Finite Group Databasebeta

← #26237050

Subgroups — #26237050

Order 12032.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252610C211yesmaximal, characteristic
2C2×#15689241C211yesmaximal, characteristic, complemented
3#20252109C211yesmaximal, characteristic, complemented
4C22×#13093952C211yesmaximal, characteristic, complemented
5#20251834C211yesmaximal, characteristic, complemented
6#20244276C211yesmaximal, characteristic, complemented
7#20244092C211yesmaximal, characteristic, complemented
8#20244037C211yesmaximal, characteristic, complemented
9#20243831C211yesmaximal, characteristic, complemented
10#20243714C211yesmaximal, characteristic, complemented
11#20243714C211yesmaximal, characteristic, complemented
12#20243666C211yesmaximal, characteristic, complemented
13#20243595C211yesmaximal, characteristic, complemented
14#20243225C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C47C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094046C2211yescharacteristic
18C2×#13094046C2211yescharacteristic
19C2×#13094030C2211yescharacteristic
20C2×#13094030C2211yescharacteristic
21C2×#13094030C2211yescharacteristic, complemented
22C22×#10625329C2211yescharacteristic
23#15689634C2211yescharacteristic
24#15689287C411yescharacteristic, complemented
25#15689287C411yescharacteristic, complemented
26#15689281C411yescharacteristic, complemented
27#15689276C411yescharacteristic, complemented
28#15689270C411yescharacteristic, complemented
29#15689270C411yescharacteristic, complemented
30#15689264C411yescharacteristic, complemented
31#15689259C411yescharacteristic, complemented
32#15689241—24no—
33#15689198—21no—
34#15689197—21no—
35#15689191—21no—
36(C22⋊D47)⋊C8—21no—
37C2×#13093960C2211yescharacteristic, complemented
38C2×#13093960C2211yescharacteristic, complemented
39#15689149C2211yescharacteristic, complemented
40C2×#13093952—24no—
41C2×#13093952C2211yescharacteristic
42C2×#13093952C2211yescharacteristic
43C2×#13093952C2211yescharacteristic
44C2×#13093952C2211yescharacteristic
45C2×#13093952C2211yescharacteristic, complemented
46C2×#13093952C2211yescharacteristic, complemented
47#15689120C2211yescharacteristic
48#15689120C2211yescharacteristic
49#15689089C2211yescharacteristic
50#15689089C2211yescharacteristic
51#15689089C2211yescharacteristic, complemented
52#15689088—21no—
53#15689088—21no—
54#15689087C2211yescharacteristic
55#15689085—21no—
56C22⋊C8×D47—21no—
57#15689078C2211yescharacteristic, complemented
58#15688888C2211yescharacteristic, complemented
59#15688888C2211yescharacteristic, complemented
60#15688883C2211yescharacteristic, complemented
61#15688883C2211yescharacteristic, complemented
62C22×C42×C47C2211yescharacteristic
63C2×C22⋊C8×C47C2211yescharacteristic
64C2×C22⋊C8×C47C2211yescharacteristic
65C2×C4×C8×C47C2211yescharacteristic, complemented
66C2×C4×C8×C47C2211yescharacteristic, complemented
67C47×#336C2211yescharacteristic, complemented
68C47×#336C2211yescharacteristic, complemented
69C2×#10625350—21no—
70C2×#10625350—21no—
71C2×#10625350—22no—
72C2×#10625350—22no—
73C2×#10625350—41no—
74C2×#10625350—41no—
75C2×#10625350C2×C411yescharacteristic
76C2×#10625350C2×C411yescharacteristic
77C2×#10625350C2311yescharacteristic
78C2×#10625350C2311yescharacteristic
79C2×#10625350C2311yescharacteristic
80C22×Dic94C2×C411yescharacteristic
81C22×D188C2×C411yescharacteristic
82C22×C22⋊D47—21no—
83C22×C4×D47—21no—
84#13094046—22no—
85#13094046—22no—
86#13094046—41no—
87#13094046—41no—
88C2×Dic188C2×C411yescharacteristic, complemented
89C2×Dic188C2×C411yescharacteristic, complemented
90C2×#10625325C2×C411yescharacteristic, complemented
91C2×#10625325C2×C411yescharacteristic, complemented
92C2×#10625325C2×C411yescharacteristic, complemented
93C2×#10625325C2×C411yescharacteristic, complemented
94C2×D376C2×C411yescharacteristic, complemented
95C2×D376C2×C411yescharacteristic, complemented
96#13094030—22no—
97#13094030—22no—
98#13094030—22no—
99#13094030—41no—
100#13094030—41no—
101#13094030—41no—
102C2×#10625329—21no—
103C2×#10625329—22no—
104C2×#10625329—41no—
105C2×#10625329C2311yescharacteristic
106C2×#10625329C2311yescharacteristic
107C2×#10625329C2311yescharacteristic
108C2×#10625329C2311yescharacteristic
109C2×#10625324—21no—
110C2×#10625324—21no—
111C2×#10625324—21no—
112C22×C47⋊C8—21no—
113C2×C8×D47—21no—
114C2×C8×D47—21no—
115C2×C8×D47—21no—
116#13094007—21no—
117#13094003C2×C411yescharacteristic
118#13094003C2×C411yescharacteristic
119#13093998C2×C411yescharacteristic
120#13093998C2×C411yescharacteristic
121#13093993—21no—
122C4×C22⋊D47—21no—
123C4×C22⋊D47—21no—
124#13093983C2311yescharacteristic
125#13093960—22no—
126#13093960—41no—
127Dic47⋊C8—21no—
128Dic47⋊C8—21no—
129#13093952—22no—
130#13093952—22no—
131#13093952—22no—
132#13093952—22no—
133#13093952—41no—
134#13093952D414yescomplemented
135#13093949C2×C411yescharacteristic, complemented
136#13093949C2×C411yescharacteristic, complemented
137#13093949C2×C411yescharacteristic, complemented
138#13093949C2×C411yescharacteristic, complemented
139#13093946C2×C411yescharacteristic, complemented
140#13093946C2×C411yescharacteristic, complemented
141#13093946C2×C411yescharacteristic, complemented
142#13093946C2×C411yescharacteristic, complemented
143C22⋊(C47⋊C8)—21no—
144C22⋊(C47⋊C8)—21no—
145(C2×D47)⋊C8—21no—
146(C2×D47)⋊C8—21no—
147(C2×D47)⋊C8—21no—
148(C2×D47)⋊C8—21no—
149(C2×D47)⋊C8—21no—
150(C2×D47)⋊C8—21no—
151#13093934—21no—
152C8×Dic47—21no—
153C23×C4×C47—21no—
154C23×C4×C47C2311yescharacteristic
155C22×C8×C47C2311yescharacteristic
156C22×C8×C47C2311yescharacteristic
157C22×C8×C47C2311yescharacteristic
158C22×C8×C47C2311yescharacteristic
159C2×C42×C47—22no—
160C2×C42×C47—21no—
161C2×C42×C47—41no—
162C2×C42×C47C2311yescharacteristic
163C2×C42×C47C2311yescharacteristic
164C22⋊C8×C47C2×C411yescharacteristic
165C22⋊C8×C47C2×C411yescharacteristic
166C22⋊C8×C47C2×C411yescharacteristic
167C22⋊C8×C47C2×C411yescharacteristic
168C22⋊C8×C47D411yescharacteristic
169C22⋊C8×C47D411yescharacteristic
170C22⋊C8×C47D411yescharacteristic
171C22⋊C8×C47D411yescharacteristic
172C4×C8×C47—22no—
173C4×C8×C47—41no—
174C24×C47#4111yescharacteristic
175C23×D47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—24no—
182C22×C4×C47—21no—
183C22×C4×C47—42no—
184C22×C4×C47—42no—
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C22×C411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47#4111yescharacteristic
190C22×C4×C47C2411yescharacteristic
191C2×C22⋊D47—21no—
192C2×C22⋊D47—21no—
193C2×C22⋊D47—21no—
194C2×C22⋊D47—21no—
195C2×C22⋊D47—21no—
196C2×C22⋊D47—21no—
197C2×C22⋊D47—21no—
198C2×C22⋊D47—42no—
199C2×C22⋊D47—42no—
200C22×Dic47—21no—
201#10625350—21no—
202#10625350—21no—
203#10625350—21no—
204#10625350—21no—
205#10625350—21no—
206#10625350—21no—
207#10625350—21no—
208#10625350—21no—
209#10625350—21no—
210#10625350—21no—
211#10625350—22no—
212#10625350—22no—
213#10625350—41no—
214#10625350—41no—
215#10625350—42no—
216#10625350—42no—
217#10625350—42no—
218#10625350—42no—
219#10625350C2×D412yes—
220#10625350#4112yes—
221C2×D188—22no—
222C2×D188—21no—
223C2×D188—41no—
224C2×D188C22×C411yescharacteristic
225C2×D188C22×C411yescharacteristic
226C2×D188C22×C411yescharacteristic
227C2×C4×D47—21no—
228C2×C4×D47—21no—
229C2×C4×D47—21no—
230C2×C4×D47—21no—
231C2×C4×D47—21no—
232C2×C4×D47—42no—
233C2×C4×D47—42no—
234C2×Dic94—22no—
235C2×Dic94—21no—
236C2×Dic94—41no—
237C2×Dic94C22×C411yescharacteristic
238C2×Dic94C22×C411yescharacteristic
239C2×Dic94C22×C411yescharacteristic
240C2×C8×C47—21no—
241C2×C8×C47—21no—
242C2×C8×C47—21no—
243C2×C8×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—21no—
248C2×C8×C47C22×C411yescharacteristic
249C2×C8×C47C22×C411yescharacteristic
250C2×C8×C47C22×C411yescharacteristic
251C2×C8×C47C22×C411yescharacteristic
252C2×C8×C47C2×D411yescharacteristic
253C2×C8×C47C2×D411yescharacteristic
254C2×C8×C47C2×D411yescharacteristic
255C2×C8×C47C2×D411yescharacteristic
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—21no—
259C42×C47—42no—
260C42×C47C2×D412yes—
261C22⋊Dic47—21no—
262C22⋊Dic47—21no—
263C22⋊Dic47—21no—
264(C2×D47)⋊C4—21no—
265(C2×D47)⋊C4—21no—
266C4⋊Dic47C22×C411yescharacteristic
267C4⋊Dic47C22×C411yescharacteristic
268Dic47⋊C4—21no—
269Dic47⋊C4—21no—
270C4×Dic47—21no—
271#10625329—21no—
272#10625329—21no—
273#10625329—21no—
274#10625329—21no—
275#10625329—21no—
276#10625329—21no—
277#10625329—21no—
278#10625329—42no—
279#10625329C2×D412yes—
280C2×C47⋊C8—21no—
281C2×C47⋊C8—21no—
282C2×C47⋊C8—21no—
283C2×C47⋊C8—21no—
284C2×C47⋊C8—42no—
285Dic188—22no—
286Dic188—41no—
287D376—22no—
288D376—41no—
289#10625325—22no—
290#10625325—22no—
291#10625325—41no—
292#10625325—41no—
293#10625324—42no—
294#10625324—42no—
295#10625324—42no—
296C8×D47—42no—
297C8×D47—42no—
298C8×D47—42no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—22no—
302C23×C47—41no—
303C23×C47C4×D411yescharacteristic
304C23×C47C4×D411yescharacteristic
305C23×C47C2×#4111yescharacteristic
306C22×D47—21no—
307C22×D47—21no—
308C22×D47—21no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—81no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—22no—
315C2×C4×C47—21no—
316C2×C4×C47—21no—
317C2×C4×C47—21no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—22no—
326C2×C4×C47—48no—
327C2×C4×C47—41no—
328C2×C4×C47—41no—
329C2×C4×C47C4×D411yescharacteristic
330C2×C4×C47C4×D411yescharacteristic
331C2×C4×C47C23×C411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C2×#4111yescharacteristic
335C2×C4×C47H(5,𝔽2)11yescharacteristic
336C2×C4×C47H(5,𝔽2)11yescharacteristic
337C22⋊D47—22no—
338C22⋊D47—22no—
339C22⋊D47—42no—
340C22⋊D47—42no—
341C22⋊D47—41no—
342C22⋊D47—41no—
343C22⋊D47—41no—
344C22⋊D47—41no—
345C22⋊D47—42no—
346C22⋊D47—81no—
347C2×Dic47—21no—
348C2×Dic47—21no—
349C2×Dic47—21no—
350C2×Dic47—21no—
351C2×Dic47—21no—
352C2×Dic47—42no—
353D188—21no—
354D188—21no—
355D188—21no—
356D188—21no—
357D188—21no—
358D188—42no—
359D188C4×D412yes—
360C4×D47—22no—
361C4×D47—22no—
362C4×D47—42no—
363C4×D47—42no—
364C4×D47—41no—
365C4×D47—41no—
366C4×D47—41no—
367C4×D47—41no—
368Dic94—21no—
369Dic94—21no—
370Dic94—21no—
371Dic94—21no—
372Dic94—21no—
373Dic94—42no—
374Dic94C4×D412yes—
375C8×C47—21no—
376C8×C47—21no—
377C8×C47—21no—
378C8×C47—21no—
379C8×C47—21no—
380C8×C47—21no—
381C8×C47—21no—
382C8×C47—21no—
383C47⋊C8—22no—
384C47⋊C8—41no—
385C47⋊C8—41no—
386C47⋊C8—41no—
387#22888—471nomaximal, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—21no—
394C22×C47—21no—
395C22×C47—42no—
396C22×C47—42no—
397C22×C47#44312yescomplemented
398C22×C47C2×C4×D411yescharacteristic
399C22×C47#54611yescharacteristic
400C22×C47#55111yescharacteristic
401C2×D47—22no—
402C2×D47—41no—
403C2×D47—41no—
404C2×D47—41no—
405C2×D47—41no—
406C2×D47—41no—
407C2×D47—41no—
408C2×D47—41no—
409C2×D47—41no—
410C2×D47—84no—
411C4×C47—24no—
412C4×C47—21no—
413C4×C47—21no—
414C4×C47—42no—
415C4×C47C2×C4×D411yescharacteristic
416C4×C47#51811yescharacteristic
417C4×C47D4211yescharacteristic
418C4×C47#54611yescharacteristic
419Dic47—22no—
420Dic47—41no—
421Dic47—41no—
422Dic47—41no—
423Dic47—41no—
424#3002—471no—
425C2×#443—471no—
426#2933—471no—
427C22×#104—471no—
428#2880—471no—
429#1974—471no—
430#1937—471no—
431#1929—471no—
432#1896—471no—
433#1876—471no—
434#1876—471no—
435#1866—471no—
436#1855—471no—
437#1764—471no—
438C4×C22⋊C8D4711yescharacteristic, complemented
439C2×C47—21no—
440C2×C47—22no—
441C2×C47—21no—
442C2×C47—41no—
443C2×C47#235811yescharacteristic
444C2×C47C2×#44311yescharacteristic
445C2×C47#295611yescharacteristic
446D47—42no—
447D47—81no—
448D47—81no—
449C22×#41—471no—
450C2×#135—471no—
451C2×#135—471no—
452C2×#131—471no—
453C2×#131—471no—
454C2×#131—471no—
455C22×M16—471no—
456#525—471no—
457C22×C42C2×D4711yescharacteristic
458#452—471no—
459#452—471no—
460#451—471no—
461#450—471no—
462#449—471no—
463#449—471no—
464#448—471no—
465#447—471no—
466#443—944no—
467#436—941no—
468#435—941no—
469#435—941no—
470C8×D4—941no—
471C2×#108—471no—
472C2×#108—471no—
473#424—471no—
474C2×#104—471no—
475C2×#104—471no—
476C2×#104—471no—
477C2×#104—471no—
478C2×#104—471no—
479C2×#104—471no—
480C2×#104—944no—
481#416—471no—
482#416—471no—
483#408—471no—
484#408—471no—
485#408—471no—
486#408—941no—
487#408—941no—
488#407—471no—
489#407—941no—
490C2×C22⋊C8—941no—
491C2×C22⋊C8C2×D4711yescharacteristic
492C2×C22⋊C8C2×D4711yescharacteristic
493#405—471no—
494C2×C4×C8C2×D4711yescharacteristic, complemented
495C2×C4×C8C2×D4711yescharacteristic, complemented
496#341—471no—
497#341—471no—
498#339—471no—
499#339—471no—
500#336C2×D4711yescharacteristic, complemented
501#336C2×D4711yescharacteristic, complemented
502C47#2288811yescharacteristic, complemented, Sylow
503C2×#41—471no—
504C2×#41—471no—
505C2×#41—471no—
506C2×#41—471no—
507C2×#41—471no—
508C2×#41—942no—
509C2×#41—942no—
510C2×#41—941no—
511C2×#41—941no—
512C2×#41—1881no—
513C2×#41—1881no—
514C22×Q8—471no—
515C22×D4—471no—
516C22×D4—941no—
517C23×C4—21no—
518C23×C4—941no—
519C23×C4C22×D4711yescharacteristic
520#135—942no—
521#135—942no—
522#135—1881no—
523#135—1881no—
524C2×Q16—471no—
525C2×Q16—471no—
526C2×SD16—471no—
527C2×SD16—471no—
528C2×SD16—471no—
529C2×SD16—471no—
530C2×D8—471no—
531C2×D8—471no—
532#131—942no—
533#131—942no—
534#131—942no—
535#131—1881no—
536#131—1881no—
537#131—1881no—
538C2×M16—471no—
539C2×M16—471no—
540C2×M16—471no—
541C2×M16—471no—
542C2×M16—941no—
543C2×M16—941no—
544C2×M16—941no—
545C2×M16—941no—
546C2×M16—942no—
547C2×M16—1881no—
548C22×C8—941no—
549C22×C8—941no—
550C22×C8—941no—
551C22×C8—941no—
552C22×C8C22×D4711yescharacteristic
553C22×C8C22×D4711yescharacteristic
554C22×C8C22×D4711yescharacteristic
555C22×C8C22×D4711yescharacteristic
556#123—941no—
557C22⋊Q8—471no—
558C22⋊Q8—471no—
559#121—471no—
560#121—471no—
561#120—941no—
562C4×D4—941no—
563C4×D4—941no—
564#117—471no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D4711yescharacteristic
569C2×C42C22×D4711yescharacteristic
570#108—942no—
571#108—1881no—
572C4⋊C8—941no—
573C4⋊C8—941no—
574#104—474no—
575#104—942no—
576#104—942no—
577#104—942no—
578#104—942no—
579#104—1881no—
580#103—471no—
581#103—471no—
582#103—471no—
583#103—471no—
584#102—471no—
585#102—471no—
586#102—471no—
587#102—471no—
588C22⋊C8—941no—
589C22⋊C8—941no—
590C22⋊C8—941no—
591C22⋊C8—941no—
592C22⋊C8—941no—
593C22⋊C8—941no—
594C22⋊C8—941no—
595C22⋊C8—941no—
596C22⋊C8C4×D4711yescharacteristic
597C22⋊C8C4×D4711yescharacteristic
598C22⋊C8C4×D4711yescharacteristic
599C22⋊C8C4×D4711yescharacteristic
600C22⋊C8D18811yescharacteristic
601C22⋊C8D18811yescharacteristic
602C22⋊C8D18811yescharacteristic
603C22⋊C8D18811yescharacteristic
604#97—941no—
605C4×C8—22no—
606C4×C8—41no—
607C4×C8—941no—
608C24—941no—
609C24#1062535011yescharacteristic
610#41—472no—
611#41—472no—
612#41—942no—
613#41—942no—
614#41—941no—
615#41—941no—
616#41—941no—
617#41—941no—
618#41—941no—
619#41—941no—
620#41—941no—
621#41—941no—
622#41—941no—
623#41—941no—
624#41—1882no—
625#41—1882no—
626#41—1881no—
627#41—1881no—
628#41—1882no—
629#41—1882no—
630C2×Q8—471no—
631C2×Q8—471no—
632C2×Q8—471no—
633C2×Q8—942no—
634C2×Q8—941no—
635C2×Q8—1881no—
636C2×D4—471no—
637C2×D4—471no—
638C2×D4—471no—
639C2×D4—942no—
640C2×D4—941no—
641C2×D4—941no—
642C2×D4—941no—
643C2×D4—941no—
644C2×D4—941no—
645C2×D4—941no—
646C2×D4—941no—
647C2×D4—941no—
648C2×D4—1881no—
649C2×D4—1882no—
650C2×D4—1882no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—941no—
661C22×C4—941no—
662C22×C4—941no—
663C22×C4—941no—
664C22×C4—941no—
665C22×C4—941no—
666C22×C4—1882no—
667C22×C4—1882no—
668C22×C4C2×C4×D4711yescharacteristic
669C22×C4C2×C4×D4711yescharacteristic
670C22×C4C2×D18811yescharacteristic
671C22×C4C2×D18811yescharacteristic
672C22×C4#1062535011yescharacteristic
673C22×C4C23×D4711yescharacteristic
674Q16—942no—
675Q16—1881no—
676SD16—942no—
677SD16—942no—
678SD16—1881no—
679SD16—1881no—
680D8—942no—
681D8—1881no—
682M16—472no—
683M16—941no—
684M16—941no—
685M16—941no—
686M16—941no—
687M16—941no—
688M16—941no—
689M16—941no—
690M16—1882no—
691M16—1882no—
692M16—1882no—
693M16—1882no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—941no—
703C2×C8—941no—
704C2×C8—941no—
705C2×C8—941no—
706C2×C8—1882no—
707C2×C8—1882no—
708C2×C8—1882no—
709C2×C8—1882no—
710C2×C8C2×C4×D4711yescharacteristic
711C2×C8C2×C4×D4711yescharacteristic
712C2×C8C2×C4×D4711yescharacteristic
713C2×C8C2×C4×D4711yescharacteristic
714C2×C8C2×D18811yescharacteristic
715C2×C8C2×D18811yescharacteristic
716C2×C8C2×D18811yescharacteristic
717C2×C8C2×D18811yescharacteristic
718C4⋊C4—471no—
719C4⋊C4—471no—
720C4⋊C4—941no—
721C4⋊C4—941no—
722C22⋊C4—941no—
723C22⋊C4—941no—
724C22⋊C4—941no—
725C22⋊C4—941no—
726C22⋊C4—941no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—941no—
732C42D4×D4712yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—41no—
737C23—941no—
738C23—941no—
739C23—941no—
740C23—3761no—
741C23—1882no—
742C23—1882no—
743C23C4×D18811yescharacteristic
744C23C4×D18811yescharacteristic
745C23C2×#1062535011yescharacteristic
746Q8—472no—
747Q8—941no—
748Q8—941no—
749Q8—941no—
750Q8—941no—
751Q8—941no—
752Q8—1882no—
753D4—472no—
754D4—942no—
755D4—942no—
756D4—941no—
757D4—941no—
758D4—941no—
759D4—941no—
760D4—941no—
761D4—3761no—
762D4—1882no—
763D4—1882no—
764D4—1882no—
765D4—1882no—
766D4—1881no—
767D4—1881no—
768D4—1881no—
769D4—1881no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
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—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—941no—
788C2×C4—942no—
789C2×C4—942no—
790C2×C4—941no—
791C2×C4—941no—
792C2×C4—941no—
793C2×C4—941no—
794C2×C4—1882no—
795C2×C4—1882no—
796C2×C4—1882no—
797C2×C4—1881no—
798C2×C4—1881no—
799C2×C4—1881no—
800C2×C4—1881no—
801C2×C4C4×D18811yescharacteristic
802C2×C4C4×D18811yescharacteristic
803C2×C4C22×C4×D4711yescharacteristic
804C2×C4C2×D4×D4711yescharacteristic
805C2×C4C22×D18811yescharacteristic
806C2×C4#41×D4711yescharacteristic
807C2×C4#1309406911yescharacteristic
808C2×C4#1309407011yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—21no—
817C8—942no—
818C8—1881no—
819C8—1881no—
820C8—1881no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—942no—
831C22—3764no—
832C22—1881no—
833C22—1881no—
834C22—1881no—
835C22—1881no—
836C22—1881no—
837C22—1881no—
838C22—1881no—
839C22—1881no—
840C22#1568924112yescomplemented
841C22C2×C4×D18811yescharacteristic
842C22#1568976311yescharacteristic
843C22#1568979711yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—42no—
848C4—942no—
849C4—1881no—
850C4—1881no—
851C4—1881no—
852C4—1881no—
853C4C4×D4×D4711yescharacteristic
854C4#1568959511yescharacteristic
855C4D4×D18811yescharacteristic
856C4#1568976811yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—3761no—
862C2—3761no—
863C2—1882no—
864C2#2024637011yescharacteristic
865C2C2×#1568924111yescharacteristic
866C2#2025229911yescharacteristic
subgroupG/H
centerC2×C4C22×D188
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC4×C22⋊C8×C47C2
socleC22×C47C2×C4×D4
prime radical#20252610C2
cosocleC22×C4×C47C24
hypercenterC4×C22⋊C8D47
hypocenterC47#22888
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#15689241C2semidirect
3. #20252109C2semidirect
4. C22×#13093952C2semidirect
5. #20251834C2semidirect
6. #20244276C2semidirect
7. #20244092C2semidirect
8. #20244037C2semidirect
9. #20243831C2semidirect
10. #20243714C2semidirect
11. #20243714C2semidirect
12. #20243666C2semidirect
13. #20243595C2semidirect
14. #20243225C2semidirect
15. C4×C22⋊C8×C47C2semidirect
21. C2×#13094030C22semidirect
24. #15689287C4semidirect
25. #15689287C4semidirect
26. #15689281C4semidirect
27. #15689276C4semidirect
28. #15689270C4semidirect
29. #15689270C4semidirect
30. #15689264C4semidirect
31. #15689259C4semidirect
37. C2×#13093960C22semidirect
38. C2×#13093960C22semidirect
39. #15689149C22semidirect
45. C2×#13093952C22semidirect
46. C2×#13093952C22semidirect
51. #15689089C22semidirect
57. #15689078C22semidirect
58. #15688888C22semidirect
59. #15688888C22semidirect
60. #15688883C22semidirect
61. #15688883C22semidirect
65. C2×C4×C8×C47C22semidirect
66. C2×C4×C8×C47C22semidirect
67. C47×#336C22semidirect
68. C47×#336C22semidirect
88. C2×Dic188C2×C4semidirect
89. C2×Dic188C2×C4semidirect
90. C2×#10625325C2×C4semidirect
91. C2×#10625325C2×C4semidirect
92. C2×#10625325C2×C4semidirect
93. C2×#10625325C2×C4semidirect
94. C2×D376C2×C4semidirect
95. C2×D376C2×C4semidirect
134. #13093952D4semidirect
135. #13093949C2×C4semidirect
136. #13093949C2×C4semidirect
137. #13093949C2×C4semidirect
138. #13093949C2×C4semidirect
139. #13093946C2×C4semidirect
140. #13093946C2×C4semidirect
141. #13093946C2×C4semidirect
142. #13093946C2×C4semidirect
397. C22×C47#443semidirect
438. C4×C22⋊C8D47semidirect
494. C2×C4×C8C2×D47semidirect
495. C2×C4×C8C2×D47semidirect
500. #336C2×D47semidirect
501. #336C2×D47semidirect
502. C47#22888semidirect
840. C22#15689241semidirect

Maximal subgroups

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

subgroupindex
#202526102
C2×#156892412
#202521092
C22×#130939522
#202518342
#202442762
#202440922
#202440372
#202438312
#202437142
#202436662
#202435952
#202432252
C4×C22⋊C8×C472
#2288847