Finite Group Databasebeta

← #26222745

Subgroups — #26222745

Order 12032.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689245C211yesmaximal, characteristic, complemented
2C2×#15689240C211yesmaximal, characteristic, complemented
3#20252106C211yesmaximal, characteristic, complemented
4#20251816C211yesmaximal, characteristic, complemented
5#20244308C211yesmaximal, characteristic, complemented
6#20244164C211yesmaximal, characteristic, complemented
7#20244038C211yesmaximal, characteristic, complemented
8#20244038C211yesmaximal, characteristic, complemented
9#20243717C211yesmaximal, characteristic, complemented
10#20243717C211yesmaximal, characteristic, complemented
11#20243408C211yesmaximal, characteristic, complemented
12#20243265C211yesmaximal, characteristic, complemented
13#20243235C211yesmaximal, characteristic, complemented
14#20243228C211yesmaximal, characteristic, complemented
15C47×#3035C211yesmaximal, characteristic
16C2×#13094031C2211yescharacteristic
17C2×#13094031C2211yescharacteristic
18C2×#13094031C2211yescharacteristic
19C2×#13094031C2211yescharacteristic
20#15689245—24no—
21#15689240—24no—
22#15689195—21no—
23#15689195—21no—
24#15689195—21no—
25#15689195—21no—
26C2×#13093960C2211yescharacteristic
27C2×#13093960C2211yescharacteristic
28#15689147C2211yescharacteristic
29C2×#13093951C2211yescharacteristic
30C2×#13093951C2211yescharacteristic
31C2×#13093951C2211yescharacteristic
32C2×#13093951C2211yescharacteristic
33C2×#13093951C2211yescharacteristic
34C2×#13093951C2211yescharacteristic
35#15689090C2211yescharacteristic
36#15689090C2211yescharacteristic
37#15689079—21no—
38#15689079—21no—
39#15689079C2211yescharacteristic
40#15689079C2211yescharacteristic
41C4×#10625329—21no—
42C4×#10625329C2211yescharacteristic
43C2×#13093935—21no—
44C2×#13093935C2211yescharacteristic
45C2×#13093934C2211yescharacteristic
46C2×C8×Dic47C2211yescharacteristic
47C4×C4⋊Dic47C2211yescharacteristic
48#15688888C2211yescharacteristic
49#15688888C2211yescharacteristic
50#15688882C2211yescharacteristic
51#15688882C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×#135×C47C2211yescharacteristic
55C2×#135×C47C2211yescharacteristic
56C47×#532C2211yescharacteristic
57C4×#41×C47C2211yescharacteristic
58C47×#464C411yescharacteristic, complemented
59C47×#464C411yescharacteristic, complemented
60C47×#463C411yescharacteristic, complemented
61C47×#463C411yescharacteristic, complemented
62C47×#462C411yescharacteristic, complemented
63C47×#461C411yescharacteristic, complemented
64C47×#460C411yescharacteristic, complemented
65C47×#459C411yescharacteristic, complemented
66C2×C4⋊C8×C47C2211yescharacteristic
67C47×#416C2211yescharacteristic
68C47×#416C2211yescharacteristic
69#13094031—22no—
70#13094031—22no—
71#13094031—22no—
72#13094031—22no—
73#13094031—22no—
74#13094031—22no—
75#13094031—22no—
76#13094031D414yescomplemented
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329—21no—
81C2×#10625329C2311yescharacteristic
82C2×#10625329C2311yescharacteristic
83C2×#10625329C2311yescharacteristic
84C2×#10625329C2311yescharacteristic
85C22×C47⋊C8—21no—
86C22×C47⋊C8—21no—
87C22×C47⋊C8—21no—
88C22×C47⋊C8—21no—
89C22×C47⋊C8C2311yescharacteristic
90C22×C47⋊C8C2311yescharacteristic
91C2×C4⋊Dic47—21no—
92C2×C4×Dic47C2311yescharacteristic
93C2×C4×Dic47C2311yescharacteristic
94#13093960—22no—
95#13093960—22no—
96C4⋊(C47⋊C8)—21no—
97C4⋊(C47⋊C8)—21no—
98#13093951—22no—
99#13093951—22no—
100#13093951—22no—
101#13093951—22no—
102#13093951—22no—
103#13093951—22no—
104C22⋊(C47⋊C8)—21no—
105C22⋊(C47⋊C8)—21no—
106C22⋊(C47⋊C8)—21no—
107C22⋊(C47⋊C8)—21no—
108#13093935—21no—
109#13093935—21no—
110#13093935—21no—
111#13093935D411yescharacteristic
112#13093935D411yescharacteristic
113#13093935D411yescharacteristic
114#13093935D411yescharacteristic
115#13093934—22no—
116C4×C47⋊C8—21no—
117C4×C47⋊C8—21no—
118C4×C47⋊C8—21no—
119C8×Dic47—22no—
120C47⋊#95—21no—
121C2×#41×C47C2311yescharacteristic
122C2×#41×C47C2311yescharacteristic
123C2×#41×C47C2311yescharacteristic
124#135×C47—22no—
125#135×C47—22no—
126#135×C47—22no—
127#135×C47—22no—
128C2×Q16×C47C2×C411yescharacteristic
129C2×Q16×C47C2×C411yescharacteristic
130C2×SD16×C47C2×C411yescharacteristic
131C2×SD16×C47C2×C411yescharacteristic
132C2×SD16×C47C2×C411yescharacteristic
133C2×SD16×C47C2×C411yescharacteristic
134C2×D8×C47C2×C411yescharacteristic
135C2×D8×C47C2×C411yescharacteristic
136C22×C8×C47C2311yescharacteristic
137C22×C8×C47C2311yescharacteristic
138C4⋊Q8×C47C2×C411yescharacteristic
139#127×C47C2×C411yescharacteristic
140#124×C47C2×C411yescharacteristic
141#124×C47C2×C411yescharacteristic
142#121×C47—21no—
143#121×C47—21no—
144C4×Q8×C47C2×C411yescharacteristic
145C4×Q8×C47C2×C411yescharacteristic
146C4×D4×C47—21no—
147C4×D4×C47—21no—
148C4×D4×C47—21no—
149C4×D4×C47—21no—
150C4×D4×C47C2×C411yescharacteristic
151C4×D4×C47C2×C411yescharacteristic
152#117×C47—21no—
153#117×C47C2311yescharacteristic
154C2×C42×C47—21no—
155C2×C42×C47C2311yescharacteristic
156C4⋊C8×C47C2×C411yescharacteristic
157C4⋊C8×C47C2×C411yescharacteristic
158C4⋊C8×C47C2×C411yescharacteristic
159C4⋊C8×C47C2×C411yescharacteristic
160#103×C47C2×C411yescharacteristic
161#103×C47C2×C411yescharacteristic
162#103×C47C2×C411yescharacteristic
163#103×C47C2×C411yescharacteristic
164#102×C47C2×C411yescharacteristic
165#102×C47C2×C411yescharacteristic
166#102×C47C2×C411yescharacteristic
167#102×C47C2×C411yescharacteristic
168#41×C47—21no—
169#41×C47—21no—
170#41×C47—21no—
171#41×C47—21no—
172#41×C47—21no—
173#41×C47—21no—
174#41×C47—21no—
175#41×C47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47C2×D412yes—
179#41×C47#4112yes—
180C2×Q8×C47C22×C411yescharacteristic
181C2×Q8×C47C22×C411yescharacteristic
182C2×Q8×C47C22×C411yescharacteristic
183C2×D4×C47—21no—
184C2×D4×C47—21no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47C22×C411yescharacteristic
189C2×D4×C47C22×C411yescharacteristic
190C2×D4×C47C22×C411yescharacteristic
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47#4111yescharacteristic
197C22×C4×C47#4111yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C22×Dic47—21no—
200C22×Dic47—21no—
201Q16×C47—22no—
202Q16×C47—22no—
203SD16×C47—22no—
204SD16×C47—22no—
205SD16×C47—22no—
206SD16×C47—22no—
207D8×C47—22no—
208D8×C47—22no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C2×C8×C47—21no—
212C2×C8×C47—21no—
213C2×C8×C47C22×C411yescharacteristic
214C2×C8×C47C22×C411yescharacteristic
215C2×C8×C47C22×C411yescharacteristic
216C2×C8×C47C22×C411yescharacteristic
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47C22×C411yescharacteristic
222C4⋊C4×C47C22×C411yescharacteristic
223C22⋊C4×C47—21no—
224C22⋊C4×C47—21no—
225C22⋊C4×C47—21no—
226C22⋊C4×C47—21no—
227C22⋊C4×C47—21no—
228C22⋊C4×C47—21no—
229C22⋊C4×C47—21no—
230C42×C47—21no—
231C42×C47—21no—
232C42×C47—21no—
233C42×C47C22×C411yescharacteristic
234C42×C47C22×C411yescharacteristic
235C42×C47C2×D411yescharacteristic
236C42×C47C2×D411yescharacteristic
237C4⋊Dic47—42no—
238C4×Dic47—21no—
239C4×Dic47—21no—
240C4×Dic47—21no—
241C4×Dic47—21no—
242#10625329—24no—
243#10625329—21no—
244#10625329—21no—
245#10625329—24no—
246#10625329—21no—
247#10625329—21no—
248#10625329—21no—
249#10625329—21no—
250#10625329—42no—
251#10625329—42no—
252#10625329C2×D412yes—
253#10625329#4112yes—
254C2×C47⋊C8—24no—
255C2×C47⋊C8—21no—
256C2×C47⋊C8—21no—
257C2×C47⋊C8—21no—
258C2×C47⋊C8—21no—
259C2×C47⋊C8—24no—
260C2×C47⋊C8—21no—
261C2×C47⋊C8—21no—
262C2×C47⋊C8—42no—
263C2×C47⋊C8—42no—
264C2×C47⋊C8C2×D411yescharacteristic
265C2×C47⋊C8C2×D411yescharacteristic
266C2×C47⋊C8C2×D412yes—
267C2×C47⋊C8C2×D411yescharacteristic
268C2×C47⋊C8C2×D411yescharacteristic
269C2×C47⋊C8#4112yes—
270C23×C47—21no—
271C23×C47—21no—
272C23×C47—21no—
273C23×C47C2×#4111yescharacteristic
274Q8×C47—21no—
275Q8×C47—21no—
276Q8×C47—21no—
277Q8×C47—21no—
278Q8×C47—21no—
279Q8×C47C4×D412yes—
280D4×C47—22no—
281D4×C47—22no—
282D4×C47—21no—
283D4×C47—21no—
284D4×C47—21no—
285D4×C47—21no—
286D4×C47—21no—
287D4×C47—41no—
288D4×C47—41no—
289D4×C47—41no—
290D4×C47—41no—
291D4×C47—81no—
292D4×C47—81no—
293D4×C47C4×D412yes—
294C2×C4×C47—21no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—21no—
298C2×C4×C47—21no—
299C2×C4×C47—21no—
300C2×C4×C47—21no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—81no—
308C2×C4×C47—81no—
309C2×C4×C47C4×D411yescharacteristic
310C2×C4×C47C4×D411yescharacteristic
311C2×C4×C47C4×D411yescharacteristic
312C2×C4×C47C4×D411yescharacteristic
313C2×C4×C47C23×C411yescharacteristic
314C2×C4×C47C22×D411yescharacteristic
315C2×C4×C47C22×D411yescharacteristic
316C2×C4×C47C2×#4111yescharacteristic
317C2×C4×C47C2×#4111yescharacteristic
318C2×C4×C47C2×#4111yescharacteristic
319C2×Dic47—22no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—41no—
324C2×Dic47—41no—
325C8×C47—21no—
326C8×C47—21no—
327C8×C47—21no—
328C8×C47—21no—
329C47⋊C8—22no—
330C47⋊C8—21no—
331C47⋊C8—22no—
332C47⋊C8—21no—
333C47⋊C8—41no—
334C47⋊C8—41no—
335C47⋊C8#12112yes—
336C47⋊C8#12112yes—
337#21519—471nomaximal, Sylow
338C22×C47—21no—
339C22×C47—21no—
340C22×C47—22no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47C2×C4×D411yescharacteristic
350C22×C47#52911yescharacteristic
351C22×C47#53211yescharacteristic
352C4×C47—21no—
353C4×C47—21no—
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—22no—
357C4×C47—41no—
358C4×C47—41no—
359C4×C47—41no—
360C4×C47—41no—
361C4×C47C2×C4×D411yescharacteristic
362C4×C47C4×#4111yescharacteristic
363C4×C47C2×#12111yescharacteristic
364C4×C47#52511yescharacteristic
365Dic47—42no—
366Dic47—81no—
367#3035D4711yescharacteristic
368C2×#444—471no—
369C2×#443—471no—
370#2932—471no—
371#2875—471no—
372#1980—471no—
373#1950—471no—
374#1929—471no—
375#1929—471no—
376#1876—471no—
377#1876—471no—
378#1806—471no—
379#1771—471no—
380#1765—471no—
381#1764—471no—
382C2×C47—21no—
383C2×C47—21no—
384C2×C47—42no—
385C2×C47—81no—
386C2×C47—81no—
387C2×C47C4×#12111yescharacteristic
388C2×C47#295611yescharacteristic
389C2×C47#295711yescharacteristic
390C2×#135C2×D4711yescharacteristic
391C2×#135C2×D4711yescharacteristic
392C2×#131—471no—
393C2×#131—471no—
394C2×#131—471no—
395C2×#131—471no—
396#532C2×D4711yescharacteristic
397C4×#41C2×D4711yescharacteristic
398#464Dic4711yescharacteristic, complemented
399#464Dic4711yescharacteristic, complemented
400#463Dic4711yescharacteristic, complemented
401#463Dic4711yescharacteristic, complemented
402#462Dic4711yescharacteristic, complemented
403#461Dic4711yescharacteristic, complemented
404#460Dic4711yescharacteristic, complemented
405#459Dic4711yescharacteristic, complemented
406#444—944no—
407#443—944no—
408#435—941no—
409#435—941no—
410#435—941no—
411#435—941no—
412C2×#108—471no—
413C2×#108—471no—
414#423—471no—
415C2×C4⋊C8C2×D4711yescharacteristic
416C2×#104—471no—
417C2×#104—471no—
418C2×#104—471no—
419C2×#104—471no—
420C2×#104—471no—
421C2×#104—471no—
422#416C2×D4711yescharacteristic
423#416C2×D4711yescharacteristic
424#408—471no—
425#408—471no—
426#405—471no—
427#405—471no—
428#405—941no—
429#405—941no—
430C4×M16—471no—
431C4×M16—941no—
432C2×#97—471no—
433C2×#97—471no—
434C2×#97—941no—
435C2×C4×C8—471no—
436C4×C4⋊C4—471no—
437#341—471no—
438#341—471no—
439#339—471no—
440#339—471no—
441#336—471no—
442#336—471no—
443C47#2151911yescharacteristic, complemented, Sylow
444C2×#41C22×D4711yescharacteristic
445C2×#41C22×D4711yescharacteristic
446C2×#41C22×D4711yescharacteristic
447#135—22no—
448#135—22no—
449#135—22no—
450#135—22no—
451C2×Q16C2×Dic4711yescharacteristic
452C2×Q16C2×Dic4711yescharacteristic
453C2×SD16C2×Dic4711yescharacteristic
454C2×SD16C2×Dic4711yescharacteristic
455C2×SD16C2×Dic4711yescharacteristic
456C2×SD16C2×Dic4711yescharacteristic
457C2×D8C2×Dic4711yescharacteristic
458C2×D8C2×Dic4711yescharacteristic
459#131—474no—
460#131—942no—
461#131—942no—
462#131—942no—
463#131—942no—
464#131—942no—
465#131—942no—
466#131—942no—
467C2×M16—471no—
468C2×M16—471no—
469C2×M16—471no—
470C2×M16—471no—
471C2×M16—941no—
472C2×M16—941no—
473C2×M16—941no—
474C2×M16—941no—
475C22×C8—471no—
476C22×C8—471no—
477C22×C8—941no—
478C22×C8—941no—
479C22×C8—941no—
480C22×C8—941no—
481C22×C8C22×D4711yescharacteristic
482C22×C8C22×D4711yescharacteristic
483C4⋊Q8C2×Dic4711yescharacteristic
484#127C2×Dic4711yescharacteristic
485#124C2×Dic4711yescharacteristic
486#124C2×Dic4711yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8C2×Dic4711yescharacteristic
490C4×Q8C2×Dic4711yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4C2×Dic4711yescharacteristic
496C4×D4C2×Dic4711yescharacteristic
497#117—21no—
498#117C22×D4711yescharacteristic
499C2×C4⋊C4—941no—
500C2×C42—21no—
501C2×C42—471no—
502C2×C42—471no—
503C2×C42C22×D4711yescharacteristic
504#108—942no—
505#108—942no—
506C4⋊C8—941no—
507C4⋊C8—941no—
508C4⋊C8C2×Dic4711yescharacteristic
509C4⋊C8C2×Dic4711yescharacteristic
510C4⋊C8C2×Dic4711yescharacteristic
511C4⋊C8C2×Dic4711yescharacteristic
512#104—942no—
513#104—942no—
514#104—942no—
515#104—942no—
516#104—942no—
517#104—942no—
518#103C2×Dic4711yescharacteristic
519#103C2×Dic4711yescharacteristic
520#103C2×Dic4711yescharacteristic
521#103C2×Dic4711yescharacteristic
522#102C2×Dic4711yescharacteristic
523#102C2×Dic4711yescharacteristic
524#102C2×Dic4711yescharacteristic
525#102C2×Dic4711yescharacteristic
526C22⋊C8—941no—
527C22⋊C8—941no—
528C22⋊C8—941no—
529C22⋊C8—941no—
530#97—471no—
531#97—471no—
532#97—471no—
533#97—471no—
534#97—941no—
535#97—941no—
536#97—942no—
537#97—941no—
538C4×C8—941no—
539C4×C8—941no—
540C4×C8—942no—
541C4×C8—941no—
542#95—941no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41D4×D4712yes—
554#41#1062535212yes—
555C2×Q8C22×Dic4711yescharacteristic
556C2×Q8C22×Dic4711yescharacteristic
557C2×Q8C22×Dic4711yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C22×Dic4711yescharacteristic
564C2×D4C22×Dic4711yescharacteristic
565C2×D4C22×Dic4711yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—941no—
572C22×C4—941no—
573C22×C4#1062535211yescharacteristic
574C22×C4#1062535211yescharacteristic
575C22×C4C23×D4711yescharacteristic
576Q16—22no—
577Q16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582D8—22no—
583D8—22no—
584M16—472no—
585M16—472no—
586M16—944no—
587M16—944no—
588M16—941no—
589M16—941no—
590M16—941no—
591M16—941no—
592M16—941no—
593M16—941no—
594M16—1882no—
595M16—1882no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—472no—
601C2×C8—471no—
602C2×C8—471no—
603C2×C8—472no—
604C2×C8—471no—
605C2×C8—471no—
606C2×C8—944no—
607C2×C8—944no—
608C2×C8—941no—
609C2×C8—941no—
610C2×C8—941no—
611C2×C8—941no—
612C2×C8—941no—
613C2×C8—941no—
614C2×C8—1882no—
615C2×C8—1882no—
616C2×C8C22×Dic4711yescharacteristic
617C2×C8C22×Dic4711yescharacteristic
618C2×C8C22×Dic4711yescharacteristic
619C2×C8C22×Dic4711yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—1882no—
625C4⋊C4C22×Dic4711yescharacteristic
626C4⋊C4C22×Dic4711yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—941no—
638C42—941no—
639C42—941no—
640C42—941no—
641C42D4×D4711yescharacteristic
642C42D4×D4711yescharacteristic
643C42C22×Dic4711yescharacteristic
644C42C22×Dic4711yescharacteristic
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×#1062535211yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8D4×Dic4712yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—81no—
668D4D4×Dic4712yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—942no—
685C2×C4—1881no—
686C2×C4—1881no—
687C2×C4—1881no—
688C2×C4—1881no—
689C2×C4—1881no—
690C2×C4D4×Dic4711yescharacteristic
691C2×C4D4×Dic4711yescharacteristic
692C2×C4D4×Dic4711yescharacteristic
693C2×C4D4×Dic4711yescharacteristic
694C2×C4C23×Dic4711yescharacteristic
695C2×C4C2×D4×D4711yescharacteristic
696C2×C4C2×D4×D4711yescharacteristic
697C2×C4#41×D4711yescharacteristic
698C2×C4#41×D4711yescharacteristic
699C2×C4C2×#1062535211yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—472no—
705C8—472no—
706C8—942no—
707C8—941no—
708C8—941no—
709C8—942no—
710C8—1881no—
711C8—1881no—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×D4×Dic4711yescharacteristic
724C22#1568965411yescharacteristic
725C22#1568966811yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—3761no—
736C4—1882no—
737C4C2×D4×Dic4711yescharacteristic
738C4#41×Dic4711yescharacteristic
739C4#121×D4711yescharacteristic
740C4#1568963311yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2#121×Dic4711yescharacteristic
747C2#2025229811yescharacteristic
748C2#2025230511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
Fitting, prime radicalC47×#3035C2
socleC22×C47C2×C4×D4
cosocleC22×C4×C47C24
hypercenter#3035D47
hypocenterC47#21519
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#15689245C2semidirect
2. C2×#15689240C2semidirect
3. #20252106C2semidirect
4. #20251816C2semidirect
5. #20244308C2semidirect
6. #20244164C2semidirect
7. #20244038C2semidirect
8. #20244038C2semidirect
9. #20243717C2semidirect
10. #20243717C2semidirect
11. #20243408C2semidirect
12. #20243265C2semidirect
13. #20243235C2semidirect
14. #20243228C2semidirect
58. C47×#464C4semidirect
59. C47×#464C4semidirect
60. C47×#463C4semidirect
61. C47×#463C4semidirect
62. C47×#462C4semidirect
63. C47×#461C4semidirect
64. C47×#460C4semidirect
65. C47×#459C4semidirect
76. #13094031D4semidirect
398. #464Dic47semidirect
399. #464Dic47semidirect
400. #463Dic47semidirect
401. #463Dic47semidirect
402. #462Dic47semidirect
403. #461Dic47semidirect
404. #460Dic47semidirect
405. #459Dic47semidirect
443. C47#21519semidirect

Maximal subgroups

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

subgroupindex
C2×#156892452
C2×#156892402
#202521062
#202518162
#202443082
#202441642
#202440382
#202437172
#202434082
#202432652
#202432352
#202432282
C47×#30352
#2151947