yes—
524Dic47⋊C4C2418yes—
525Dic47⋊C4C2414yes—
526Dic47⋊C4C2414yes—
527Dic47⋊C4C2418yes—
528Dic47⋊C4C2418yes—
529Dic47⋊C4C2418yes—
530C4×Dic47C2414yes—
531C4×Dic47C2414yes—
532C4×Dic47C2414yes—
533C4×Dic47C2414yes—
534C4×Dic47C2414yes—
535C4×Dic47C2414yes—
536C4×Dic47C2414yes—
537C4×Dic47C2414yes—
538C4×Dic47C2414yes—
539C4×Dic47C2418yes—
540C4×Dic47C2418yes—
541C23×C47—22no—
542C23×C47—22no—
543C23×C47—22no—
544C23×C47—24no—
545C23×C47—24no—
546C23×C47—22no—
547C23×C47—24no—
548C23×C47—24no—
549C23×C47—24no—
550C23×C47—22no—
551C23×C47—24no—
552C23×C47—216no—
553C23×C47—48no—
554C23×C47—48no—
555C23×C47—816no—
556C23×C47C2×#4114yes—
557C23×C47C2514yes—
558C23×C47C2514yes—
559C23×C47C2512yes—
560C23×C47C2512yes—
561C23×C47C2511yescharacteristic
562C22×D47—22no—
563C22×D47—24no—
564C22×D47—24no—
565C22×D47—22no—
566C22×D47—22no—
567C22×D47—24no—
568C22×D47—24no—
569C22×D47—24no—
570C22×D47—24no—
571C22×D47—216no—
572C22×D47—48no—
573C22×D47—48no—
574C22×D47—816no—
575C22×D47C2514yes—
576C22×D47C2514yes—
577C22×D47C2512yes—
578Q8×C47—28no—
579D4×C47—28no—
580D4×C47—28no—
581D4×C47—28no—
582D4×C47—48no—
583D4×C47—48no—
584D4×C47—48no—
585C2×C4×C47—22no—
586C2×C4×C47—24no—
587C2×C4×C47—22no—
588C2×C4×C47—22no—
589C2×C4×C47—24no—
590C2×C4×C47—22no—
591C2×C4×C47—28no—
592C2×C4×C47—28no—
593C2×C4×C47—48no—
594C2×C4×C47—48no—
595C2×C4×C47H(5,𝔽2)14yes—
596C2×C4×C47C2512yes—
597C2×C4×C47C2512yes—
598C2×C4×C47C2514yes—
599C2×C4×C47C2512yes—
600C2×C4×C47C2514yes—
601C2×C4×C47C2512yes—
602C2×C4×C47C2512yes—
603C22⋊D47—28no—
604C22⋊D47—28no—
605C22⋊D47—216no—
606C22⋊D47—216no—
607C22⋊D47—216no—
608C22⋊D47—216no—
609C22⋊D47—216no—
610C22⋊D47—216no—
611C22⋊D47—48no—
612C22⋊D47—48no—
613C22⋊D47—48no—
614C22⋊D47—48no—
615C22⋊D47—48no—
616C22⋊D47—48no—
617C2×Dic47—22no—
618C2×Dic47—24no—
619C2×Dic47—24no—
620C2×Dic47—22no—
621C2×Dic47—22no—
622C2×Dic47—22no—
623C2×Dic47—28no—
624C2×Dic47—28no—
625C2×Dic47—28no—
626C2×Dic47—48no—
627C2×Dic47—48no—
628C2×Dic47C2×#4114yes—
629C2×Dic47C2×#4114yes—
630C2×Dic47C2×#41116yescomplemented
631C2×Dic47H(5,𝔽2)14yes—
632C2×Dic47C2512yes—
633C2×Dic47C2512yes—
634C2×Dic47C2512yes—
635C2×Dic47C2512yes—
636C2×Dic47C2514yes—
637C2×Dic47C2514yes—
638C2×Dic47C2512yes—
639C2×Dic47C2512yes—
640C2×Dic47C2512yes—
641D188—28no—
642D188—28no—
643D188—48no—
644D188—48no—
645D188—48no—
646C4×D47—28no—
647C4×D47—28no—
648C4×D47—28no—
649C4×D47—48no—
650C4×D47—48no—
651C4×D47—48no—
652C4×D47—48no—
653Dic94—28no—
654Dic94—28no—
655Dic94—216no—
656C2×#3508—471nomaximal, Sylow
657C22×C47—22no—
658C22×C47—22no—
659C22×C47—28no—
660C22×C47—22no—
661C22×C47—24no—
662C22×C47—24no—
663C22×C47—22no—
664C22×C47—24no—
665C22×C47—24no—
666C22×C47—24no—
667C22×C47—22no—
668C22×C47—24no—
669C22×C47—44no—
670C22×C47—48no—
671C22×C47—48no—
672C22×C47—816no—
673C22×C47C22×#4114yes—
674C22×C47C22×#4112yes—
675C22×C47C2×H(5,𝔽2)12yes—
676C22×C47C2×H(5,𝔽2)12yes—
677C22×C47C2611yescharacteristic
678C2×D47—22no—
679C2×D47—24no—
680C2×D47—24no—
681C2×D47—22no—
682C2×D47—22no—
683C2×D47—24no—
684C2×D47—24no—
685C2×D47—24no—
686C2×D47—24no—
687C2×D47—44no—
688C2×D47—48no—
689C2×D47—48no—
690C2×D47—816no—
691C4×C47—22no—
692C4×C47—24no—
693C4×C47—22no—
694C4×C47—22no—
695C4×C47—24no—
696C4×C47—22no—
697C4×C47C2×H(5,𝔽2)14yes—
698Dic47—22no—
699Dic47—24no—
700Dic47—24no—
701Dic47—22no—
702Dic47—22no—
703Dic47—22no—
704Dic47C22×#4114yes—
705Dic47C22×#4114yes—
706Dic47C2×H(5,𝔽2)14yes—
707#3508—4732no—
708C2×#559—471no—
709C2×#559—472no—
710C2×#559—471no—
711C2×#550—471no—
712C2×#550—471no—
713C2×#550—472no—
714C2×#546—471no—
715C2×#546—471no—
716C2×#546—472no—
717C2×#546—471no—
718C2×#546—472no—
719C2×#546D4711yescharacteristic, complemented
720C2×#540—472no—
721C2×#540—472no—
722C2×#535—472no—
723C2×#533—471no—
724C2×#532—471no—
725C2×#532—471no—
726C2×#532—471no—
727C2×#532—471no—
728C22×#127—471no—
729C2×#518—472no—
730C2×C4×#41—471no—
731C2×C47—24no—
732C2×C47—42no—
733C2×C47—44no—
734C2×C47—44no—
735C2×C47#350814yescomplemented
736C2×C47C23×#4111yescharacteristic
737C2×C47C22×H(5,𝔽2)11yescharacteristic
738C2×C47C22×H(5,𝔽2)11yescharacteristic
739D47—42no—
740D47—44no—
741D47—44no—
742C22×#41—471no—
743C22×#41—471no—
744C22×#41—472no—
745C22×#41—471no—
746C22×#41—472no—
747C22×#41—471no—
748C22×#41C2×D4711yescharacteristic, complemented
749C23×D4—472no—
750C23×D4—472no—
751C23×D4—471no—
752C23×D4C2×D4711yescharacteristic
753#559—4716no—
754#559—4732no—
755#559—4716no—
756#550—4716no—
757#550—4716no—
758#550—4732no—
759#546—4716no—
760#546—4716no—
761#546—4732no—
762#546—4716no—
763#546—4732no—
764#546C2×D47116yescomplemented
765#540—4732no—
766#540—4732no—
767#535—4732no—
768#533—4716no—
769#532—4716no—
770#532—4716no—
771#532—4716no—
772#532—4716no—
773C2×C4⋊Q8—471no—
774C2×C4⋊Q8—471no—
775C2×#127—471no—
776C2×#127—471no—
777C2×#127—472no—
778C2×#127—472no—
779C2×#127—471no—
780C2×#127—471no—
781C2×#127—4716no—
782C2×#127—472no—
783C2×#127—472no—
784C2×#125—472no—
785C2×#124—471no—
786C2×#124—471no—
787C2×#124—472no—
788C2×#124—472no—
789C2×#124—472no—
790C2×#124—472no—
791C2×#124—471no—
792C2×#124C2×D4711yescharacteristic, complemented
793C2×#123—472no—
794C2×#123—472no—
795C2×#123—472no—
796C2×#123—472no—
797C2×#123—472no—
798C2×#123—472no—
799C2×#123—472no—
800C2×#123C2×D4712yescomplemented
801C2×C22⋊Q8—471no—
802C2×C22⋊Q8—472no—
803C2×C22⋊Q8C2×D4711yescharacteristic
804C2×#121—472no—
805C2×#121—472no—
806C2×#121—471no—
807C2×#121—472no—
808C2×#121—472no—
809C2×#121—472no—
810C2×#121—472no—
811C2×#121—471no—
812C2×#121—472no—
813C2×#121—471no—
814C2×#121—472no—
815C2×#121—472no—
816C2×#121—472no—
817C2×#121—472no—
818C2×#121—472no—
819C2×#121—472no—
820C2×#121C2×D4711yescharacteristic, complemented
821C2×#121C2×D4712yescomplemented
822C2×#120—472no—
823C2×#120—472no—
824C2×#120—472no—
825C2×#120C2×D4712yes—
826#518—4732no—
827C4×#41—4716no—
828C2×C4×Q8—471no—
829C2×C4×Q8—471no—
830C2×C4×Q8—472no—
831C2×C4×Q8—471no—
832C2×C4×Q8—471no—
833C2×C4×D4—471no—
834C2×C4×D4—471no—
835C2×C4×D4—471no—
836C2×C4×D4—471no—
837C2×C4×D4—472no—
838C2×C4×D4—472no—
839C2×C4×D4—472no—
840C2×C4×D4—472no—
841C2×C4×D4—472no—
842C2×C4×D4—471no—
843C2×C4×D4—471no—
844C2×C4×D4—471no—
845C2×C4×D4—472no—
846C2×C4×D4—472no—
847C2×C4×D4—472no—
848C2×C4×D4—472no—
849C2×C4×D4—472no—
850C2×C4×D4—471no—
851C2×C4×D4C2×D4711yescharacteristic
852C2×C4×D4C2×D4711yescharacteristic, complemented
853C2×#117—471no—
854C2×#117—471no—
855C2×#117—471no—
856C2×#117—472no—
857C22×C22⋊C4—472no—
858C22×C22⋊C4—472no—
859C22×C22⋊C4—472no—
860C22×C22⋊C4C2×D4712yes—
861C22×C42—471no—
862C22×C42—471no—
863C22×C42—471no—
864C47C2×#350811yescharacteristic, complemented, Sylow
865C25—472no—
866C25C22×D4712yes—
867C2×#41—44no—
868C2×#41—478no—
869C2×#41—478no—
870C2×#41—4716no—
871C2×#41—478no—
872C2×#41—4716no—
873C2×#41—478no—
874C2×#41—948no—
875C2×#41—1884no—
876C2×#41—1888no—
877C2×#41—1884no—
878C2×#41—1888no—
879C2×#41—1884no—
880C2×#41C22×D4718yescomplemented
881C22×Q8—471no—
882C22×Q8—472no—
883C22×Q8—471no—
884C22×Q8C22×D4711yescharacteristic
885C22×D4—44no—
886C22×D4—471no—
887C22×D4—472no—
888C22×D4—472no—
889C22×D4—472no—
890C22×D4—472no—
891C22×D4—471no—
892C22×D4—472no—
893C22×D4—472no—
894C22×D4—4716no—
895C22×D4—472no—
896C22×D4—472no—
897C22×D4—472no—
898C22×D4—472no—
899C22×D4—472no—
900C22×D4—472no—
901C22×D4—4716no—
902C22×D4—471no—
903C22×D4—471no—
904C22×D4—472no—
905C22×D4—472no—
906C22×D4—472no—
907C22×D4—478no—
908C22×D4—9416no—
909C22×D4—1884no—
910C22×D4—1888no—
911C22×D4C22×D4711yescharacteristic
912C22×D4C22×D4711yescharacteristic
913C22×D4C22×D4711yescharacteristic
914C22×D4C22×D4712yes—
915C22×D4C22×D4712yes—
916C22×D4C22×D4712yes—
917C22×D4C22×D4718yes—
918C23×C4—471no—
919C23×C4—471no—
920C23×C4—471no—
921C23×C4—471no—
922C23×C4—472no—
923C23×C4—472no—
924C23×C4—471no—
925C23×C4—471no—
926C23×C4—471no—
927C23×C4—472no—
928C23×C4—472no—
929C23×C4—472no—
930C23×C4—472no—
931C23×C4C22×D4711yescharacteristic
932C23×C4C22×D4711yescharacteristic
933C23×C4C22×D4712yes—
934C23×C4C22×D4712yes—
935C4⋊Q8—478no—
936C4⋊Q8—478no—
937#127—478no—
938#127—478no—
939#127—4716no—
940#127—4716no—
941#127—478no—
942#127—478no—
943#127—4716no—
944#127—4716no—
945#125—4716no—
946#124—478no—
947#124—478no—
948#124—4716no—
949#124—4716no—
950#124—4716no—
951#124—4716no—
952#124—478no—
953#124C22×D4718yescomplemented
954#123—4716no—
955#123—4716no—
956#123—4716no—
957#123—4716no—
958#123—4716no—
959#123—4716no—
960#123—4716no—
961#123C22×D47116yescomplemented
962C22⋊Q8—478no—
963C22⋊Q8—4716no—
964C22⋊Q8C22×D4718yes—
965#121—4716no—
966#121—4716no—
967#121—478no—
968#121—4716no—
969#121—4716no—
970#121—4716no—
971#121—4716no—
972#121—478no—
973#121—4716no—
974#121—478no—
975#121—4716no—
976#121—4716no—
977#121—4716no—
978#121—4716no—
979#121—4716no—
980#121—4716no—
981#121C22×D4718yescomplemented
982#121C22×D47116yescomplemented
983#120—4716no—
984#120—4716no—
985#120—4716no—
986#120C22×D47116yes—
987C4×Q8—478no—
988C4×Q8—478no—
989C4×Q8—4716no—
990C4×Q8—478no—
991C4×Q8—478no—
992C4×D4—478no—
993C4×D4—478no—
994C4×D4—478no—
995C4×D4—478no—
996C4×D4—4716no—
997C4×D4—4716no—
998C4×D4—4716no—
999C4×D4—4716no—
1000C4×D4—4716no—
1001C4×D4—478no—
1002C4×D4—478no—
1003C4×D4—478no—
1004C4×D4—4716no—
1005C4×D4—4716no—
1006C4×D4—4716no—
1007C4×D4—4716no—
1008C4×D4—4716no—
1009C4×D4—478no—
1010C4×D4C22×D4718yes—
1011C4×D4C22×D4718yescomplemented
1012#117—478no—
1013#117—478no—
1014#117—478no—
1015#117—4716no—
1016C2×C4⋊C4—471no—
1017C2×C4⋊C4—471no—
1018C2×C4⋊C4—472no—
1019C2×C4⋊C4—472no—
1020C2×C4⋊C4—471no—
1021C2×C4⋊C4—471no—
1022C2×C4⋊C4—471no—
1023C2×C4⋊C4—472no—
1024C2×C4⋊C4—471no—
1025C2×C4⋊C4—472no—
1026C2×C4⋊C4—472no—
1027C2×C4⋊C4—472no—
1028C2×C4⋊C4C22×D4711yescharacteristic
1029C2×C4⋊C4C22×D4711yescharacteristic
1030C2×C4⋊C4C22×D4712yes—
1031C2×C22⋊C4—471no—
1032C2×C22⋊C4—472no—
1033C2×C22⋊C4—472no—
1034C2×C22⋊C4—472no—
1035C2×C22⋊C4—4716no—
1036C2×C22⋊C4—471no—
1037C2×C22⋊C4—472no—
1038C2×C22⋊C4—472no—
1039C2×C22⋊C4—472no—
1040C2×C22⋊C4—472no—
1041C2×C22⋊C4—472no—
1042C2×C22⋊C4—472no—
1043C2×C22⋊C4—471no—
1044C2×C22⋊C4—471no—
1045C2×C22⋊C4—472no—
1046C2×C22⋊C4—472no—
1047C2×C22⋊C4—472no—
1048C2×C22⋊C4—472no—
1049C2×C22⋊C4—4716no—
1050C2×C22⋊C4—4716no—
1051C2×C22⋊C4C22×D4711yescharacteristic
1052C2×C22⋊C4C22×D4712yes—
1053C2×C22⋊C4C22×D4712yes—
1054C2×C22⋊C4C22×D4712yes—
1055C2×C22⋊C4C22×D47116yes—
1056C2×C22⋊C4C22×D4711yescharacteristic
1057C2×C22⋊C4C22×D4712yes—
1058C2×C22⋊C4C22×D4712yes—
1059C2×C42—471no—
1060C2×C42—471no—
1061C2×C42—471no—
1062C2×C42—472no—
1063C2×C42—472no—
1064C2×C42—471no—
1065C2×C42—471no—
1066C2×C42—471no—
1067C2×C42—471no—
1068C2×C42—471no—
1069C2×C42—478no—
1070C2×C42—478no—
1071C2×C42—471no—
1072C2×C42—478no—
1073C2×C42C22×D4711yescharacteristic
1074C24—28no—
1075C24—44no—
1076C24—44no—
1077C24—472no—
1078C24—472no—
1079C24—471no—
1080C24—478no—
1081C24—948no—
1082C24—1884no—
1083C24—1884no—
1084C24C23×D4712yes—
1085C24C23×D4712yes—
1086C24C23×D4711yescharacteristic
1087C24C23×D4711yescharacteristic
1088C24C23×D4718yes—
1089#41—416no—
1090#41—9432no—
1091#41—18816no—
1092#41—18832no—
1093#41—18816no—
1094#41—18832no—
1095#41—18816no—
1096C2×Q8—24no—
1097C2×Q8—474no—
1098C2×Q8—478no—
1099C2×Q8—474no—
1100C2×Q8—944no—
1101C2×Q8—948no—
1102C2×Q8—944no—
1103C2×Q8C23×D4714yes—
1104C2×D4—24no—
1105C2×D4—24no—
1106C2×D4—24no—
1107C2×D4—416no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—474no—
1112C2×D4—478no—
1113C2×D4—478no—
1114C2×D4—478no—
1115C2×D4—478no—
1116C2×D4—474no—
1117C2×D4—478no—
1118C2×D4—478no—
1119C2×D4—478no—
1120C2×D4—478no—
1121C2×D4—478no—
1122C2×D4—478no—
1123C2×D4—478no—
1124C2×D4—478no—
1125C2×D4—474no—
1126C2×D4—474no—
1127C2×D4—478no—
1128C2×D4—478no—
1129C2×D4—478no—
1130C2×D4—948no—
1131C2×D4—948no—
1132C2×D4—948no—
1133C2×D4—948no—
1134C2×D4—9464no—
1135C2×D4—948no—
1136C2×D4—948no—
1137C2×D4—944no—
1138C2×D4—944no—
1139C2×D4—944no—
1140C2×D4—944no—
1141C2×D4—18816no—
1142C2×D4—1884no—
1143C2×D4—1884no—
1144C2×D4—1884no—
1145C2×D4—18832no—
1146C2×D4—1884no—
1147C2×D4—1884no—
1148C2×D4—1884no—
1149C2×D4—1884no—
1150C2×D4—1884no—
1151C2×D4—1884no—
1152C2×D4C23×D4714yes—
1153C2×D4C23×D4714yes—
1154C2×D4C23×D4714yes—
1155C2×D4C23×D4718yes—
1156C2×D4C23×D4718yes—
1157C2×D4C23×D4718yes—
1158C22×C4—24no—
1159C22×C4—24no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—478no—
1163C22×C4—474no—
1164C22×C4—471no—
1165C22×C4—471no—
1166C22×C4—471no—
1167C22×C4—474no—
1168C22×C4—474no—
1169C22×C4—474no—
1170C22×C4—471no—
1171C22×C4—471no—
1172C22×C4—471no—
1173C22×C4—471no—
1174C22×C4—472no—
1175C22×C4—472no—
1176C22×C4—478no—
1177C22×C4—478no—
1178C22×C4—474no—
1179C22×C4—474no—
1180C22×C4—474no—
1181C22×C4—478no—
1182C22×C4—478no—
1183C22×C4—478no—
1184C22×C4—478no—
1185C22×C4—944no—
1186C22×C4—944no—
1187C22×C4—944no—
1188C22×C4—944no—
1189C22×C4—944no—
1190C22×C4—944no—
1191C22×C4—1884no—
1192C22×C4—1884no—
1193C22×C4—1884no—
1194C22×C4—1884no—
1195C22×C4—1884no—
1196C22×C4—1884no—
1197C22×C4C23×D4714yes—
1198C22×C4C23×D4714yes—
1199C22×C4C23×D4711yescharacteristic
1200C22×C4C23×D4711yescharacteristic
1201C22×C4C23×D4711yescharacteristic
1202C22×C4C23×D4711yescharacteristic
1203C22×C4C23×D4712yes—
1204C22×C4C23×D4712yes—
1205C22×C4C23×D4718yes—
1206C22×C4C23×D4718yes—
1207C22×C4C23×D4711yescharacteristic
1208C4⋊C4—474no—
1209C4⋊C4—474no—
1210C4⋊C4—478no—
1211C4⋊C4—478no—
1212C4⋊C4—474no—
1213C4⋊C4—474no—
1214C4⋊C4—478no—
1215C4⋊C4—478no—
1216C4⋊C4—478no—
1217C4⋊C4—474no—
1218C4⋊C4—474no—
1219C4⋊C4—478no—
1220C4⋊C4C23×D4714yes—
1221C4⋊C4C23×D4714yes—
1222C4⋊C4C23×D4718yes—
1223C22⋊C4—474no—
1224C22⋊C4—478no—
1225C22⋊C4—478no—
1226C22⋊C4—478no—
1227C22⋊C4—474no—
1228C22⋊C4—478no—
1229C22⋊C4—478no—
1230C22⋊C4—478no—
1231C22⋊C4—478no—
1232C22⋊C4—478no—
1233C22⋊C4—478no—
1234C22⋊C4—474no—
1235C22⋊C4—474no—
1236C22⋊C4—478no—
1237C22⋊C4—478no—
1238C22⋊C4—478no—
1239C22⋊C4—478no—
1240C22⋊C4C23×D4714yes—
1241C22⋊C4C23×D4718yes—
1242C22⋊C4C23×D4718yes—
1243C22⋊C4C23×D4718yes—
1244C22⋊C4C23×D4714yes—
1245C22⋊C4C23×D4718yes—
1246C22⋊C4C23×D4718yes—
1247C42—474no—
1248C42—474no—
1249C42—474no—
1250C42—474no—
1251C42—474no—
1252C42—474no—
1253C42—474no—
1254C42—474no—
1255C42—474no—
1256C42—478no—
1257C42—478no—
1258C42C23×D4714yes—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—22no—
1266C23—24no—
1267C23—22no—
1268C23—24no—
1269C23—24no—
1270C23—216no—
1271C23—48no—
1272C23—48no—
1273C23—816no—
1274C23—474no—
1275C23—474no—
1276C23—472no—
1277C23—9416no—
1278C23—942no—
1279C23—944no—
1280C23—944no—
1281C23—942no—
1282C23—944no—
1283C23—944no—
1284C23—942no—
1285C23—944no—
1286C23—944no—
1287C23—37616no—
1288C23—1888no—
1289C23—1888no—
1290C23#41×D4714yes—
1291C23C24×D4714yes—
1292C23C24×D4714yes—
1293C23C24×D4712yes—
1294C23C24×D4712yes—
1295C23C24×D4711yescharacteristic
1296Q8—28no—
1297Q8—948no—
1298Q8—9416no—
1299Q8—948no—
1300D4—28no—
1301D4—28no—
1302D4—28no—
1303D4—48no—
1304D4—48no—
1305D4—48no—
1306D4—9416no—
1307D4—9416no—
1308D4—9416no—
1309D4—9416no—
1310D4—9416no—
1311D4—9416no—
1312D4—948no—
1313D4—948no—
1314D4—948no—
1315D4—948no—
1316D4—1888no—
1317D4—1888no—
1318D4—1888no—
1319D4—1888no—
1320D4—1888no—
1321D4—1888no—
1322D4—1888no—
1323D4—1888no—
1324D4—1888no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—28no—
1332C2×C4—28no—
1333C2×C4—48no—
1334C2×C4—48no—
1335C2×C4—474no—
1336C2×C4—474no—
1337C2×C4—4716no—
1338C2×C4—474no—
1339C2×C4—472no—
1340C2×C4—472no—
1341C2×C4—472no—
1342C2×C4—472no—
1343C2×C4—472no—
1344C2×C4—472no—
1345C2×C4—472no—
1346C2×C4—474no—
1347C2×C4—474no—
1348C2×C4—948no—
1349C2×C4—948no—
1350C2×C4—948no—
1351C2×C4—948no—
1352C2×C4—948no—
1353C2×C4—942no—
1354C2×C4—942no—
1355C2×C4—942no—
1356C2×C4—944no—
1357C2×C4—942no—
1358C2×C4—944no—
1359C2×C4—948no—
1360C2×C4—1888no—
1361C2×C4—1888no—
1362C2×C4—1888no—
1363C2×C4—1888no—
1364C2×C4—1888no—
1365C2×C4—1888no—
1366C2×C4#1309406914yes—
1367C2×C4C24×D4712yes—
1368C2×C4C24×D4712yes—
1369C2×C4C24×D4712yes—
1370C2×C4C24×D4712yes—
1371C2×C4C24×D4714yes—
1372C2×C4C24×D4714yes—
1373C2×C4C24×D4712yes—
1374C22—22no—
1375C22—22no—
1376C22—28no—
1377C22—22no—
1378C22—24no—
1379C22—24no—
1380C22—24no—
1381C22—22no—
1382C22—24no—
1383C22—22no—
1384C22—24no—
1385C22—24no—
1386C22—48no—
1387C22—48no—
1388C22—44no—
1389C22—816no—
1390C22—942no—
1391C22—944no—
1392C22—944no—
1393C22—942no—
1394C22—944no—
1395C22—944no—
1396C22—942no—
1397C22—944no—
1398C22—944no—
1399C22—37616no—
1400C22—1888no—
1401C22—1888no—
1402C22—1884no—
1403C22C2×#41×D4714yes—
1404C22C2×#41×D4712yes—
1405C22H(5,𝔽2)×D4712yes—
1406C22C2×#1309406912yes—
1407C22C25×D4711yescharacteristic
1408C4—22no—
1409C4—22no—
1410C4—24no—
1411C4—22no—
1412C4—22no—
1413C4—24no—
1414C4—474no—
1415C4—474no—
1416C4—474no—
1417C4—942no—
1418C4—942no—
1419C4—942no—
1420C4—944no—
1421C4—942no—
1422C4—944no—
1423C4C2×#1309406914yes—
1424C2—24no—
1425C2—44no—
1426C2—44no—
1427C2—42no—
1428C2—1884no—
1429C2—1884no—
1430C2—1882no—
1431C2#2025725614yesdirect product factor
1432C2C22×#41×D4711yescharacteristic
1433C2C2×H(5,𝔽2)×D4711yescharacteristic
1434C2C22×#1309406911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#546C2
socleC23×C47C25
hypercenterC2×#546D47
hypocenterC47C2×#3508
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. #20257256C2direct (N × H)
2. C2×#15689857C2semidirect
3. C2×#15689856C2semidirect
4. C2×#15689855C2semidirect
5. C2×#15689792C2semidirect
6. C2×#15689791C2semidirect
7. C2×#15689791C2semidirect
8. C2×#15689769C2semidirect
9. C2×#15689767C2semidirect
10. C2×#15689764C2semidirect
11. C2×#15689763C2semidirect
12. C2×#15689760C2semidirect
13. C2×#15689725C2semidirect
14. C2×#15689723C2semidirect
15. C2×#15689688C2semidirect
16. C2×#15689675C2semidirect
17. C2×#15689672C2semidirect
18. C2×#15689670C2semidirect
19. C2×#15689669C2semidirect
20. C2×#15689668C2semidirect
21. C22×#13094020C2semidirect
22. C2×#15689596C2semidirect
23. C2×C4×#10625352C2semidirect
24. C2×C47×#546C2semidirect
25. C22×#10625354C22semidirect
26. C22×#10625350C22semidirect
27. C22×#10625350C22semidirect
29. C22×#10625352C22semidirect
30. C22×#10625352C22semidirect
34. #15689857C22semidirect
35. #15689856C22semidirect
36. #15689855C22semidirect
37. #15689792C22semidirect
38. #15689791C22semidirect
39. #15689791C22semidirect
40. #15689769C22semidirect
41. #15689767C22semidirect
42. #15689764C22semidirect
43. #15689763C22semidirect
44. #15689760C22semidirect
45. #15689725C22semidirect
46. #15689723C22semidirect
47. #15689688C22semidirect
48. #15689675C22semidirect
49. #15689672C22semidirect
50. #15689670C22semidirect
51. #15689669C22semidirect
52. #15689668C22semidirect
53. C2×#13094023C22semidirect
54. C2×#13094022C22semidirect
61. C2×#13094020C22semidirect
62. C2×#13094020C22semidirect
63. C2×#13094020C22semidirect
64. C2×#13094014C22semidirect
65. C2×#13094013C22semidirect
66. C2×#13094012C22semidirect
67. C2×#13094011C22semidirect
68. C2×#13094010C22semidirect
69. C2×#13094010C22semidirect
70. C2×#13094010C22semidirect
71. C2×#13094010C22semidirect
72. C2×#13094009C22semidirect
73. C2×#13094009C22semidirect
74. C2×#13094008C22semidirect
75. C2×#13094007C22semidirect
76. C2×#13094006C22semidirect
77. C2×#13094006C22semidirect
78. C2×#13094005C22semidirect
81. C2×#13093999C22semidirect
82. C2×#13093999C22semidirect
83. C2×#13093998C22semidirect
84. C2×#13093998C22semidirect
85. C2×#13093997C22semidirect
86. C2×#13093997C22semidirect
87. C2×#13093997C22semidirect
88. C2×#13093997C22semidirect
89. C2×#13093997C22semidirect
90. C2×#13093996C22semidirect
91. C2×#13093996C22semidirect
92. C2×#13093996C22semidirect
93. C2×#13093996C22semidirect
94. C2×#13093996C22semidirect
95. C2×#13093995C22semidirect
96. C2×#13093995C22semidirect
100. #15689596C22semidirect
101. C4×#10625352C22semidirect
102. C2×Q8×Dic47C22semidirect
103. C2×C4×Dic94C22semidirect
104. C2×#13093989C22semidirect
105. C2×#13093989C22semidirect
106. C2×#13093989C22semidirect
107. C2×C4×D188C22semidirect
109. C2×D4×Dic47C22semidirect
110. C2×#13093986C22semidirect
112. C2×C4×C22⋊D47C22semidirect
113. C2×C4×C22⋊D47C22semidirect
114. C2×C4×C22⋊D47C22semidirect
115. C2×C4×C22⋊D47C22semidirect
116. C2×C4×C22⋊D47C22semidirect
117. C2×C4×C22⋊D47C22semidirect
119. C2×(C22⋊D47)⋊C4C22semidirect
120. C2×(C22⋊D47)⋊C4C22semidirect
121. C2×(C22⋊D47)⋊C4C22semidirect
122. C2×(C22⋊D47)⋊C4C22semidirect
123. C2×(C22⋊D47)⋊C4C22semidirect
124. C2×(C22⋊D47)⋊C4C22semidirect
125. C2×#13093982C22semidirect
128. C2×#13093980C22semidirect
133. C22×C4×Dic47C22semidirect
134. C2×C42×D47C22semidirect
135. C22×#41×C47C22semidirect
137. C47×#546C22semidirect
138. C2×#124×C47C22semidirect
139. C2×#123×C47C22semidirect
141. C2×#121×C47C22semidirect
142. C2×#121×C47C22semidirect
145. C2×C4×D4×C47C22semidirect
149. C2×#10625354C23semidirect
152. C2×#10625350C23semidirect
153. C2×#10625350C23semidirect
158. C2×#10625352C23semidirect
159. C2×#10625352C23semidirect
201. #13094023C23semidirect
202. #13094022C23semidirect
209. #13094020C23semidirect
210. #13094020C23semidirect
211. #13094014C23semidirect
212. #13094013C23semidirect
213. #13094012C23semidirect
214. #13094011C23semidirect
215. #13094010C23semidirect
216. #13094010C23semidirect
217. #13094010C23semidirect
218. #13094010C23semidirect
219. #13094009C23semidirect
220. #13094009C23semidirect
221. #13094008C23semidirect
222. #13094007C23semidirect
223. #13094006C23semidirect
224. #13094006C23semidirect
225. #13094005C23semidirect
228. #13093999C23semidirect
229. #13093999C23semidirect
230. #13093998C23semidirect
231. #13093998C23semidirect
232. #13093997C23semidirect
233. #13093997C23semidirect
234. #13093997C23semidirect
235. #13093997C23semidirect
236. #13093997C23semidirect
237. #13093996C23semidirect
238. #13093996C23semidirect
239. #13093996C23semidirect
240. #13093996C23semidirect
241. #13093996C23semidirect
242. #13093995C23semidirect
243. #13093995C23semidirect
247. Q8×Dic47C23semidirect
248. C4×Dic94C23semidirect
249. #13093989C23semidirect
250. #13093989C23semidirect
251. #13093989C23semidirect
252. C4×D188C23semidirect
254. D4×Dic47C23semidirect
255. #13093986C23semidirect
257. C4×C22⋊D47C23semidirect
258. C4×C22⋊D47C23semidirect
259. C4×C22⋊D47C23semidirect
260. C4×C22⋊D47C23semidirect
261. C4×C22⋊D47C23semidirect
262. C4×C22⋊D47C23semidirect
264. (C22⋊D47)⋊C4C23semidirect
265. (C22⋊D47)⋊C4C23semidirect
266. (C22⋊D47)⋊C4C23semidirect
267. (C22⋊D47)⋊C4C23semidirect
268. (C22⋊D47)⋊C4C23semidirect
269. (C22⋊D47)⋊C4C23semidirect
270. #13093982C23semidirect
273. #13093980C23semidirect
318. C2×C4×Dic47C23semidirect
319. C42×D47C23semidirect
322. C2×#41×C47C23semidirect
336. #124×C47C23semidirect
337. #123×C47C23semidirect
339. #121×C47C23semidirect
340. #121×C47C23semidirect
343. C4×D4×C47C23semidirect
437. C22×Dic47#41semidirect
630. C2×Dic47C2×#41semidirect
719. C2×#546D47semidirect
735. C2×C47#3508semidirect
748. C22×#41C2×D47semidirect
764. #546C2×D47semidirect
792. C2×#124C2×D47semidirect
800. C2×#123C2×D47semidirect
820. C2×#121C2×D47semidirect
821. C2×#121C2×D47semidirect
852. C2×C4×D4C2×D47semidirect
864. C47C2×#3508semidirect
880. C2×#41C22×D47semidirect
953. #124C22×D47semidirect
961. #123C22×D47semidirect
981. #121C22×D47semidirect
982. #121C22×D47semidirect
1011. C4×D4C22×D47semidirect
1431. C2#20257256direct (N × H)

Maximal subgroups

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

subgroupindex
#202572562
C2×#156898572
C2×#156898562
C2×#156898552
C2×#156897922
C2×#156897912
C2×#156897692
C2×#156897672
C2×#156897642
C2×#156897632
C2×#156897602
C2×#156897252
C2×#156897232
C2×#156896882
C2×#156896752
C2×#156896722
C2×#156896702
C2×#156896692
C2×#156896682
C22×#130940202
C2×#156895962
C2×C4×#106253522
C2×C47×#5462
C2×#350847