Finite Group Databasebeta

← #25107991

Subgroups — #25107991

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143815C211yesmaximal, characteristic
2#19143288C211yesmaximal, characteristic, complemented
3#408×D43C211yesmaximal, characteristic, complemented
4#19135483C211yesmaximal, characteristic, complemented
5#19135482C211yesmaximal, characteristic, complemented
6#19135298C211yesmaximal, characteristic, complemented
7#19135245C211yesmaximal, characteristic, complemented
8#19135241C211yesmaximal, characteristic, complemented
9#19134923C211yesmaximal, characteristic, complemented
10#19134919C211yesmaximal, characteristic, complemented
11#19134896C211yesmaximal, characteristic, complemented
12#19134801C211yesmaximal, characteristic, complemented
13#19134537C211yesmaximal, characteristic, complemented
14C8×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C43×#1937C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063347C2211yescharacteristic
18C2×#13063345C2211yescharacteristic
19C2×#13063333C2211yescharacteristic, complemented
20C2×M16×D43C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583411C2211yescharacteristic
23#14583064C411yescharacteristic, complemented
24#14583062C411yescharacteristic, complemented
25#14583056C411yescharacteristic, complemented
26#14583051C411yescharacteristic, complemented
27#14583047C411yescharacteristic, complemented
28#14583045C411yescharacteristic, complemented
29#14583039C411yescharacteristic, complemented
30#14583034C411yescharacteristic, complemented
31#14582969—21no—
32#14582969—21no—
33#14582964—21no—
34#14582964—21no—
35C2×#13063261C2211yescharacteristic, complemented
36C2×#13063260C2211yescharacteristic, complemented
37C2×#13063253C2211yescharacteristic
38C2×#13063253C2211yescharacteristic, complemented
39C2×#13063252C2211yescharacteristic
40C2×#13063251C2211yescharacteristic
41C2×#13063251C2211yescharacteristic, complemented
42#14582893C2211yescharacteristic
43#14582867C2211yescharacteristic
44#14582866C2211yescharacteristic
45#14582865C2211yescharacteristic
46#14582865C2211yescharacteristic, complemented
47#14582864—21no—
48#14582864—21no—
49#14582862C2211yescharacteristic
50C2×(C2×D43)⋊C8C2211yescharacteristic
51C22⋊C8×D43—21no—
52C22⋊C8×D43—21no—
53#14582855C2211yescharacteristic, complemented
54C2×C8×Dic43C2211yescharacteristic, complemented
55C4×(C2×D43)⋊C4C2211yescharacteristic
56#14582663C2211yescharacteristic, complemented
57#14582658C2211yescharacteristic, complemented
58#14582654C2211yescharacteristic, complemented
59#14582653C2211yescharacteristic, complemented
60C43×#424C2211yescharacteristic, complemented
61C2×#104×C43C2211yescharacteristic
62C43×#416C2211yescharacteristic
63C43×#408C2211yescharacteristic
64C2×C4×C8×C43C2211yescharacteristic, complemented
65C43×#341C2211yescharacteristic, complemented
66C43×#339C2211yescharacteristic, complemented
67C2×#10621902C2×C411yescharacteristic
68C2×#10621898—21no—
69C2×#10621898C2311yescharacteristic
70C2×#10621898C2311yescharacteristic
71C2×#10621900—21no—
72C2×#10621900C2×C411yescharacteristic
73#41×D43—41no—
74#41×D43—41no—
75#41×D43—41no—
76#41×D43—41no—
77C2×Q8×D43C2×C411yescharacteristic
78C2×D4×D43—21no—
79C2×D4×D43C2×C411yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43C2311yescharacteristic
82#13063347—41no—
83#13063347—41no—
84#13063345—41no—
85#13063345—41no—
86C2×Dic172C2×C411yescharacteristic
87C2×#10621885C2×C411yescharacteristic
88C2×#10621873C2×C411yescharacteristic
89C2×#10621873C2×C411yescharacteristic
90C2×#10621883C2×C411yescharacteristic
91C2×#10621884C2×C411yescharacteristic
92C2×D344C2×C411yescharacteristic
93C2×#10621882C2×C411yescharacteristic
94#13063333—41no—
95#13063333—41no—
96C2×#10621877C2311yescharacteristic
97C2×#10621877C2311yescharacteristic
98C2×#10621872—21no—
99C2×#10621872—21no—
100M16×D43—41no—
101M16×D43—41no—
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C2×C8×D43—21no—
105C2×C8×D43—21no—
106C2×C8×D43—41no—
107C2×C8×D43—41no—
108C2×C8×D43D411yescharacteristic
109C2×C8×D43D411yescharacteristic
110C2×C8×D43D411yescharacteristic
111C2×C8×D43D411yescharacteristic
112#13063309—21no—
113#13063305C2×C411yescharacteristic
114#13063305C2×C411yescharacteristic
115#13063300C2×C411yescharacteristic
116#13063300C2×C411yescharacteristic
117#13063295—21no—
118C4×D172—21no—
119C4×D172—21no—
120C2×(C2×D43)⋊C4—21no—
121C2×C4×Dic43C2311yescharacteristic
122#13063261—41no—
123#13063260—41no—
124#13063253—41no—
125#13063253—41no—
126#13063252—41no—
127#13063251—41no—
128#13063251—41no—
129#13063248C2×C411yescharacteristic
130#13063248C2×C411yescharacteristic
131#13063245C2×C411yescharacteristic
132#13063245C2×C411yescharacteristic
133C22⋊(C43⋊C8)—21no—
134C22⋊(C43⋊C8)—21no—
135(C2×D43)⋊C8—21no—
136(C2×D43)⋊C8—21no—
137(C2×D43)⋊C8—21no—
138(C2×D43)⋊C8—21no—
139(C2×D43)⋊C8—21no—
140(C2×D43)⋊C8—21no—
141(C2×D43)⋊C8—21no—
142(C2×D43)⋊C8—21no—
143(C2×D43)⋊C8C2×C411yescharacteristic
144(C2×D43)⋊C8C2×C411yescharacteristic
145(C2×D43)⋊C8C2×C411yescharacteristic
146(C2×D43)⋊C8C2×C411yescharacteristic
147#13063236—21no—
148C4×C43⋊C8—21no—
149C8×Dic43—41no—
150C43⋊#95—21no—
151C2×#41×C43C2311yescharacteristic
152C2×M16×C43C2311yescharacteristic
153C2×M16×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C22×C8×C43C2311yescharacteristic
156#117×C43C2311yescharacteristic
157C2×C42×C43C2311yescharacteristic
158C4⋊C8×C43—21no—
159C4⋊C8×C43—21no—
160#104×C43—41no—
161#103×C43C2×C411yescharacteristic
162#103×C43C2×C411yescharacteristic
163#102×C43C2×C411yescharacteristic
164#102×C43C2×C411yescharacteristic
165C22⋊C8×C43—21no—
166C22⋊C8×C43—21no—
167C4×C8×C43—41no—
168C23×D43—21no—
169C23×D43#4111yescharacteristic
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—21no—
173#41×C43—21no—
174C2×Q8×C43C22×C411yescharacteristic
175C2×D4×C43—21no—
176C2×D4×C43C22×C411yescharacteristic
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43C2411yescharacteristic
180C2×C22⋊D43—21no—
181C2×C22⋊D43—21no—
182C2×C22⋊D43—21no—
183C2×C22⋊D43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43#4111yescharacteristic
187#10621902—41no—
188#10621902—41no—
189Q8×D43—41no—
190Q8×D43—41no—
191#10621900—41no—
192#10621900—41no—
193#10621900—42no—
194#10621900—42no—
195D4×D43—42no—
196D4×D43—42no—
197D4×D43—41no—
198D4×D43—41no—
199#10621898—21no—
200#10621898—21no—
201#10621898—21no—
202#10621898—21no—
203#10621898—21no—
204#10621898—21no—
205#10621898—21no—
206#10621898—21no—
207#10621898—42no—
208#10621898—42no—
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172C22×C411yescharacteristic
213C2×D172C22×C411yescharacteristic
214C2×C4×D43—21no—
215C2×C4×D43—21no—
216C2×C4×D43—21no—
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—42no—
223C2×C4×D43—42no—
224C2×C4×D43C22×C411yescharacteristic
225C2×C4×D43C22×C411yescharacteristic
226C2×C4×D43C2×D411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×Dic86—21no—
229C2×Dic86C22×C411yescharacteristic
230C2×Dic86C22×C411yescharacteristic
231M16×C43—21no—
232M16×C43—21no—
233M16×C43—21no—
234M16×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43C22×C411yescharacteristic
242C2×C8×C43C22×C411yescharacteristic
243C2×C8×C43C2×D411yescharacteristic
244C2×C8×C43C2×D411yescharacteristic
245C4⋊C4×C43C22×C411yescharacteristic
246C4⋊C4×C43C22×C411yescharacteristic
247C22⋊C4×C43—21no—
248C42×C43—21no—
249C42×C43—21no—
250C42×C43—21no—
251#10621885—41no—
252#10621884—41no—
253#10621883—41no—
254#10621882—41no—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4×Dic43—21no—
263C4×Dic43—21no—
264#10621877—21no—
265#10621877—21no—
266#10621877—21no—
267#10621877—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8C22×C411yescharacteristic
275C2×C43⋊C8C22×C411yescharacteristic
276C2×C43⋊C8C2×D411yescharacteristic
277C2×C43⋊C8C2×D411yescharacteristic
278Dic172—41no—
279D344—41no—
280#10621873—41no—
281#10621873—41no—
282#10621872—42no—
283#10621872—42no—
284C8×D43—41no—
285C8×D43—41no—
286C8×D43—41no—
287C8×D43—41no—
288C8×D43—42no—
289C8×D43—42no—
290C23×C43—21no—
291C23×C43C2×#4111yescharacteristic
292C22×D43—21no—
293C22×D43—21no—
294C22×D43—22no—
295C22×D43—21no—
296C22×D43—21no—
297C22×D43—41no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43C4×D411yescharacteristic
302C22×D43C4×D411yescharacteristic
303Q8×C43—21no—
304Q8×C43—21no—
305D4×C43—21no—
306D4×C43—21no—
307D4×C43—41no—
308D4×C43—41no—
309C2×C4×C43—22no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43C23×C411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C2×C4×C43H(5,𝔽2)11yescharacteristic
322C2×C4×C43H(5,𝔽2)11yescharacteristic
323C22⋊D43—42no—
324C22⋊D43—42no—
325C22⋊D43—41no—
326C22⋊D43—41no—
327C22⋊D43—41no—
328C22⋊D43—41no—
329C2×Dic43—21no—
330C2×Dic43—21no—
331C2×Dic43—22no—
332C2×Dic43—21no—
333C2×Dic43—21no—
334C2×Dic43—42no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43C4×D411yescharacteristic
338C2×Dic43C4×D411yescharacteristic
339D172—21no—
340D172—21no—
341D172—21no—
342D172—21no—
343D172—42no—
344D172—42no—
345D172—42no—
346C4×D43—21no—
347C4×D43—21no—
348C4×D43—21no—
349C4×D43—21no—
350C4×D43—21no—
351C4×D43—21no—
352C4×D43—21no—
353C4×D43—21no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43—41no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43—41no—
360Dic86—21no—
361Dic86—21no—
362Dic86—21no—
363Dic86—21no—
364Dic86—42no—
365C8×C43—21no—
366C8×C43—21no—
367C8×C43—21no—
368C8×C43—21no—
369C8×C43—41no—
370C8×C43—41no—
371C43⋊C8—21no—
372C43⋊C8—21no—
373C43⋊C8—21no—
374C43⋊C8—21no—
375C43⋊C8—41no—
376C43⋊C8—41no—
377#22060—431nomaximal, Sylow
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43C2×C4×D411yescharacteristic
384C22×C43#53811yescharacteristic
385C22×C43#53811yescharacteristic
386C2×D43—21no—
387C2×D43—21no—
388C2×D43—21no—
389C2×D43—21no—
390C2×D43—21no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—41no—
394C2×D43—41no—
395C2×D43—41no—
396C2×D43—41no—
397C2×D43—41no—
398C2×D43—41no—
399C2×D43—84no—
400C2×D43#44312yes—
401C4×C43—42no—
402C4×C43—41no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43#51811yescharacteristic
406C4×C43#51811yescharacteristic
407C4×C43#53411yescharacteristic
408C4×C43#53511yescharacteristic
409Dic43—21no—
410Dic43—21no—
411Dic43—42no—
412Dic43—41no—
413Dic43—41no—
414#3002—431no—
415#2929—431no—
416C2×#408—431no—
417#1974—431no—
418#1974—431no—
419#1937—431no—
420#1937D4311yescharacteristic, complemented
421#1929—431no—
422#1929—431no—
423#1876—431no—
424#1876—431no—
425#1871—431no—
426#1855—431no—
427#1789—431no—
428C8×C22⋊C4—431no—
429C2×C43—21no—
430C2×C43—21no—
431C2×C43—81no—
432C2×C43#232111yescharacteristic
433C2×C43C2×#44311yescharacteristic
434C2×C43#295511yescharacteristic
435D43—22no—
436D43—41no—
437D43—81no—
438D43—81no—
439C22×#41—431no—
440C2×#135—431no—
441C2×#135—431no—
442C2×#131—431no—
443C22×M16—431no—
444C23×C8—431no—
445#525—431no—
446#452—431no—
447#452—431no—
448#451—431no—
449#450—431no—
450#449—431no—
451#449—431no—
452#448—431no—
453#447—431no—
454#435—861no—
455#435—861no—
456C8×D4—861no—
457C8×D4—861no—
458C2×#108—431no—
459C2×#108—431no—
460#424C2×D4311yescharacteristic, complemented
461C2×#104—431no—
462C2×#104—431no—
463C2×#104—431no—
464C2×#104—431no—
465C2×#104—431no—
466C2×#104C2×D4311yescharacteristic
467#416—431no—
468#416C2×D4311yescharacteristic
469#408—431no—
470#408—431no—
471#408—431no—
472#408—431no—
473#408—861no—
474#408—861no—
475#408C2×D4311yescharacteristic
476#407—431no—
477C2×C22⋊C8—431no—
478C2×C22⋊C8—861no—
479C2×C22⋊C8—861no—
480#405—431no—
481C2×C4×C8—431no—
482C2×C4×C8C2×D4311yescharacteristic, complemented
483C4×C22⋊C4—431no—
484#341—431no—
485#341C2×D4311yescharacteristic, complemented
486#339—431no—
487#339C2×D4311yescharacteristic, complemented
488#336—431no—
489#336—431no—
490C43#2206011yescharacteristic, complemented, Sylow
491C2×#41—431no—
492C2×#41—431no—
493C2×#41—431no—
494C2×#41—431no—
495C2×#41—861no—
496C2×#41—861no—
497C2×#41—1721no—
498C2×#41—1721no—
499C2×#41—1721no—
500C2×#41—1721no—
501C2×#41C22×D4311yescharacteristic
502C22×Q8—431no—
503C22×D4—431no—
504C22×D4—861no—
505C23×C4—431no—
506C23×C4—861no—
507#135—1721no—
508#135—1721no—
509#135—1721no—
510#135—1721no—
511C2×Q16—431no—
512C2×Q16—431no—
513C2×SD16—431no—
514C2×SD16—431no—
515C2×SD16—431no—
516C2×SD16—431no—
517C2×D8—431no—
518C2×D8—431no—
519#131—1721no—
520#131—1721no—
521C2×M16—431no—
522C2×M16—431no—
523C2×M16—861no—
524C2×M16—861no—
525C2×M16—1721no—
526C2×M16—1721no—
527C2×M16C22×D4311yescharacteristic
528C2×M16C22×D4311yescharacteristic
529C22×C8—431no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—431no—
533C22×C8—431no—
534C22×C8—431no—
535C22×C8—861no—
536C22×C8—861no—
537C22×C8—1721no—
538C22×C8—1721no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
541#123—861no—
542C22⋊Q8—431no—
543C22⋊Q8—431no—
544#121—431no—
545#121—431no—
546#120—861no—
547C4×D4—861no—
548C4×D4—861no—
549#117C22×D4311yescharacteristic
550C2×C22⋊C4—861no—
551C2×C42—431no—
552C2×C42C22×D4311yescharacteristic
553#108—1721no—
554#108—1721no—
555C4⋊C8—21no—
556C4⋊C8—21no—
557#104—41no—
558#104—1721no—
559#104—1721no—
560#104—1721no—
561#104—1721no—
562#104—1721no—
563#103—431no—
564#103—431no—
565#103C4×D4311yescharacteristic
566#103C4×D4311yescharacteristic
567#102—431no—
568#102—431no—
569#102C4×D4311yescharacteristic
570#102C4×D4311yescharacteristic
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—431no—
574C22⋊C8—431no—
575C22⋊C8—431no—
576C22⋊C8—431no—
577C22⋊C8—861no—
578C22⋊C8—861no—
579C22⋊C8—861no—
580C22⋊C8—861no—
581C22⋊C8—861no—
582C22⋊C8—861no—
583C22⋊C8—861no—
584C22⋊C8—861no—
585C22⋊C8—861no—
586C22⋊C8—861no—
587#97—861no—
588C4×C8—41no—
589C4×C8—861no—
590C4×C8—1721no—
591#95—861no—
592C24—431no—
593C24—861no—
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—861no—
599#41—861no—
600#41—861no—
601#41—861no—
602#41—861no—
603#41—861no—
604#41—861no—
605#41—861no—
606#41—1722no—
607#41—1722no—
608#41—1721no—
609#41—1721no—
610#41—1722no—
611#41—1722no—
612#41—1721no—
613#41—1721no—
614C2×Q8—431no—
615C2×Q8—431no—
616C2×Q8—861no—
617C2×Q8—1721no—
618C2×Q8—1721no—
619C2×Q8C2×C4×D4311yescharacteristic
620C2×D4—21no—
621C2×D4—431no—
622C2×D4—431no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—1721no—
631C2×D4—1721no—
632C2×D4—1722no—
633C2×D4—1722no—
634C2×D4C2×C4×D4311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—431no—
638C22×C4—431no—
639C22×C4—431no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—861no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—861no—
650C22×C4—861no—
651C22×C4—861no—
652C22×C4—1722no—
653C22×C4—1722no—
654C22×C4C23×D4311yescharacteristic
655Q16—1721no—
656Q16—1721no—
657SD16—1721no—
658SD16—1721no—
659SD16—1721no—
660SD16—1721no—
661D8—1721no—
662D8—1721no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—861no—
668M16—861no—
669M16—861no—
670M16—861no—
671M16—1722no—
672M16—1722no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—431no—
680C2×C8—431no—
681C2×C8—431no—
682C2×C8—431no—
683C2×C8—861no—
684C2×C8—861no—
685C2×C8—861no—
686C2×C8—861no—
687C2×C8—861no—
688C2×C8—861no—
689C2×C8—1721no—
690C2×C8—1721no—
691C2×C8—1721no—
692C2×C8—1721no—
693C2×C8—1722no—
694C2×C8—1722no—
695C2×C8C2×C4×D4311yescharacteristic
696C2×C8C2×C4×D4311yescharacteristic
697C2×C8D4×D4311yescharacteristic
698C2×C8D4×D4311yescharacteristic
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4C2×C4×D4311yescharacteristic
702C4⋊C4C2×C4×D4311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—861no—
705C22⋊C4—861no—
706C22⋊C4—861no—
707C22⋊C4—861no—
708C22⋊C4—864no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—861no—
713C42—861no—
714C23—21no—
715C23—431no—
716C23—431no—
717C23—862no—
718C23—861no—
719C23—861no—
720C23—861no—
721C23—861no—
722C23—1721no—
723C23—1722no—
724C23—1722no—
725C23—1722no—
726C23#41×D4311yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—861no—
730Q8—861no—
731Q8—861no—
732Q8—861no—
733Q8—1722no—
734D4—21no—
735D4—21no—
736D4—41no—
737D4—41no—
738D4—861no—
739D4—861no—
740D4—861no—
741D4—861no—
742D4—1722no—
743D4—1722no—
744D4—1722no—
745D4—1722no—
746D4—1722no—
747D4—1721no—
748D4—1721no—
749D4—1721no—
750D4—1721no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—431no—
760C2×C4—431no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—861no—
765C2×C4—861no—
766C2×C4—861no—
767C2×C4—861no—
768C2×C4—861no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—862no—
772C2×C4—861no—
773C2×C4—861no—
774C2×C4—1722no—
775C2×C4—1722no—
776C2×C4—1722no—
777C2×C4—1721no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4C22×C4×D4311yescharacteristic
784C2×C4C2×D4×D4311yescharacteristic
785C2×C4#1306337011yescharacteristic
786C2×C4#1306337111yescharacteristic
787C2×C4#1306337111yescharacteristic
788C2×C4#1306337111yescharacteristic
789C8—21no—
790C8—21no—
791C8—21no—
792C8—21no—
793C8—41no—
794C8—41no—
795C8—861no—
796C8—861no—
797C8—861no—
798C8—861no—
799C8—1721no—
800C8—1721no—
801C22—21no—
802C22—21no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—432no—
807C22—861no—
808C22—861no—
809C22—861no—
810C22—861no—
811C22—861no—
812C22—3444no—
813C22—1722no—
814C22—1722no—
815C22—1721no—
816C22—1721no—
817C22—1721no—
818C22—1721no—
819C22—1721no—
820C22—1721no—
821C22C4×D4×D4311yescharacteristic
822C22#1458348511yescharacteristic
823C22#1458348811yescharacteristic
824C4—42no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—861no—
829C4—861no—
830C4—1722no—
831C4—1721no—
832C4—1721no—
833C4#1458337111yescharacteristic
834C4#1458337311yescharacteristic
835C4#1458345711yescharacteristic
836C4#1458346711yescharacteristic
837C2—21no—
838C2—21no—
839C2—81no—
840C2—862no—
841C2—3441no—
842C2—3441no—
843C2—1721no—
844C2#1913724811yescharacteristic
845C2#443×D4311yescharacteristic
846C2#1914349311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1937C2
socleC22×C43C2×C4×D4
prime radical#19143815C2
cosocleC22×C4×C43C24
hypercenter#1937D43
hypocenterC43#22060
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1937

Complements

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

NH ≅ G/Ntype
2. #19143288C2semidirect
3. #408×D43C2semidirect
4. #19135483C2semidirect
5. #19135482C2semidirect
6. #19135298C2semidirect
7. #19135245C2semidirect
8. #19135241C2semidirect
9. #19134923C2semidirect
10. #19134919C2semidirect
11. #19134896C2semidirect
12. #19134801C2semidirect
13. #19134537C2semidirect
14. C8×(C2×D43)⋊C4C2semidirect
15. C43×#1937C2semidirect
19. C2×#13063333C22semidirect
23. #14583064C4semidirect
24. #14583062C4semidirect
25. #14583056C4semidirect
26. #14583051C4semidirect
27. #14583047C4semidirect
28. #14583045C4semidirect
29. #14583039C4semidirect
30. #14583034C4semidirect
35. C2×#13063261C22semidirect
36. C2×#13063260C22semidirect
38. C2×#13063253C22semidirect
41. C2×#13063251C22semidirect
46. #14582865C22semidirect
53. #14582855C22semidirect
54. C2×C8×Dic43C22semidirect
56. #14582663C22semidirect
57. #14582658C22semidirect
58. #14582654C22semidirect
59. #14582653C22semidirect
60. C43×#424C22semidirect
64. C2×C4×C8×C43C22semidirect
65. C43×#341C22semidirect
66. C43×#339C22semidirect
420. #1937D43semidirect
460. #424C2×D43semidirect
482. C2×C4×C8C2×D43semidirect
485. #341C2×D43semidirect
487. #339C2×D43semidirect
490. C43#22060semidirect

Maximal subgroups

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

subgroupindex
#191438152
#191432882
#408×D432
#191354832
#191354822
#191352982
#191352452
#191352412
#191349232
#191349192
#191348962
#191348012
#191345372
C8×(C2×D43)⋊C42
C43×#19372
#2206043