Finite Group Databasebeta

← #26217340

Subgroups — #26217340

Order 12032.

1358 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689888C211yesmaximal, characteristic
2C2×#15689170C211yesmaximal, characteristic, complemented
3#20251949C211yesmaximal, characteristic, complemented
4C2×#104×D47C211yesmaximal, characteristic
5#20251903C211yesmaximal, characteristic
6#20243666C211yesmaximal, characteristic, complemented
7#20243665C211yesmaximal, characteristic, complemented
8#20243664C211yesmaximal, characteristic, complemented
9#20243663C211yesmaximal, characteristic, complemented
10#20243662C211yesmaximal, characteristic, complemented
11#20243661C211yesmaximal, characteristic, complemented
12#20243660C211yesmaximal, characteristic, complemented
13#339×D47C211yesmaximal, characteristic, complemented
14#20243080C211yesmaximal, characteristic, complemented
15C47×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D47C2211yescharacteristic
17#15689888—24no—
18#15689888—24no—
19C2×#13094032—21no—
20C2×#13094032C2211yescharacteristic
21C2×#13094031C2211yescharacteristic
22C2×#13094030—21no—
23C2×#13094030C2211yescharacteristic
24C22×#10625324—21no—
25C22×#10625324C2211yescharacteristic
26C22×#10625324C2211yescharacteristic
27C2×M16×D47—21no—
28C2×M16×D47C2211yescharacteristic
29C2×M16×D47C2211yescharacteristic
30#117×D47C2211yescharacteristic
31C2×C42×D47C2211yescharacteristic
32#15689170—24no—
33C2×#13093960C2211yescharacteristic, complemented
34C2×#13093959C2211yescharacteristic, complemented
35C2×#13093959C2211yescharacteristic, complemented
36#15689151C2211yescharacteristic, complemented
37#15689150C2211yescharacteristic, complemented
38#15689149C2211yescharacteristic, complemented
39#15689148—21no—
40#15689148—21no—
41#15689145—21no—
42#15689145—21no—
43C2×#13093952C2211yescharacteristic
44C2×#13093951C2211yescharacteristic
45C2×#13093950C2211yescharacteristic
46#104×D47—24no—
47#15689130C411yescharacteristic, complemented
48#15689130C411yescharacteristic, complemented
49#15689126C411yescharacteristic, complemented
50#15689126C411yescharacteristic, complemented
51#15689123C411yescharacteristic, complemented
52#15689123C411yescharacteristic, complemented
53#15689121C411yescharacteristic, complemented
54#15689121C411yescharacteristic, complemented
55#15689120C2211yescharacteristic
56#15689119C2211yescharacteristic
57#15689117C2211yescharacteristic
58#15688884C2211yescharacteristic, complemented
59#15688883C2211yescharacteristic, complemented
60#15688882C2211yescharacteristic, complemented
61#15688878C2211yescharacteristic, complemented
62#15688877C2211yescharacteristic, complemented
63#15688877C2211yescharacteristic, complemented
64C2×#131×C47C2211yescharacteristic
65C2×#108×C47C2211yescharacteristic, complemented
66C47×#424C2211yescharacteristic, complemented
67C2×#104×C47C2211yescharacteristic
68C47×#416C2211yescharacteristic
69C47×#339C2211yescharacteristic, complemented
70C47×#336C2211yescharacteristic, complemented
71C2×#10625354C2×C411yescharacteristic
72C2×#10625350—21no—
73C2×#10625350C2311yescharacteristic
74C2×#10625352—21no—
75C2×#10625352C2×C411yescharacteristic
76#41×D47—22no—
77#41×D47—22no—
78#41×D47D414yes—
79#41×D47Q814yes—
80C2×Q8×D47C2×C411yescharacteristic
81C2×D4×D47—21no—
82C2×D4×D47C2×C411yescharacteristic
83C22×C4×D47—21no—
84C22×C4×D47—21no—
85C22×C4×D47C2311yescharacteristic
86#13094032—28no—
87#13094032—22no—
88#13094032—22no—
89#13094031—22no—
90#13094031—22no—
91#13094030—28no—
92#13094030—22no—
93#13094030—22no—
94C2×#10625329—21no—
95C2×#10625329C2311yescharacteristic
96C2×#10625329C2311yescharacteristic
97C2×#10625324—28no—
98C2×#10625324—21no—
99C2×#10625324—22no—
100C2×#10625324—22no—
101C2×#10625324—22no—
102C2×#10625324—22no—
103C2×#10625324—21no—
104C2×#10625324—21no—
105C2×#10625324—21no—
106C2×#10625324C2×C411yescharacteristic
107C2×#10625324C2×C411yescharacteristic
108C2×#10625324C2×C411yescharacteristic
109C2×#10625324C2×C411yescharacteristic
110C2×#10625324D411yescharacteristic
111C2×#10625324D411yescharacteristic
112C2×#10625324D411yescharacteristic
113C2×#10625324D411yescharacteristic
114M16×D47—28no—
115M16×D47—22no—
116M16×D47—22no—
117M16×D47—22no—
118M16×D47D414yes—
119C22×C47⋊C8—21no—
120C22×C47⋊C8C2311yescharacteristic
121C22×C47⋊C8C2311yescharacteristic
122C2×C8×D47—21no—
123C2×C8×D47—21no—
124C2×C8×D47—21no—
125C2×C8×D47—21no—
126#13093983C2311yescharacteristic
127#13093982C2×C411yescharacteristic
128#13093982C2×C411yescharacteristic
129#13093981—21no—
130#13093980—21no—
131C4⋊C4×D47C2×C411yescharacteristic
132C4⋊C4×D47C2×C411yescharacteristic
133C22⋊C4×D47—21no—
134C2×C4×Dic47—21no—
135C2×C4×Dic47C2311yescharacteristic
136C42×D47—21no—
137C42×D47—22no—
138C42×D47—22no—
139#13093960—22no—
140#13093959—22no—
141#13093959—22no—
142C4⋊(C47⋊C8)—21no—
143C4⋊(C47⋊C8)—21no—
144Dic47⋊C8—21no—
145Dic47⋊C8—21no—
146Dic47⋊C8—21no—
147Dic47⋊C8—21no—
148#13093952—22no—
149#13093951—22no—
150#13093950—22no—
151#13093949C2×C411yescharacteristic, complemented
152#13093949C2×C411yescharacteristic, complemented
153#13093948C2×C411yescharacteristic, complemented
154#13093948C2×C411yescharacteristic, complemented
155#13093947C2×C411yescharacteristic, complemented
156#13093947C2×C411yescharacteristic, complemented
157#13093946C2×C411yescharacteristic, complemented
158#13093946C2×C411yescharacteristic, complemented
159#13093945C2×C411yescharacteristic, complemented
160#13093945C2×C411yescharacteristic, complemented
161#13093944C2×C411yescharacteristic, complemented
162#13093944C2×C411yescharacteristic, complemented
163C2×#41×C47C2311yescharacteristic
164#131×C47—22no—
165#131×C47—22no—
166C2×M16×C47—21no—
167C2×M16×C47C2311yescharacteristic
168C2×M16×C47C2311yescharacteristic
169C22×C8×C47—21no—
170C22×C8×C47C2311yescharacteristic
171C22×C8×C47C2311yescharacteristic
172#117×C47C2311yescharacteristic
173C2×C42×C47C2311yescharacteristic
174#108×C47—22no—
175C4⋊C8×C47—21no—
176C4⋊C8×C47—21no—
177#104×C47—22no—
178#103×C47C2×C411yescharacteristic, complemented
179#103×C47C2×C411yescharacteristic, complemented
180#102×C47C2×C411yescharacteristic, complemented
181#102×C47C2×C411yescharacteristic, complemented
182C23×D47—21no—
183C23×D47#4111yescharacteristic
184#41×C47—21no—
185#41×C47—21no—
186#41×C47C2×D412yes—
187#41×C47C2×Q812yes—
188C2×Q8×C47C22×C411yescharacteristic
189C2×D4×C47—21no—
190C2×D4×C47C22×C411yescharacteristic
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47C2411yescharacteristic
194C2×C22⋊D47—21no—
195C2×C22⋊D47—21no—
196C2×C22⋊D47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47#4111yescharacteristic
200#10625354—22no—
201#10625354C4⋊C414yes—
202Q8×D47—22no—
203Q8×D47C4⋊C414yes—
204#10625352—24no—
205#10625352—24no—
206#10625352—22no—
207#10625352C4⋊C414yes—
208D4×D47—24no—
209D4×D47—24no—
210D4×D47—22no—
211D4×D47C4⋊C414yes—
212#10625350—21no—
213#10625350—21no—
214#10625350—24no—
215#10625350—24no—
216#10625350C2×D412yes—
217#10625350C2×Q812yes—
218C2×D188—21no—
219C2×D188C22×C411yescharacteristic
220C2×C4×D47—21no—
221C2×C4×D47—21no—
222C2×C4×D47—21no—
223C2×C4×D47—24no—
224C2×C4×D47—24no—
225C2×C4×D47—21no—
226C2×C4×D47—21no—
227C2×C4×D47—42no—
228C2×C4×D47—42no—
229C2×C4×D47—42no—
230C2×C4×D47C22×C411yescharacteristic
231C2×C4×D47C22×C411yescharacteristic
232C2×C4×D47C2×D412yes—
233C2×C4×D47C2×D412yes—
234C2×C4×D47C2×D411yescharacteristic
235C2×C4×D47C2×D411yescharacteristic
236C2×C4×D47C2×Q812yes—
237C2×C4×D47#4112yes—
238C2×Dic94—21no—
239C2×Dic94C22×C411yescharacteristic
240M16×C47—24no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—21no—
244M16×C47C2×D412yes—
245C2×C8×C47—24no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47—21no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47C22×C411yescharacteristic
253C2×C8×C47C22×C411yescharacteristic
254C2×C8×C47C2×D411yescharacteristic
255C2×C8×C47C2×D411yescharacteristic
256C4⋊C4×C47C22×C411yescharacteristic
257C4⋊C4×C47C22×C411yescharacteristic
258C22⋊C4×C47—21no—
259C42×C47—21no—
260C42×C47—21no—
261C42×C47—21no—
262C22⋊Dic47—21no—
263(C2×D47)⋊C4—21no—
264(C2×D47)⋊C4—21no—
265C4⋊Dic47C22×C411yescharacteristic
266C4⋊Dic47C22×C411yescharacteristic
267Dic47⋊C4—21no—
268Dic47⋊C4—21no—
269C4×Dic47—21no—
270C4×Dic47—21no—
271C4×Dic47—21no—
272C4×Dic47—21no—
273C4×Dic47—21no—
274C4×Dic47—42no—
275#10625329—24no—
276#10625329—21no—
277#10625329—21no—
278#10625329—21no—
279#10625329C2×D412yes—
280C2×C47⋊C8—24no—
281C2×C47⋊C8—21no—
282C2×C47⋊C8—21no—
283C2×C47⋊C8—21no—
284C2×C47⋊C8—21no—
285C2×C47⋊C8—21no—
286C2×C47⋊C8—21no—
287C2×C47⋊C8C22×C411yescharacteristic
288C2×C47⋊C8C22×C411yescharacteristic
289C2×C47⋊C8C2×D411yescharacteristic
290C2×C47⋊C8C2×D411yescharacteristic
291#10625324—24no—
292#10625324—24no—
293#10625324—22no—
294#10625324—22no—
295#10625324—22no—
296#10625324—22no—
297#10625324—22no—
298#10625324—24no—
299#10625324—22no—
300#10625324—22no—
301#10625324—22no—
302#10625324—42no—
303C8×D47—24no—
304C8×D47—24no—
305C8×D47—24no—
306C8×D47—42no—
307C23×C47—21no—
308C23×C47C2×#4111yescharacteristic
309C22×D47—21no—
310C22×D47—24no—
311C22×D47—41no—
312C22×D47—41no—
313C22×D47—81no—
314C22×D47—81no—
315C22×D47C4×D411yescharacteristic
316C22×D47C4×D411yescharacteristic
317C22×D47C22⋊Q812yes—
318C22×D47#12312yes—
319Q8×C47—21no—
320Q8×C47C2×C4⋊C412yes—
321D4×C47—22no—
322D4×C47—22no—
323D4×C47—21no—
324D4×C47C2×C4⋊C412yes—
325C2×C4×C47—21no—
326C2×C4×C47—22no—
327C2×C4×C47—22no—
328C2×C4×C47—22no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—41no—
332C2×C4×C47—41no—
333C2×C4×C47C23×C411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C22×D411yescharacteristic
336C2×C4×C47C22×D411yescharacteristic
337C2×C4×C47C22×Q811yescharacteristic
338C2×C4×C47C2×#4111yescharacteristic
339C22⋊D47—22no—
340C22⋊D47—22no—
341C22⋊D47—24no—
342C22⋊D47—24no—
343C2×Dic47—21no—
344C2×Dic47—24no—
345C2×Dic47—22no—
346C2×Dic47—21no—
347C2×Dic47—21no—
348C2×Dic47—41no—
349C2×Dic47—41no—
350C2×Dic47C4×D411yescharacteristic
351C2×Dic47C4×D411yescharacteristic
352C2×Dic47C22⋊Q812yes—
353C2×Dic47#12312yes—
354D188—24no—
355D188—21no—
356D188C2×C4⋊C412yes—
357C4×D47—24no—
358C4×D47—22no—
359C4×D47—22no—
360C4×D47—24no—
361C4×D47—48no—
362C4×D47—81no—
363C4×D47—81no—
364C4×D47C2×C4⋊C412yes—
365C4×D47C2×C4⋊C412yes—
366C4×D47C4×D412yes—
367C4×D47C4×D412yes—
368C4×D47#12012yes—
369C4×D47#12012yes—
370C4×D47C22⋊Q812yes—
371C4×D47C22⋊Q812yes—
372Dic94—21no—
373Dic94—24no—
374Dic94C2×C4⋊C412yes—
375C8×C47—21no—
376C8×C47—21no—
377C8×C47—22no—
378C8×C47—21no—
379C8×C47—21no—
380C8×C47—41no—
381C47⋊C8—21no—
382C47⋊C8—21no—
383C47⋊C8—22no—
384C47⋊C8—21no—
385C47⋊C8—21no—
386C47⋊C8—41no—
387#20885—471nomaximal, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—22no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47C2×C4×D411yescharacteristic
394C22×C47C2×C22⋊Q811yescharacteristic
395C22×C47C2×#12311yescharacteristic
396C2×D47—21no—
397C2×D47—21no—
398C2×D47—21no—
399C2×D47—21no—
400C2×D47—22no—
401C2×D47—42no—
402C2×D47—42no—
403C2×D47—41no—
404C2×D47—41no—
405C2×D47—84no—
406C2×D47#38512yes—
407C2×D47#38512yes—
408C4×C47—22no—
409C4×C47—42no—
410C4×C47—41no—
411C4×C47—41no—
412C4×C47C22×C4⋊C411yescharacteristic
413C4×C47C2×C4×D411yescharacteristic
414C4×C47C2×#12011yescharacteristic
415C4×C47C2×C22⋊Q811yescharacteristic
416Dic47—22no—
417Dic47—42no—
418Dic47—41no—
419Dic47—41no—
420Dic47#38512yes—
421Dic47#38512yes—
422C2×#568—471no—
423C2×#430—471no—
424#2905—471no—
425C22×#104—471no—
426#2896—471no—
427#1866—471no—
428#1866—471no—
429#1866—471no—
430#1866—471no—
431#1866—471no—
432#1866—471no—
433#1866—471no—
434#1866D4711yescharacteristic, complemented
435C2×#339—471no—
436#1728—471no—
437C2×C47—21no—
438C2×C47—21no—
439C2×C47—42no—
440C2×C47C2×#38511yescharacteristic
441C2×C47#295611yescharacteristic
442C2×C47#295611yescharacteristic
443D47—22no—
444D47—22no—
445D47—42no—
446C22×#41—471no—
447#568—944no—
448#568—944no—
449C2×#131—471no—
450C2×#131—471no—
451C2×#131—471no—
452C2×#131—941no—
453C2×#131—941no—
454C2×#131C2×D4711yescharacteristic
455C22×M16—471no—
456C22×M16—471no—
457C22×M16—471no—
458C22×M16—471no—
459C22×M16—941no—
460C22×M16—941no—
461C2×#117—471no—
462C22×C42—471no—
463#430—944no—
464C2×#108—471no—
465C2×#108—471no—
466C2×#108—471no—
467C2×#108C2×D4711yescharacteristic, complemented
468#424—471no—
469#424—471no—
470#424—471no—
471#424—941no—
472#424—941no—
473#424C2×D4711yescharacteristic, complemented
474#423—941no—
475#423—941no—
476C2×#104—471no—
477C2×#104—471no—
478C2×#104—471no—
479C2×#104—944no—
480C2×#104C2×D4711yescharacteristic
481#419—471no—
482#419—471no—
483#418—471no—
484#418—471no—
485#417—471no—
486#417—471no—
487#417—471no—
488#417—471no—
489#416—471no—
490#416—471no—
491#416—471no—
492#416C2×D4711yescharacteristic
493#339—471no—
494#339—471no—
495#339—471no—
496#339C2×D4711yescharacteristic, complemented
497#336—471no—
498#336—471no—
499#336—471no—
500#336C2×D4711yescharacteristic, complemented
501C47#2088511yescharacteristic, complemented, Sylow
502C2×#41—474no—
503C2×#41—474no—
504C2×#41—471no—
505C2×#41—471no—
506C2×#41—471no—
507C2×#41—941no—
508C2×#41—941no—
509C2×#41—942no—
510C2×#41—942no—
511C2×#41C22×D4711yescharacteristic
512C22×Q8—471no—
513C22×D4—471no—
514C22×D4—941no—
515C23×C4—471no—
516C23×C4—941no—
517C23×C4—941no—
518#131—22no—
519#131—22no—
520#131—942no—
521#131—942no—
522#131—948no—
523#131—942no—
524#131—948no—
525#131—942no—
526#131—942no—
527#131—942no—
528C2×M16—21no—
529C2×M16—471no—
530C2×M16—471no—
531C2×M16—471no—
532C2×M16—471no—
533C2×M16—471no—
534C2×M16—471no—
535C2×M16—471no—
536C2×M16—471no—
537C2×M16—471no—
538C2×M16—474no—
539C2×M16—471no—
540C2×M16—941no—
541C2×M16—941no—
542C2×M16—942no—
543C2×M16—942no—
544C2×M16—942no—
545C2×M16—942no—
546C2×M16—948no—
547C2×M16—941no—
548C2×M16—941no—
549C2×M16—942no—
550C2×M16—948no—
551C2×M16—941no—
552C2×M16—942no—
553C2×M16—942no—
554C2×M16C22×D4711yescharacteristic
555C2×M16C22×D4711yescharacteristic
556C22×C8—21no—
557C22×C8—471no—
558C22×C8—471no—
559C22×C8—941no—
560C22×C8—941no—
561C22×C8—941no—
562C22×C8—941no—
563C22×C8—941no—
564C22×C8C22×D4711yescharacteristic
565C22×C8C22×D4711yescharacteristic
566#117—471no—
567#117—471no—
568#117—471no—
569#117—941no—
570#117—941no—
571#117C22×D4711yescharacteristic
572C2×C4⋊C4—471no—
573C2×C4⋊C4—471no—
574C2×C22⋊C4—941no—
575C2×C42—471no—
576C2×C42—941no—
577C2×C42—942no—
578C2×C42—942no—
579C2×C42—941no—
580C2×C42C22×D4711yescharacteristic
581#108—22no—
582#108—942no—
583#108—942no—
584#108—942no—
585C4⋊C8—21no—
586C4⋊C8—21no—
587C4⋊C8—941no—
588C4⋊C8—941no—
589C4⋊C8—941no—
590C4⋊C8—941no—
591C4⋊C8—941no—
592C4⋊C8—941no—
593#104—22no—
594#104—942no—
595#104—942no—
596#104—942no—
597#103—471no—
598#103—471no—
599#103—471no—
600#103—471no—
601#103—471no—
602#103—471no—
603#103C4×D4711yescharacteristic, complemented
604#103C4×D4711yescharacteristic, complemented
605#102—471no—
606#102—471no—
607#102—471no—
608#102—471no—
609#102—471no—
610#102—471no—
611#102C4×D4711yescharacteristic, complemented
612#102C4×D4711yescharacteristic, complemented
613C24—471no—
614C24—941no—
615#41—21no—
616#41—21no—
617#41—474no—
618#41—474no—
619#41—472no—
620#41—472no—
621#41—944no—
622#41—944no—
623#41—944no—
624#41—944no—
625#41—942no—
626#41—942no—
627#41—941no—
628#41—941no—
629#41D4×D4712yes—
630#41Q8×D4712yes—
631C2×Q8—474no—
632C2×Q8—471no—
633C2×Q8—941no—
634C2×Q8—942no—
635C2×Q8C2×C4×D4711yescharacteristic
636C2×D4—21no—
637C2×D4—474no—
638C2×D4—471no—
639C2×D4—941no—
640C2×D4—942no—
641C2×D4—941no—
642C2×D4—944no—
643C2×D4—944no—
644C2×D4—941no—
645C2×D4—941no—
646C2×D4C2×C4×D4711yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—471no—
650C22×C4—471no—
651C22×C4—471no—
652C22×C4—472no—
653C22×C4—472no—
654C22×C4—471no—
655C22×C4—471no—
656C22×C4—472no—
657C22×C4—472no—
658C22×C4—944no—
659C22×C4—941no—
660C22×C4—944no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—941no—
666C22×C4—941no—
667C22×C4—1882no—
668C22×C4—1882no—
669C22×C4—1882no—
670C22×C4C23×D4711yescharacteristic
671M16—24no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—472no—
676M16—942no—
677M16—942no—
678M16—942no—
679M16—942no—
680M16—942no—
681M16—944no—
682M16—942no—
683M16—942no—
684M16—942no—
685M16—944no—
686M16—944no—
687M16—944no—
688M16—941no—
689M16—941no—
690M16—941no—
691M16—1882no—
692M16D4×D4712yes—
693C2×C8—24no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—471no—
701C2×C8—471no—
702C2×C8—471no—
703C2×C8—471no—
704C2×C8—944no—
705C2×C8—944no—
706C2×C8—944no—
707C2×C8—944no—
708C2×C8—941no—
709C2×C8—941no—
710C2×C8—941no—
711C2×C8—941no—
712C2×C8—941no—
713C2×C8—941no—
714C2×C8—1882no—
715C2×C8C2×C4×D4711yescharacteristic
716C2×C8C2×C4×D4711yescharacteristic
717C2×C8D4×D4711yescharacteristic
718C2×C8D4×D4711yescharacteristic
719C4⋊C4—471no—
720C4⋊C4—471no—
721C4⋊C4—941no—
722C4⋊C4—941no—
723C4⋊C4C2×C4×D4711yescharacteristic
724C4⋊C4C2×C4×D4711yescharacteristic
725C22⋊C4—21no—
726C22⋊C4—941no—
727C22⋊C4—941no—
728C22⋊C4—941no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—941no—
733C42—941no—
734C42—941no—
735C42—941no—
736C42—941no—
737C42—1882no—
738C23—21no—
739C23—471no—
740C23—471no—
741C23—472no—
742C23—472no—
743C23—944no—
744C23—941no—
745C23—3761no—
746C23—3761no—
747C23—1881no—
748C23—1881no—
749C23#41×D4711yescharacteristic
750Q8—21no—
751Q8—472no—
752Q8—944no—
753Q8—941no—
754Q8C4⋊C4×D4712yes—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—472no—
759D4—944no—
760D4—944no—
761D4—944no—
762D4—942no—
763D4—942no—
764D4—941no—
765D4C4⋊C4×D4712yes—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—471no—
775C2×C4—471no—
776C2×C4—472no—
777C2×C4—472no—
778C2×C4—472no—
779C2×C4—472no—
780C2×C4—472no—
781C2×C4—472no—
782C2×C4—472no—
783C2×C4—472no—
784C2×C4—472no—
785C2×C4—472no—
786C2×C4—944no—
787C2×C4—944no—
788C2×C4—944no—
789C2×C4—941no—
790C2×C4—942no—
791C2×C4—942no—
792C2×C4—942no—
793C2×C4—941no—
794C2×C4—941no—
795C2×C4—3761no—
796C2×C4—3761no—
797C2×C4—1888no—
798C2×C4—1881no—
799C2×C4—1881no—
800C2×C4C22×C4×D4711yescharacteristic
801C2×C4C2×D4×D4711yescharacteristic
802C2×C4C2×D4×D4711yescharacteristic
803C2×C4C2×D4×D4711yescharacteristic
804C2×C4C2×Q8×D4711yescharacteristic
805C2×C4#41×D4711yescharacteristic
806C8—21no—
807C8—21no—
808C8—21no—
809C8—22no—
810C8—21no—
811C8—41no—
812C8—941no—
813C8—941no—
814C8—941no—
815C8—941no—
816C8—942no—
817C8—1881no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—41no—
822C22—41no—
823C22—472no—
824C22—472no—
825C22—941no—
826C22—941no—
827C22—941no—
828C22—941no—
829C22—942no—
830C22—3764no—
831C22—1882no—
832C22—1882no—
833C22—1881no—
834C22—1881no—
835C22C4×D4×D4711yescharacteristic
836C22C22⋊Q8×D4711yescharacteristic
837C22#123×D4711yescharacteristic
838C4—22no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—472no—
843C4—472no—
844C4—942no—
845C4—1882no—
846C4—1881no—
847C4—1881no—
848C4C2×C4⋊C4×D4711yescharacteristic
849C4C4×D4×D4711yescharacteristic
850C4#120×D4711yescharacteristic
851C4C22⋊Q8×D4711yescharacteristic
852C2—21no—
853C2—21no—
854C2—42no—
855C2—942no—
856C2—942no—
857C2—1882no—
858C2#385×D4711yescharacteristic
859C2#2025229311yescharacteristic
860C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1866C2
socleC22×C47C2×C4×D4
prime radicalC2×#41×D47C22
cosocleC22×C4×C47C24
hypercenter#1866D47
hypocenterC47#20885
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. C2×#15689170C2semidirect
3. #20251949C2semidirect
6. #20243666C2semidirect
7. #20243665C2semidirect
8. #20243664C2semidirect
9. #20243663C2semidirect
10. #20243662C2semidirect
11. #20243661C2semidirect
12. #20243660C2semidirect
13. #339×D47C2semidirect
14. #20243080C2semidirect
15. C47×#1866C2semidirect
33. C2×#13093960C22semidirect
34. C2×#13093959C22semidirect
35. C2×#13093959C22semidirect
36. #15689151C22semidirect
37. #15689150C22semidirect
38. #15689149C22semidirect
47. #15689130C4semidirect
48. #15689130C4semidirect
49. #15689126C4semidirect
50. #15689126C4semidirect
51. #15689123C4semidirect
52. #15689123C4semidirect
53. #15689121C4semidirect
54. #15689121C4semidirect
58. #15688884C22semidirect
59. #15688883C22semidirect
60. #15688882C22semidirect
61. #15688878C22semidirect
62. #15688877C22semidirect
63. #15688877C22semidirect
65. C2×#108×C47C22semidirect
66. C47×#424C22semidirect
69. C47×#339C22semidirect
70. C47×#336C22semidirect
151. #13093949C2×C4semidirect
152. #13093949C2×C4semidirect
153. #13093948C2×C4semidirect
154. #13093948C2×C4semidirect
155. #13093947C2×C4semidirect
156. #13093947C2×C4semidirect
157. #13093946C2×C4semidirect
158. #13093946C2×C4semidirect
159. #13093945C2×C4semidirect
160. #13093945C2×C4semidirect
161. #13093944C2×C4semidirect
162. #13093944C2×C4semidirect
178. #103×C47C2×C4semidirect
179. #103×C47C2×C4semidirect
180. #102×C47C2×C4semidirect
181. #102×C47C2×C4semidirect
434. #1866D47semidirect
467. C2×#108C2×D47semidirect
473. #424C2×D47semidirect
496. #339C2×D47semidirect
500. #336C2×D47semidirect
501. C47#20885semidirect
603. #103C4×D47semidirect
604. #103C4×D47semidirect
611. #102C4×D47semidirect
612. #102C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156898882
C2×#156891702
#202519492
C2×#104×D472
#202519032
#202436662
#202436652
#202436642
#202436632
#202436622
#202436612
#202436602
#339×D472
#202430802
C47×#18662
#2088547