Finite Group Databasebeta

← #26237012

Subgroups — #26237012

Order 12032.

1058 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#20252604C211yesmaximal, characteristic
2C2×#15689242C211yesmaximal, characteristic, complemented
3#20252115C211yesmaximal, characteristic, complemented
4C22×#13093952C211yesmaximal, characteristic, complemented
5#20251838C211yesmaximal, characteristic, complemented
6#20244278C211yesmaximal, characteristic, complemented
7#20244100C211yesmaximal, characteristic, complemented
8#20244034C211yesmaximal, characteristic, complemented
9#20243713C211yesmaximal, characteristic, complemented
10#20243712C211yesmaximal, characteristic, complemented
11#20243664C211yesmaximal, characteristic, complemented
12#20243592C211yesmaximal, characteristic, complemented
13#20243229C211yesmaximal, characteristic, complemented
14#20243150C211yesmaximal, characteristic, complemented
15C47×#1896C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C2×#13094044C2211yescharacteristic
18C2×#13094044C2211yescharacteristic
19C2×#13094032C2211yescharacteristic
20C2×#13094032C2211yescharacteristic
21C2×#13094031C2211yescharacteristic, complemented
22C22×#10625329C2211yescharacteristic
23#15689283C411yescharacteristic, complemented
24#15689283C411yescharacteristic, complemented
25#15689278C411yescharacteristic, complemented
26#15689273C411yescharacteristic, complemented
27#15689266C411yescharacteristic, complemented
28#15689266C411yescharacteristic, complemented
29#15689261C411yescharacteristic, complemented
30#15689256C411yescharacteristic, complemented
31#15689242—24no—
32#15689201—21no—
33#15689195—21no—
34#15689195—21no—
35D4×C47⋊C8—21no—
36C2×#13093959C2211yescharacteristic, complemented
37C2×#13093959C2211yescharacteristic, complemented
38#15689150C2211yescharacteristic, complemented
39C2×#13093952—24no—
40C2×#13093952C2211yescharacteristic
41C2×#13093952C2211yescharacteristic
42C2×#13093952C2211yescharacteristic
43C2×#13093952C2211yescharacteristic
44#15689117C2211yescharacteristic
45#15689117C2211yescharacteristic
46#15689091C2211yescharacteristic
47#15689091C2211yescharacteristic
48#15689090C2211yescharacteristic, complemented
49#15689088—21no—
50#15689088—21no—
51#15689085—21no—
52C2×C22⋊(C47⋊C8)C2211yescharacteristic
53C2×C22⋊(C47⋊C8)C2211yescharacteristic
54C22⋊C8×D47—21no—
55#15689079C2211yescharacteristic, complemented
56C2×#13093935C2211yescharacteristic, complemented
57C2×#13093935C2211yescharacteristic, complemented
58#15688887C2211yescharacteristic, complemented
59#15688887C2211yescharacteristic, complemented
60#15688878C2211yescharacteristic, complemented
61#15688878C2211yescharacteristic, complemented
62C47×#525C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C2×#104×C47C2211yescharacteristic, complemented
65C2×#104×C47C2211yescharacteristic, complemented
66C47×#407C2211yescharacteristic
67C47×#339C2211yescharacteristic, complemented
68C47×#339C2211yescharacteristic, 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
79C22×Dic94C2×C411yescharacteristic
80C22×D188C2×C411yescharacteristic
81C22×C22⋊D47—21no—
82C22×C4×D47—21no—
83#13094044—22no—
84#13094044—22no—
85#13094044—41no—
86#13094044—41no—
87C2×#10625337C2×C411yescharacteristic, complemented
88C2×#10625337C2×C411yescharacteristic, complemented
89C2×#10625335C2×C411yescharacteristic, complemented
90C2×#10625335C2×C411yescharacteristic, complemented
91C2×#10625336C2×C411yescharacteristic, complemented
92C2×#10625336C2×C411yescharacteristic, complemented
93C2×#10625334C2×C411yescharacteristic, complemented
94C2×#10625334C2×C411yescharacteristic, complemented
95#13094032—22no—
96#13094032—22no—
97#13094032—41no—
98#13094032—41no—
99#13094031—22no—
100#13094031—41no—
101C2×#10625329—21no—
102C2×#10625329—21no—
103C2×#10625329—22no—
104C2×#10625329—41no—
105C2×#10625329C2311yescharacteristic
106C2×#10625329C2311yescharacteristic
107C2×#10625324—21no—
108C2×#10625324—21no—
109C22×C47⋊C8—21no—
110C22×C47⋊C8—21no—
111C22×C47⋊C8C2311yescharacteristic
112C22×C47⋊C8C2311yescharacteristic
113C22×C47⋊C8C2311yescharacteristic
114C22×C47⋊C8C2311yescharacteristic
115C2×C8×D47—21no—
116C2×C8×D47—21no—
117#13093959—22no—
118#13093959—41no—
119C4⋊(C47⋊C8)—21no—
120C4⋊(C47⋊C8)—21no—
121#13093952—22no—
122#13093952—22no—
123#13093952—22no—
124#13093952D414yescomplemented
125#13093947C2×C411yescharacteristic, complemented
126#13093947C2×C411yescharacteristic, complemented
127#13093947C2×C411yescharacteristic, complemented
128#13093947C2×C411yescharacteristic, complemented
129#13093944C2×C411yescharacteristic, complemented
130#13093944C2×C411yescharacteristic, complemented
131#13093944C2×C411yescharacteristic, complemented
132#13093944C2×C411yescharacteristic, complemented
133C22⋊(C47⋊C8)—21no—
134C22⋊(C47⋊C8)—21no—
135C22⋊(C47⋊C8)C2×C411yescharacteristic
136C22⋊(C47⋊C8)C2×C411yescharacteristic
137C22⋊(C47⋊C8)C2×C411yescharacteristic
138C22⋊(C47⋊C8)C2×C411yescharacteristic
139C22⋊(C47⋊C8)D411yescharacteristic
140C22⋊(C47⋊C8)D411yescharacteristic
141C22⋊(C47⋊C8)D411yescharacteristic
142C22⋊(C47⋊C8)D411yescharacteristic
143(C2×D47)⋊C8—21no—
144(C2×D47)⋊C8—21no—
145(C2×D47)⋊C8—21no—
146(C2×D47)⋊C8—21no—
147#13093935—22no—
148#13093935—21no—
149#13093935—41no—
150C4×C47⋊C8—21no—
151C2×#41×C47C2311yescharacteristic
152C23×C4×C47—21no—
153C23×C4×C47C2311yescharacteristic
154C2×M16×C47C2311yescharacteristic
155C2×M16×C47C2311yescharacteristic
156#123×C47—21no—
157C22⋊Q8×C47C2×C411yescharacteristic
158C22⋊Q8×C47C2×C411yescharacteristic
159#121×C47C2×C411yescharacteristic
160#121×C47C2×C411yescharacteristic
161#120×C47—21no—
162C4×D4×C47—21no—
163C4×D4×C47—21no—
164#117×C47C2311yescharacteristic
165C2×C42×C47—22no—
166C2×C42×C47—21no—
167C2×C42×C47—41no—
168C2×C42×C47C2311yescharacteristic
169C2×C42×C47C2311yescharacteristic
170#104×C47—22no—
171#104×C47—41no—
172C22⋊C8×C47—21no—
173C22⋊C8×C47—21no—
174C24×C47#4111yescharacteristic
175C23×D47—21no—
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—21no—
179#41×C47—21no—
180C2×Q8×C47C22×C411yescharacteristic
181C2×D4×C47—21no—
182C2×D4×C47—21no—
183C2×D4×C47—21no—
184C2×D4×C47C22×C411yescharacteristic
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—42no—
193C22×C4×C47—42no—
194C22×C4×C47—42no—
195C22×C4×C47C22×C411yescharacteristic
196C22×C4×C47C22×C411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47#4111yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—21no—
202C2×C22⋊D47—21no—
203C2×C22⋊D47—21no—
204C2×C22⋊D47—21no—
205C2×C22⋊D47—42no—
206C2×C22⋊D47—42no—
207C22×Dic47—21no—
208#10625350—21no—
209#10625350—21no—
210#10625350—21no—
211#10625350—21no—
212#10625350—21no—
213#10625350—21no—
214#10625350—22no—
215#10625350—22no—
216#10625350—41no—
217#10625350—41no—
218#10625350—42no—
219#10625350—42no—
220#10625350—42no—
221#10625350—42no—
222#10625350C2×D412yes—
223#10625350#4112yes—
224C2×D188—22no—
225C2×D188—21no—
226C2×D188—41no—
227C2×D188C22×C411yescharacteristic
228C2×D188C22×C411yescharacteristic
229C2×C4×D47—21no—
230C2×C4×D47—21no—
231C2×C4×D47—21no—
232C2×C4×D47—21no—
233C2×C4×D47—42no—
234C2×C4×D47—42no—
235C2×Dic94—22no—
236C2×Dic94—21no—
237C2×Dic94—41no—
238C2×Dic94C22×C411yescharacteristic
239C2×Dic94C22×C411yescharacteristic
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—21no—
244C2×C8×C47—21no—
245C2×C8×C47—21no—
246C4⋊C4×C47—21no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47C22×C411yescharacteristic
249C4⋊C4×C47C22×C411yescharacteristic
250C22⋊C4×C47—21no—
251C22⋊C4×C47—21no—
252C22⋊C4×C47—21no—
253C22⋊C4×C47—21no—
254C22⋊C4×C47—21no—
255C42×C47—21no—
256C42×C47—21no—
257C42×C47—21no—
258C42×C47—21no—
259C42×C47—42no—
260C42×C47C2×D412yes—
261#10625337—22no—
262#10625337—41no—
263#10625336—22no—
264#10625336—41no—
265#10625335—22no—
266#10625335—41no—
267#10625334—22no—
268#10625334—41no—
269#10625329—21no—
270#10625329—21no—
271#10625329—21no—
272#10625329—42no—
273#10625329—42no—
274#10625329C2×D412yes—
275C2×C47⋊C8—21no—
276C2×C47⋊C8—21no—
277C2×C47⋊C8—21no—
278C2×C47⋊C8—21no—
279C2×C47⋊C8—21no—
280C2×C47⋊C8—21no—
281C2×C47⋊C8—21no—
282C2×C47⋊C8—21no—
283C2×C47⋊C8—21no—
284C2×C47⋊C8—21no—
285C2×C47⋊C8—42no—
286C2×C47⋊C8—42no—
287C2×C47⋊C8C22×C411yescharacteristic
288C2×C47⋊C8C22×C411yescharacteristic
289C2×C47⋊C8C22×C411yescharacteristic
290C2×C47⋊C8C22×C411yescharacteristic
291C2×C47⋊C8C2×D411yescharacteristic
292C2×C47⋊C8C2×D411yescharacteristic
293C2×C47⋊C8C2×D411yescharacteristic
294C2×C47⋊C8C2×D411yescharacteristic
295#10625324—42no—
296#10625324—42no—
297C8×D47—42no—
298C8×D47—42no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—22no—
302C23×C47—21no—
303C23×C47—41no—
304C23×C47C4×D411yescharacteristic
305C23×C47C4×D411yescharacteristic
306C23×C47C2×#4111yescharacteristic
307C22×D47—21no—
308C22×D47—21no—
309C22×D47—42no—
310C22×D47—42no—
311C22×D47—81no—
312Q8×C47—21no—
313Q8×C47—21no—
314D4×C47—21no—
315D4×C47—21no—
316D4×C47—41no—
317D4×C47—41no—
318D4×C47—42no—
319D4×C47—81no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—22no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—22no—
335C2×C4×C47—41no—
336C2×C4×C47—41no—
337C2×C4×C47—41no—
338C2×C4×C47—48no—
339C2×C4×C47—41no—
340C2×C4×C47—41no—
341C2×C4×C47—41no—
342C2×C4×C47C4×D411yescharacteristic
343C2×C4×C47C4×D411yescharacteristic
344C2×C4×C47C23×C411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C2×#4111yescharacteristic
348C2×C4×C47H(5,𝔽2)11yescharacteristic
349C2×C4×C47H(5,𝔽2)11yescharacteristic
350C22⋊D47—22no—
351C22⋊D47—22no—
352C22⋊D47—42no—
353C22⋊D47—42no—
354C22⋊D47—41no—
355C22⋊D47—41no—
356C2×Dic47—21no—
357C2×Dic47—21no—
358C2×Dic47—42no—
359D188—21no—
360D188—21no—
361D188—21no—
362D188—42no—
363D188C4×D412yes—
364C4×D47—22no—
365C4×D47—22no—
366C4×D47—42no—
367C4×D47—42no—
368C4×D47—41no—
369C4×D47—41no—
370Dic94—21no—
371Dic94—21no—
372Dic94—21no—
373Dic94—42no—
374Dic94C4×D412yes—
375C8×C47—41no—
376C8×C47—41no—
377C47⋊C8—21no—
378C47⋊C8—21no—
379C47⋊C8—21no—
380C47⋊C8—21no—
381C47⋊C8—21no—
382C47⋊C8—21no—
383C47⋊C8—22no—
384C47⋊C8—21no—
385C47⋊C8—21no—
386C47⋊C8—41no—
387#22886—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—41no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47#44412yescomplemented
401C22×C47C2×C4×D411yescharacteristic
402C22×C47#54611yescharacteristic
403C22×C47#55111yescharacteristic
404C2×D47—22no—
405C2×D47—41no—
406C2×D47—41no—
407C2×D47—41no—
408C2×D47—41no—
409C2×D47—41no—
410C2×D47—84no—
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—42no—
414C4×C47—42no—
415C4×C47—41no—
416C4×C47—41no—
417C4×C47—41no—
418C4×C47C2×C4×D411yescharacteristic
419C4×C47#51811yescharacteristic
420C4×C47D4211yescharacteristic
421C4×C47#54611yescharacteristic
422Dic47—22no—
423Dic47—41no—
424#3002—471no—
425C2×#444—471no—
426#2933—471no—
427C22×#104—471no—
428#2880—471no—
429#1975—471no—
430#1938—471no—
431#1929—471no—
432#1896D4711yescharacteristic, complemented
433#1876—471no—
434#1876—471no—
435#1866—471no—
436#1855—471no—
437#1765—471no—
438#1749—471no—
439C2×C47—21no—
440C2×C47—22no—
441C2×C47—21no—
442C2×C47—41no—
443C2×C47—81no—
444C2×C47#235811yescharacteristic
445C2×C47C2×#44411yescharacteristic
446C2×C47#295611yescharacteristic
447D47—42no—
448D47—81no—
449C22×#41—471no—
450C2×#135—471no—
451C2×#135—471no—
452C2×#131—471no—
453C2×#131—471no—
454C2×#131—471no—
455C22×M16—471no—
456#525C2×D4711yescharacteristic
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#444—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—944no—
479C2×#104C2×D4711yescharacteristic, complemented
480C2×#104C2×D4711yescharacteristic, complemented
481#416—471no—
482#416—471no—
483#408—471no—
484#408—471no—
485#408—471no—
486#408—941no—
487#408—941no—
488#407—941no—
489#407C2×D4711yescharacteristic
490C2×C22⋊C8—471no—
491C2×C22⋊C8—471no—
492C2×C22⋊C8—941no—
493#405—471no—
494C2×#97—471no—
495C2×#97—471no—
496#341—471no—
497#341—471no—
498#339C2×D4711yescharacteristic, complemented
499#339C2×D4711yescharacteristic, complemented
500#336—471no—
501#336—471no—
502C47#2288611yescharacteristic, complemented, Sylow
503C2×#41—471no—
504C2×#41—471no—
505C2×#41—471no—
506C2×#41—471no—
507C2×#41—942no—
508C2×#41—942no—
509C2×#41—941no—
510C2×#41—941no—
511C2×#41—1881no—
512C2×#41—1881no—
513C2×#41C22×D4711yescharacteristic
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—941no—
541C2×M16—941no—
542C2×M16—941no—
543C2×M16—941no—
544C2×M16—942no—
545C2×M16—1881no—
546C2×M16C22×D4711yescharacteristic
547C2×M16C22×D4711yescharacteristic
548C22×C8—471no—
549C22×C8—471no—
550C22×C8—471no—
551C22×C8—471no—
552C22×C8—941no—
553C22×C8—941no—
554C22×C8—941no—
555C22×C8—941no—
556#123—21no—
557C22⋊Q8C4×D4711yescharacteristic
558C22⋊Q8C4×D4711yescharacteristic
559#121C4×D4711yescharacteristic
560#121C4×D4711yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D4711yescharacteristic
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—22no—
575#104—41no—
576#104—474no—
577#104—942no—
578#104—942no—
579#104—942no—
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—21no—
589C22⋊C8—21no—
590C22⋊C8—471no—
591C22⋊C8—471no—
592C22⋊C8—471no—
593C22⋊C8—471no—
594C22⋊C8—471no—
595C22⋊C8—471no—
596C22⋊C8—471no—
597C22⋊C8—471no—
598C22⋊C8—941no—
599C22⋊C8—941no—
600C22⋊C8—941no—
601C22⋊C8—941no—
602C22⋊C8—941no—
603C22⋊C8—941no—
604#97—941no—
605#97—942no—
606#97—1881no—
607C4×C8—941no—
608C24—941no—
609C24#1062535211yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—472no—
615#41—472no—
616#41—942no—
617#41—942no—
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—942no—
633C2×Q8—941no—
634C2×Q8—1881no—
635C2×Q8C2×C4×D4711yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—471no—
640C2×D4—471no—
641C2×D4—942no—
642C2×D4—941no—
643C2×D4—941no—
644C2×D4—941no—
645C2×D4—941no—
646C2×D4—941no—
647C2×D4—1881no—
648C2×D4—1882no—
649C2×D4—1882no—
650C2×D4C2×C4×D4711yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
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×C4D4×D4711yescharacteristic
671C22×C4D4×D4711yescharacteristic
672C22×C4#1062535211yescharacteristic
673C22×C4C23×D4711yescharacteristic
674Q16—942no—
675Q16—1881no—
676SD16—942no—
677SD16—942no—
678SD16—1881no—
679SD16—1881no—
680D8—942no—
681D8—1881no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—472no—
687M16—941no—
688M16—941no—
689M16—941no—
690M16—1882no—
691M16—1882no—
692M16—1882no—
693M16—1882no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—471no—
697C2×C8—471no—
698C2×C8—471no—
699C2×C8—471no—
700C2×C8—471no—
701C2×C8—471no—
702C2×C8—471no—
703C2×C8—471no—
704C2×C8—941no—
705C2×C8—941no—
706C2×C8—941no—
707C2×C8—941no—
708C2×C8—941no—
709C2×C8—941no—
710C2×C8—941no—
711C2×C8—941no—
712C2×C8—941no—
713C2×C8—941no—
714C2×C8—1882no—
715C2×C8—1882no—
716C2×C8—1882no—
717C2×C8—1882no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D4711yescharacteristic
721C4⋊C4C2×C4×D4711yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42D4×D4712yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—941no—
739C23—941no—
740C23—3761no—
741C23—1882no—
742C23—1882no—
743C23(C22⋊D47)⋊C411yescharacteristic
744C23(C22⋊D47)⋊C411yescharacteristic
745C23C2×#1062535211yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—472no—
749Q8—941no—
750Q8—941no—
751Q8—941no—
752Q8—1882no—
753D4—21no—
754D4—21no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—81no—
759D4—472no—
760D4—942no—
761D4—942no—
762D4—941no—
763D4—941no—
764D4—941no—
765D4—1882no—
766D4—1882no—
767D4—1882no—
768D4—1881no—
769D4—1881no—
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—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—48no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—941no—
793C2×C4—942no—
794C2×C4—942no—
795C2×C4—941no—
796C2×C4—1882no—
797C2×C4—1882no—
798C2×C4—1882no—
799C2×C4—1881no—
800C2×C4—1881no—
801C2×C4(C22⋊D47)⋊C411yescharacteristic
802C2×C4(C22⋊D47)⋊C411yescharacteristic
803C2×C4C22×C4×D4711yescharacteristic
804C2×C4C2×D4×D4711yescharacteristic
805C2×C4C2×D4×D4711yescharacteristic
806C2×C4#41×D4711yescharacteristic
807C2×C4#1309406911yescharacteristic
808C2×C4#1309407011yescharacteristic
809C8—41no—
810C8—41no—
811C8—941no—
812C8—941no—
813C8—942no—
814C8—941no—
815C8—941no—
816C8—941no—
817C8—941no—
818C8—941no—
819C8—941no—
820C8—1881no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—942no—
834C22—3764no—
835C22—1881no—
836C22—1881no—
837C22—1881no—
838C22—1881no—
839C22—1881no—
840C22#1568924212yescomplemented
841C22C2×(C22⋊D47)⋊C411yescharacteristic
842C22#1568976011yescharacteristic
843C22#1568979611yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—942no—
852C4—1881no—
853C4C4×D4×D4711yescharacteristic
854C4#1568959511yescharacteristic
855C4#1568975711yescharacteristic
856C4#1568976211yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—3761no—
863C2—1882no—
864C2#2024636811yescharacteristic
865C2C2×#1568924211yescharacteristic
866C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1896C2
socleC22×C47C2×C4×D4
prime radical#20252604C2
cosocleC22×C4×C47C24
hypercenter#1896D47
hypocenterC47#22886
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#15689242C2semidirect
3. #20252115C2semidirect
4. C22×#13093952C2semidirect
5. #20251838C2semidirect
6. #20244278C2semidirect
7. #20244100C2semidirect
8. #20244034C2semidirect
9. #20243713C2semidirect
10. #20243712C2semidirect
11. #20243664C2semidirect
12. #20243592C2semidirect
13. #20243229C2semidirect
14. #20243150C2semidirect
15. C47×#1896C2semidirect
21. C2×#13094031C22semidirect
23. #15689283C4semidirect
24. #15689283C4semidirect
25. #15689278C4semidirect
26. #15689273C4semidirect
27. #15689266C4semidirect
28. #15689266C4semidirect
29. #15689261C4semidirect
30. #15689256C4semidirect
36. C2×#13093959C22semidirect
37. C2×#13093959C22semidirect
38. #15689150C22semidirect
48. #15689090C22semidirect
55. #15689079C22semidirect
56. C2×#13093935C22semidirect
57. C2×#13093935C22semidirect
58. #15688887C22semidirect
59. #15688887C22semidirect
60. #15688878C22semidirect
61. #15688878C22semidirect
64. C2×#104×C47C22semidirect
65. C2×#104×C47C22semidirect
67. C47×#339C22semidirect
68. C47×#339C22semidirect
87. C2×#10625337C2×C4semidirect
88. C2×#10625337C2×C4semidirect
89. C2×#10625335C2×C4semidirect
90. C2×#10625335C2×C4semidirect
91. C2×#10625336C2×C4semidirect
92. C2×#10625336C2×C4semidirect
93. C2×#10625334C2×C4semidirect
94. C2×#10625334C2×C4semidirect
124. #13093952D4semidirect
125. #13093947C2×C4semidirect
126. #13093947C2×C4semidirect
127. #13093947C2×C4semidirect
128. #13093947C2×C4semidirect
129. #13093944C2×C4semidirect
130. #13093944C2×C4semidirect
131. #13093944C2×C4semidirect
132. #13093944C2×C4semidirect
400. C22×C47#444semidirect
432. #1896D47semidirect
479. C2×#104C2×D47semidirect
480. C2×#104C2×D47semidirect
498. #339C2×D47semidirect
499. #339C2×D47semidirect
502. C47#22886semidirect
840. C22#15689242semidirect

Maximal subgroups

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

subgroupindex
#202526042
C2×#156892422
#202521152
C22×#130939522
#202518382
#202442782
#202441002
#202440342
#202437132
#202437122
#202436642
#202435922
#202432292
#202431502
C47×#18962
#2288647