Finite Group Databasebeta

← #25117330

Subgroups — #25117330

Order 11008.

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#19143813C211yesmaximal, characteristic
2C2×#14583019C211yesmaximal, characteristic, complemented
3#19143316C211yesmaximal, characteristic, complemented
4C22×#13063252C211yesmaximal, characteristic, complemented
5#19135487C211yesmaximal, characteristic, complemented
6#19135309C211yesmaximal, characteristic, complemented
7#19135240C211yesmaximal, characteristic, complemented
8#19135036C211yesmaximal, characteristic, complemented
9#19134925C211yesmaximal, characteristic, complemented
10#19134922C211yesmaximal, characteristic, complemented
11#19134870C211yesmaximal, characteristic, complemented
12#19134799C211yesmaximal, characteristic, complemented
13#19134437C211yesmaximal, characteristic, complemented
14#19134359C211yesmaximal, characteristic, complemented
15C43×#2880C211yesmaximal, characteristic, complemented
16C2×#13063345C2211yescharacteristic
17C2×#13063345C2211yescharacteristic
18C2×#13063331C2211yescharacteristic, complemented
19C22×#10621877C2211yescharacteristic
20#14583410C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14583061C411yescharacteristic, complemented
23#14583061C411yescharacteristic, complemented
24#14583055C411yescharacteristic, complemented
25#14583050C411yescharacteristic, complemented
26#14583044C411yescharacteristic, complemented
27#14583044C411yescharacteristic, complemented
28#14583038C411yescharacteristic, complemented
29#14583033C411yescharacteristic, complemented
30#14583019—24no—
31#14582974—21no—
32#14582973—21no—
33#14582967—21no—
34(C22⋊D43)⋊C8—21no—
35C2×#13063260C2211yescharacteristic, complemented
36C2×#13063260C2211yescharacteristic, complemented
37#14582925C2211yescharacteristic, complemented
38C2×#13063252—24no—
39C2×#13063252C2211yescharacteristic
40C2×#13063252C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42C2×#13063252C2211yescharacteristic
43C2×#13063251C2211yescharacteristic, complemented
44C2×#13063251C2211yescharacteristic, complemented
45#14582895C2211yescharacteristic
46#14582895C2211yescharacteristic
47#14582865C2211yescharacteristic, complemented
48C2×C22⋊(C43⋊C8)C2211yescharacteristic
49#14582854C2211yescharacteristic, complemented
50C2×#13063235C2211yescharacteristic, complemented
51C2×#13063235C2211yescharacteristic, complemented
52#14582663C2211yescharacteristic, complemented
53#14582663C2211yescharacteristic, complemented
54#14582660C2211yescharacteristic, complemented
55#14582660C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57#14582653C2211yescharacteristic, complemented
58C22×#41×C43C2211yescharacteristic
59C2×#131×C43C2211yescharacteristic
60C2×#131×C43C2211yescharacteristic
61C43×#408—21no—
62C43×#408—21no—
63C43×#408C2211yescharacteristic
64C43×#408C2211yescharacteristic
65C43×#407—21no—
66C43×#407C2211yescharacteristic
67C2×C22⋊C8×C43—21no—
68C2×C22⋊C8×C43C2211yescharacteristic
69C2×#10621898C2311yescharacteristic
70C23×Dic43—21no—
71#13063345—22no—
72#13063345—22no—
73#13063345—41no—
74#13063345—41no—
75C2×#10621885C2×C411yescharacteristic, complemented
76C2×#10621885C2×C411yescharacteristic, complemented
77C2×#10621883C2×C411yescharacteristic, complemented
78C2×#10621883C2×C411yescharacteristic, complemented
79C2×#10621884C2×C411yescharacteristic, complemented
80C2×#10621884C2×C411yescharacteristic, complemented
81C2×#10621882C2×C411yescharacteristic, complemented
82C2×#10621882C2×C411yescharacteristic, complemented
83#13063331—22no—
84#13063331—41no—
85C2×#10621877—21no—
86C2×#10621877—22no—
87C2×#10621877—41no—
88C2×#10621877C2311yescharacteristic
89C2×#10621877C2311yescharacteristic
90C2×#10621872—21no—
91C22×C43⋊C8—21no—
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94C2×C8×D43—21no—
95#13063308—21no—
96#13063304C2×C411yescharacteristic
97#13063304C2×C411yescharacteristic
98#13063299C2×C411yescharacteristic
99#13063299C2×C411yescharacteristic
100#13063294—21no—
101C4×C22⋊D43—21no—
102C4×C22⋊D43—21no—
103#13063284C2311yescharacteristic
104C2×C4×Dic43—22no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—41no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109#13063260—22no—
110#13063260—41no—
111Dic43⋊C8—21no—
112Dic43⋊C8—21no—
113#13063252—22no—
114#13063252—22no—
115#13063252—22no—
116#13063252D414yescomplemented
117#13063251—22no—
118#13063251—41no—
119#13063249C2×C411yescharacteristic, complemented
120#13063249C2×C411yescharacteristic, complemented
121#13063249C2×C411yescharacteristic, complemented
122#13063249C2×C411yescharacteristic, complemented
123#13063246C2×C411yescharacteristic, complemented
124#13063246C2×C411yescharacteristic, complemented
125#13063246C2×C411yescharacteristic, complemented
126#13063246C2×C411yescharacteristic, complemented
127C22⋊(C43⋊C8)C2×C411yescharacteristic
128C22⋊(C43⋊C8)C2×C411yescharacteristic
129C22⋊(C43⋊C8)C2×C411yescharacteristic
130C22⋊(C43⋊C8)C2×C411yescharacteristic
131(C2×D43)⋊C8—21no—
132(C2×D43)⋊C8—21no—
133#13063235—21no—
134#13063235—22no—
135#13063235—41no—
136C8×Dic43—21no—
137C2×#41×C43—21no—
138C2×#41×C43—21no—
139C2×#41×C43—22no—
140C2×#41×C43—22no—
141C2×#41×C43—41no—
142C2×#41×C43—41no—
143C2×#41×C43C2×C411yescharacteristic
144C2×#41×C43C2×C411yescharacteristic
145C2×#41×C43C2311yescharacteristic
146C2×#41×C43C2311yescharacteristic
147C22×Q8×C43C2×C411yescharacteristic
148C22×D4×C43—21no—
149C22×D4×C43C2×C411yescharacteristic
150C23×C4×C43—21no—
151C23×C4×C43C2311yescharacteristic
152#131×C43—22no—
153#131×C43—22no—
154#131×C43—41no—
155#131×C43—41no—
156C2×M16×C43—21no—
157C2×M16×C43—21no—
158C2×M16×C43C2311yescharacteristic
159C2×M16×C43C2311yescharacteristic
160C22×C8×C43—21no—
161C22×C8×C43—21no—
162C22×C8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22⋊C8×C43—21no—
165C22⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C22⋊C8×C43—21no—
168C22⋊C8×C43—21no—
169C22⋊C8×C43—21no—
170C22⋊C8×C43D411yescharacteristic
171C22⋊C8×C43D411yescharacteristic
172C22⋊C8×C43D411yescharacteristic
173C22⋊C8×C43D411yescharacteristic
174C24×C43—21no—
175C24×C43#4111yescharacteristic
176#41×C43—21no—
177#41×C43—21no—
178#41×C43—22no—
179#41×C43—22no—
180#41×C43—21no—
181#41×C43—21no—
182#41×C43—21no—
183#41×C43—21no—
184#41×C43—42no—
185#41×C43—42no—
186#41×C43—41no—
187#41×C43—41no—
188#41×C43—42no—
189#41×C43—42no—
190#41×C43C2×D412yes—
191#41×C43#4112yes—
192C2×Q8×C43—21no—
193C2×Q8×C43—22no—
194C2×Q8×C43—41no—
195C2×Q8×C43C22×C411yescharacteristic
196C2×Q8×C43C22×C411yescharacteristic
197C2×D4×C43—21no—
198C2×D4×C43—21no—
199C2×D4×C43—21no—
200C2×D4×C43—21no—
201C2×D4×C43—21no—
202C2×D4×C43—22no—
203C2×D4×C43—42no—
204C2×D4×C43—42no—
205C2×D4×C43—41no—
206C2×D4×C43C22×C411yescharacteristic
207C2×D4×C43C22×C411yescharacteristic
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—42no—
218C22×C4×C43—42no—
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43#4111yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—42no—
231C22×Dic43—42no—
232C22×Dic43—42no—
233#10621898—21no—
234#10621898—21no—
235#10621898—21no—
236#10621898—21no—
237C2×D172C22×C411yescharacteristic
238C2×C4×D43—21no—
239C2×Dic86C22×C411yescharacteristic
240M16×C43—21no—
241M16×C43—21no—
242M16×C43—21no—
243M16×C43—21no—
244M16×C43—42no—
245M16×C43—42no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—21no—
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—42no—
253C2×C8×C43—42no—
254C2×C8×C43C2×D411yescharacteristic
255C2×C8×C43C2×D411yescharacteristic
256C2×C8×C43C2×D411yescharacteristic
257C2×C8×C43C2×D411yescharacteristic
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261#10621885—22no—
262#10621885—41no—
263#10621884—22no—
264#10621884—41no—
265#10621883—22no—
266#10621883—41no—
267#10621882—22no—
268#10621882—41no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271C4⋊Dic43C22×C411yescharacteristic
272C4⋊Dic43C22×C411yescharacteristic
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—42no—
280C4×Dic43C2×D412yes—
281#10621877—21no—
282#10621877—21no—
283#10621877—21no—
284#10621877—42no—
285#10621877C2×D412yes—
286C2×C43⋊C8—21no—
287C2×C43⋊C8—21no—
288C2×C43⋊C8—21no—
289C2×C43⋊C8—21no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—42no—
293C2×C43⋊C8C22×C411yescharacteristic
294C2×C43⋊C8C22×C411yescharacteristic
295C2×C43⋊C8C22×C411yescharacteristic
296C2×C43⋊C8C22×C411yescharacteristic
297#10621872—42no—
298C8×D43—42no—
299C23×C43—21no—
300C23×C43—21no—
301C23×C43—21no—
302C23×C43—22no—
303C23×C43—21no—
304C23×C43—41no—
305C23×C43—42no—
306C23×C43—42no—
307C23×C43—81no—
308C23×C43C4×D411yescharacteristic
309C23×C43C4×D411yescharacteristic
310C23×C43C2×#4111yescharacteristic
311C22×D43—21no—
312Q8×C43—21no—
313Q8×C43—21no—
314Q8×C43—21no—
315Q8×C43—42no—
316Q8×C43C4×D412yes—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—21no—
320D4×C43—21no—
321D4×C43—21no—
322D4×C43—42no—
323D4×C43—42no—
324D4×C43—42no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43C4×D412yes—
328C2×C4×C43—21no—
329C2×C4×C43—21no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—42no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43C4×D411yescharacteristic
348C2×C4×C43C4×D411yescharacteristic
349C2×C4×C43C23×C411yescharacteristic
350C2×C4×C43C22×D411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C2×#4111yescharacteristic
353C2×C4×C43H(5,𝔽2)11yescharacteristic
354C2×C4×C43H(5,𝔽2)11yescharacteristic
355C22⋊D43—41no—
356C22⋊D43—41no—
357C22⋊D43—42no—
358C22⋊D43—81no—
359C2×Dic43—22no—
360C2×Dic43—21no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—22no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—48no—
368C2×Dic43—41no—
369D172—21no—
370D172—21no—
371C4×D43—41no—
372C4×D43—41no—
373Dic86—21no—
374Dic86—21no—
375C8×C43—21no—
376C8×C43—21no—
377C8×C43—21no—
378C8×C43—21no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—21no—
382C43⋊C8—21no—
383C43⋊C8—21no—
384C43⋊C8—21no—
385C43⋊C8—22no—
386C43⋊C8—41no—
387#22886—431nomaximal, Sylow
388C22×C43—21no—
389C22×C43—21no—
390C22×C43—21no—
391C22×C43—21no—
392C22×C43—21no—
393C22×C43—22no—
394C22×C43—21no—
395C22×C43—21no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—84no—
404C22×C43#44412yescomplemented
405C22×C43C2×C4×D411yescharacteristic
406C22×C43#54611yescharacteristic
407C22×C43#55111yescharacteristic
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—22no—
414C4×C43—41no—
415C4×C43C2×C4×D411yescharacteristic
416C4×C43#51811yescharacteristic
417C4×C43D4211yescharacteristic
418C4×C43#54611yescharacteristic
419Dic43—42no—
420Dic43—42no—
421Dic43—41no—
422Dic43—41no—
423Dic43—41no—
424#3002—431no—
425C2×#444—431no—
426#2933—431no—
427C22×#104—431no—
428#2880D4311yescharacteristic, complemented
429#1975—431no—
430#1938—431no—
431#1929—431no—
432#1896—431no—
433#1876—431no—
434#1876—431no—
435#1866—431no—
436#1855—431no—
437#1765—431no—
438#1749—431no—
439C2×C43—21no—
440C2×C43—22no—
441C2×C43—21no—
442C2×C43—41no—
443C2×C43—42no—
444C2×C43—81no—
445C2×C43#235811yescharacteristic
446C2×C43C2×#44411yescharacteristic
447C2×C43#295611yescharacteristic
448D43—81no—
449C22×#41C2×D4311yescharacteristic
450C2×#135—431no—
451C2×#135—431no—
452C2×#131—431no—
453C2×#131C2×D4311yescharacteristic
454C2×#131C2×D4311yescharacteristic
455C22×M16—431no—
456#525—431no—
457C22×C42—431no—
458#452—431no—
459#452—431no—
460#451—431no—
461#450—431no—
462#449—431no—
463#449—431no—
464#448—431no—
465#447—431no—
466#444—864no—
467#436—861no—
468#435—861no—
469#435—861no—
470C8×D4—861no—
471C2×#108—431no—
472C2×#108—431no—
473#424—431no—
474C2×#104—431no—
475C2×#104—431no—
476C2×#104—431no—
477C2×#104—431no—
478C2×#104—431no—
479C2×#104—431no—
480C2×#104—864no—
481#416—431no—
482#416—431no—
483#408—21no—
484#408—21no—
485#408—431no—
486#408C2×D4311yescharacteristic
487#408C2×D4311yescharacteristic
488#407—21no—
489#407C2×D4311yescharacteristic
490C2×C22⋊C8—21no—
491C2×C22⋊C8—431no—
492C2×C22⋊C8C2×D4311yescharacteristic
493#405—431no—
494C2×#97—431no—
495C2×#97—431no—
496#341—431no—
497#341—431no—
498#339—431no—
499#339—431no—
500#336—431no—
501#336—431no—
502C43#2288611yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—431no—
510C2×#41C4×D4311yescharacteristic
511C2×#41C4×D4311yescharacteristic
512C2×#41C22×D4311yescharacteristic
513C2×#41C22×D4311yescharacteristic
514C22×Q8C4×D4311yescharacteristic
515C22×D4—21no—
516C22×D4C4×D4311yescharacteristic
517C23×C4—21no—
518C23×C4—861no—
519C23×C4C22×D4311yescharacteristic
520#135—862no—
521#135—862no—
522#135—1721no—
523#135—1721no—
524C2×Q16—431no—
525C2×Q16—431no—
526C2×SD16—431no—
527C2×SD16—431no—
528C2×SD16—431no—
529C2×SD16—431no—
530C2×D8—431no—
531C2×D8—431no—
532#131—22no—
533#131—22no—
534#131—41no—
535#131—41no—
536#131—862no—
537#131—1721no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—431no—
541C2×M16—431no—
542C2×M16—861no—
543C2×M16—861no—
544C2×M16—862no—
545C2×M16—1721no—
546C2×M16C22×D4311yescharacteristic
547C2×M16C22×D4311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—431no—
551C22×C8—431no—
552C22×C8—861no—
553C22×C8—861no—
554C22×C8C22×D4311yescharacteristic
555C22×C8C22×D4311yescharacteristic
556#123—861no—
557C22⋊Q8—431no—
558C22⋊Q8—431no—
559#121—431no—
560#121—431no—
561#120—861no—
562C4×D4—861no—
563C4×D4—861no—
564#117—431no—
565C2×C42—431no—
566C2×C42—431no—
567C2×C42—862no—
568C2×C42—861no—
569C2×C42—1721no—
570#108—862no—
571#108—1721no—
572C4⋊C8—861no—
573C4⋊C8—861no—
574#104—434no—
575#104—862no—
576#104—862no—
577#104—862no—
578#104—862no—
579#104—1721no—
580#103—431no—
581#103—431no—
582#103—431no—
583#103—431no—
584#102—431no—
585#102—431no—
586#102—431no—
587#102—431no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—431no—
595C22⋊C8—431no—
596C22⋊C8—431no—
597C22⋊C8—431no—
598C22⋊C8—861no—
599C22⋊C8—861no—
600C22⋊C8C22⋊D4311yescharacteristic
601C22⋊C8C22⋊D4311yescharacteristic
602C22⋊C8C22⋊D4311yescharacteristic
603C22⋊C8C22⋊D4311yescharacteristic
604#97—862no—
605#97—861no—
606#97—1721no—
607C4×C8—861no—
608C24—21no—
609C24#1062189811yescharacteristic
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—861no—
625#41—861no—
626#41—861no—
627#41—861no—
628#41D4×D4312yes—
629#41#1062190012yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—431no—
634C2×Q8C2×C4×D4311yescharacteristic
635C2×Q8C2×C4×D4311yescharacteristic
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—431no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4C2×C4×D4311yescharacteristic
650C2×D4C2×C4×D4311yescharacteristic
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—42no—
661C22×C4—42no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4—1722no—
668C22×C4C2×C4×D4311yescharacteristic
669C22×C4C2×C4×D4311yescharacteristic
670C22×C4#1062189811yescharacteristic
671C22×C4C2×C22⋊D4311yescharacteristic
672C22×C4C2×C22⋊D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674Q16—862no—
675Q16—1721no—
676SD16—862no—
677SD16—862no—
678SD16—1721no—
679SD16—1721no—
680D8—862no—
681D8—1721no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—42no—
687M16—42no—
688M16—432no—
689M16—861no—
690M16—861no—
691M16—861no—
692M16—1722no—
693M16—1722no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—431no—
703C2×C8—431no—
704C2×C8—431no—
705C2×C8—431no—
706C2×C8—861no—
707C2×C8—861no—
708C2×C8—861no—
709C2×C8—861no—
710C2×C8—861no—
711C2×C8—861no—
712C2×C8—1722no—
713C2×C8—1722no—
714C2×C8C2×C22⋊D4311yescharacteristic
715C2×C8C2×C22⋊D4311yescharacteristic
716C2×C8C2×C22⋊D4311yescharacteristic
717C2×C8C2×C22⋊D4311yescharacteristic
718C4⋊C4—431no—
719C4⋊C4—431no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C42—432no—
728C42—861no—
729C42—861no—
730C42—861no—
731C42—861no—
732C42—1722no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—861no—
743C23C4×C22⋊D4311yescharacteristic
744C23C4×C22⋊D4311yescharacteristic
745C23C2×#1062189811yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—861no—
751Q8—861no—
752Q8(C22⋊D43)⋊C412yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—861no—
764D4—861no—
765D4—3441no—
766D4—1721no—
767D4—1722no—
768D4—1721no—
769D4(C22⋊D43)⋊C412yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—862no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—862no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1728no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4C4×C22⋊D4311yescharacteristic
802C2×C4C4×C22⋊D4311yescharacteristic
803C2×C4C22×C4×D4311yescharacteristic
804C2×C4C2×D4×D4311yescharacteristic
805C2×C4C22×C22⋊D4311yescharacteristic
806C2×C4C2×#1062190011yescharacteristic
807C2×C4#1306337011yescharacteristic
808C2×C4#1306337011yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—861no—
816C8—861no—
817C8—861no—
818C8—861no—
819C8—862no—
820C8—1721no—
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—1721no—
838C22—1721no—
839C22—1721no—
840C22#1458301912yescomplemented
841C22C2×C4×C22⋊D4311yescharacteristic
842C22#1458353911yescharacteristic
843C22#1458357511yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—1722no—
849C4—1722no—
850C4—1721no—
851C4—1721no—
852C4—1721no—
853C4C2×(C22⋊D43)⋊C411yescharacteristic
854C4#1458337211yescharacteristic
855C4D4×C22⋊D4311yescharacteristic
856C4#1458354311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—3441no—
864C2#1913757411yescharacteristic
865C2C2×#1458301911yescharacteristic
866C2#1914350211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2880C2
socleC22×C43C2×C4×D4
prime radical#19143813C2
cosocleC22×C4×C43C24
hypercenter#2880D43
hypocenterC43#22886
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#14583019C2semidirect
3. #19143316C2semidirect
4. C22×#13063252C2semidirect
5. #19135487C2semidirect
6. #19135309C2semidirect
7. #19135240C2semidirect
8. #19135036C2semidirect
9. #19134925C2semidirect
10. #19134922C2semidirect
11. #19134870C2semidirect
12. #19134799C2semidirect
13. #19134437C2semidirect
14. #19134359C2semidirect
15. C43×#2880C2semidirect
18. C2×#13063331C22semidirect
22. #14583061C4semidirect
23. #14583061C4semidirect
24. #14583055C4semidirect
25. #14583050C4semidirect
26. #14583044C4semidirect
27. #14583044C4semidirect
28. #14583038C4semidirect
29. #14583033C4semidirect
35. C2×#13063260C22semidirect
36. C2×#13063260C22semidirect
37. #14582925C22semidirect
43. C2×#13063251C22semidirect
44. C2×#13063251C22semidirect
47. #14582865C22semidirect
49. #14582854C22semidirect
50. C2×#13063235C22semidirect
51. C2×#13063235C22semidirect
52. #14582663C22semidirect
53. #14582663C22semidirect
54. #14582660C22semidirect
55. #14582660C22semidirect
56. #14582653C22semidirect
57. #14582653C22semidirect
75. C2×#10621885C2×C4semidirect
76. C2×#10621885C2×C4semidirect
77. C2×#10621883C2×C4semidirect
78. C2×#10621883C2×C4semidirect
79. C2×#10621884C2×C4semidirect
80. C2×#10621884C2×C4semidirect
81. C2×#10621882C2×C4semidirect
82. C2×#10621882C2×C4semidirect
116. #13063252D4semidirect
119. #13063249C2×C4semidirect
120. #13063249C2×C4semidirect
121. #13063249C2×C4semidirect
122. #13063249C2×C4semidirect
123. #13063246C2×C4semidirect
124. #13063246C2×C4semidirect
125. #13063246C2×C4semidirect
126. #13063246C2×C4semidirect
404. C22×C43#444semidirect
428. #2880D43semidirect
502. C43#22886semidirect
840. C22#14583019semidirect

Maximal subgroups

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

subgroupindex
#191438132
C2×#145830192
#191433162
C22×#130632522
#191354872
#191353092
#191352402
#191350362
#191349252
#191349222
#191348702
#191347992
#191344372
#191343592
C43×#28802
#2288643