Finite Group Databasebeta

← #26237015

Subgroups — #26237015

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#20252606C211yesmaximal, characteristic
2C2×#15689242C211yesmaximal, characteristic, complemented
3#20252113C211yesmaximal, characteristic, complemented
4#20251837C211yesmaximal, characteristic, complemented
5#20244278C211yesmaximal, characteristic, complemented
6#20244096C211yesmaximal, characteristic, complemented
7#20244039C211yesmaximal, characteristic, complemented
8#20243831C211yesmaximal, characteristic, complemented
9#20243713C211yesmaximal, characteristic, complemented
10#20243712C211yesmaximal, characteristic, complemented
11#20243661C211yesmaximal, characteristic, complemented
12#20243593C211yesmaximal, characteristic, complemented
13#20243233C211yesmaximal, characteristic, complemented
14#20243150C211yesmaximal, characteristic, complemented
15C22×#104×C47C211yesmaximal, characteristic, complemented
16C2×#13094044C2211yescharacteristic
17C2×#13094044C2211yescharacteristic
18C2×#13094032C2211yescharacteristic, complemented
19C2×#13094031C2211yescharacteristic
20C2×#13094031C2211yescharacteristic
21#15689634C2211yescharacteristic
22#15689285C411yescharacteristic, complemented
23#15689285C411yescharacteristic, complemented
24#15689279C411yescharacteristic, complemented
25#15689274C411yescharacteristic, complemented
26#15689268C411yescharacteristic, complemented
27#15689268C411yescharacteristic, complemented
28#15689262C411yescharacteristic, complemented
29#15689257C411yescharacteristic, complemented
30#15689242—24no—
31#15689199—21no—
32#15689194—21no—
33#15689192—21no—
34C8×C22⋊D47—21no—
35C2×#13093959C2211yescharacteristic, complemented
36C2×#13093959C2211yescharacteristic, complemented
37#15689151C2211yescharacteristic, complemented
38C2×#13093952C2211yescharacteristic, complemented
39C2×#13093952C2211yescharacteristic, complemented
40#15689119C2211yescharacteristic
41#15689119C2211yescharacteristic
42#15689091C2211yescharacteristic, complemented
43#15689090—21no—
44#15689090—21no—
45#15689090C2211yescharacteristic
46#15689090C2211yescharacteristic
47#15689087—21no—
48#15689087C2211yescharacteristic
49C2×C22⋊(C47⋊C8)—21no—
50C2×C22⋊(C47⋊C8)C2211yescharacteristic
51C2×C22⋊(C47⋊C8)C2211yescharacteristic
52#15689081C2211yescharacteristic, complemented
53C2×#13093935C2211yescharacteristic, complemented
54C2×#13093935C2211yescharacteristic, complemented
55#15688887C2211yescharacteristic, complemented
56#15688887C2211yescharacteristic, complemented
57#15688883C2211yescharacteristic, complemented
58#15688883C2211yescharacteristic, complemented
59#15688878C2211yescharacteristic, complemented
60#15688878C2211yescharacteristic, complemented
61C22×#41×C47C2211yescharacteristic
62C22×M16×C47C2211yescharacteristic
63C22×C42×C47C2211yescharacteristic
64C2×#104×C47—24no—
65C2×#104×C47C2211yescharacteristic
66C2×#104×C47C2211yescharacteristic
67C2×#104×C47C2211yescharacteristic
68C2×#104×C47C2211yescharacteristic
69C2×#10625350C2311yescharacteristic
70#13094044—22no—
71#13094044—22no—
72#13094044—41no—
73#13094044—41no—
74C2×#10625337C2×C411yescharacteristic, complemented
75C2×#10625337C2×C411yescharacteristic, complemented
76C2×#10625335C2×C411yescharacteristic, complemented
77C2×#10625335C2×C411yescharacteristic, complemented
78C2×#10625336C2×C411yescharacteristic, complemented
79C2×#10625336C2×C411yescharacteristic, complemented
80C2×#10625334C2×C411yescharacteristic, complemented
81C2×#10625334C2×C411yescharacteristic, complemented
82#13094032—22no—
83#13094032—41no—
84#13094031—22no—
85#13094031—22no—
86#13094031—41no—
87#13094031—41no—
88C2×#10625329—21no—
89C2×#10625329—21no—
90C2×#10625329C2311yescharacteristic
91C2×#10625329C2311yescharacteristic
92C2×#10625324—21no—
93C22×C47⋊C8—21no—
94C22×C47⋊C8—21no—
95C22×C47⋊C8C2311yescharacteristic
96C22×C47⋊C8C2311yescharacteristic
97C22×C47⋊C8C2311yescharacteristic
98C22×C47⋊C8C2311yescharacteristic
99C2×C8×D47—21no—
100#13094007—21no—
101#13094003C2×C411yescharacteristic
102#13094003C2×C411yescharacteristic
103#13093998C2×C411yescharacteristic
104#13093998C2×C411yescharacteristic
105#13093993—21no—
106C4×C22⋊D47—21no—
107C4×C22⋊D47—21no—
108#13093983C2311yescharacteristic
109#13093959—22no—
110#13093959—41no—
111Dic47⋊C8—21no—
112Dic47⋊C8—21no—
113#13093952—22no—
114#13093952—41no—
115#13093948C2×C411yescharacteristic, complemented
116#13093948C2×C411yescharacteristic, complemented
117#13093948C2×C411yescharacteristic, complemented
118#13093948C2×C411yescharacteristic, complemented
119#13093945C2×C411yescharacteristic, complemented
120#13093945C2×C411yescharacteristic, complemented
121#13093945C2×C411yescharacteristic, complemented
122#13093945C2×C411yescharacteristic, complemented
123C22⋊(C47⋊C8)—21no—
124C22⋊(C47⋊C8)—21no—
125C22⋊(C47⋊C8)—21no—
126C22⋊(C47⋊C8)—21no—
127C22⋊(C47⋊C8)—21no—
128C22⋊(C47⋊C8)—21no—
129C22⋊(C47⋊C8)C2×C411yescharacteristic
130C22⋊(C47⋊C8)C2×C411yescharacteristic
131C22⋊(C47⋊C8)C2×C411yescharacteristic
132C22⋊(C47⋊C8)C2×C411yescharacteristic
133C22⋊(C47⋊C8)D411yescharacteristic
134C22⋊(C47⋊C8)D411yescharacteristic
135C22⋊(C47⋊C8)D411yescharacteristic
136C22⋊(C47⋊C8)D411yescharacteristic
137(C2×D47)⋊C8—21no—
138(C2×D47)⋊C8—21no—
139#13093935—22no—
140#13093935—41no—
141#13093934—21no—
142C8×Dic47—21no—
143C2×#41×C47—21no—
144C2×#41×C47—21no—
145C2×#41×C47—22no—
146C2×#41×C47—22no—
147C2×#41×C47—41no—
148C2×#41×C47—41no—
149C2×#41×C47C2×C411yescharacteristic
150C2×#41×C47C2×C411yescharacteristic
151C2×#41×C47C2311yescharacteristic
152C2×#41×C47C2311yescharacteristic
153C22×Q8×C47C2×C411yescharacteristic
154C22×D4×C47—21no—
155C22×D4×C47C2×C411yescharacteristic
156C23×C4×C47—21no—
157C23×C4×C47—21no—
158C23×C4×C47C2311yescharacteristic
159C2×M16×C47—21no—
160C2×M16×C47—22no—
161C2×M16×C47—41no—
162C2×M16×C47C2311yescharacteristic
163C2×M16×C47C2311yescharacteristic
164C22×C8×C47—21no—
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—22no—
172#104×C47—22no—
173#104×C47D414yescomplemented
174C24×C47—21no—
175C24×C47#4111yescharacteristic
176#41×C47—21no—
177#41×C47—21no—
178#41×C47—22no—
179#41×C47—22no—
180#41×C47—21no—
181#41×C47—21no—
182#41×C47—21no—
183#41×C47—21no—
184#41×C47—42no—
185#41×C47—42no—
186#41×C47—41no—
187#41×C47—41no—
188#41×C47—42no—
189#41×C47—42no—
190#41×C47C2×D412yes—
191#41×C47#4112yes—
192C2×Q8×C47—21no—
193C2×Q8×C47—22no—
194C2×Q8×C47—41no—
195C2×Q8×C47C22×C411yescharacteristic
196C2×Q8×C47C22×C411yescharacteristic
197C2×D4×C47—21no—
198C2×D4×C47—22no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—41no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47C22×C411yescharacteristic
207C2×D4×C47C22×C411yescharacteristic
208C22×C4×C47—21no—
209C22×C4×C47—21no—
210C22×C4×C47—21no—
211C22×C4×C47—21no—
212C22×C4×C47—21no—
213C22×C4×C47—21no—
214C22×C4×C47—21no—
215C22×C4×C47—21no—
216C22×C4×C47—21no—
217C22×C4×C47—21no—
218C22×C4×C47—21no—
219C22×C4×C47—42no—
220C22×C4×C47—42no—
221C22×C4×C47—42no—
222C22×C4×C47—42no—
223C22×C4×C47—42no—
224C22×C4×C47C22×C411yescharacteristic
225C22×C4×C47C22×C411yescharacteristic
226C22×C4×C47C2×D411yescharacteristic
227C22×C4×C47C2×D411yescharacteristic
228C22×C4×C47#4111yescharacteristic
229C22×C4×C47C2411yescharacteristic
230C2×C22⋊D47—21no—
231C2×C22⋊D47—21no—
232C2×C22⋊D47—21no—
233#10625350—21no—
234#10625350—21no—
235#10625350—21no—
236#10625350—21no—
237C2×D188C22×C411yescharacteristic
238C2×C4×D47—21no—
239C2×Dic94C22×C411yescharacteristic
240M16×C47—21no—
241M16×C47—21no—
242M16×C47—21no—
243M16×C47—42no—
244M16×C47C2×D412yes—
245C2×C8×C47—21no—
246C2×C8×C47—21no—
247C2×C8×C47—42no—
248C42×C47—21no—
249C42×C47—21no—
250C42×C47—21no—
251C42×C47—42no—
252C42×C47C2×D412yes—
253C22⋊Dic47—21no—
254C22⋊Dic47—21no—
255C22⋊Dic47—21no—
256#10625337—22no—
257#10625337—41no—
258#10625336—22no—
259#10625336—41no—
260#10625335—22no—
261#10625335—41no—
262#10625334—22no—
263#10625334—41no—
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—42no—
276#10625329—42no—
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—21no—
286C2×C47⋊C8—21no—
287C2×C47⋊C8—42no—
288C2×C47⋊C8—42no—
289C2×C47⋊C8C22×C411yescharacteristic
290C2×C47⋊C8C22×C411yescharacteristic
291C2×C47⋊C8C22×C411yescharacteristic
292C2×C47⋊C8C22×C411yescharacteristic
293C2×C47⋊C8C2×D411yescharacteristic
294C2×C47⋊C8C2×D411yescharacteristic
295C2×C47⋊C8C2×D411yescharacteristic
296C2×C47⋊C8C2×D411yescharacteristic
297#10625324—42no—
298C8×D47—42no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—21no—
302C23×C47—22no—
303C23×C47—21no—
304C23×C47—41no—
305C23×C47—42no—
306C23×C47—42no—
307C23×C47—81no—
308C23×C47C4×D411yescharacteristic
309C23×C47C4×D411yescharacteristic
310C23×C47C2×#4111yescharacteristic
311C22×D47—21no—
312Q8×C47—21no—
313Q8×C47—21no—
314Q8×C47—21no—
315Q8×C47—42no—
316Q8×C47C4×D412yes—
317D4×C47—22no—
318D4×C47—22no—
319D4×C47—21no—
320D4×C47—21no—
321D4×C47—21no—
322D4×C47—42no—
323D4×C47—42no—
324D4×C47—42no—
325D4×C47—41no—
326D4×C47—41no—
327D4×C47C4×D412yes—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—22no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—22no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—22no—
342C2×C4×C47—21no—
343C2×C4×C47—22no—
344C2×C4×C47—42no—
345C2×C4×C47—42no—
346C2×C4×C47—42no—
347C2×C4×C47—41no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—48no—
351C2×C4×C47—41no—
352C2×C4×C47—41no—
353C2×C4×C47—41no—
354C2×C4×C47C4×D411yescharacteristic
355C2×C4×C47C4×D411yescharacteristic
356C2×C4×C47C23×C411yescharacteristic
357C2×C4×C47C22×D411yescharacteristic
358C2×C4×C47C22×D411yescharacteristic
359C2×C4×C47C2×#4111yescharacteristic
360C2×C4×C47H(5,𝔽2)11yescharacteristic
361C2×C4×C47H(5,𝔽2)11yescharacteristic
362C22⋊D47—41no—
363C22⋊D47—41no—
364C22⋊D47—42no—
365C22⋊D47—81no—
366C2×Dic47—21no—
367C2×Dic47—21no—
368C2×Dic47—21no—
369D188—21no—
370D188—21no—
371C4×D47—41no—
372C4×D47—41no—
373Dic94—21no—
374Dic94—21no—
375C8×C47—22no—
376C8×C47—41no—
377C47⋊C8—21no—
378C47⋊C8—21no—
379C47⋊C8—21no—
380C47⋊C8—21no—
381C47⋊C8—21no—
382C47⋊C8—21no—
383C47⋊C8—21no—
384C47⋊C8—21no—
385C47⋊C8—41no—
386C47⋊C8—41no—
387#22886—471nomaximal, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—21no—
392C22×C47—21no—
393C22×C47—22no—
394C22×C47—21no—
395C22×C47—21no—
396C22×C47—42no—
397C22×C47—42no—
398C22×C47—41no—
399C22×C47—41no—
400C22×C47—41no—
401C22×C47—41no—
402C22×C47—41no—
403C22×C47—84no—
404C22×C47#44412yescomplemented
405C22×C47C2×C4×D411yescharacteristic
406C22×C47#54611yescharacteristic
407C22×C47#55111yescharacteristic
408C2×D47—41no—
409C2×D47—41no—
410C2×D47—41no—
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—22no—
414C4×C47—42no—
415C4×C47—42no—
416C4×C47—41no—
417C4×C47C2×C4×D411yescharacteristic
418C4×C47#51811yescharacteristic
419C4×C47D4211yescharacteristic
420C4×C47#54611yescharacteristic
421Dic47—41no—
422Dic47—41no—
423Dic47—41no—
424#3002—471no—
425C2×#444—471no—
426#2933—471no—
427C22×#104D4711yescharacteristic, complemented
428#2880—471no—
429#1975—471no—
430#1938—471no—
431#1929—471no—
432#1896—471no—
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—42no—
444C2×C47—81no—
445C2×C47#235811yescharacteristic
446C2×C47C2×#44411yescharacteristic
447C2×C47#295611yescharacteristic
448D47—81no—
449C22×#41C2×D4711yescharacteristic
450C2×#135—471no—
451C2×#135—471no—
452C2×#131—471no—
453C2×#131—471no—
454C2×#131—471no—
455C22×M16C2×D4711yescharacteristic
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#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—24no—
475C2×#104—471no—
476C2×#104—471no—
477C2×#104C2×D4711yescharacteristic
478C2×#104C2×D4711yescharacteristic
479C2×#104C2×D4711yescharacteristic
480C2×#104C2×D4711yescharacteristic
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—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#339—471no—
499#339—471no—
500#336—471no—
501#336—471no—
502C47#2288611yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—471no—
510C2×#41C4×D4711yescharacteristic
511C2×#41C4×D4711yescharacteristic
512C2×#41C22×D4711yescharacteristic
513C2×#41C22×D4711yescharacteristic
514C22×Q8C4×D4711yescharacteristic
515C22×D4—21no—
516C22×D4C4×D4711yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
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—21no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—471no—
542C2×M16—471no—
543C2×M16—941no—
544C2×M16—941no—
545C2×M16—941no—
546C2×M16C22×D4711yescharacteristic
547C2×M16C22×D4711yescharacteristic
548C22×C8—21no—
549C22×C8—471no—
550C22×C8—471no—
551C22×C8—471no—
552C22×C8—471no—
553C22×C8—941no—
554C22×C8—941no—
555C22×C8—941no—
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—22no—
575#104—22no—
576#104—22no—
577#104—942no—
578#104—1881no—
579#104C22⋊D4714yescomplemented
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—471no—
589C22⋊C8—471no—
590C22⋊C8—471no—
591C22⋊C8—471no—
592C22⋊C8—471no—
593C22⋊C8—471no—
594C22⋊C8—471no—
595C22⋊C8—471no—
596C22⋊C8—941no—
597C22⋊C8—941no—
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—21no—
609C24#1062535211yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41—941no—
625#41—941no—
626#41—941no—
627#41—941no—
628#41#1062535012yes—
629#41C2×C22⋊D4712yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—471no—
634C2×Q8C2×C4×D4711yescharacteristic
635C2×Q8C2×C4×D4711yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—471no—
646C2×D4—941no—
647C2×D4—941no—
648C2×D4—941no—
649C2×D4C2×C4×D4711yescharacteristic
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—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—941no—
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—42no—
686M16—941no—
687M16—941no—
688M16—941no—
689M16—941no—
690M16—1882no—
691M16—1882no—
692M16—1882no—
693M16C2×C22⋊D4712yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—42no—
697C2×C8—471no—
698C2×C8—471no—
699C2×C8—471no—
700C2×C8—471no—
701C2×C8—471no—
702C2×C8—471no—
703C2×C8—471no—
704C2×C8—471no—
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—941no—
715C2×C8—1882no—
716C2×C8—1882no—
717C2×C8—1882no—
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—
732C42C2×C22⋊D4712yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—941no—
743C23(C22⋊D47)⋊C411yescharacteristic
744C23(C22⋊D47)⋊C411yescharacteristic
745C23C2×#1062535211yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—941no—
751Q8—941no—
752Q8C4×C22⋊D4712yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—941no—
764D4—941no—
765D4—3761no—
766D4—1882no—
767D4—1881no—
768D4—1881no—
769D4C4×C22⋊D4712yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—941no—
797C2×C4—941no—
798C2×C4—941no—
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×C4C22×C22⋊D4711yescharacteristic
806C2×C4C2×#1062535011yescharacteristic
807C2×C4#1309406911yescharacteristic
808C2×C4#1309406911yescharacteristic
809C8—22no—
810C8—41no—
811C8—941no—
812C8—941no—
813C8—941no—
814C8—941no—
815C8—941no—
816C8—941no—
817C8—941no—
818C8—941no—
819C8—1881no—
820C8—1881no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—1881no—
838C22—1881no—
839C22—1881no—
840C22#1568924212yescomplemented
841C22C2×(C22⋊D47)⋊C411yescharacteristic
842C22#1568976711yescharacteristic
843C22#1568979911yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—1881no—
851C4—1881no—
852C4—1881no—
853C4C2×C4×C22⋊D4711yescharacteristic
854C4#1568959611yescharacteristic
855C4D4×C22⋊D4711yescharacteristic
856C4#1568976311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—3761no—
864C2#2024636711yescharacteristic
865C2C2×#1568924211yescharacteristic
866C2#2025229411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC22×#104×C47C2
socleC22×C47C2×C4×D4
prime radical#20252606C2
cosocleC22×C4×C47C24
hypercenterC22×#104D47
hypocenterC47#22886
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#15689242C2semidirect
3. #20252113C2semidirect
4. #20251837C2semidirect
5. #20244278C2semidirect
6. #20244096C2semidirect
7. #20244039C2semidirect
8. #20243831C2semidirect
9. #20243713C2semidirect
10. #20243712C2semidirect
11. #20243661C2semidirect
12. #20243593C2semidirect
13. #20243233C2semidirect
14. #20243150C2semidirect
15. C22×#104×C47C2semidirect
18. C2×#13094032C22semidirect
22. #15689285C4semidirect
23. #15689285C4semidirect
24. #15689279C4semidirect
25. #15689274C4semidirect
26. #15689268C4semidirect
27. #15689268C4semidirect
28. #15689262C4semidirect
29. #15689257C4semidirect
35. C2×#13093959C22semidirect
36. C2×#13093959C22semidirect
37. #15689151C22semidirect
38. C2×#13093952C22semidirect
39. C2×#13093952C22semidirect
42. #15689091C22semidirect
52. #15689081C22semidirect
53. C2×#13093935C22semidirect
54. C2×#13093935C22semidirect
55. #15688887C22semidirect
56. #15688887C22semidirect
57. #15688883C22semidirect
58. #15688883C22semidirect
59. #15688878C22semidirect
60. #15688878C22semidirect
74. C2×#10625337C2×C4semidirect
75. C2×#10625337C2×C4semidirect
76. C2×#10625335C2×C4semidirect
77. C2×#10625335C2×C4semidirect
78. C2×#10625336C2×C4semidirect
79. C2×#10625336C2×C4semidirect
80. C2×#10625334C2×C4semidirect
81. C2×#10625334C2×C4semidirect
115. #13093948C2×C4semidirect
116. #13093948C2×C4semidirect
117. #13093948C2×C4semidirect
118. #13093948C2×C4semidirect
119. #13093945C2×C4semidirect
120. #13093945C2×C4semidirect
121. #13093945C2×C4semidirect
122. #13093945C2×C4semidirect
173. #104×C47D4semidirect
404. C22×C47#444semidirect
427. C22×#104D47semidirect
502. C47#22886semidirect
579. #104C22⋊D47semidirect
840. C22#15689242semidirect

Maximal subgroups

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

subgroupindex
#202526062
C2×#156892422
#202521132
#202518372
#202442782
#202440962
#202440392
#202438312
#202437132
#202437122
#202436612
#202435932
#202432332
#202431502
C22×#104×C472
#2288647