Finite Group Databasebeta

← C2×#20257606 #27123496

Subgroups — C2×#20257606 #27123496

Order 12032.

7962 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257606C2132yesmaximal, direct product factor
2C2×#15689868C212yesmaximal, complemented
3C2×#15689868C212yesmaximal, complemented
4C2×#15689831C211yesmaximal, characteristic, complemented
5C2×#15689828C211yesmaximal, characteristic, complemented
6C2×#15689783C211yesmaximal, characteristic, complemented
7C2×#15689780C211yesmaximal, characteristic, complemented
8C2×#15689774C211yesmaximal, characteristic, complemented
9C2×#15689773C211yesmaximal, characteristic, complemented
10C2×#15689770C211yesmaximal, characteristic, complemented
11C2×#15689770C212yesmaximal, complemented
12C2×#15689762C212yesmaximal, complemented
13C2×#15689761C211yesmaximal, characteristic, complemented
14C2×#15689748C212yesmaximal, complemented
15C2×#15689746C211yesmaximal, characteristic, complemented
16C2×#15689740C211yesmaximal, characteristic, complemented
17C2×#15689719C212yesmaximal, complemented
18C2×#15689705C212yesmaximal, complemented
19C2×#15689702C212yesmaximal, complemented
20C2×#15689701C211yesmaximal, characteristic, complemented
21C2×#15689630C211yesmaximal, characteristic, complemented
22C2×C22⋊Q8×D47C211yesmaximal, characteristic, complemented
23C2×#121×D47C211yesmaximal, characteristic, complemented
24C2×C47×#537C211yesmaximal, characteristic, complemented
25C22×#10625350C2212yescomplemented
26C22×#10625350C2211yescharacteristic, complemented
27C22×#10625352C2212yescomplemented
28C22×Q8×D47C2211yescharacteristic, complemented
29C22×D4×D47C2211yescharacteristic
30C22×D4×D47C2212yes—
31C23×C4×D47C2211yescharacteristic
32#15689868C22132yescomplemented
33#15689868C22132yescomplemented
34#15689831C22116yescomplemented
35#15689828C22116yescomplemented
36#15689783C22116yescomplemented
37#15689780C22116yescomplemented
38#15689774C22116yescomplemented
39#15689773C22116yescomplemented
40#15689770C22116yescomplemented
41#15689770C22132yescomplemented
42#15689762C22132yescomplemented
43#15689761C22116yescomplemented
44#15689748C22132yescomplemented
45#15689746C22116yescomplemented
46#15689740C22116yescomplemented
47#15689719C22132yescomplemented
48#15689705C22132yescomplemented
49#15689702C22132yescomplemented
50#15689701C22116yescomplemented
51C2×#13094023C2211yescharacteristic, complemented
52C2×#13094023C2211yescharacteristic, complemented
53C2×#13094019C2212yescomplemented
54C2×#13094017C2212yescomplemented
55C2×#13094014C2212yescomplemented
56C2×#13094014C2212yescomplemented
57C2×#13094013C2211yescharacteristic, complemented
58C2×#13094011C2211yescharacteristic, complemented
59C2×#13094011C2212yescomplemented
60C2×#13094011C2212yescomplemented
61C2×#13094010C2212yescomplemented
62C2×#13094010C2212yescomplemented
63#15689630C22116yescomplemented
64C2×#13094009C2212yescomplemented
65C2×#13094007C2212yescomplemented
66C2×#13094007C2212yescomplemented
67C2×#13094006C2212yescomplemented
68C2×#13094006C2212yescomplemented
69C2×#13094006C2212yescomplemented
70C2×#13094005C2212yescomplemented
71C2×#13094005C2212yescomplemented
72C2×#13094005C2211yescharacteristic, complemented
73C2×#13094005C2211yescharacteristic, complemented
74C2×#13094004C2212yes—
75C2×#13094004C2211yescharacteristic
76C2×#13094004C2212yescomplemented
77C2×#13094003C2212yescomplemented
78C2×#13094003C2211yescharacteristic, complemented
79C2×#13094003C2211yescharacteristic, complemented
80C2×#13094003C2212yescomplemented
81C2×#13094002C2212yes—
82C2×#13094002C2212yes—
83C2×#13094002C2212yescomplemented
84C2×#13094002C2212yescomplemented
85C2×#13094001C2212yescomplemented
86C2×#13094001C2212yescomplemented
87C2×#13094001C2212yescomplemented
88C2×#13094001C2212yescomplemented
89C2×#13094000C2211yescharacteristic
90C2×#13094000C2211yescharacteristic
91C2×#13094000C2212yescomplemented
92C2×#13094000C2211yescharacteristic, complemented
93C22⋊Q8×D47C22116yescomplemented
94C2×#13093999C2211yescharacteristic
95C2×#13093998C2211yescharacteristic
96C2×#13093998C2211yescharacteristic, complemented
97C2×#13093997C2212yes—
98C2×#13093997C2212yescomplemented
99C2×#13093996C2212yes—
100C2×#13093996C2212yescomplemented
101C2×#13093996C2212yescomplemented
102C2×#13093996C2212yescomplemented
103C2×#13093995C2211yescharacteristic
104C2×#13093995C2211yescharacteristic
105C2×#13093995C2212yescomplemented
106C2×#13093995C2212yescomplemented
107C2×#13093995C2212yescomplemented
108C2×#13093995C2211yescharacteristic, complemented
109#121×D47C22116yescomplemented
110C2×#13093992C2212yes—
111C2×#13093992C2211yescharacteristic
112C2×#13093992C2212yes—
113C2×#13093992C2211yescharacteristic
114C2×Q8×Dic47C2211yescharacteristic, complemented
115C2×#13093989C2211yescharacteristic, complemented
116C2×D4×Dic47C2211yescharacteristic, complemented
117C2×#13093986C2211yescharacteristic, complemented
118C2×#13093986C2212yescomplemented
119C2×C4×C22⋊D47C2211yescharacteristic
120C2×C4×C22⋊D47C2211yescharacteristic
121C2×C4×C22⋊D47C2212yes—
122C2×C4×C22⋊D47C2212yescomplemented
123C2×C4×C22⋊D47C2211yescharacteristic, complemented
124C2×C4×C22⋊D47C2211yescharacteristic, complemented
125C2×(C22⋊D47)⋊C4C2212yes—
126C2×#13093983C2211yescharacteristic, complemented
127C22×C4⋊Dic47C2211yescharacteristic, complemented
128C2×C4⋊C4×D47C2211yescharacteristic
129C2×C4⋊C4×D47C2211yescharacteristic, complemented
130C2×C4⋊C4×D47C2212yescomplemented
131C22×(C2×D47)⋊C4C2212yes—
132C2×C22⋊C4×D47C2212yes—
133C2×C22⋊C4×D47C2212yes—
134C2×C22⋊C4×D47C2212yes—
135C22×#41×C47C2211yescharacteristic, complemented
136C22×#41×C47C2211yescharacteristic, complemented
137C47×#537C22116yescomplemented
138C2×C22⋊Q8×C47C2211yescharacteristic, complemented
139C2×C22⋊Q8×C47C2212yescomplemented
140C2×C22⋊Q8×C47C2211yescharacteristic, complemented
141C2×#121×C47C2211yescharacteristic
142C2×#121×C47C2212yescomplemented
143C2×#121×C47C2211yescharacteristic, complemented
144C2×#121×C47C2212yescomplemented
145C2×#121×C47C2212yescomplemented
146C22×C4⋊C4×C47C2211yescharacteristic, complemented
147C24×D47C2311yescharacteristic
148C24×D47C2312yes—
149C2×#10625350—44no—
150C2×#10625350—48no—
151C2×#10625350C23116yescomplemented
152C2×#10625350C2318yescomplemented
153C2×#10625352—48no—
154C2×#10625352C23116yescomplemented
155C22×Dic94C2311yescharacteristic
156C22×Dic94C2312yes—
157C22×Dic94C2312yes—
158C22×Dic94C2312yes—
159C2×Q8×D47—44no—
160C2×Q8×D47C2318yescomplemented
161C22×D188C2312yes—
162C22×D188C2311yescharacteristic
163C22×C22⋊D47C2311yescharacteristic
164C22×C22⋊D47C2311yescharacteristic
165C22×C22⋊D47C2311yescharacteristic
166C22×C22⋊D47C2311yescharacteristic
167C22×C22⋊D47C2312yes—
168C22×C22⋊D47C2312yes—
169C22×C22⋊D47C2312yes—
170C22×C22⋊D47C2312yes—
171C22×C22⋊D47C2312yes—
172C2×D4×D47—44no—
173C2×D4×D47—48no—
174C2×D4×D47C2318yes—
175C2×D4×D47C23116yes—
176C23×Dic47C2312yes—
177C23×Dic47C2312yes—
178C23×Dic47C2311yescharacteristic
179C22×C4×D47—44no—
180C22×C4×D47C2312yes—
181C22×C4×D47C2311yescharacteristic
182C22×C4×D47C2311yescharacteristic
183C22×C4×D47C2311yescharacteristic
184C22×C4×D47C2312yes—
185C22×C4×D47C2312yes—
186C22×C4×D47C2312yes—
187C22×C4×D47C2312yes—
188C22×C4×D47C2311yescharacteristic
189C22×C4×D47C2318yes—
190#13094023C2318yescomplemented
191#13094023C2318yescomplemented
192#13094019C23116yescomplemented
193#13094017C23116yescomplemented
194#13094014C23116yescomplemented
195#13094014C23116yescomplemented
196#13094013C2318yescomplemented
197#13094011C2318yescomplemented
198#13094011C23116yescomplemented
199#13094011C23116yescomplemented
200#13094010C23116yescomplemented
201#13094010C23116yescomplemented
202#13094009C23116yescomplemented
203#13094007C23116yescomplemented
204#13094007C23116yescomplemented
205#13094006C23116yescomplemented
206#13094006C23116yescomplemented
207#13094006C23116yescomplemented
208#13094005C23116yescomplemented
209#13094005C23116yescomplemented
210#13094005C2318yescomplemented
211#13094005C2318yescomplemented
212#13094004C23116yes—
213#13094004C2318yes—
214#13094004C23116yescomplemented
215#13094003C2318yescomplemented
216#13094003C23116yescomplemented
217#13094003C2318yescomplemented
218#13094003C23116yescomplemented
219#13094002C23116yes—
220#13094002C23116yes—
221#13094002C23116yescomplemented
222#13094002C23116yescomplemented
223#13094001C23116yescomplemented
224#13094001C23116yescomplemented
225#13094001C23116yescomplemented
226#13094001C23116yescomplemented
227#13094000C2318yes—
228#13094000C2318yes—
229#13094000C23116yescomplemented
230#13094000C2318yescomplemented
231#13093999C2318yes—
232#13093998C2318yes—
233#13093998C2318yescomplemented
234#13093997C23116yes—
235#13093997C23116yescomplemented
236#13093996C23116yes—
237#13093996C23116yescomplemented
238#13093996C23116yescomplemented
239#13093996C23116yescomplemented
240#13093995C2318yes—
241#13093995C2318yes—
242#13093995C23116yescomplemented
243#13093995C23116yescomplemented
244#13093995C23116yescomplemented
245#13093995C2318yescomplemented
246#13093992C23116yes—
247#13093992C2318yes—
248#13093992C23116yes—
249#13093992C2318yes—
250Q8×Dic47C2318yescomplemented
251#13093989C2318yescomplemented
252D4×Dic47C2318yescomplemented
253#13093986C2318yescomplemented
254#13093986C23116yescomplemented
255C4×C22⋊D47C2318yes—
256C4×C22⋊D47C23116yes—
257C4×C22⋊D47C2318yes—
258C4×C22⋊D47C23116yescomplemented
259C4×C22⋊D47C2318yescomplemented
260C4×C22⋊D47C2318yescomplemented
261(C22⋊D47)⋊C4C23116yes—
262#13093983C2318yescomplemented
263C2×C4⋊Dic47C2311yescharacteristic
264C2×C4⋊Dic47C2311yescharacteristic
265C2×C4⋊Dic47C2312yes—
266C2×C4⋊Dic47C2312yes—
267C2×C4⋊Dic47C2311yescharacteristic
268C2×C4⋊Dic47C2311yescharacteristic
269C2×C4⋊Dic47C2312yes—
270C2×C4⋊Dic47C2318yescomplemented
271C2×Dic47⋊C4C2312yes—
272C2×Dic47⋊C4C2312yes—
273C2×Dic47⋊C4C2312yes—
274C2×Dic47⋊C4C2312yes—
275C2×Dic47⋊C4C2312yes—
276C2×Dic47⋊C4C2311yescharacteristic
277C2×Dic47⋊C4C2311yescharacteristic
278C2×Dic47⋊C4C2312yes—
279C2×Dic47⋊C4C2312yes—
280C2×Dic47⋊C4C2311yescharacteristic
281C2×Dic47⋊C4C2311yescharacteristic
282C2×Dic47⋊C4C2312yes—
283C4⋊C4×D47C2318yes—
284C4⋊C4×D47C2318yescomplemented
285C4⋊C4×D47C23116yescomplemented
286C2×C22⋊Dic47C2312yes—
287C2×C22⋊Dic47C2312yes—
288C2×C22⋊Dic47C2312yes—
289C2×C22⋊Dic47C2311yescharacteristic
290C2×C22⋊Dic47C2311yescharacteristic
291C2×C22⋊Dic47C2311yescharacteristic
292C2×C22⋊Dic47C2312yes—
293C2×C22⋊Dic47C2311yescharacteristic
294C2×C22⋊Dic47C2312yes—
295C2×C22⋊Dic47C2311yescharacteristic
296C2×C22⋊Dic47C2311yescharacteristic
297C2×C22⋊Dic47C2312yes—
298C2×(C2×D47)⋊C4C23116yes—
299C2×(C2×D47)⋊C4C2311yescharacteristic
300C2×(C2×D47)⋊C4C2312yes—
301C2×(C2×D47)⋊C4C2312yes—
302C2×(C2×D47)⋊C4C2312yes—
303C2×(C2×D47)⋊C4C2312yes—
304C2×(C2×D47)⋊C4C2311yescharacteristic
305C2×(C2×D47)⋊C4C2312yes—
306C2×(C2×D47)⋊C4C2312yes—
307C2×(C2×D47)⋊C4C2311yescharacteristic
308C2×(C2×D47)⋊C4C2311yescharacteristic
309C2×(C2×D47)⋊C4C2312yes—
310C2×(C2×D47)⋊C4C2312yes—
311C22⋊C4×D47C23116yes—
312C22⋊C4×D47C23116yes—
313C22⋊C4×D47C23116yes—
314C2×C4×Dic47C2311yescharacteristic
315C2×C4×Dic47C2311yescharacteristic
316C2×C4×Dic47C2312yes—
317C2×C4×Dic47C2312yes—
318C2×#41×C47—44no—
319C2×#41×C47—44no—
320C2×#41×C47C2318yescomplemented
321C2×#41×C47C2318yescomplemented
322C22×Q8×C47C2311yescharacteristic
323C22×Q8×C47C2311yescharacteristic
324C22×D4×C47C2311yescharacteristic
325C22×D4×C47C2312yes—
326C22×D4×C47C2312yes—
327C22×D4×C47C2311yescharacteristic
328C22×D4×C47C2312yes—
329C22×D4×C47C2311yescharacteristic
330C22×D4×C47C2311yescharacteristic
331C23×C4×C47C2311yescharacteristic
332C23×C4×C47C2311yescharacteristic
333C23×C4×C47C2311yescharacteristic
334C23×C4×C47C2312yes—
335C23×C4×C47C2312yes—
336C22⋊Q8×C47C2318yescomplemented
337C22⋊Q8×C47C23116yescomplemented
338C22⋊Q8×C47C2318yescomplemented
339#121×C47C2318yes—
340#121×C47C23116yescomplemented
341#121×C47C2318yescomplemented
342#121×C47C23116yescomplemented
343#121×C47C23116yescomplemented
344C2×C4⋊C4×C47C2311yescharacteristic
345C2×C4⋊C4×C47C2311yescharacteristic
346C2×C4⋊C4×C47C2312yes—
347C2×C4⋊C4×C47C2312yes—
348C2×C4⋊C4×C47C2312yes—
349C2×C4⋊C4×C47C2318yescomplemented
350C2×C22⋊C4×C47C2312yes—
351C2×C22⋊C4×C47C2312yes—
352C2×C22⋊C4×C47C2312yes—
353C2×C22⋊C4×C47C2312yes—
354C24×C47C2412yes—
355C24×C47C2411yescharacteristic
356C24×C47C2411yescharacteristic
357C24×C47C2411yescharacteristic
358C23×D47—24no—
359C23×D47—24no—
360C23×D47—28no—
361C23×D47—42no—
362C23×D47—44no—
363C23×D47—44no—
364C23×D47C2412yes—
365C23×D47C2414yes—
366C23×D47C2411yescharacteristic
367C23×D47C2411yescharacteristic
368C23×D47C2418yes—
369#41×C47—416no—
370#41×C47—416no—
371C2×Q8×C47—24no—
372C2×Q8×C47—42no—
373C2×Q8×C47C2414yes—
374C2×Q8×C47C2414yes—
375C2×D4×C47—24no—
376C2×D4×C47—44no—
377C2×D4×C47—42no—
378C2×D4×C47—42no—
379C2×D4×C47—42no—
380C2×D4×C47—44no—
381C2×D4×C47—44no—
382C2×D4×C47C2414yes—
383C2×D4×C47C2418yes—
384C2×D4×C47C2418yes—
385C2×D4×C47C2414yes—
386C2×D4×C47C2418yes—
387C2×D4×C47C2414yes—
388C2×D4×C47C2414yes—
389C22×C4×C47—24no—
390C22×C4×C47—24no—
391C22×C4×C47—24no—
392C22×C4×C47—44no—
393C22×C4×C47—44no—
394C22×C4×C47C2412yes—
395C22×C4×C47C2412yes—
396C22×C4×C47C2412yes—
397C22×C4×C47C2411yescharacteristic
398C22×C4×C47C2411yescharacteristic
399C22×C4×C47C2411yescharacteristic
400C22×C4×C47C2414yes—
401C22×C4×C47C2414yes—
402C22×C4×C47C2414yes—
403C22×C4×C47C2418yes—
404C22×C4×C47C2418yes—
405C22×C4×C47C2411yescharacteristic
406C2×C22⋊D47—28no—
407C2×C22⋊D47—24no—
408C2×C22⋊D47—24no—
409C2×C22⋊D47—24no—
410C2×C22⋊D47—24no—
411C2×C22⋊D47—44no—
412C2×C22⋊D47—44no—
413C2×C22⋊D47—44no—
414C2×C22⋊D47—44no—
415C2×C22⋊D47C2414yes—
416C2×C22⋊D47C2414yes—
417C2×C22⋊D47C2414yes—
418C2×C22⋊D47C2414yes—
419C2×C22⋊D47C2418yes—
420C2×C22⋊D47C2418yes—
421C2×C22⋊D47C2418yes—
422C2×C22⋊D47C2418yes—
423C2×C22⋊D47C2418yes—
424C22×Dic47—42no—
425C22×Dic47—44no—
426C22×Dic47—44no—
427C22×Dic47C2411yescharacteristic
428C22×Dic47C2411yescharacteristic
429C22×Dic47C2411yescharacteristic
430C22×Dic47C2412yes—
431C22×Dic47C2411yescharacteristic
432C22×Dic47C2412yes—
433C22×Dic47C2411yescharacteristic
434C22×Dic47C2412yes—
435C22×Dic47C2411yescharacteristic
436C22×Dic47C2418yes—
437C22×Dic47C2418yes—
438C22×Dic47C2414yes—
439Q8×D47—416no—
440#10625352—432no—
441D4×D47—416no—
442D4×D47—432no—
443#10625350—416no—
444#10625350—432no—
445C2×D188—28no—
446C2×D188—24no—
447C2×D188C2418yes—
448C2×D188C2414yes—
449C2×C4×D47—28no—
450C2×C4×D47—24no—
451C2×C4×D47—24no—
452C2×C4×D47—416no—
453C2×C4×D47—42no—
454C2×C4×D47—42no—
455C2×C4×D47—44no—
456C2×C4×D47—44no—
457C2×C4×D47—44no—
458C2×C4×D47—44no—
459C2×C4×D47C2418yes—
460C2×C4×D47C2414yes—
461C2×C4×D47C2414yes—
462C2×C4×D47C2414yes—
463C2×C4×D47C2418yes—
464C2×C4×D47C2418yes—
465C2×C4×D47C2418yes—
466C2×C4×D47C2418yes—
467C2×C4×D47C2414yes—
468C2×Dic94—24no—
469C2×Dic94—44no—
470C2×Dic94—44no—
471C2×Dic94—44no—
472C2×Dic94C2414yes—
473C2×Dic94C2418yes—
474C2×Dic94C2418yes—
475C2×Dic94C2418yes—
476C4⋊C4×C47C2414yes—
477C4⋊C4×C47C2414yes—
478C4⋊C4×C47C2418yes—
479C4⋊C4×C47C2418yes—
480C4⋊C4×C47C2418yes—
481C22⋊C4×C47C2418yes—
482C22⋊C4×C47C2418yes—
483C22⋊C4×C47C2418yes—
484C22⋊C4×C47C2418yes—
485C22⋊Dic47C2418yes—
486C22⋊Dic47C2418yes—
487C22⋊Dic47C2418yes—
488C22⋊Dic47C2414yes—
489C22⋊Dic47C2414yes—
490C22⋊Dic47C2414yes—
491C22⋊Dic47C2418yes—
492C22⋊Dic47C2414yes—
493C22⋊Dic47C2418yes—
494C22⋊Dic47C2414yes—
495C22⋊Dic47C2414yes—
496C22⋊Dic47C2418yes—
497(C2×D47)⋊C4C2414yes—
498(C2×D47)⋊C4C2418yes—
499(C2×D47)⋊C4C2418yes—
500(C2×D47)⋊C4C2418yes—
501(C2×D47)⋊C4C2418yes—
502(C2×D47)⋊C4C2414yes—
503(C2×D47)⋊C4C2418yes—
504(C2×D47)⋊C4C2418yes—
505(C2×D47)⋊C4C2414yes—
506(C2×D47)⋊C4C2414yes—
507(C2×D47)⋊C4C2418yes—
508(C2×D47)⋊C4C2418yes—
509C4⋊Dic47C2414yes—
510C4⋊Dic47C2414yes—
511C4⋊Dic47C2418yes—
512C4⋊Dic47C2418yes—
513C4⋊Dic47C2414yes—
514C4⋊Dic47C2414yes—
515C4⋊Dic47C2418yes—
516Dic47⋊C4C2418yes—
517Dic47⋊C4C2418yes—
518Dic47⋊C4C2418yes—
519Dic47⋊C4C2418yes—
520Dic47⋊C4C2418yes—
521Dic47⋊C4C2414yes—
522Dic47⋊C4C2414yes—
523Dic47⋊C4C2418yes—
524Dic47⋊C4C2418yes—
525Dic47⋊C4C2414yes—
526Dic47⋊C4C2414yes—
527Dic47⋊C4C2418yes—
528C4×Dic47C2414yes—
529C4×Dic47C2414yes—
530C4×Dic47C2418yes—
531C4×Dic47C2418yes—
532C23×C47—22no—
533C23×C47—24no—
534C23×C47—22no—
535C23×C47—22no—
536C23×C47—22no—
537C23×C47—22no—
538C23×C47—24no—
539C23×C47—22no—
540C23×C47—22no—
541C23×C47—22no—
542C23×C47—22no—
543C23×C47—24no—
544C23×C47C2514yes—
545C23×C47C2512yes—
546C23×C47C2512yes—
547C23×C47C2512yes—
548C23×C47C2511yescharacteristic
549C22×D47—22no—
550C22×D47—22no—
551C22×D47—22no—
552C22×D47—22no—
553C22×D47—24no—
554C22×D47—24no—
555C22×D47—24no—
556C22×D47—28no—
557C22×D47—28no—
558C22×D47—216no—
559C22×D47—44no—
560C22×D47—416no—
561C22×D47—48no—
562C22×D47—48no—
563C22×D47—816no—
564C22×D47H(5,𝔽2)14yes—
565C22×D472−1+414yes—
566C22×D47C2514yes—
567C22×D47C2512yes—
568C22×D47C2512yes—
569Q8×C47—28no—
570Q8×C47—44no—
571D4×C47—28no—
572D4×C47—48no—
573D4×C47—48no—
574D4×C47—48no—
575D4×C47—44no—
576D4×C47—44no—
577D4×C47—44no—
578C2×C4×C47—24no—
579C2×C4×C47—24no—
580C2×C4×C47—24no—
581C2×C4×C47—22no—
582C2×C4×C47—22no—
583C2×C4×C47—22no—
584C2×C4×C47—28no—
585C2×C4×C47—28no—
586C2×C4×C47—28no—
587C2×C4×C47—48no—
588C2×C4×C47—48no—
589C2×C4×C47H(5,𝔽2)14yes—
590C2×C4×C47C2514yes—
591C2×C4×C47C2514yes—
592C2×C4×C47C2512yes—
593C2×C4×C47C2512yes—
594C2×C4×C47C2512yes—
595C2×C4×C47C2514yes—
596C2×C4×C47C2512yes—
597C22⋊D47—28no—
598C22⋊D47—216no—
599C22⋊D47—28no—
600C22⋊D47—28no—
601C22⋊D47—28no—
602C22⋊D47—48no—
603C22⋊D47—48no—
604C22⋊D47—48no—
605C22⋊D47—48no—
606C2×Dic47—24no—
607C2×Dic47—22no—
608C2×Dic47—22no—
609C2×Dic47—22no—
610C2×Dic47—24no—
611C2×Dic47—24no—
612C2×Dic47—22no—
613C2×Dic47—22no—
614C2×Dic47—22no—
615C2×Dic47—44no—
616C2×Dic47—48no—
617C2×Dic47—48no—
618C2×Dic47C2512yes—
619C2×Dic47C2512yes—
620C2×Dic47C2514yes—
621C2×Dic47C2512yes—
622C2×Dic47C2514yes—
623C2×Dic47C2512yes—
624C2×Dic47C2512yes—
625C2×Dic47C2514yes—
626C2×Dic47C2512yes—
627D188—216no—
628D188—28no—
629C4×D47—216no—
630C4×D47—28no—
631C4×D47—28no—
632C4×D47—44no—
633C4×D47—44no—
634C4×D47—48no—
635C4×D47—48no—
636C4×D47—48no—
637C4×D47—48no—
638Dic94—28no—
639Dic94—48no—
640Dic94—48no—
641Dic94—48no—
642C2×#3536—471nomaximal, Sylow
643C22×C47—22no—
644C22×C47—24no—
645C22×C47—22no—
646C22×C47—22no—
647C22×C47—22no—
648C22×C47—22no—
649C22×C47—24no—
650C22×C47—22no—
651C22×C47—22no—
652C22×C47—22no—
653C22×C47—22no—
654C22×C47—24no—
655C22×C47—44no—
656C22×C47—48no—
657C22×C47—44no—
658C22×C47—44no—
659C22×C47C2×H(5,𝔽2)12yes—
660C22×C47C2×H(5,𝔽2)12yes—
661C22×C47C2×2−1+412yes—
662C22×C47C2611yescharacteristic
663C2×D47—22no—
664C2×D47—22no—
665C2×D47—22no—
666C2×D47—22no—
667C2×D47—28no—
668C2×D47—28no—
669C2×D47—24no—
670C2×D47—24no—
671C2×D47—24no—
672C2×D47—416no—
673C2×D47—48no—
674C2×D47—816no—
675C2×D47C2×H(5,𝔽2)14yes—
676C2×D47C2×2−1+414yes—
677C4×C47—24no—
678C4×C47—24no—
679C4×C47—24no—
680C4×C47—22no—
681C4×C47—22no—
682C4×C47—22no—
683C4×C47C2×H(5,𝔽2)14yes—
684Dic47—24no—
685Dic47—22no—
686Dic47—22no—
687Dic47—22no—
688Dic47—24no—
689Dic47—24no—
690Dic47—22no—
691Dic47—22no—
692Dic47—22no—
693#3536—4732no—
694C2×#562—472no—
695C2×#562—472no—
696C2×#554—471no—
697C2×#554—471no—
698C2×#548—471no—
699C2×#548—471no—
700C2×#547—471no—
701C2×#547—471no—
702C2×#546—471no—
703C2×#546—472no—
704C2×#546—472no—
705C2×#546—471no—
706C2×#543—472no—
707C2×#542—471no—
708C2×#542—471no—
709C2×#539—472no—
710C2×#538—472no—
711C2×#537—471no—
712C2×#537—472no—
713C2×#537D4711yescharacteristic, complemented
714C2×#525—471no—
715C22×C22⋊Q8—471no—
716C22×#121—471no—
717C2×C47—42no—
718C2×C47—44no—
719C2×C47—42no—
720C2×C47—42no—
721C2×C47#353614yescomplemented
722C2×C47C22×H(5,𝔽2)11yescharacteristic
723C2×C47C22×H(5,𝔽2)11yescharacteristic
724C2×C47C22×2−1+411yescharacteristic
725D47—24no—
726D47—24no—
727D47—44no—
728C22×#41—472no—
729C22×#41—472no—
730C22×#41—471no—
731C22×#41C2×D4711yescharacteristic, complemented
732C22×#41C2×D4711yescharacteristic, complemented
733C23×Q8—471no—
734C23×D4—471no—
735C23×D4—472no—
736C24×C4—471no—
737#562—4732no—
738#562—4732no—
739#554—4716no—
740#554—4716no—
741#548—4716no—
742#548—4716no—
743#547—4716no—
744#547—4716no—
745#546—4716no—
746#546—4732no—
747#546—4732no—
748#546—4716no—
749#543—4732no—
750#542—4716no—
751#542—4716no—
752#539—4732no—
753#538—4732no—
754#537—4716no—
755#537—4732no—
756#537C2×D47116yescomplemented
757C2×C4⋊Q8—471no—
758C2×C4⋊Q8—471no—
759C2×#126—472no—
760C2×#126—472no—
761C2×#125—472no—
762C2×#125—472no—
763C2×#124—471no—
764C2×#124—472no—
765C2×#124—471no—
766C2×#124—472no—
767C2×#124—472no—
768C2×#124—472no—
769#525—4716no—
770C2×#123—471no—
771C2×#123—471no—
772C2×#123—472no—
773C2×#123—472no—
774C2×#123—472no—
775C2×#123—472no—
776C2×#123—472no—
777C2×#123—472no—
778C2×#123—472no—
779C2×#123—472no—
780C2×C22⋊Q8—471no—
781C2×C22⋊Q8—471no—
782C2×C22⋊Q8—471no—
783C2×C22⋊Q8—472no—
784C2×C22⋊Q8—471no—
785C2×C22⋊Q8—471no—
786C2×C22⋊Q8—472no—
787C2×C22⋊Q8—472no—
788C2×C22⋊Q8—4716no—
789C2×C22⋊Q8—472no—
790C2×C22⋊Q8—471no—
791C2×C22⋊Q8—472no—
792C2×C22⋊Q8—472no—
793C2×C22⋊Q8—472no—
794C2×C22⋊Q8—472no—
795C2×C22⋊Q8—472no—
796C2×C22⋊Q8—472no—
797C2×C22⋊Q8—472no—
798C2×C22⋊Q8—472no—
799C2×C22⋊Q8—472no—
800C2×C22⋊Q8C2×D4711yescharacteristic, complemented
801C2×C22⋊Q8C2×D4712yescomplemented
802C2×C22⋊Q8C2×D4711yescharacteristic, complemented
803C2×#121—471no—
804C2×#121—472no—
805C2×#121—471no—
806C2×#121—471no—
807C2×#121—472no—
808C2×#121—472no—
809C2×#121—472no—
810C2×#121—472no—
811C2×#121—472no—
812C2×#121—472no—
813C2×#121—471no—
814C2×#121—471no—
815C2×#121—4716no—
816C2×#121—471no—
817C2×#121—472no—
818C2×#121—472no—
819C2×#121C2×D4711yescharacteristic
820C2×#121C2×D4712yescomplemented
821C2×#121C2×D4711yescharacteristic, complemented
822C2×#121C2×D4712yescomplemented
823C2×#121C2×D4712yescomplemented
824C2×#120—471no—
825C2×#120—471no—
826C2×#120—472no—
827C2×#120—472no—
828C2×C4×Q8—471no—
829C2×C4×Q8—471no—
830C2×C4×D4—471no—
831C2×C4×D4—471no—
832C2×C4×D4—471no—
833C2×C4×D4—471no—
834C2×C4×D4—471no—
835C2×C4×D4—472no—
836C2×C4×D4—472no—
837C2×C4×D4—472no—
838C2×C4×D4—471no—
839C2×C4×D4—472no—
840C2×#117—471no—
841C22×C4⋊C4—471no—
842C22×C4⋊C4—471no—
843C22×C4⋊C4—472no—
844C22×C4⋊C4—471no—
845C22×C4⋊C4C2×D4711yescharacteristic, complemented
846C22×C22⋊C4—472no—
847C22×C22⋊C4—472no—
848C22×C22⋊C4—472no—
849C22×C22⋊C4—472no—
850C47C2×#353611yescharacteristic, complemented, Sylow
851C25—471no—
852C25—472no—
853C2×#41—44no—
854C2×#41—44no—
855C2×#41—4716no—
856C2×#41—4716no—
857C2×#41—478no—
858C2×#41—1884no—
859C2×#41—1888no—
860C2×#41—1888no—
861C2×#41C22×D4718yescomplemented
862C2×#41C22×D4718yescomplemented
863C22×Q8—478no—
864C22×Q8—471no—
865C22×Q8—472no—
866C22×Q8—472no—
867C22×Q8—472no—
868C22×Q8—1884no—
869C22×Q8C22×D4711yescharacteristic
870C22×Q8C22×D4711yescharacteristic
871C22×D4—471no—
872C22×D4—471no—
873C22×D4—471no—
874C22×D4—471no—
875C22×D4—472no—
876C22×D4—472no—
877C22×D4—472no—
878C22×D4—472no—
879C22×D4—472no—
880C22×D4—478no—
881C22×D4—4716no—
882C22×D4—472no—
883C22×D4—471no—
884C22×D4—1884no—
885C22×D4—1888no—
886C22×D4C22×D4711yescharacteristic
887C22×D4C22×D4711yescharacteristic
888C22×D4C22×D4711yescharacteristic
889C22×D4C22×D4712yes—
890C22×D4C22×D4712yes—
891C22×D4C22×D4711yescharacteristic
892C22×D4C22×D4712yes—
893C23×C4—472no—
894C23×C4—472no—
895C23×C4—471no—
896C23×C4—472no—
897C23×C4—471no—
898C23×C4—471no—
899C23×C4—471no—
900C23×C4—472no—
901C23×C4—472no—
902C23×C4—472no—
903C23×C4—472no—
904C23×C4—471no—
905C23×C4—478no—
906C23×C4—1884no—
907C23×C4C22×D4711yescharacteristic
908C23×C4C22×D4711yescharacteristic
909C23×C4C22×D4711yescharacteristic
910C23×C4C22×D4712yes—
911C23×C4C22×D4712yes—
912C4⋊Q8—478no—
913C4⋊Q8—478no—
914#126—4716no—
915#126—4716no—
916#125—4716no—
917#125—4716no—
918#124—478no—
919#124—4716no—
920#124—478no—
921#124—4716no—
922#124—4716no—
923#124—4716no—
924#123—478no—
925#123—478no—
926#123—4716no—
927#123—4716no—
928#123—4716no—
929#123—4716no—
930#123—4716no—
931#123—4716no—
932#123—4716no—
933#123—4716no—
934C22⋊Q8—478no—
935C22⋊Q8—478no—
936C22⋊Q8—478no—
937C22⋊Q8—4716no—
938C22⋊Q8—478no—
939C22⋊Q8—478no—
940C22⋊Q8—4716no—
941C22⋊Q8—4716no—
942C22⋊Q8—4716no—
943C22⋊Q8—478no—
944C22⋊Q8—4716no—
945C22⋊Q8—4716no—
946C22⋊Q8—4716no—
947C22⋊Q8—4716no—
948C22⋊Q8—4716no—
949C22⋊Q8—4716no—
950C22⋊Q8—4716no—
951C22⋊Q8—4716no—
952C22⋊Q8—4716no—
953C22⋊Q8C22×D4718yescomplemented
954C22⋊Q8C22×D47116yescomplemented
955C22⋊Q8C22×D4718yescomplemented
956#121—478no—
957#121—4716no—
958#121—478no—
959#121—478no—
960#121—4716no—
961#121—4716no—
962#121—4716no—
963#121—4716no—
964#121—4716no—
965#121—4716no—
966#121—478no—
967#121—478no—
968#121—478no—
969#121—4716no—
970#121—4716no—
971#121C22×D4718yes—
972#121C22×D47116yescomplemented
973#121C22×D4718yescomplemented
974#121C22×D47116yescomplemented
975#121C22×D47116yescomplemented
976#120—478no—
977#120—478no—
978#120—4716no—
979#120—4716no—
980C4×Q8—478no—
981C4×Q8—478no—
982C4×D4—478no—
983C4×D4—478no—
984C4×D4—478no—
985C4×D4—478no—
986C4×D4—478no—
987C4×D4—4716no—
988C4×D4—4716no—
989C4×D4—4716no—
990C4×D4—478no—
991C4×D4—4716no—
992#117—478no—
993C2×C4⋊C4—471no—
994C2×C4⋊C4—471no—
995C2×C4⋊C4—472no—
996C2×C4⋊C4—472no—
997C2×C4⋊C4—472no—
998C2×C4⋊C4—472no—
999C2×C4⋊C4—472no—
1000C2×C4⋊C4—472no—
1001C2×C4⋊C4—478no—
1002C2×C4⋊C4—471no—
1003C2×C4⋊C4—471no—
1004C2×C4⋊C4—472no—
1005C2×C4⋊C4—471no—
1006C2×C4⋊C4—471no—
1007C2×C4⋊C4—471no—
1008C2×C4⋊C4—471no—
1009C2×C4⋊C4—472no—
1010C2×C4⋊C4—472no—
1011C2×C4⋊C4—472no—
1012C2×C4⋊C4—472no—
1013C2×C4⋊C4—478no—
1014C2×C4⋊C4—4716no—
1015C2×C4⋊C4—478no—
1016C2×C4⋊C4C22×D4711yescharacteristic
1017C2×C4⋊C4C22×D4711yescharacteristic
1018C2×C4⋊C4C22×D4712yes—
1019C2×C4⋊C4C22×D4712yes—
1020C2×C4⋊C4C22×D4712yes—
1021C2×C4⋊C4C22×D4718yescomplemented
1022C2×C22⋊C4—472no—
1023C2×C22⋊C4—472no—
1024C2×C22⋊C4—472no—
1025C2×C22⋊C4—471no—
1026C2×C22⋊C4—471no—
1027C2×C22⋊C4—472no—
1028C2×C22⋊C4—472no—
1029C2×C22⋊C4—471no—
1030C2×C22⋊C4—471no—
1031C2×C22⋊C4—472no—
1032C2×C22⋊C4—471no—
1033C2×C22⋊C4—471no—
1034C2×C22⋊C4—471no—
1035C2×C22⋊C4—471no—
1036C2×C22⋊C4—472no—
1037C2×C22⋊C4—472no—
1038C2×C22⋊C4—472no—
1039C2×C22⋊C4—472no—
1040C2×C22⋊C4—472no—
1041C2×C22⋊C4—472no—
1042C2×C22⋊C4—4716no—
1043C2×C22⋊C4—471no—
1044C2×C22⋊C4—471no—
1045C2×C22⋊C4—472no—
1046C2×C22⋊C4—472no—
1047C2×C22⋊C4—4716no—
1048C2×C22⋊C4—4716no—
1049C2×C22⋊C4—4716no—
1050C2×C22⋊C4C22×D4712yes—
1051C2×C22⋊C4C22×D4712yes—
1052C2×C22⋊C4C22×D4712yes—
1053C2×C22⋊C4C22×D4712yes—
1054C2×C42—471no—
1055C2×C42—471no—
1056C2×C42—472no—
1057C2×C42—472no—
1058C24—471no—
1059C24—471no—
1060C24—472no—
1061C24—474no—
1062C24—478no—
1063C24—948no—
1064C24—944no—
1065C24—944no—
1066C24—1884no—
1067C24—1884no—
1068C24—1882no—
1069C24C23×D4712yes—
1070C24C23×D4711yescharacteristic
1071C24C23×D4711yescharacteristic
1072C24C23×D4711yescharacteristic
1073#41—416no—
1074#41—416no—
1075#41—18816no—
1076#41—18832no—
1077#41—18832no—
1078C2×Q8—24no—
1079C2×Q8—42no—
1080C2×Q8—474no—
1081C2×Q8—478no—
1082C2×Q8—478no—
1083C2×Q8—478no—
1084C2×Q8—944no—
1085C2×Q8—1884no—
1086C2×Q8—1884no—
1087C2×Q8—1884no—
1088C2×Q8—18816no—
1089C2×Q8C23×D4714yes—
1090C2×Q8C23×D4714yes—
1091C2×D4—24no—
1092C2×D4—44no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—474no—
1099C2×D4—474no—
1100C2×D4—474no—
1101C2×D4—474no—
1102C2×D4—478no—
1103C2×D4—478no—
1104C2×D4—478no—
1105C2×D4—478no—
1106C2×D4—478no—
1107C2×D4—478no—
1108C2×D4—474no—
1109C2×D4—948no—
1110C2×D4—944no—
1111C2×D4—944no—
1112C2×D4—948no—
1113C2×D4—944no—
1114C2×D4—944no—
1115C2×D4—944no—
1116C2×D4—18816no—
1117C2×D4—1884no—
1118C2×D4—1884no—
1119C2×D4—1884no—
1120C2×D4—1884no—
1121C2×D4—18832no—
1122C2×D4C23×D4714yes—
1123C2×D4C23×D4714yes—
1124C2×D4C23×D4714yes—
1125C2×D4C23×D4718yes—
1126C2×D4C23×D4718yes—
1127C2×D4C23×D4714yes—
1128C2×D4C23×D4718yes—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—471no—
1135C22×C4—471no—
1136C22×C4—471no—
1137C22×C4—471no—
1138C22×C4—472no—
1139C22×C4—472no—
1140C22×C4—471no—
1141C22×C4—472no—
1142C22×C4—471no—
1143C22×C4—478no—
1144C22×C4—478no—
1145C22×C4—474no—
1146C22×C4—478no—
1147C22×C4—474no—
1148C22×C4—474no—
1149C22×C4—474no—
1150C22×C4—478no—
1151C22×C4—478no—
1152C22×C4—478no—
1153C22×C4—478no—
1154C22×C4—474no—
1155C22×C4—948no—
1156C22×C4—944no—
1157C22×C4—944no—
1158C22×C4—18816no—
1159C22×C4—1882no—
1160C22×C4—1882no—
1161C22×C4—1884no—
1162C22×C4—1884no—
1163C22×C4—1884no—
1164C22×C4—1884no—
1165C22×C4—1882no—
1166C22×C4—1884no—
1167C22×C4—1884no—
1168C22×C4C23×D4714yes—
1169C22×C4C23×D4714yes—
1170C22×C4C23×D4714yes—
1171C22×C4C23×D4712yes—
1172C22×C4C23×D4712yes—
1173C22×C4C23×D4711yescharacteristic
1174C22×C4C23×D4711yescharacteristic
1175C22×C4C23×D4711yescharacteristic
1176C22×C4C23×D4712yes—
1177C22×C4C23×D4718yes—
1178C22×C4C23×D4718yes—
1179C22×C4C23×D4711yescharacteristic
1180C4⋊C4—478no—
1181C4⋊C4—478no—
1182C4⋊C4—478no—
1183C4⋊C4—478no—
1184C4⋊C4—478no—
1185C4⋊C4—474no—
1186C4⋊C4—474no—
1187C4⋊C4—474no—
1188C4⋊C4—474no—
1189C4⋊C4—478no—
1190C4⋊C4—478no—
1191C4⋊C4—478no—
1192C4⋊C4—474no—
1193C4⋊C4—474no—
1194C4⋊C4—478no—
1195C4⋊C4—478no—
1196C4⋊C4—474no—
1197C4⋊C4—474no—
1198C4⋊C4—478no—
1199C4⋊C4C23×D4714yes—
1200C4⋊C4C23×D4714yes—
1201C4⋊C4C23×D4718yes—
1202C4⋊C4C23×D4718yes—
1203C4⋊C4C23×D4718yes—
1204C22⋊C4—478no—
1205C22⋊C4—478no—
1206C22⋊C4—478no—
1207C22⋊C4—474no—
1208C22⋊C4—474no—
1209C22⋊C4—478no—
1210C22⋊C4—478no—
1211C22⋊C4—474no—
1212C22⋊C4—474no—
1213C22⋊C4—478no—
1214C22⋊C4—474no—
1215C22⋊C4—474no—
1216C22⋊C4—474no—
1217C22⋊C4—474no—
1218C22⋊C4—478no—
1219C22⋊C4—478no—
1220C22⋊C4—478no—
1221C22⋊C4—478no—
1222C22⋊C4—478no—
1223C22⋊C4—478no—
1224C22⋊C4—474no—
1225C22⋊C4—474no—
1226C22⋊C4—478no—
1227C22⋊C4—478no—
1228C22⋊C4C23×D4718yes—
1229C22⋊C4C23×D4718yes—
1230C22⋊C4C23×D4718yes—
1231C22⋊C4C23×D4718yes—
1232C42—474no—
1233C42—474no—
1234C42—478no—
1235C42—478no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—24no—
1244C23—22no—
1245C23—22no—
1246C23—24no—
1247C23—22no—
1248C23—474no—
1249C23—474no—
1250C23—472no—
1251C23—472no—
1252C23—474no—
1253C23—9416no—
1254C23—948no—
1255C23—948no—
1256C23—942no—
1257C23—942no—
1258C23—942no—
1259C23—942no—
1260C23—944no—
1261C23—944no—
1262C23—944no—
1263C23—37616no—
1264C23—1888no—
1265C23—1888no—
1266C23—1884no—
1267C23—18816no—
1268C23C24×D4714yes—
1269C23C24×D4712yes—
1270C23C24×D4712yes—
1271C23C24×D4712yes—
1272C23C24×D4711yescharacteristic
1273Q8—28no—
1274Q8—44no—
1275Q8—948no—
1276Q8—1888no—
1277Q8—1888no—
1278Q8—1888no—
1279D4—28no—
1280D4—48no—
1281D4—44no—
1282D4—44no—
1283D4—44no—
1284D4—48no—
1285D4—48no—
1286D4—9416no—
1287D4—948no—
1288D4—948no—
1289D4—9416no—
1290D4—948no—
1291D4—948no—
1292D4—948no—
1293D4—1888no—
1294D4—1888no—
1295D4—1888no—
1296D4—1888no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—28no—
1304C2×C4—28no—
1305C2×C4—28no—
1306C2×C4—48no—
1307C2×C4—48no—
1308C2×C4—472no—
1309C2×C4—472no—
1310C2×C4—472no—
1311C2×C4—472no—
1312C2×C4—474no—
1313C2×C4—474no—
1314C2×C4—472no—
1315C2×C4—474no—
1316C2×C4—472no—
1317C2×C4—9416no—
1318C2×C4—944no—
1319C2×C4—944no—
1320C2×C4—942no—
1321C2×C4—942no—
1322C2×C4—942no—
1323C2×C4—942no—
1324C2×C4—944no—
1325C2×C4—942no—
1326C2×C4—942no—
1327C2×C4—948no—
1328C2×C4—948no—
1329C2×C4—1884no—
1330C2×C4—1884no—
1331C2×C4—1888no—
1332C2×C4—1888no—
1333C2×C4—1888no—
1334C2×C4—1888no—
1335C2×C4—1884no—
1336C2×C4—1888no—
1337C2×C4—1888no—
1338C2×C4#1309406914yes—
1339C2×C4C24×D4714yes—
1340C2×C4C24×D4714yes—
1341C2×C4C24×D4712yes—
1342C2×C4C24×D4712yes—
1343C2×C4C24×D4712yes—
1344C2×C4C24×D4714yes—
1345C2×C4C24×D4712yes—
1346C22—22no—
1347C22—22no—
1348C22—24no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—24no—
1354C22—22no—
1355C22—22no—
1356C22—24no—
1357C22—22no—
1358C22—48no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—474no—
1363C22—474no—
1364C22—948no—
1365C22—948no—
1366C22—942no—
1367C22—942no—
1368C22—942no—
1369C22—942no—
1370C22—944no—
1371C22—944no—
1372C22—944no—
1373C22—37616no—
1374C22—18816no—
1375C22—1888no—
1376C22H(5,𝔽2)×D4712yes—
1377C22C2×#1309406912yes—
1378C222−1+4×D4712yes—
1379C22C25×D4711yescharacteristic
1380C4—24no—
1381C4—24no—
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—24no—
1386C4—944no—
1387C4—944no—
1388C4—942no—
1389C4—942no—
1390C4—942no—
1391C4—942no—
1392C4—944no—
1393C4—942no—
1394C4—942no—
1395C4C2×#1309406914yes—
1396C2—44no—
1397C2—42no—
1398C2—42no—
1399C2—42no—
1400C2—944no—
1401C2—944no—
1402C2—1884no—
1403C2#2025760614yesdirect product factor
1404C2C2×H(5,𝔽2)×D4711yescharacteristic
1405C2C22×#1309406911yescharacteristic
1406C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#537C2
socleC23×C47C25
hypercenterC2×#537D47
hypocenterC47C2×#3536
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #20257606C2direct (N × H)
2. C2×#15689868C2semidirect
3. C2×#15689868C2semidirect
4. C2×#15689831C2semidirect
5. C2×#15689828C2semidirect
6. C2×#15689783C2semidirect
7. C2×#15689780C2semidirect
8. C2×#15689774C2semidirect
9. C2×#15689773C2semidirect
10. C2×#15689770C2semidirect
11. C2×#15689770C2semidirect
12. C2×#15689762C2semidirect
13. C2×#15689761C2semidirect
14. C2×#15689748C2semidirect
15. C2×#15689746C2semidirect
16. C2×#15689740C2semidirect
17. C2×#15689719C2semidirect
18. C2×#15689705C2semidirect
19. C2×#15689702C2semidirect
20. C2×#15689701C2semidirect
21. C2×#15689630C2semidirect
22. C2×C22⋊Q8×D47C2semidirect
23. C2×#121×D47C2semidirect
24. C2×C47×#537C2semidirect
25. C22×#10625350C22semidirect
26. C22×#10625350C22semidirect
27. C22×#10625352C22semidirect
28. C22×Q8×D47C22semidirect
32. #15689868C22semidirect
33. #15689868C22semidirect
34. #15689831C22semidirect
35. #15689828C22semidirect
36. #15689783C22semidirect
37. #15689780C22semidirect
38. #15689774C22semidirect
39. #15689773C22semidirect
40. #15689770C22semidirect
41. #15689770C22semidirect
42. #15689762C22semidirect
43. #15689761C22semidirect
44. #15689748C22semidirect
45. #15689746C22semidirect
46. #15689740C22semidirect
47. #15689719C22semidirect
48. #15689705C22semidirect
49. #15689702C22semidirect
50. #15689701C22semidirect
51. C2×#13094023C22semidirect
52. C2×#13094023C22semidirect
53. C2×#13094019C22semidirect
54. C2×#13094017C22semidirect
55. C2×#13094014C22semidirect
56. C2×#13094014C22semidirect
57. C2×#13094013C22semidirect
58. C2×#13094011C22semidirect
59. C2×#13094011C22semidirect
60. C2×#13094011C22semidirect
61. C2×#13094010C22semidirect
62. C2×#13094010C22semidirect
63. #15689630C22semidirect
64. C2×#13094009C22semidirect
65. C2×#13094007C22semidirect
66. C2×#13094007C22semidirect
67. C2×#13094006C22semidirect
68. C2×#13094006C22semidirect
69. C2×#13094006C22semidirect
70. C2×#13094005C22semidirect
71. C2×#13094005C22semidirect
72. C2×#13094005C22semidirect
73. C2×#13094005C22semidirect
76. C2×#13094004C22semidirect
77. C2×#13094003C22semidirect
78. C2×#13094003C22semidirect
79. C2×#13094003C22semidirect
80. C2×#13094003C22semidirect
83. C2×#13094002C22semidirect
84. C2×#13094002C22semidirect
85. C2×#13094001C22semidirect
86. C2×#13094001C22semidirect
87. C2×#13094001C22semidirect
88. C2×#13094001C22semidirect
91. C2×#13094000C22semidirect
92. C2×#13094000C22semidirect
93. C22⋊Q8×D47C22semidirect
96. C2×#13093998C22semidirect
98. C2×#13093997C22semidirect
100. C2×#13093996C22semidirect
101. C2×#13093996C22semidirect
102. C2×#13093996C22semidirect
105. C2×#13093995C22semidirect
106. C2×#13093995C22semidirect
107. C2×#13093995C22semidirect
108. C2×#13093995C22semidirect
109. #121×D47C22semidirect
114. C2×Q8×Dic47C22semidirect
115. C2×#13093989C22semidirect
116. C2×D4×Dic47C22semidirect
117. C2×#13093986C22semidirect
118. C2×#13093986C22semidirect
122. C2×C4×C22⋊D47C22semidirect
123. C2×C4×C22⋊D47C22semidirect
124. C2×C4×C22⋊D47C22semidirect
126. C2×#13093983C22semidirect
127. C22×C4⋊Dic47C22semidirect
129. C2×C4⋊C4×D47C22semidirect
130. C2×C4⋊C4×D47C22semidirect
135. C22×#41×C47C22semidirect
136. C22×#41×C47C22semidirect
137. C47×#537C22semidirect
138. C2×C22⋊Q8×C47C22semidirect
139. C2×C22⋊Q8×C47C22semidirect
140. C2×C22⋊Q8×C47C22semidirect
142. C2×#121×C47C22semidirect
143. C2×#121×C47C22semidirect
144. C2×#121×C47C22semidirect
145. C2×#121×C47C22semidirect
146. C22×C4⋊C4×C47C22semidirect
151. C2×#10625350C23semidirect
152. C2×#10625350C23semidirect
154. C2×#10625352C23semidirect
160. C2×Q8×D47C23semidirect
190. #13094023C23semidirect
191. #13094023C23semidirect
192. #13094019C23semidirect
193. #13094017C23semidirect
194. #13094014C23semidirect
195. #13094014C23semidirect
196. #13094013C23semidirect
197. #13094011C23semidirect
198. #13094011C23semidirect
199. #13094011C23semidirect
200. #13094010C23semidirect
201. #13094010C23semidirect
202. #13094009C23semidirect
203. #13094007C23semidirect
204. #13094007C23semidirect
205. #13094006C23semidirect
206. #13094006C23semidirect
207. #13094006C23semidirect
208. #13094005C23semidirect
209. #13094005C23semidirect
210. #13094005C23semidirect
211. #13094005C23semidirect
214. #13094004C23semidirect
215. #13094003C23semidirect
216. #13094003C23semidirect
217. #13094003C23semidirect
218. #13094003C23semidirect
221. #13094002C23semidirect
222. #13094002C23semidirect
223. #13094001C23semidirect
224. #13094001C23semidirect
225. #13094001C23semidirect
226. #13094001C23semidirect
229. #13094000C23semidirect
230. #13094000C23semidirect
233. #13093998C23semidirect
235. #13093997C23semidirect
237. #13093996C23semidirect
238. #13093996C23semidirect
239. #13093996C23semidirect
242. #13093995C23semidirect
243. #13093995C23semidirect
244. #13093995C23semidirect
245. #13093995C23semidirect
250. Q8×Dic47C23semidirect
251. #13093989C23semidirect
252. D4×Dic47C23semidirect
253. #13093986C23semidirect
254. #13093986C23semidirect
258. C4×C22⋊D47C23semidirect
259. C4×C22⋊D47C23semidirect
260. C4×C22⋊D47C23semidirect
262. #13093983C23semidirect
270. C2×C4⋊Dic47C23semidirect
284. C4⋊C4×D47C23semidirect
285. C4⋊C4×D47C23semidirect
320. C2×#41×C47C23semidirect
321. C2×#41×C47C23semidirect
336. C22⋊Q8×C47C23semidirect
337. C22⋊Q8×C47C23semidirect
338. C22⋊Q8×C47C23semidirect
340. #121×C47C23semidirect
341. #121×C47C23semidirect
342. #121×C47C23semidirect
343. #121×C47C23semidirect
349. C2×C4⋊C4×C47C23semidirect
713. C2×#537D47semidirect
721. C2×C47#3536semidirect
731. C22×#41C2×D47semidirect
732. C22×#41C2×D47semidirect
756. #537C2×D47semidirect
800. C2×C22⋊Q8C2×D47semidirect
801. C2×C22⋊Q8C2×D47semidirect
802. C2×C22⋊Q8C2×D47semidirect
820. C2×#121C2×D47semidirect
821. C2×#121C2×D47semidirect
822. C2×#121C2×D47semidirect
823. C2×#121C2×D47semidirect
845. C22×C4⋊C4C2×D47semidirect
850. C47C2×#3536semidirect
861. C2×#41C22×D47semidirect
862. C2×#41C22×D47semidirect
953. C22⋊Q8C22×D47semidirect
954. C22⋊Q8C22×D47semidirect
955. C22⋊Q8C22×D47semidirect
972. #121C22×D47semidirect
973. #121C22×D47semidirect
974. #121C22×D47semidirect
975. #121C22×D47semidirect
1021. C2×C4⋊C4C22×D47semidirect
1403. C2#20257606direct (N × H)

Maximal subgroups

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

subgroupindex
#202576062
C2×#156898682
C2×#156898312
C2×#156898282
C2×#156897832
C2×#156897802
C2×#156897742
C2×#156897732
C2×#156897702
C2×#156897622
C2×#156897612
C2×#156897482
C2×#156897462
C2×#156897402
C2×#156897192
C2×#156897052
C2×#156897022
C2×#156897012
C2×#156896302
C2×C22⋊Q8×D472
C2×#121×D472
C2×C47×#5372
C2×#353647