Finite Group Databasebeta

← #26369022

Subgroups — #26369022

Order 12032.

1236 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
1C2×#15689107C211yesmaximal, characteristic, complemented
2C2×#15689097C211yesmaximal, characteristic, complemented
3#20245042C212yesmaximal, complemented
4#20245038C212yesmaximal, complemented
5#20245034C214yesmaximal, complemented
6#20245029C214yesmaximal, complemented
7C47×#3449C211yesmaximal, characteristic
8C22×#10625329—21no—
9C2×#13093983—21no—
10#15689107—21no—
11#15689107—21no—
12#15689107C2212yes—
13#15689107C2212yes—
14C2×#13093943—21no—
15C2×#13093941C2212yes—
16#15689097—21no—
17#15689097—21no—
18#15689097C2212yes—
19#15689097C2212yes—
20C2×#13093939—21no—
21C2×#13093939C2212yes—
22#15688913C2218yescomplemented
23#15688910C2218yescomplemented
24C22×#41×C47C411yescharacteristic, complemented
25C22×#41×C47C2211yescharacteristic
26C47×#537—21no—
27C47×#537—21no—
28C47×#536—21no—
29C47×#536C411yescharacteristic, complemented
30C47×#536C2211yescharacteristic
31C47×#535—21no—
32C47×#535C411yescharacteristic, complemented
33C47×#535C2211yescharacteristic
34C47×#534C412yescomplemented
35C47×#534C2212yes—
36C47×#532—21no—
37C47×#532—21no—
38C47×#525—21no—
39C47×#525—21no—
40C47×#525C412yescomplemented
41C47×#525C2212yes—
42C2×#117×C47C411yescharacteristic, complemented
43C2×#10625329—22no—
44C2×#10625329—22no—
45C2×#10625329—22no—
46C2×#10625329—41no—
47C2×#10625329—41no—
48C2×#10625329—41no—
49C22×C47⋊C8—41no—
50#13093983—22no—
51#13093983—22no—
52#13093983—41no—
53#13093983—41no—
54C2×C4⋊Dic47—41no—
55C2×C22⋊Dic47—22no—
56C2×C4×Dic47—41no—
57#13093943—22no—
58#13093943—22no—
59#13093941—22no—
60#13093941C2314yes—
61#13093939—22no—
62#13093939—22no—
63#13093939—22no—
64#13093939C2314yes—
65C2×#41×C47—21no—
66C2×#41×C47—21no—
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C2×#41×C47—41no—
70C2×#41×C47—41no—
71C2×#41×C47—41no—
72C2×#41×C47—41no—
73C2×#41×C47—41no—
74C2×#41×C47—41no—
75C2×#41×C47—41no—
76C2×#41×C47—41no—
77C2×#41×C47C2×C411yescharacteristic
78C2×#41×C47C2×C411yescharacteristic
79C2×#41×C47D411yescharacteristic
80C2×#41×C47D411yescharacteristic
81C2×#41×C47D411yescharacteristic
82C2×#41×C47D411yescharacteristic
83C2×#41×C47C2311yescharacteristic
84C2×#41×C47C2311yescharacteristic
85C22×Q8×C47C2×C411yescharacteristic, complemented
86C22×Q8×C47D411yescharacteristic
87C22×D4×C47C2×C411yescharacteristic
88C22×D4×C47C2×C412yes—
89C22×D4×C47C2×C411yescharacteristic, complemented
90C22×D4×C47D411yescharacteristic
91C22×D4×C47C2311yescharacteristic
92C23×C4×C47C2×C411yescharacteristic
93C23×C4×C47C2×C412yescomplemented
94C23×C4×C47D411yescharacteristic
95C23×C4×C47D411yescharacteristic
96C4⋊Q8×C47—21no—
97C4⋊Q8×C47—21no—
98#127×C47—21no—
99#127×C47—21no—
100#124×C47—21no—
101#124×C47—21no—
102#124×C47—21no—
103#124×C47—21no—
104#123×C47—22no—
105#123×C47—22no—
106#123×C47C2×C412yes—
107#123×C47C2×C412yescomplemented
108#123×C47C2×C412yescomplemented
109#123×C47C2312yes—
110C22⋊Q8×C47—22no—
111C22⋊Q8×C47—22no—
112C22⋊Q8×C47—21no—
113C22⋊Q8×C47—21no—
114C22⋊Q8×C47—21no—
115C22⋊Q8×C47—21no—
116#121×C47—22no—
117#121×C47—22no—
118#121×C47—22no—
119#121×C47—22no—
120#121×C47—22no—
121#121×C47—22no—
122#121×C47—21no—
123#121×C47—21no—
124#121×C47—21no—
125#121×C47—21no—
126#120×C47—22no—
127#120×C47—22no—
128#120×C47C2×C412yes—
129#120×C47C2×C412yescomplemented
130#120×C47C2×C412yescomplemented
131#120×C47C2312yes—
132C4×D4×C47—22no—
133C4×D4×C47—22no—
134C4×D4×C47—22no—
135C4×D4×C47—22no—
136#117×C47—21no—
137#117×C47—21no—
138#117×C47C2×C412yescomplemented
139#117×C47C2×C411yescharacteristic, complemented
140#117×C47C2×C411yescharacteristic, complemented
141C2×C4⋊C4×C47—21no—
142C2×C22⋊C4×C47C2×C412yes—
143C2×C42×C47—21no—
144C24×C47C22⋊C411yescharacteristic
145C24×C47C22×C411yescharacteristic
146C24×C47C22×C412yes—
147C24×C47C2×D411yescharacteristic
148#41×C47—41no—
149#41×C47—41no—
150#41×C47—41no—
151#41×C47—41no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
155#41×C47—41no—
156#41×C47—41no—
157#41×C47—41no—
158#41×C47—41no—
159#41×C47—41no—
160#41×C47—41no—
161#41×C47—41no—
162#41×C47—41no—
163#41×C47—41no—
164#41×C47—42no—
165#41×C47—42no—
166#41×C47—42no—
167#41×C47—42no—
168#41×C47—42no—
169#41×C47—42no—
170#41×C47—41no—
171#41×C47—41no—
172#41×C47—41no—
173#41×C47—41no—
174C2×Q8×C47—21no—
175C2×Q8×C47—21no—
176C2×Q8×C47—41no—
177C2×Q8×C47—41no—
178C2×Q8×C47—41no—
179C2×Q8×C47—41no—
180C2×Q8×C47C22⋊C411yescharacteristic
181C2×Q8×C47C22⋊C411yescharacteristic
182C2×Q8×C47C2×D411yescharacteristic
183C2×Q8×C47C2×D411yescharacteristic
184C2×D4×C47—22no—
185C2×D4×C47—22no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47—22no—
189C2×D4×C47—22no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—41no—
193C2×D4×C47—41no—
194C2×D4×C47—41no—
195C2×D4×C47—41no—
196C2×D4×C47—41no—
197C2×D4×C47—41no—
198C2×D4×C47—41no—
199C2×D4×C47—41no—
200C2×D4×C47—42no—
201C2×D4×C47—42no—
202C2×D4×C47C22⋊C411yescharacteristic
203C2×D4×C47C22⋊C411yescharacteristic
204C2×D4×C47C22⋊C411yescharacteristic
205C2×D4×C47C22⋊C411yescharacteristic
206C2×D4×C47C22×C411yescharacteristic
207C2×D4×C47C22×C411yescharacteristic
208C2×D4×C47C22×C411yescharacteristic
209C2×D4×C47C2×D411yescharacteristic
210C2×D4×C47C2×D411yescharacteristic
211C2×D4×C47C2×D411yescharacteristic
212C2×D4×C47C2×D411yescharacteristic
213C2×D4×C47C2411yescharacteristic
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—22no—
227C22×C4×C47—22no—
228C22×C4×C47—22no—
229C22×C4×C47—42no—
230C22×C4×C47—42no—
231C22×C4×C47C22⋊C411yescharacteristic
232C22×C4×C47C22⋊C411yescharacteristic
233C22×C4×C47C22⋊C411yescharacteristic
234C22×C4×C47C22⋊C411yescharacteristic
235C22×C4×C47C22⋊C411yescharacteristic
236C22×C4×C47C22⋊C411yescharacteristic
237C22×C4×C47C22⋊C411yescharacteristic
238C22×C4×C47C22⋊C411yescharacteristic
239C22×C4×C47C22⋊C411yescharacteristic
240C22×C4×C47C22×C411yescharacteristic
241C22×C4×C47C22×C411yescharacteristic
242C22×C4×C47C22×C412yes—
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D411yescharacteristic
245C22×C4×C47C2×D411yescharacteristic
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2×D411yescharacteristic
248C22×Dic47—42no—
249C4⋊C4×C47—22no—
250C4⋊C4×C47—21no—
251C4⋊C4×C47—21no—
252C4⋊C4×C47—22no—
253C4⋊C4×C47—22no—
254C4⋊C4×C47—22no—
255C4⋊C4×C47—22no—
256C22⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
259C22⋊C4×C47—22no—
260C22⋊C4×C47—22no—
261C22⋊C4×C47—22no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—22no—
264C22⋊C4×C47—22no—
265C22⋊C4×C47C22×C412yes—
266C22⋊C4×C47C22×C412yes—
267C42×C47—22no—
268C42×C47—21no—
269C42×C47—21no—
270C22⋊Dic47—24no—
271C22⋊Dic47—42no—
272C4⋊Dic47—42no—
273C4⋊Dic47—42no—
274C4×Dic47—42no—
275C4×Dic47—42no—
276#10625329—24no—
277#10625329—42no—
278#10625329—42no—
279#10625329—42no—
280C2×C47⋊C8—42no—
281C2×C47⋊C8—42no—
282C2×C47⋊C8—42no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—22no—
290C23×C47—42no—
291C23×C47—81no—
292C23×C47—81no—
293C23×C47—81no—
294C23×C47—82no—
295C23×C47C2×C22⋊C411yescharacteristic
296C23×C47C2×C22⋊C411yescharacteristic
297C23×C47C2×C22⋊C411yescharacteristic
298C23×C47C2×C22⋊C411yescharacteristic
299C23×C47C2×C22⋊C411yescharacteristic
300C23×C47C23×C411yescharacteristic
301C23×C47C22×D411yescharacteristic
302Q8×C47—41no—
303Q8×C47—41no—
304Q8×C47—41no—
305Q8×C47—41no—
306Q8×C47—42no—
307Q8×C47—41no—
308Q8×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—41no—
319D4×C47—41no—
320D4×C47—41no—
321D4×C47—42no—
322D4×C47—44no—
323D4×C47—42no—
324D4×C47—42no—
325D4×C47—41no—
326D4×C47—41no—
327D4×C47—82no—
328D4×C47—82no—
329D4×C47—82no—
330D4×C47—82no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47—21no—
349C2×C4×C47—21no—
350C2×C4×C47—21no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—21no—
354C2×C4×C47—21no—
355C2×C4×C47—21no—
356C2×C4×C47—21no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—21no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—22no—
364C2×C4×C47—44no—
365C2×C4×C47—42no—
366C2×C4×C47—42no—
367C2×C4×C47—42no—
368C2×C4×C47—82no—
369C2×C4×C47#9911yescharacteristic
370C2×C4×C47#9911yescharacteristic
371C2×C4×C47#9911yescharacteristic
372C2×C4×C47#9911yescharacteristic
373C2×C4×C47C2×C22⋊C411yescharacteristic
374C2×C4×C47C2×C22⋊C411yescharacteristic
375C2×C4×C47C2×C22⋊C411yescharacteristic
376C2×C4×C47C2×C22⋊C411yescharacteristic
377C2×C4×C47C2×C22⋊C411yescharacteristic
378C2×C4×C47C2×C22⋊C411yescharacteristic
379C2×C4×C47C2×C22⋊C411yescharacteristic
380C2×C4×C47C22×D411yescharacteristic
381C2×Dic47—44no—
382C2×Dic47—84no—
383C47⋊C8—44no—
384#33347—471nomaximal, Sylow
385C22×C47—21no—
386C22×C47—21no—
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—42no—
401C22×C47—42no—
402C22×C47—42no—
403C22×C47—81no—
404C22×C47—81no—
405C22×C47—81no—
406C22×C47—81no—
407C22×C47—84no—
408C22×C47C2×#9911yescharacteristic
409C22×C47C2×#9911yescharacteristic
410C22×C47C22×C22⋊C411yescharacteristic
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—21no—
414C4×C47—21no—
415C4×C47—21no—
416C4×C47—21no—
417C4×C47—42no—
418C4×C47—42no—
419C4×C47—42no—
420C4×C47C2×#9911yescharacteristic
421C4×C47C2×#9911yescharacteristic
422C4×C47C2×#9911yescharacteristic
423C4×C47C2×#9911yescharacteristic
424Dic47—84no—
425#3449D4711yescharacteristic
426C2×#413—471no—
427C2×#410—471no—
428#2123—472no—
429#2122—472no—
430#2121—474no—
431#2120—474no—
432C2×C47—21no—
433C2×C47—21no—
434C2×C47—21no—
435C2×C47—41no—
436C2×C47—41no—
437C2×C47—41no—
438C2×C47—41no—
439C2×C47—41no—
440C2×C47—41no—
441C2×C47—82no—
442C2×C47C22×#9911yescharacteristic
443C22×#41Dic4711yescharacteristic, complemented
444C22×#41C2×D4711yescharacteristic
445C22×M16—941no—
446#537—21no—
447#537—21no—
448#536—21no—
449#536Dic4711yescharacteristic, complemented
450#536C2×D4711yescharacteristic
451#535—21no—
452#535Dic4711yescharacteristic, complemented
453#535C2×D4711yescharacteristic
454#534Dic4712yescomplemented
455#534C2×D4712yes—
456#532—21no—
457#532—21no—
458#525—21no—
459#525—21no—
460#525Dic4712yescomplemented
461#525C2×D4712yes—
462C2×#117—941no—
463C2×#117Dic4711yescharacteristic, complemented
464#413—472no—
465#413—472no—
466#413—941no—
467#413—941no—
468C2×#101—941no—
469C2×#100—472no—
470#410—472no—
471#410—472no—
472#410—941no—
473#410—941no—
474C2×#99—472no—
475C2×#99—941no—
476#352—478no—
477AΣL(1,𝔽16)—478no—
478C47#3334711yescharacteristic, complemented, Sylow
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41—41no—
484C2×#41—41no—
485C2×#41—41no—
486C2×#41—41no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41C2×Dic4711yescharacteristic
492C2×#41C2×Dic4711yescharacteristic
493C2×#41C22⋊D4711yescharacteristic
494C2×#41C22⋊D4711yescharacteristic
495C2×#41C22⋊D4711yescharacteristic
496C2×#41C22⋊D4711yescharacteristic
497C2×#41C22×D4711yescharacteristic
498C2×#41C22×D4711yescharacteristic
499C22×Q8C2×Dic4711yescharacteristic, complemented
500C22×Q8C22⋊D4711yescharacteristic
501C22×D4C2×Dic4711yescharacteristic
502C22×D4C2×Dic4712yes—
503C22×D4C2×Dic4711yescharacteristic, complemented
504C22×D4C22⋊D4711yescharacteristic
505C22×D4C22×D4711yescharacteristic
506C23×C4C2×Dic4711yescharacteristic
507C23×C4C2×Dic4712yescomplemented
508C23×C4C22⋊D4711yescharacteristic
509C23×C4C22⋊D4711yescharacteristic
510C2×M16—942no—
511C2×M16—942no—
512C2×M16—942no—
513C2×M16—1881no—
514C2×M16—1881no—
515C2×M16—1881no—
516C22×C8—1881no—
517C4⋊Q8—21no—
518C4⋊Q8—21no—
519#127—21no—
520#127—21no—
521#124—21no—
522#124—21no—
523#124—21no—
524#124—21no—
525#123—22no—
526#123—22no—
527#123C2×Dic4712yes—
528#123C2×Dic4712yescomplemented
529#123C2×Dic4712yescomplemented
530#123C22×D4712yes—
531C22⋊Q8—22no—
532C22⋊Q8—22no—
533C22⋊Q8—21no—
534C22⋊Q8—21no—
535C22⋊Q8—21no—
536C22⋊Q8—21no—
537#121—22no—
538#121—22no—
539#121—22no—
540#121—22no—
541#121—22no—
542#121—22no—
543#121—21no—
544#121—21no—
545#121—21no—
546#121—21no—
547#120—22no—
548#120—22no—
549#120C2×Dic4712yes—
550#120C2×Dic4712yescomplemented
551#120C2×Dic4712yescomplemented
552#120C22×D4712yes—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557#117—21no—
558#117—21no—
559#117—942no—
560#117—942no—
561#117—1881no—
562#117—1881no—
563#117C2×Dic4712yescomplemented
564#117C2×Dic4711yescharacteristic, complemented
565#117C2×Dic4711yescharacteristic, complemented
566C2×C4⋊C4—21no—
567C2×C4⋊C4—1881no—
568C2×C22⋊C4—942no—
569C2×C22⋊C4C2×Dic4712yes—
570C2×C42—21no—
571C2×C42—1881no—
572#101—942no—
573#101—942no—
574#100—474no—
575#100—942no—
576#99—474no—
577#99—942no—
578#99—942no—
579#99—942no—
580C24C22⋊Dic4711yescharacteristic
581C24C22×Dic4711yescharacteristic
582C24C22×Dic4712yes—
583C24C2×C22⋊D4711yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—42no—
601#41—42no—
602#41—42no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—41no—
607#41—41no—
608#41—41no—
609#41—41no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—41no—
613C2×Q8—41no—
614C2×Q8—41no—
615C2×Q8—41no—
616C2×Q8C22⋊Dic4711yescharacteristic
617C2×Q8C22⋊Dic4711yescharacteristic
618C2×Q8C2×C22⋊D4711yescharacteristic
619C2×Q8C2×C22⋊D4711yescharacteristic
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—41no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4C22⋊Dic4711yescharacteristic
639C2×D4C22⋊Dic4711yescharacteristic
640C2×D4C22⋊Dic4711yescharacteristic
641C2×D4C22⋊Dic4711yescharacteristic
642C2×D4C22×Dic4711yescharacteristic
643C2×D4C22×Dic4711yescharacteristic
644C2×D4C22×Dic4711yescharacteristic
645C2×D4C2×C22⋊D4711yescharacteristic
646C2×D4C2×C22⋊D4711yescharacteristic
647C2×D4C2×C22⋊D4711yescharacteristic
648C2×D4C2×C22⋊D4711yescharacteristic
649C2×D4C23×D4711yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1882no—
668C22×C4C22⋊Dic4711yescharacteristic
669C22×C4C22⋊Dic4711yescharacteristic
670C22×C4C22⋊Dic4711yescharacteristic
671C22×C4C22⋊Dic4711yescharacteristic
672C22×C4C22⋊Dic4711yescharacteristic
673C22×C4C22⋊Dic4711yescharacteristic
674C22×C4C22⋊Dic4711yescharacteristic
675C22×C4C22⋊Dic4711yescharacteristic
676C22×C4C22⋊Dic4711yescharacteristic
677C22×C4C22×Dic4711yescharacteristic
678C22×C4C22×Dic4711yescharacteristic
679C22×C4C22×Dic4712yes—
680C22×C4C2×C22⋊D4711yescharacteristic
681C22×C4C2×C22⋊D4711yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C2×C22⋊D4711yescharacteristic
684C22×C4C2×C22⋊D4711yescharacteristic
685M16—944no—
686M16—1882no—
687M16—1882no—
688M16—1882no—
689C2×C8—1882no—
690C2×C8—1882no—
691C2×C8—1882no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—22no—
699C4⋊C4—1882no—
700C4⋊C4—1882no—
701C22⋊C4—22no—
702C22⋊C4—22no—
703C22⋊C4—22no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—944no—
711C22⋊C4—1882no—
712C22⋊C4C22×Dic4712yes—
713C22⋊C4C22×Dic4712yes—
714C42—22no—
715C42—21no—
716C42—21no—
717C42—1882no—
718C42—1882no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—22no—
726C23—42no—
727C23—81no—
728C23—81no—
729C23—81no—
730C23—82no—
731C23C2×C22⋊Dic4711yescharacteristic
732C23C2×C22⋊Dic4711yescharacteristic
733C23C2×C22⋊Dic4711yescharacteristic
734C23C2×C22⋊Dic4711yescharacteristic
735C23C2×C22⋊Dic4711yescharacteristic
736C23C23×Dic4711yescharacteristic
737C23C22×C22⋊D4711yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—42no—
743Q8—41no—
744Q8—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—44no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—82no—
764D4—82no—
765D4—82no—
766D4—82no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—82no—
805C2×C4—3764no—
806C2×C4—1884no—
807C2×C4#1309393911yescharacteristic
808C2×C4#1309393911yescharacteristic
809C2×C4#1309393911yescharacteristic
810C2×C4#1309393911yescharacteristic
811C2×C4C2×C22⋊Dic4711yescharacteristic
812C2×C4C2×C22⋊Dic4711yescharacteristic
813C2×C4C2×C22⋊Dic4711yescharacteristic
814C2×C4C2×C22⋊Dic4711yescharacteristic
815C2×C4C2×C22⋊Dic4711yescharacteristic
816C2×C4C2×C22⋊Dic4711yescharacteristic
817C2×C4C2×C22⋊Dic4711yescharacteristic
818C2×C4C22×C22⋊D4711yescharacteristic
819C8—1884no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—84no—
843C22C2×#1309393911yescharacteristic
844C22C2×#1309393911yescharacteristic
845C22C22×C22⋊Dic4711yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—42no—
853C4—42no—
854C4—42no—
855C4—3764no—
856C4C2×#1309393911yescharacteristic
857C4C2×#1309393911yescharacteristic
858C4C2×#1309393911yescharacteristic
859C4C2×#1309393911yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—82no—
870C2C22×#1309393911yescharacteristic
subgroupG/H
centerC4C2×#13093939
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
Fitting, prime radicalC47×#3449C2
socleC2×C47C22×#99
cosocleC2×D4×C47C24
hypercenter#3449D47
hypocenterC47#33347
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#15689107C2semidirect
2. C2×#15689097C2semidirect
3. #20245042C2semidirect
4. #20245038C2semidirect
5. #20245034C2semidirect
6. #20245029C2semidirect
22. #15688913C22semidirect
23. #15688910C22semidirect
24. C22×#41×C47C4semidirect
29. C47×#536C4semidirect
32. C47×#535C4semidirect
34. C47×#534C4semidirect
40. C47×#525C4semidirect
42. C2×#117×C47C4semidirect
85. C22×Q8×C47C2×C4semidirect
89. C22×D4×C47C2×C4semidirect
93. C23×C4×C47C2×C4semidirect
107. #123×C47C2×C4semidirect
108. #123×C47C2×C4semidirect
129. #120×C47C2×C4semidirect
130. #120×C47C2×C4semidirect
138. #117×C47C2×C4semidirect
139. #117×C47C2×C4semidirect
140. #117×C47C2×C4semidirect
443. C22×#41Dic47semidirect
449. #536Dic47semidirect
452. #535Dic47semidirect
454. #534Dic47semidirect
460. #525Dic47semidirect
463. C2×#117Dic47semidirect
478. C47#33347semidirect
499. C22×Q8C2×Dic47semidirect
503. C22×D4C2×Dic47semidirect
507. C23×C4C2×Dic47semidirect
528. #123C2×Dic47semidirect
529. #123C2×Dic47semidirect
550. #120C2×Dic47semidirect
551. #120C2×Dic47semidirect
563. #117C2×Dic47semidirect
564. #117C2×Dic47semidirect
565. #117C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
C2×#156891072
C2×#156890972
#202450422
#202450382
#202450342
#202450292
C47×#34492
#3334747