Finite Group Databasebeta

← C2×#20257818 #27123890

Subgroups — C2×#20257818 #27123890

Order 12032.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257818C2132yesmaximal, direct product factor
2C2×#15689875C214yesmaximal, complemented
3C2×#15689852C211yesmaximal, characteristic, complemented
4C2×#15689831C212yesmaximal, complemented
5C2×#15689817C212yesmaximal, complemented
6C2×Q8×D188C212yesmaximal, complemented
7C2×#15689788C211yesmaximal, characteristic, complemented
8C2×#15689781C212yesmaximal, complemented
9C2×#15689777C211yesmaximal, characteristic, complemented
10C2×#15689751C212yesmaximal, complemented
11C2×#15689746C212yesmaximal, complemented
12C2×#15689731C212yesmaximal, complemented
13C2×#15689714C214yesmaximal, complemented
14C2×#15689693C212yesmaximal, complemented
15C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
16C2×#15689660C211yesmaximal, characteristic, complemented
17C2×#15689655C211yesmaximal, characteristic, complemented
18C2×C47×#556C211yesmaximal, characteristic, complemented
19C22×#10625352C2212yes—
20C22×Q8×D47C2212yes—
21C22×Q8×D47C2212yes—
22#15689875C22164yescomplemented
23#15689852C22116yescomplemented
24#15689831C22132yescomplemented
25#15689817C22132yescomplemented
26Q8×D188C22132yescomplemented
27#15689788C22116yescomplemented
28#15689781C22132yescomplemented
29#15689777C22116yescomplemented
30#15689751C22132yescomplemented
31#15689746C22132yescomplemented
32#15689731C22132yescomplemented
33#15689714C22164yescomplemented
34#15689693C22132yescomplemented
35C2×#13094024C2214yes—
36C2×#13094024C2211yescharacteristic
37C2×#13094024C2212yes—
38C2×#13094023C2212yes—
39C2×#13094023C2212yes—
40C2×#13094023C2212yes—
41C2×#13094022C2212yes—
42C4⋊Q8×D47C22116yescomplemented
43#15689660C22116yescomplemented
44#15689655C22116yescomplemented
45C2×#13094019C2214yes—
46C2×#13094019C2212yes—
47C2×#13094018C2214yes—
48C2×#13094017C2212yes—
49C2×#13094016C2214yes—
50C2×#13094015C2211yescharacteristic
51C2×#13094015C2212yes—
52C2×#13094015C2211yescharacteristic
53C2×#13094015C2214yes—
54C2×#13094014C2214yes—
55C2×#13094013C2211yescharacteristic
56C2×#13094011C2211yescharacteristic
57C2×#13094010C2214yes—
58C2×#13094009C2212yes—
59C2×#13094008C2214yes—
60C2×#13094006C2214yes—
61C2×#13094006C2214yes—
62C2×#13094006C2212yes—
63C2×#13094004C2214yes—
64C2×#13094004C2212yes—
65C2×#13094004C2211yescharacteristic
66C2×#13094004C2214yes—
67C2×#13094002C2214yes—
68C2×#13094001C2214yes—
69C2×#13094001C2214yes—
70C2×#13094001C2214yes—
71C2×#13094000C2212yes—
72C2×#13094000C2211yescharacteristic
73C2×#13093999C2211yescharacteristic
74C2×#13093998C2212yes—
75C2×#13093997C2214yes—
76C2×#13093995C2211yescharacteristic
77C2×Q8×Dic47C2212yes—
78C2×C4×Dic94C2212yes—
79C2×C4×Dic94C2211yescharacteristic
80C2×C4×D188C2211yescharacteristic
81C2×C4×D188C2212yes—
82C2×C4×D188C2214yes—
83C2×#13093986C2212yes—
84C2×C4×C22⋊D47C2212yes—
85C2×(C22⋊D47)⋊C4C2214yes—
86C2×#13093983C2212yes—
87C2×#13093981C2212yes—
88C22×C4⋊Dic47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C4⋊C4×D47C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#556C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#126×C47C2214yes—
95C2×#124×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2212yes—
98C2×C4×Q8×C47C2211yescharacteristic
99C2×C4×D4×C47C2211yescharacteristic
100C2×#117×C47C2212yes—
101C2×#10625352—48no—
102C2×#10625352C23116yes—
103C22×Dic94C2311yescharacteristic
104C22×Dic94C2312yes—
105C22×Dic94C2314yes—
106C22×Dic94C2314yes—
107C2×Q8×D47—48no—
108C2×Q8×D47—48no—
109C2×Q8×D47C23116yes—
110C2×Q8×D47C23116yes—
111C22×D188C2311yescharacteristic
112C22×D188C2312yes—
113C22×C22⋊D47C2312yes—
114C22×C22⋊D47C2314yes—
115C23×Dic47C2314yes—
116C22×C4×D47C2311yescharacteristic
117C22×C4×D47C2311yescharacteristic
118C22×C4×D47C2311yescharacteristic
119C22×C4×D47C2312yes—
120C22×C4×D47C2314yes—
121C22×C4×D47C2314yes—
122#13094024C23132yes—
123#13094024C2318yes—
124#13094024C23116yes—
125#13094023C23116yes—
126#13094023C23116yes—
127#13094023C23116yes—
128#13094022C23116yes—
129#13094019C23132yes—
130#13094019C23116yes—
131#13094018C23132yes—
132#13094017C23116yes—
133#13094016C23132yes—
134#13094015C2318yes—
135#13094015C2318yes—
136#13094015C23116yes—
137#13094015C23132yes—
138#13094014C23132yes—
139#13094013C2318yes—
140#13094011C2318yes—
141#13094010C23132yes—
142#13094009C23116yes—
143#13094008C23132yes—
144#13094006C23132yes—
145#13094006C23132yes—
146#13094006C23116yes—
147#13094004C23116yes—
148#13094004C23132yes—
149#13094004C2318yes—
150#13094004C23132yes—
151#13094002C23132yes—
152#13094001C23132yes—
153#13094001C23132yes—
154#13094001C23132yes—
155#13094000C23116yes—
156#13094000C2318yes—
157#13093999C2318yes—
158#13093998C23116yes—
159#13093997C23132yes—
160#13093995C2318yes—
161Q8×Dic47C23116yes—
162C4×Dic94C23116yes—
163C4×Dic94C2318yes—
164C4×D188C2318yes—
165C4×D188C23116yes—
166C4×D188C23132yes—
167#13093986C23116yes—
168C4×C22⋊D47C23116yes—
169(C22⋊D47)⋊C4C23132yes—
170#13093983C23116yes—
171#13093981C23116yes—
172C2×C4⋊Dic47C23116yes—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2311yescharacteristic
176C2×C4⋊Dic47C2314yes—
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2312yes—
180C2×C4⋊Dic47C2314yes—
181C2×C4⋊Dic47C2311yescharacteristic
182C2×C4⋊Dic47C2314yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2314yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2314yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2314yes—
190C2×Dic47⋊C4C2312yes—
191C4⋊C4×D47C23116yes—
192C4⋊C4×D47C23116yes—
193C2×C22⋊Dic47C2312yes—
194C2×C22⋊Dic47C2312yes—
195C2×C22⋊Dic47C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2314yes—
201C2×(C2×D47)⋊C4C2314yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×(C2×D47)⋊C4C2312yes—
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2312yes—
208C2×C4×Dic47C2314yes—
209C42×D47C2318yes—
210C22×Q8×C47C2311yescharacteristic
211C22×Q8×C47C2312yes—
212C22×D4×C47C2311yescharacteristic
213C23×C4×C47C2312yes—
214C4⋊Q8×C47C2318yes—
215#126×C47C23132yes—
216#124×C47C23116yes—
217C22⋊Q8×C47C23116yes—
218C4×Q8×C47C23116yes—
219C4×Q8×C47C2318yes—
220C4×D4×C47C2318yes—
221#117×C47C23116yes—
222C2×C4⋊C4×C47C2311yescharacteristic
223C2×C4⋊C4×C47C2312yes—
224C2×C4⋊C4×C47C2311yescharacteristic
225C2×C4⋊C4×C47C2314yes—
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C2312yes—
228C2×C22⋊C4×C47C2314yes—
229C2×C22⋊C4×C47C2312yes—
230C2×C22⋊C4×C47C2314yes—
231C2×C42×C47C2314yes—
232C2×C42×C47C2311yescharacteristic
233C2×C42×C47C2312yes—
234C24×C47C2412yes—
235C23×D47C2412yes—
236C23×D47C2411yescharacteristic
237C2×Q8×C47—28no—
238C2×Q8×C47—24no—
239C2×Q8×C47C2414yes—
240C2×Q8×C47C2418yes—
241C2×D4×C47—24no—
242C2×D4×C47C2414yes—
243C22×C4×C47—28no—
244C22×C4×C47C2412yes—
245C22×C4×C47C2412yes—
246C22×C4×C47C2411yescharacteristic
247C22×C4×C47C2412yes—
248C22×C4×C47C2414yes—
249C22×C4×C47C2418yes—
250C22×C4×C47C2411yescharacteristic
251C22×C4×C47C2411yescharacteristic
252C2×C22⋊D47—28no—
253C2×C22⋊D47—48no—
254C2×C22⋊D47C2418yes—
255C2×C22⋊D47C24116yes—
256C22×Dic47—48no—
257C22×Dic47C2412yes—
258C22×Dic47C2411yescharacteristic
259C22×Dic47C2411yescharacteristic
260C22×Dic47C2411yescharacteristic
261C22×Dic47C2412yes—
262C22×Dic47C2414yes—
263C22×Dic47C2412yes—
264C22×Dic47C24116yes—
265Q8×D47—432no—
266Q8×D47—432no—
267#10625352—432no—
268C2×D188—28no—
269C2×D188—24no—
270C2×D188C2414yes—
271C2×D188C2418yes—
272C2×C4×D47—24no—
273C2×C4×D47—24no—
274C2×C4×D47—28no—
275C2×C4×D47—24no—
276C2×C4×D47—48no—
277C2×C4×D47—48no—
278C2×C4×D47C2414yes—
279C2×C4×D47C2414yes—
280C2×C4×D47C2414yes—
281C2×C4×D47C2418yes—
282C2×C4×D47C24116yes—
283C2×C4×D47C24116yes—
284C2×Dic94—24no—
285C2×Dic94—28no—
286C2×Dic94—48no—
287C2×Dic94—48no—
288C2×Dic94C2414yes—
289C2×Dic94C2418yes—
290C2×Dic94C24116yes—
291C2×Dic94C24116yes—
292C4⋊C4×C47C2414yes—
293C4⋊C4×C47C2418yes—
294C4⋊C4×C47C2414yes—
295C4⋊C4×C47C24116yes—
296C4⋊C4×C47C2418yes—
297C4⋊C4×C47C2418yes—
298C22⋊C4×C47C24116yes—
299C22⋊C4×C47C2418yes—
300C22⋊C4×C47C24116yes—
301C42×C47C24116yes—
302C42×C47C2414yes—
303C42×C47C2418yes—
304C22⋊Dic47C2418yes—
305C22⋊Dic47C2418yes—
306C22⋊Dic47C2418yes—
307(C2×D47)⋊C4C2418yes—
308(C2×D47)⋊C4C2418yes—
309(C2×D47)⋊C4C2418yes—
310(C2×D47)⋊C4C2418yes—
311(C2×D47)⋊C4C24116yes—
312(C2×D47)⋊C4C24116yes—
313(C2×D47)⋊C4C2418yes—
314(C2×D47)⋊C4C2418yes—
315C4⋊Dic47C2418yes—
316C4⋊Dic47C2418yes—
317C4⋊Dic47C2414yes—
318C4⋊Dic47C24116yes—
319C4⋊Dic47C2418yes—
320C4⋊Dic47C2418yes—
321C4⋊Dic47C2418yes—
322C4⋊Dic47C24116yes—
323C4⋊Dic47C2414yes—
324C4⋊Dic47C24116yes—
325Dic47⋊C4C24116yes—
326Dic47⋊C4C24116yes—
327Dic47⋊C4C2418yes—
328Dic47⋊C4C2418yes—
329Dic47⋊C4C24116yes—
330Dic47⋊C4C2418yes—
331Dic47⋊C4C24116yes—
332Dic47⋊C4C2418yes—
333C4×Dic47C2414yes—
334C4×Dic47C2414yes—
335C4×Dic47C2414yes—
336C4×Dic47C2418yes—
337C4×Dic47C24116yes—
338C23×C47—24no—
339C23×C47—24no—
340C23×C47—24no—
341C23×C47C2514yes—
342C23×C47C2511yescharacteristic
343C22×D47—22no—
344C22×D47—22no—
345C22×D47—24no—
346C22×D47—24no—
347C22×D47—24no—
348C22×D472−1+414yes—
349C22×D47C2514yes—
350C22×D47C2512yes—
351Q8×C47—216no—
352Q8×C47—28no—
353D4×C47—28no—
354C2×C4×C47—28no—
355C2×C4×C47—22no—
356C2×C4×C47—24no—
357C2×C4×C47—24no—
358C2×C4×C47—24no—
359C2×C4×C47—216no—
360C2×C4×C47H(5,𝔽2)14yes—
361C2×C4×C472−1+414yes—
362C2×C4×C47C2514yes—
363C2×C4×C47C2512yes—
364C2×C4×C47C2514yes—
365C2×C4×C47C2518yes—
366C2×C4×C47C2514yes—
367C2×C4×C47C2512yes—
368C2×C4×C47C2512yes—
369C22⋊D47—216no—
370C22⋊D47—416no—
371C2×Dic47—24no—
372C2×Dic47—28no—
373C2×Dic47—22no—
374C2×Dic47—24no—
375C2×Dic47—22no—
376C2×Dic47—22no—
377C2×Dic47—24no—
378C2×Dic47—416no—
379C2×Dic47C2514yes—
380C2×Dic47C2512yes—
381C2×Dic47C2512yes—
382C2×Dic47C2512yes—
383C2×Dic47C2518yes—
384C2×Dic47C2514yes—
385C2×Dic47C2514yes—
386D188—216no—
387D188—28no—
388C4×D47—28no—
389C4×D47—216no—
390C4×D47—28no—
391C4×D47—28no—
392C4×D47—416no—
393C4×D47—416no—
394Dic94—216no—
395Dic94—28no—
396Dic94—416no—
397Dic94—416no—
398C2×#3552—471nomaximal, Sylow
399C22×C47—24no—
400C22×C47—24no—
401C22×C47—24no—
402C22×C47—48no—
403C22×C47C2×H(5,𝔽2)12yes—
404C22×C47C2×2−1+412yes—
405C22×C47C2×2−1+412yes—
406C22×C47C2611yescharacteristic
407C2×D47—22no—
408C2×D47—22no—
409C2×D47—28no—
410C2×D47—24no—
411C2×D47—24no—
412C2×D47—24no—
413C2×D47—48no—
414C2×D47C2×2−1+414yes—
415C4×C47—28no—
416C4×C47—22no—
417C4×C47—24no—
418C4×C47—24no—
419C4×C47—24no—
420C4×C47C2×H(5,𝔽2)14yes—
421C4×C47C2×2−1+414yes—
422Dic47—24no—
423Dic47—28no—
424Dic47—22no—
425Dic47—24no—
426Dic47—22no—
427Dic47—22no—
428Dic47—24no—
429#3552—4732no—
430C2×#563—474no—
431C2×#557—471no—
432C2×#556D4711yescharacteristic, complemented
433C2×#554—472no—
434C2×#553—472no—
435C2×D4×Q8—471no—
436C2×D4×Q8—472no—
437C2×#548—472no—
438C2×#547—471no—
439C2×#544—472no—
440C2×#542—472no—
441C2×#541—472no—
442C2×#539—474no—
443C2×#536—472no—
444C22×C4⋊Q8—471no—
445C2×#529—471no—
446C2×#529—471no—
447C2×C47—44no—
448C2×C47#355214yescomplemented
449C2×C47C22×H(5,𝔽2)11yescharacteristic
450C2×C47C22×2−1+411yescharacteristic
451C2×C47C22×2−1+411yescharacteristic
452D47—24no—
453D47—44no—
454C22×#41—472no—
455C23×Q8—472no—
456C23×Q8—472no—
457#563—4764no—
458#557—4716no—
459#556C2×D47116yescomplemented
460#554—4732no—
461#553—4732no—
462D4×Q8—4716no—
463D4×Q8—4732no—
464#548—4732no—
465#547—4716no—
466#544—4732no—
467#542—4732no—
468#541—4732no—
469#539—4764no—
470#536—4732no—
471C2×C4⋊Q8—472no—
472C2×C4⋊Q8—4716no—
473C2×C4⋊Q8—472no—
474C2×C4⋊Q8—472no—
475C2×C4⋊Q8—472no—
476C2×C4⋊Q8—471no—
477C2×C4⋊Q8—472no—
478C2×C4⋊Q8—474no—
479C2×C4⋊Q8C2×D4711yescharacteristic
480#529—4716no—
481#529—4716no—
482C2×#126—472no—
483C2×#126—474no—
484C2×#126—472no—
485C2×#126—474no—
486C2×#126C2×D4714yes—
487C2×#125—471no—
488C2×#125—471no—
489C2×#125—474no—
490C2×#125—474no—
491C2×#125—472no—
492C2×#125—474no—
493C2×#124—471no—
494C2×#124—471no—
495C2×#124—474no—
496C2×#124C2×D4712yes—
497C2×#123—472no—
498C2×#123—472no—
499C2×#123—474no—
500C2×#123—474no—
501C2×#123—474no—
502C2×C22⋊Q8—471no—
503C2×C22⋊Q8—472no—
504C2×C22⋊Q8—471no—
505C2×C22⋊Q8—474no—
506C2×C22⋊Q8—474no—
507C2×C22⋊Q8—472no—
508C2×C22⋊Q8—474no—
509C2×C22⋊Q8—474no—
510C2×C22⋊Q8—474no—
511C2×C22⋊Q8—474no—
512C2×C22⋊Q8C2×D4712yes—
513C2×#121—471no—
514C2×#121—472no—
515C2×#121—471no—
516C2×#121—474no—
517C2×C4×Q8—472no—
518C2×C4×Q8—471no—
519C2×C4×Q8—472no—
520C2×C4×Q8C2×D4711yescharacteristic
521C2×C4×Q8C2×D4712yes—
522C2×C4×D4—472no—
523C2×C4×D4—472no—
524C2×C4×D4—474no—
525C2×C4×D4—471no—
526C2×C4×D4—472no—
527C2×C4×D4—474no—
528C2×C4×D4C2×D4711yescharacteristic
529C2×#117—472no—
530C2×#117—472no—
531C2×#117C2×D4712yes—
532C22×C4⋊C4—472no—
533C22×C4⋊C4—472no—
534C22×C4⋊C4—472no—
535C22×C42—471no—
536C47C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—4716no—
538C2×#41—1888no—
539C22×Q8—4716no—
540C22×Q8—4716no—
541C22×Q8—471no—
542C22×Q8—472no—
543C22×Q8—474no—
544C22×Q8—474no—
545C22×Q8—1888no—
546C22×Q8—1888no—
547C22×Q8C22×D4711yescharacteristic
548C22×Q8C22×D4712yes—
549C22×D4—472no—
550C22×D4—474no—
551C22×D4—472no—
552C22×D4—471no—
553C22×D4C22×D4711yescharacteristic
554C23×C4—474no—
555C23×C4—471no—
556C23×C4—471no—
557C23×C4—472no—
558C23×C4—471no—
559C23×C4—474no—
560C23×C4—474no—
561C23×C4C22×D4712yes—
562C4⋊Q8—4716no—
563C4⋊Q8—4716no—
564C4⋊Q8—4716no—
565C4⋊Q8—4716no—
566C4⋊Q8—478no—
567C4⋊Q8—4716no—
568C4⋊Q8—4732no—
569C4⋊Q8C22×D4718yes—
570#126—4716no—
571#126—4732no—
572#126—4716no—
573#126—4732no—
574#126C22×D47132yes—
575#125—478no—
576#125—478no—
577#125—4732no—
578#125—4732no—
579#125—4716no—
580#125—4732no—
581#124—478no—
582#124—478no—
583#124—4732no—
584#124C22×D47116yes—
585#123—4716no—
586#123—4716no—
587#123—4732no—
588#123—4732no—
589#123—4732no—
590C22⋊Q8—478no—
591C22⋊Q8—4716no—
592C22⋊Q8—478no—
593C22⋊Q8—4732no—
594C22⋊Q8—4732no—
595C22⋊Q8—4716no—
596C22⋊Q8—4732no—
597C22⋊Q8—4732no—
598C22⋊Q8—4732no—
599C22⋊Q8—4732no—
600C22⋊Q8C22×D47116yes—
601#121—478no—
602#121—4716no—
603#121—478no—
604#121—4732no—
605C4×Q8—4716no—
606C4×Q8—478no—
607C4×Q8—4716no—
608C4×Q8C22×D4718yes—
609C4×Q8C22×D47116yes—
610C4×D4—4716no—
611C4×D4—4716no—
612C4×D4—4732no—
613C4×D4—478no—
614C4×D4—4716no—
615C4×D4—4732no—
616C4×D4C22×D4718yes—
617#117—4716no—
618#117—4716no—
619#117C22×D47116yes—
620C2×C4⋊C4—471no—
621C2×C4⋊C4—472no—
622C2×C4⋊C4—474no—
623C2×C4⋊C4—474no—
624C2×C4⋊C4—474no—
625C2×C4⋊C4—472no—
626C2×C4⋊C4—4716no—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—472no—
629C2×C4⋊C4—472no—
630C2×C4⋊C4—472no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—472no—
633C2×C4⋊C4—474no—
634C2×C4⋊C4—472no—
635C2×C4⋊C4—471no—
636C2×C4⋊C4—474no—
637C2×C4⋊C4—474no—
638C2×C4⋊C4—472no—
639C2×C4⋊C4—4716no—
640C2×C4⋊C4—4716no—
641C2×C4⋊C4C22×D4712yes—
642C2×C4⋊C4C22×D4712yes—
643C2×C4⋊C4C22×D4711yescharacteristic
644C2×C4⋊C4C22×D4711yescharacteristic
645C2×C4⋊C4C22×D4714yes—
646C2×C4⋊C4C22×D4712yes—
647C2×C22⋊C4—472no—
648C2×C22⋊C4—472no—
649C2×C22⋊C4—472no—
650C2×C22⋊C4—472no—
651C2×C22⋊C4—472no—
652C2×C22⋊C4—472no—
653C2×C22⋊C4—472no—
654C2×C22⋊C4—474no—
655C2×C22⋊C4—474no—
656C2×C22⋊C4—472no—
657C2×C22⋊C4—472no—
658C2×C22⋊C4C22×D4714yes—
659C2×C22⋊C4C22×D4714yes—
660C2×C22⋊C4C22×D4712yes—
661C2×C42—471no—
662C2×C42—471no—
663C2×C42—472no—
664C2×C42—474no—
665C2×C42—471no—
666C2×C42—478no—
667C2×C42C22×D4712yes—
668C2×C42C22×D4714yes—
669C2×C42C22×D4711yescharacteristic
670C24—471no—
671C24—472no—
672C24C23×D4712yes—
673#41—18832no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—474no—
677C2×Q8—478no—
678C2×Q8—4716no—
679C2×Q8—4716no—
680C2×Q8—944no—
681C2×Q8—948no—
682C2×Q8—1888no—
683C2×Q8—1888no—
684C2×Q8—18832no—
685C2×Q8—18832no—
686C2×Q8C23×D4714yes—
687C2×Q8C23×D4718yes—
688C2×D4—24no—
689C2×D4—478no—
690C2×D4—4716no—
691C2×D4—478no—
692C2×D4—474no—
693C2×D4—948no—
694C2×D4—948no—
695C2×D4—944no—
696C2×D4—1888no—
697C2×D4C23×D4714yes—
698C22×C4—28no—
699C22×C4—472no—
700C22×C4—471no—
701C22×C4—471no—
702C22×C4—471no—
703C22×C4—472no—
704C22×C4—474no—
705C22×C4—472no—
706C22×C4—4716no—
707C22×C4—474no—
708C22×C4—474no—
709C22×C4—474no—
710C22×C4—478no—
711C22×C4—4716no—
712C22×C4—4716no—
713C22×C4—944no—
714C22×C4—944no—
715C22×C4—948no—
716C22×C4—944no—
717C22×C4—1888no—
718C22×C4—1888no—
719C22×C4—1888no—
720C22×C4C23×D4718yes—
721C22×C4C23×D4712yes—
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4712yes—
724C22×C4C23×D4712yes—
725C22×C4C23×D4714yes—
726C22×C4C23×D4711yescharacteristic
727C22×C4C23×D4711yescharacteristic
728C4⋊C4—4716no—
729C4⋊C4—4716no—
730C4⋊C4—478no—
731C4⋊C4—478no—
732C4⋊C4—4716no—
733C4⋊C4—478no—
734C4⋊C4—4716no—
735C4⋊C4—478no—
736C4⋊C4—474no—
737C4⋊C4—478no—
738C4⋊C4—4716no—
739C4⋊C4—478no—
740C4⋊C4—478no—
741C4⋊C4—478no—
742C4⋊C4—478no—
743C4⋊C4—4716no—
744C4⋊C4—474no—
745C4⋊C4—4716no—
746C4⋊C4C23×D4718yes—
747C4⋊C4C23×D4718yes—
748C4⋊C4C23×D4714yes—
749C4⋊C4C23×D4714yes—
750C4⋊C4C23×D47116yes—
751C4⋊C4C23×D4718yes—
752C22⋊C4—478no—
753C22⋊C4—478no—
754C22⋊C4—478no—
755C22⋊C4—478no—
756C22⋊C4—478no—
757C22⋊C4—478no—
758C22⋊C4—478no—
759C22⋊C4—4716no—
760C22⋊C4—4716no—
761C22⋊C4—478no—
762C22⋊C4—478no—
763C22⋊C4C23×D47116yes—
764C22⋊C4C23×D47116yes—
765C22⋊C4C23×D4718yes—
766C42—474no—
767C42—474no—
768C42—474no—
769C42—478no—
770C42—4716no—
771C42C23×D4714yes—
772C42C23×D4718yes—
773C42C23×D47116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—474no—
778C23—472no—
779C23—474no—
780C23—942no—
781C23—942no—
782C23—944no—
783C23—944no—
784C23—944no—
785C23C24×D4714yes—
786C23C24×D4711yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—948no—
790Q8—9416no—
791Q8—18816no—
792Q8—18816no—
793D4—28no—
794D4—9416no—
795D4—9416no—
796D4—948no—
797D4—18816no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—474no—
805C2×C4—472no—
806C2×C4—472no—
807C2×C4—472no—
808C2×C4—474no—
809C2×C4—478no—
810C2×C4—474no—
811C2×C4—948no—
812C2×C4—944no—
813C2×C4—942no—
814C2×C4—948no—
815C2×C4—944no—
816C2×C4—942no—
817C2×C4—944no—
818C2×C4—942no—
819C2×C4—948no—
820C2×C4—9416no—
821C2×C4—948no—
822C2×C4—18816no—
823C2×C4—18816no—
824C2×C4—18816no—
825C2×C4#1309407014yes—
826C2×C4#1309407114yes—
827C2×C4C24×D4714yes—
828C2×C4C24×D4712yes—
829C2×C4C24×D4714yes—
830C2×C4C24×D4714yes—
831C2×C4C24×D4718yes—
832C2×C4C24×D4712yes—
833C2×C4C24×D4712yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—474no—
839C22—948no—
840C22—942no—
841C22—942no—
842C22—944no—
843C22—944no—
844C22—944no—
845C22—1888no—
846C22C2×#1309407012yes—
847C222−1+4×D4712yes—
848C22C2×#1309407112yes—
849C22C25×D4711yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—944no—
856C4—942no—
857C4—948no—
858C4—944no—
859C4—942no—
860C4—944no—
861C4—942no—
862C4C2×#1309407014yes—
863C4C2×#1309407114yes—
864C2—44no—
865C2—944no—
866C2—1884no—
867C2#2025781814yesdirect product factor
868C2C22×#1309407011yescharacteristic
869C2C2×2−1+4×D4711yescharacteristic
870C2C22×#1309407111yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#556C2
socleC23×C47C25
hypercenterC2×#556D47
hypocenterC47C2×#3552
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20257818C2direct (N × H)
2. C2×#15689875C2semidirect
3. C2×#15689852C2semidirect
4. C2×#15689831C2semidirect
5. C2×#15689817C2semidirect
6. C2×Q8×D188C2semidirect
7. C2×#15689788C2semidirect
8. C2×#15689781C2semidirect
9. C2×#15689777C2semidirect
10. C2×#15689751C2semidirect
11. C2×#15689746C2semidirect
12. C2×#15689731C2semidirect
13. C2×#15689714C2semidirect
14. C2×#15689693C2semidirect
15. C2×C4⋊Q8×D47C2semidirect
16. C2×#15689660C2semidirect
17. C2×#15689655C2semidirect
18. C2×C47×#556C2semidirect
22. #15689875C22semidirect
23. #15689852C22semidirect
24. #15689831C22semidirect
25. #15689817C22semidirect
26. Q8×D188C22semidirect
27. #15689788C22semidirect
28. #15689781C22semidirect
29. #15689777C22semidirect
30. #15689751C22semidirect
31. #15689746C22semidirect
32. #15689731C22semidirect
33. #15689714C22semidirect
34. #15689693C22semidirect
42. C4⋊Q8×D47C22semidirect
43. #15689660C22semidirect
44. #15689655C22semidirect
92. C47×#556C22semidirect
432. C2×#556D47semidirect
448. C2×C47#3552semidirect
459. #556C2×D47semidirect
536. C47C2×#3552semidirect
867. C2#20257818direct (N × H)

Maximal subgroups

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

subgroupindex
#202578182
C2×#156898752
C2×#156898522
C2×#156898312
C2×#156898172
C2×Q8×D1882
C2×#156897882
C2×#156897812
C2×#156897772
C2×#156897512
C2×#156897462
C2×#156897312
C2×#156897142
C2×#156896932
C2×C4⋊Q8×D472
C2×#156896602
C2×#156896552
C2×C47×#5562
C2×#355247