Finite Group Databasebeta

← #25102232

Subgroups — #25102232

Order 11008.

1480 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2C2×#14583059C211yesmaximal, characteristic
3C2×#14582991C211yesmaximal, characteristic, complemented
4C2×#14582984C211yesmaximal, characteristic, complemented
5C22⋊Q8×Dic43C211yesmaximal, characteristic, complemented
6#19134933C211yesmaximal, characteristic, complemented
7#19134926C211yesmaximal, characteristic, complemented
8#19134864C211yesmaximal, characteristic, complemented
9#19134843C211yesmaximal, characteristic, complemented
10#19134794C211yesmaximal, characteristic, complemented
11#19134536C211yesmaximal, characteristic
12#19134414C211yesmaximal, characteristic, complemented
13#19134409C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic43C211yesmaximal, characteristic, complemented
15C43×#1873C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19#14583367—24no—
20#14583367—24no—
21C2×Q8×Dic43C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24C2×#13063287C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×(C22⋊D43)⋊C4—21no—
27C2×(C22⋊D43)⋊C4—21no—
28C2×#13063282—21no—
29C22×C4×Dic43C2211yescharacteristic
30C2×C42×D43—21no—
31#14583059C418yescomplemented
32#14582991—24no—
33#14582984—24no—
34C2×#13063258C2211yescharacteristic
35C2×#13063256C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44C2×C8×Dic43C2211yescharacteristic
45#14582806C2211yescharacteristic
46#14582798C2211yescharacteristic
47#14582785—21no—
48#14582774—21no—
49#14582759C2211yescharacteristic
50C4⋊C4×Dic43—21no—
51C4⋊C4×Dic43C2211yescharacteristic
52C22⋊C4×Dic43—21no—
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×#117×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#103×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—22no—
69C2×#10621898C2×C414yes—
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C23×Dic43D411yescharacteristic
74C23×Dic43D411yescharacteristic
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78C2×#10621885—22no—
79C2×#10621885—22no—
80C2×#10621885C2×C414yescomplemented
81C2×#10621884—22no—
82C2×#10621884—22no—
83C2×#10621884C2×C414yescomplemented
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86Q8×Dic43—22no—
87Q8×Dic43—22no—
88#13063290—22no—
89#13063290—22no—
90#13063290—22no—
91#13063290D414yes—
92#13063287—22no—
93#13063287—22no—
94#13063287—22no—
95#13063287D414yes—
96(C22⋊D43)⋊C4—28no—
97(C22⋊D43)⋊C4—28no—
98#13063282—28no—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×C22⋊Dic43—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—22no—
111C2×C4×Dic43—22no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43D411yescharacteristic
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118C42×D43—28no—
119#13063258—22no—
120#13063256—22no—
121#13063250—22no—
122#13063250—22no—
123#13063248C2×C414yescomplemented
124#13063247—22no—
125#13063247—22no—
126#13063245C2×C414yescomplemented
127C22⋊(C43⋊C8)C2×C414yescomplemented
128C8×Dic43—22no—
129C8×Dic43—22no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×Q8×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22⋊Q8×C43—22no—
140C22⋊Q8×C43C2×C414yescomplemented
141#117×C43—22no—
142#117×C43—22no—
143C2×C4⋊C4×C43—21no—
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C4⋊C4×C43C2311yescharacteristic
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150#103×C43—22no—
151#103×C43—22no—
152C22⋊C8×C43—22no—
153C24×C43C2×D411yescharacteristic
154C23×D43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43C22×C412yes—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43C22×C412yes—
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43#4112yes—
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—24no—
174C2×C22⋊D43—24no—
175C2×C22⋊D43—24no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—41no—
185C22×Dic43C2×D411yescharacteristic
186C22×Dic43C2×D411yescharacteristic
187C22×Dic43C2×D411yescharacteristic
188C22×Dic43C2×D411yescharacteristic
189#10621898—28no—
190#10621898—28no—
191#10621898—28no—
192#10621898—28no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172C22×C412yes—
197C2×D172C2×D412yes—
198C2×D172#4112yes—
199C2×C4×D43—24no—
200C2×C4×D43—24no—
201C2×C4×D43—24no—
202C2×C4×D43—24no—
203C2×C4×D43—24no—
204C2×C4×D43—42no—
205C2×C4×D43—42no—
206C2×C4×D43—42no—
207C2×C4×D43—42no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86—21no—
211C2×Dic86C22×C412yes—
212C2×Dic86C2×D412yes—
213C2×Dic86#4112yes—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C4⋊C4×C43—24no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43C22×C412yes—
225C4⋊C4×C43C2×D412yes—
226C4⋊C4×C43C2×D412yes—
227C22⋊C4×C43—24no—
228C22⋊C4×C43—24no—
229C42×C43—24no—
230C22⋊Dic43—42no—
231#10621885—28no—
232#10621884—28no—
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—42no—
240C4⋊Dic43—42no—
241Dic43⋊C4—24no—
242Dic43⋊C4—24no—
243C4×Dic43—24no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—22no—
247C4×Dic43—24no—
248C4×Dic43—22no—
249C4×Dic43—42no—
250C4×Dic43—42no—
251C4×Dic43C2×D412yes—
252C4×Dic43C2×D412yes—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8—21no—
257C2×C43⋊C8C22×C412yes—
258C2×C43⋊C8C22×C412yes—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43C4×D412yes—
266C23×C43C22×D411yescharacteristic
267C22×D43—22no—
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—41no—
273C22×D43—41no—
274Q8×C43—22no—
275Q8×C43—22no—
276Q8×C43—41no—
277Q8×C43—41no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43C4×D412yes—
297C2×C4×C43C23×C411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C22⋊D43—216no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—44no—
315C2×Dic43—44no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43#12012yes—
323C2×Dic43#12012yes—
324C2×Dic43#13512yes—
325C2×Dic43#13512yes—
326C2×Dic43#13712yes—
327D172—22no—
328D172—22no—
329D172—22no—
330D172C4×D414yes—
331C4×D43—216no—
332C4×D43—48no—
333C4×D43—48no—
334Dic86—22no—
335Dic86—22no—
336Dic86—22no—
337Dic86C4×D414yes—
338C8×C43—41no—
339C8×C43—41no—
340C43⋊C8—22no—
341C43⋊C8—22no—
342C4×#452—431nomaximal, Sylow
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43C2×C4×D411yescharacteristic
351C22×C43C2×#12011yescharacteristic
352C22×C43#52511yescharacteristic
353C22×C43C2×#13511yescharacteristic
354C22×C43C2×#13511yescharacteristic
355C22×C43C2×#13711yescharacteristic
356C22×C43#57511yescharacteristic
357C2×D43—24no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C4×C43—22no—
365C4×C43—42no—
366C4×C43—42no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43C2×C4×D411yescharacteristic
370C4×C43C2×C4×D411yescharacteristic
371C4×C43#52511yescharacteristic
372C4×C43#52511yescharacteristic
373Dic43—22no—
374Dic43—22no—
375Dic43—24no—
376Dic43—41no—
377Dic43—81no—
378Dic43—81no—
379Dic43#45214yescomplemented
380C2×C4×#41—431no—
381C2×#452—431no—
382C2×C4×Q16—431no—
383C2×C4×SD16—431no—
384C4×C22⋊Q8—431no—
385#1878—431no—
386#1877—431no—
387#1873D4311yescharacteristic, complemented
388#1865—431no—
389#1862—431no—
390#1854—431no—
391#1788—431no—
392C4×#103—431no—
393C4×#102—431no—
394C4×C22⋊C8—431no—
395C2×C43—42no—
396C2×C43C4×#12011yescharacteristic
397C2×C43C4×#13511yescharacteristic
398C2×C43C4×#13711yescharacteristic
399C2×C43C2×#45211yescharacteristic
400C2×C43#300211yescharacteristic
401C2×C43#310211yescharacteristic
402C2×C43#310711yescharacteristic
403D43—44no—
404C22×#41—431no—
405C22×Q16—431no—
406C22×SD16—431no—
407C2×C22⋊Q8C2×D4311yescharacteristic
408C4×#41—864no—
409C4×#41—864no—
410C2×C4×Q8—431no—
411C2×C4×Q8—431no—
412C2×C4×Q8—431no—
413C2×C4×D4—431no—
414C2×C4×D4—431no—
415C2×C4×D4—861no—
416C2×C4×D4—861no—
417C2×#117—861no—
418C2×#117C2×D4311yescharacteristic
419C22×C42—431no—
420C22×C42—861no—
421#452—438no—
422C4×Q16—864no—
423C4×SD16—864no—
424C2×#107—431no—
425C2×#106—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#103—431no—
429C2×#103C2×D4311yescharacteristic
430C2×#103C2×D4311yescharacteristic
431C2×#102—431no—
432C2×#102—431no—
433C2×#102—431no—
434C2×C22⋊C8—431no—
435C2×C22⋊C8C2×D4311yescharacteristic
436C2×C4×C8—431no—
437C2×C4×C8—431no—
438#391—431no—
439#389—431no—
440#387—861no—
441#385—861no—
442#380—431no—
443C4×C4⋊C4—431no—
444C4×C4⋊C4—861no—
445C4×C22⋊C4—861no—
446#340—431no—
447#340—431no—
448#340C2×D4311yescharacteristic
449#340C2×D4311yescharacteristic
450#336—431no—
451#336—431no—
452C43C4×#45211yescharacteristic, complemented, Sylow
453C2×#41—434no—
454C2×#41—862no—
455C2×#41—862no—
456C2×#41—862no—
457C2×#41—862no—
458C2×#41—862no—
459C22×Q8—431no—
460C22×Q8C22×D4311yescharacteristic
461C22×D4—431no—
462C22×D4—861no—
463C23×C4—431no—
464C23×C4—431no—
465C23×C4—861no—
466C23×C4—861no—
467C23×C4—861no—
468C23×C4C22×D4311yescharacteristic
469C2×Q16—434no—
470C2×Q16—862no—
471C2×Q16—862no—
472C2×SD16—434no—
473C2×SD16—862no—
474C2×SD16—862no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479C22⋊Q8—22no—
480C22⋊Q8C4×D4314yescomplemented
481C4×Q8—434no—
482C4×Q8—862no—
483C4×Q8—862no—
484C4×Q8—862no—
485C4×Q8—862no—
486C4×Q8—862no—
487C4×D4—434no—
488C4×D4—862no—
489C4×D4—868no—
490C4×D4—868no—
491C4×D4—862no—
492C4×D4—862no—
493#117—22no—
494#117—22no—
495#117—868no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—431no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C22×D4311yescharacteristic
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C42—21no—
512C2×C42—431no—
513C2×C42—431no—
514C2×C42—431no—
515C2×C42—431no—
516C2×C42—868no—
517C2×C42—862no—
518C2×C42—862no—
519C2×C42—861no—
520C2×C42—861no—
521C2×C42—861no—
522C2×C42—861no—
523#107—862no—
524#106—862no—
525#103—22no—
526#103—22no—
527#103—434no—
528#103—862no—
529#103—862no—
530#102—434no—
531#102—862no—
532#102—862no—
533C22⋊C8—22no—
534C22⋊C8—434no—
535C4×C8—862no—
536C4×C8—862no—
537#95—861no—
538#95—861no—
539#95—861no—
540#95—861no—
541#95—861no—
542C24—861no—
543C24D4×D4311yescharacteristic
544#41—868no—
545#41—868no—
546#41—868no—
547#41—868no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—432no—
554C2×Q8—432no—
555C2×Q8—432no—
556C2×Q8—861no—
557C2×Q8—861no—
558C2×Q8—861no—
559C2×Q8C2×C4×D4312yes—
560C2×D4—432no—
561C2×D4—432no—
562C2×D4—432no—
563C2×D4—864no—
564C2×D4—864no—
565C2×D4—864no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—861no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—864no—
582C22×C4—864no—
583C22×C4—864no—
584C22×C4—864no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—861no—
591C22×C4—864no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—1722no—
595C22×C4—1722no—
596C22×C4—1722no—
597C22×C4—1722no—
598C22×C4—1721no—
599C22×C4C2×C4×D4312yes—
600C22×C4D4×D4311yescharacteristic
601C22×C4#1062190012yes—
602C22×C4C23×D4311yescharacteristic
603Q16—868no—
604SD16—868no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—432no—
612C2×C8—432no—
613C2×C8—861no—
614C2×C8—861no—
615C2×C8—861no—
616C2×C8—861no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—864no—
622C4⋊C4—864no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—861no—
626C4⋊C4—861no—
627C4⋊C4—1722no—
628C4⋊C4—1722no—
629C4⋊C4C2×C4×D4312yes—
630C4⋊C4D4×D4312yes—
631C4⋊C4D4×D4312yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—864no—
635C22⋊C4—864no—
636C22⋊C4—1722no—
637C42—24no—
638C42—432no—
639C42—432no—
640C42—862no—
641C42—862no—
642C42—864no—
643C42—864no—
644C42—861no—
645C42—861no—
646C42—1722no—
647C42—1722no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—862no—
655C23—862no—
656C23—862no—
657C23—1721no—
658C23—1721no—
659C23—1721no—
660C23—1721no—
661C23(C22⋊D43)⋊C412yes—
662C23C2×D4×D4311yescharacteristic
663Q8—22no—
664Q8—22no—
665Q8—41no—
666Q8—41no—
667Q8—434no—
668Q8—862no—
669Q8—862no—
670Q8—862no—
671D4—434no—
672D4—8616no—
673D4—862no—
674D4—862no—
675D4—862no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—432no—
695C2×C4—432no—
696C2×C4—432no—
697C2×C4—432no—
698C2×C4—432no—
699C2×C4—8616no—
700C2×C4—862no—
701C2×C4—861no—
702C2×C4—862no—
703C2×C4—862no—
704C2×C4—861no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—1728no—
711C2×C4—1728no—
712C2×C4—1724no—
713C2×C4—1724no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4(C22⋊D43)⋊C412yes—
721C2×C4C22×C4×D4311yescharacteristic
722C2×C4C2×D4×D4311yescharacteristic
723C2×C4C2×D4×D4311yescharacteristic
724C2×C4#41×D4311yescharacteristic
725C2×C4#41×D4311yescharacteristic
726C2×C4C2×#1062190011yescharacteristic
727C8—41no—
728C8—41no—
729C8—862no—
730C8—862no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—864no—
739C22—1722no—
740C22—1722no—
741C22—1722no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22C2×(C22⋊D43)⋊C411yescharacteristic
746C22#120×D4311yescharacteristic
747C22#1458340711yescharacteristic
748C22#135×D4311yescharacteristic
749C22#135×D4311yescharacteristic
750C22#137×D4311yescharacteristic
751C22#1458369811yescharacteristic
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—434no—
758C4—864no—
759C4—862no—
760C4—862no—
761C4—3441no—
762C4—3441no—
763C4—1721no—
764C4C4×D4×D4311yescharacteristic
765C4C4×D4×D4311yescharacteristic
766C4#1458340911yescharacteristic
767C4#1458340911yescharacteristic
768C2—42no—
769C2—1724no—
770C2#1913710011yescharacteristic
771C2#1914336311yescharacteristic
772C2#1914341011yescharacteristic
773C2#452×D4311yescharacteristic
774C2#1914381611yescharacteristic
775C2#1914461611yescharacteristic
776C2#1914466111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1873C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1873D43
hypocenterC43C4×#452
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
3. C2×#14582991C2semidirect
4. C2×#14582984C2semidirect
5. C22⋊Q8×Dic43C2semidirect
6. #19134933C2semidirect
7. #19134926C2semidirect
8. #19134864C2semidirect
9. #19134843C2semidirect
10. #19134794C2semidirect
12. #19134414C2semidirect
13. #19134409C2semidirect
14. C22⋊C8×Dic43C2semidirect
15. C43×#1873C2semidirect
31. #14583059C4semidirect
80. C2×#10621885C2×C4semidirect
83. C2×#10621884C2×C4semidirect
123. #13063248C2×C4semidirect
126. #13063245C2×C4semidirect
127. C22⋊(C43⋊C8)C2×C4semidirect
140. C22⋊Q8×C43C2×C4semidirect
379. Dic43#452semidirect
387. #1873D43semidirect
452. C43C4×#452semidirect
480. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
C2×#145830592
C2×#145829912
C2×#145829842
C22⋊Q8×Dic432
#191349332
#191349262
#191348642
#191348432
#191347942
#191345362
#191344142
#191344092
C22⋊C8×Dic432
C43×#18732
C4×#45243