Finite Group Databasebeta

← C43×#61484 #24981501

Subgroups — C43×#61484 #24981501

Order 11008.

1750 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3523C212yesmaximal
2C43×#3395C211yesmaximal, characteristic, complemented
3C43×#3383C211yesmaximal, characteristic, complemented
4C43×#3374C212yesmaximal, complemented
5C43×#3342C211yesmaximal, characteristic, complemented
6C43×#3336C212yesmaximal, complemented
7C43×#3328C212yesmaximal, complemented
8C43×#3312C214yesmaximal, complemented
9D4×Q16×C43C212yesmaximal, complemented
10D4×Q16×C43C211yesmaximal, characteristic, complemented
11C43×#3177C212yesmaximal, complemented
12C43×#3170C211yesmaximal, characteristic, complemented
13C43×#3127C214yesmaximal, complemented
14C43×#3113C212yesmaximal, complemented
15C43×#2966C211yesmaximal, characteristic
16C43×#2950C212yesmaximal, complemented
17C2×C4×Q16×C43C211yesmaximal, characteristic, complemented
18C22×Q16×C43C2211yescharacteristic
19C22×Q16×C43C2212yes—
20C43×#557—22no—
21C43×#557C2212yes—
22C43×#557C2212yes—
23C43×#556—22no—
24C43×#556C2212yes—
25C43×#552—24no—
26C43×#552C2214yes—
27D4×Q8×C43C2214yes—
28D4×Q8×C43C2212yes—
29C43×#541—24no—
30C43×#541C2214yes—
31C43×#533—22no—
32C43×#533C2212yes—
33C43×#529—22no—
34C43×#529C2211yescharacteristic
35C43×#519C2214yes—
36C2×C4×Q8×C43C2212yes—
37C43×#500C2211yescharacteristic
38C43×#499C2212yes—
39C43×#494C2211yescharacteristic
40C43×#494C2212yes—
41C43×#491C2214yes—
42C43×#487C2212yes—
43C43×#485C2214yes—
44C43×#485C2214yes—
45C43×#483C2214yes—
46C43×#479C2214yes—
47C43×#479C2214yes—
48C43×#475C2212yes—
49C43×#475C2212yes—
50C43×#470C2214yes—
51C43×#467C2212yes—
52C43×#467C2212yes—
53C43×#467C2212yes—
54C43×#467C2212yes—
55C43×#462C2212yes—
56C43×#462C2212yes—
57C43×#462C2214yes—
58C43×#462C2214yes—
59C43×#451C2214yes—
60C43×#451C2214yes—
61C43×#451C2214yes—
62C43×#446C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#441C2214yes—
65C43×#441C2214yes—
66C43×#441C2214yes—
67C4×Q16×C43C2212yes—
68C4×Q16×C43C2212yes—
69C4×Q16×C43C2212yes—
70C4×Q16×C43C2211yescharacteristic
71C4×Q16×C43C2212yes—
72C4×Q16×C43C2211yescharacteristic
73C4×Q16×C43C2212yes—
74C4×Q16×C43C2212yes—
75C4×Q16×C43C2211yescharacteristic
76C4×Q16×C43C2211yescharacteristic
77C43×#436C2211yescharacteristic
78C43×#435C2212yes—
79C8×D4×C43C2212yes—
80C8×D4×C43C2211yescharacteristic
81C43×#433C2212yes—
82C43×#432C2211yescharacteristic
83C43×#427C2212yes—
84C2×#107×C43C2211yescharacteristic
85C43×#419C2214yes—
86C2×#103×C43C2212yes—
87C43×#405C2212yes—
88C2×C4×C8×C43C2211yescharacteristic
89C22×Q8×C43C2312yes—
90C22×Q8×C43C2314yes—
91C2×Q16×C43—24no—
92C2×Q16×C43—28no—
93C2×Q16×C43C2312yes—
94C2×Q16×C43C2311yescharacteristic
95C2×Q16×C43C2312yes—
96C2×Q16×C43C2314yes—
97C2×Q16×C43C2312yes—
98C2×Q16×C43C2314yes—
99C2×Q16×C43C2311yescharacteristic
100C2×M16×C43C2312yes—
101C22×C8×C43C2311yescharacteristic
102C22×C8×C43C2312yes—
103C22×C8×C43C2311yescharacteristic
104C4⋊Q8×C43—22no—
105C4⋊Q8×C43—22no—
106C4⋊Q8×C43—24no—
107C4⋊Q8×C43C2312yes—
108C4⋊Q8×C43C2314yes—
109C4⋊Q8×C43C2312yes—
110#126×C43—24no—
111#126×C43—24no—
112#126×C43—24no—
113#126×C43—24no—
114#126×C43D412yes—
115#125×C43—22no—
116#125×C43—24no—
117#125×C43—24no—
118#125×C43—24no—
119#125×C43—24no—
120#125×C43—24no—
121#125×C43—22no—
122#125×C43D411yescharacteristic
123#125×C43C2314yes—
124#124×C43—22no—
125#124×C43D411yescharacteristic
126#123×C43—24no—
127#123×C43D412yes—
128C22⋊Q8×C43—22no—
129C22⋊Q8×C43—24no—
130C22⋊Q8×C43—24no—
131C22⋊Q8×C43—24no—
132C22⋊Q8×C43D411yescharacteristic
133C22⋊Q8×C43C2314yes—
134C22⋊Q8×C43C2314yes—
135C22⋊Q8×C43C2314yes—
136#121×C43D411yescharacteristic
137C4×Q8×C43—22no—
138C4×Q8×C43—24no—
139C4×Q8×C43—24no—
140C4×Q8×C43—22no—
141C4×Q8×C43—22no—
142C4×Q8×C43—22no—
143C4×Q8×C43—22no—
144C4×Q8×C43—22no—
145C4×Q8×C43C2312yes—
146C4×Q8×C43C2312yes—
147C4×Q8×C43C2312yes—
148C4×Q8×C43C2312yes—
149C4×Q8×C43C2314yes—
150C4×Q8×C43C2314yes—
151C4×Q8×C43C2314yes—
152C4×Q8×C43C2311yescharacteristic
153C4×D4×C43—24no—
154C4×D4×C43—22no—
155C4×D4×C43C2312yes—
156C4×D4×C43C2311yescharacteristic
157#117×C43—22no—
158#117×C43—24no—
159#117×C43—24no—
160#117×C43—24no—
161#117×C43C2314yes—
162#117×C43C2312yes—
163C2×C4⋊C4×C43—22no—
164C2×C4⋊C4×C43C2312yes—
165C2×C42×C43—22no—
166C2×C42×C43C2311yescharacteristic
167#107×C43C2311yescharacteristic
168#107×C43C2312yes—
169#107×C43C2312yes—
170#107×C43C2311yescharacteristic
171#107×C43C2312yes—
172#106×C43C2314yes—
173#106×C43C2314yes—
174C4⋊C8×C43C2311yescharacteristic
175C4⋊C8×C43C2311yescharacteristic
176C4⋊C8×C43C2312yes—
177C4⋊C8×C43C2312yes—
178#103×C43C2312yes—
179#103×C43C2312yes—
180#103×C43C2312yes—
181#103×C43C2312yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#103×C43C2314yes—
185#103×C43C2314yes—
186#103×C43C2314yes—
187#103×C43C2314yes—
188C22⋊C8×C43C2312yes—
189C22⋊C8×C43C2312yes—
190C22⋊C8×C43C2312yes—
191#97×C43C2312yes—
192#97×C43C2312yes—
193C4×C8×C43C2312yes—
194C4×C8×C43C2311yescharacteristic
195C4×C8×C43C2311yescharacteristic
196C4×C8×C43C2311yescharacteristic
197C4×C8×C43C2311yescharacteristic
198C2×Q8×C43—22no—
199C2×Q8×C43—24no—
200C2×Q8×C43—22no—
201C2×Q8×C43—24no—
202C2×Q8×C43—28no—
203C2×Q8×C43—42no—
204C2×Q8×C43—44no—
205C2×Q8×C43C2×D411yescharacteristic
206C2×Q8×C43C2412yes—
207C2×Q8×C43C2414yes—
208C2×Q8×C43C2412yes—
209C2×D4×C43C2×D412yes—
210C2×D4×C43C2×D411yescharacteristic
211C22×C4×C43—22no—
212C22×C4×C43—22no—
213C22×C4×C43—24no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C22×C4×C43C2412yes—
218Q16×C43—24no—
219Q16×C43—28no—
220Q16×C43—22no—
221Q16×C43—24no—
222Q16×C43—42no—
223Q16×C43—44no—
224Q16×C43#4114yes—
225M16×C43—42no—
226C2×C8×C43—22no—
227C2×C8×C43—24no—
228C2×C8×C43—41no—
229C2×C8×C43C2411yescharacteristic
230C2×C8×C43C2411yescharacteristic
231C2×C8×C43C2411yescharacteristic
232C2×C8×C43C2412yes—
233C2×C8×C43C2412yes—
234C2×C8×C43C2411yescharacteristic
235C4⋊C4×C43—22no—
236C4⋊C4×C43—22no—
237C4⋊C4×C43—22no—
238C4⋊C4×C43—22no—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—22no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—22no—
248C4⋊C4×C43—24no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43—24no—
251C4⋊C4×C43—24no—
252C4⋊C4×C43—24no—
253C4⋊C4×C43C2×D412yes—
254C4⋊C4×C43C2×D412yes—
255C4⋊C4×C43C2×D411yescharacteristic
256C4⋊C4×C43C2×D412yes—
257C4⋊C4×C43C2×D411yescharacteristic
258C4⋊C4×C43C2×D412yes—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2414yes—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—24no—
266C22⋊C4×C43C2×D412yes—
267C22⋊C4×C43C2×D412yes—
268C22⋊C4×C43C2×D412yes—
269C22⋊C4×C43C2×D412yes—
270C22⋊C4×C43C2×D412yes—
271C42×C43—22no—
272C42×C43—22no—
273C42×C43—22no—
274C42×C43—22no—
275C42×C43—24no—
276C42×C43—24no—
277C42×C43—24no—
278C42×C43—24no—
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2411yescharacteristic
282C42×C43C2411yescharacteristic
283C42×C43C2412yes—
284C23×C43C22×D412yes—
285C23×C43C22×D411yescharacteristic
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—24no—
290Q8×C43—24no—
291Q8×C43—22no—
292Q8×C43—44no—
293Q8×C43—48no—
294Q8×C43—44no—
295Q8×C43C2×#4114yes—
296D4×C43—24no—
297D4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—21no—
302C2×C4×C43—22no—
303C2×C4×C43—21no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—24no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—44no—
311C2×C4×C43—48no—
312C2×C4×C43—44no—
313C2×C4×C43C22×D411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2511yescharacteristic
322C8×C43—21no—
323C8×C43—22no—
324C8×C43—21no—
325C8×C43—21no—
326C8×C43—22no—
327C8×C43C2×#4112yes—
328#61484C4311yesmaximal, characteristic, direct product factor, Sylow
329C22×C43—21no—
330C22×C43—21no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43#57812yes—
335C22×C43C23×D411yescharacteristic
336C4×C43—21no—
337C4×C43—22no—
338C4×C43—24no—
339C4×C43—21no—
340C4×C43—21no—
341C4×C43—21no—
342C4×C43—22no—
343C4×C43—22no—
344C4×C43—42no—
345C4×C43—44no—
346C4×C43—42no—
347C4×C43—42no—
348C4×C43—44no—
349C4×C43#57812yes—
350C4×C43C22×#4111yescharacteristic
351C4×C43#58511yescharacteristic
352#3523C2×C4312yes—
353#3395C2×C4311yescharacteristic, complemented
354#3383C2×C4311yescharacteristic, complemented
355#3374C2×C4312yescomplemented
356#3342C2×C4311yescharacteristic, complemented
357#3336C2×C4312yescomplemented
358#3328C2×C4312yescomplemented
359#3312C2×C4314yescomplemented
360D4×Q16C2×C4311yescharacteristic, complemented
361D4×Q16C2×C4312yescomplemented
362#3177C2×C4312yescomplemented
363#3170C2×C4311yescharacteristic, complemented
364#3127C2×C4314yescomplemented
365#3113C2×C4312yescomplemented
366#2966C2×C4311yescharacteristic
367#2950C2×C4312yescomplemented
368C2×C4×Q16C2×C4311yescharacteristic, complemented
369C2×C43—22no—
370C2×C43—42no—
371C2×C43D4×#4111yescharacteristic
372C2×C43C2×#57811yescharacteristic
373C2×C43C2×#57811yescharacteristic
374C22×Q16C22×C4311yescharacteristic
375C22×Q16C22×C4312yes—
376#557—22no—
377#557C22×C4312yes—
378#557C22×C4312yes—
379#556—22no—
380#556C22×C4312yes—
381#552—24no—
382#552C22×C4314yes—
383D4×Q8C22×C4312yes—
384D4×Q8C22×C4314yes—
385#541—24no—
386#541C22×C4314yes—
387#533—22no—
388#533C22×C4312yes—
389#529—22no—
390#529C22×C4311yescharacteristic
391#519C22×C4314yes—
392C2×C4×Q8C22×C4312yes—
393#500C22×C4311yescharacteristic
394#499C22×C4312yes—
395#494C22×C4311yescharacteristic
396#494C22×C4312yes—
397#491C22×C4314yes—
398#487C22×C4312yes—
399#485C22×C4314yes—
400#485C22×C4314yes—
401#483C22×C4314yes—
402#479C22×C4314yes—
403#479C22×C4314yes—
404#475C22×C4312yes—
405#475C22×C4312yes—
406#470C22×C4314yes—
407#467C22×C4312yes—
408#467C22×C4312yes—
409#467C22×C4312yes—
410#467C22×C4312yes—
411#462C22×C4312yes—
412#462C22×C4312yes—
413#462C22×C4314yes—
414#462C22×C4314yes—
415#451C22×C4314yes—
416#451C22×C4314yes—
417#451C22×C4314yes—
418#446C22×C4311yescharacteristic
419C8×Q8C22×C4311yescharacteristic
420#441C22×C4314yes—
421#441C22×C4314yes—
422#441C22×C4314yes—
423C4×Q16C22×C4312yes—
424C4×Q16C22×C4312yes—
425C4×Q16C22×C4311yescharacteristic
426C4×Q16C22×C4312yes—
427C4×Q16C22×C4312yes—
428C4×Q16C22×C4311yescharacteristic
429C4×Q16C22×C4312yes—
430C4×Q16C22×C4312yes—
431C4×Q16C22×C4311yescharacteristic
432C4×Q16C22×C4311yescharacteristic
433#436C22×C4311yescharacteristic
434#435C22×C4312yes—
435C8×D4C22×C4312yes—
436C8×D4C22×C4311yescharacteristic
437#433C22×C4312yes—
438#432C22×C4311yescharacteristic
439#427C22×C4312yes—
440C2×#107C22×C4311yescharacteristic
441#419C22×C4314yes—
442C2×#103C22×C4312yes—
443#405C22×C4312yes—
444C2×C4×C8C22×C4311yescharacteristic
445C43#6148411yescharacteristic, direct product factor, Sylow
446C22×Q8C23×C4312yes—
447C22×Q8C23×C4314yes—
448C2×Q16—24no—
449C2×Q16—28no—
450C2×Q16C23×C4312yes—
451C2×Q16C23×C4311yescharacteristic
452C2×Q16C23×C4312yes—
453C2×Q16C23×C4314yes—
454C2×Q16C23×C4312yes—
455C2×Q16C23×C4314yes—
456C2×Q16C23×C4311yescharacteristic
457C2×M16C23×C4312yes—
458C22×C8C23×C4311yescharacteristic
459C22×C8C23×C4312yes—
460C22×C8C23×C4311yescharacteristic
461C4⋊Q8—22no—
462C4⋊Q8—22no—
463C4⋊Q8—24no—
464C4⋊Q8C23×C4312yes—
465C4⋊Q8C23×C4314yes—
466C4⋊Q8C23×C4312yes—
467#126—24no—
468#126—24no—
469#126—24no—
470#126—24no—
471#126D4×C4312yes—
472#125—22no—
473#125—24no—
474#125—24no—
475#125—24no—
476#125—24no—
477#125—24no—
478#125—22no—
479#125D4×C4311yescharacteristic
480#125C23×C4314yes—
481#124—22no—
482#124D4×C4311yescharacteristic
483#123—24no—
484#123D4×C4312yes—
485C22⋊Q8—22no—
486C22⋊Q8—24no—
487C22⋊Q8—24no—
488C22⋊Q8—24no—
489C22⋊Q8D4×C4311yescharacteristic
490C22⋊Q8C23×C4314yes—
491C22⋊Q8C23×C4314yes—
492C22⋊Q8C23×C4314yes—
493#121D4×C4311yescharacteristic
494C4×Q8—22no—
495C4×Q8—24no—
496C4×Q8—24no—
497C4×Q8—22no—
498C4×Q8—22no—
499C4×Q8—22no—
500C4×Q8—22no—
501C4×Q8—22no—
502C4×Q8C23×C4312yes—
503C4×Q8C23×C4312yes—
504C4×Q8C23×C4312yes—
505C4×Q8C23×C4312yes—
506C4×Q8C23×C4314yes—
507C4×Q8C23×C4314yes—
508C4×Q8C23×C4314yes—
509C4×Q8C23×C4311yescharacteristic
510C4×D4—24no—
511C4×D4—22no—
512C4×D4C23×C4312yes—
513C4×D4C23×C4311yescharacteristic
514#117—22no—
515#117—24no—
516#117—24no—
517#117—24no—
518#117C23×C4314yes—
519#117C23×C4312yes—
520C2×C4⋊C4—22no—
521C2×C4⋊C4C23×C4312yes—
522C2×C42—22no—
523C2×C42C23×C4311yescharacteristic
524#107C23×C4311yescharacteristic
525#107C23×C4311yescharacteristic
526#107C23×C4312yes—
527#107C23×C4312yes—
528#107C23×C4312yes—
529#106C23×C4314yes—
530#106C23×C4314yes—
531C4⋊C8C23×C4311yescharacteristic
532C4⋊C8C23×C4311yescharacteristic
533C4⋊C8C23×C4312yes—
534C4⋊C8C23×C4312yes—
535#103C23×C4312yes—
536#103C23×C4312yes—
537#103C23×C4312yes—
538#103C23×C4312yes—
539#103C23×C4314yes—
540#103C23×C4314yes—
541#103C23×C4314yes—
542#103C23×C4314yes—
543#103C23×C4314yes—
544#103C23×C4314yes—
545C22⋊C8C23×C4312yes—
546C22⋊C8C23×C4312yes—
547C22⋊C8C23×C4312yes—
548#97C23×C4312yes—
549#97C23×C4312yes—
550C4×C8C23×C4311yescharacteristic
551C4×C8C23×C4311yescharacteristic
552C4×C8C23×C4311yescharacteristic
553C4×C8C23×C4311yescharacteristic
554C4×C8C23×C4312yes—
555C2×Q8—22no—
556C2×Q8—24no—
557C2×Q8—22no—
558C2×Q8—24no—
559C2×Q8—28no—
560C2×Q8—42no—
561C2×Q8—44no—
562C2×Q8C2×D4×C4311yescharacteristic
563C2×Q8C24×C4312yes—
564C2×Q8C24×C4314yes—
565C2×Q8C24×C4312yes—
566C2×D4C2×D4×C4312yes—
567C2×D4C2×D4×C4311yescharacteristic
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4C2×D4×C4311yescharacteristic
572C22×C4C2×D4×C4311yescharacteristic
573C22×C4C24×C4311yescharacteristic
574C22×C4C24×C4312yes—
575Q16—24no—
576Q16—28no—
577Q16—22no—
578Q16—24no—
579Q16—42no—
580Q16—44no—
581Q16#41×C4314yes—
582M16—42no—
583C2×C8—22no—
584C2×C8—24no—
585C2×C8—41no—
586C2×C8C24×C4311yescharacteristic
587C2×C8C24×C4311yescharacteristic
588C2×C8C24×C4311yescharacteristic
589C2×C8C24×C4312yes—
590C2×C8C24×C4312yes—
591C2×C8C24×C4311yescharacteristic
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—22no—
601C4⋊C4—24no—
602C4⋊C4—22no—
603C4⋊C4—24no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—24no—
610C4⋊C4C2×D4×C4312yes—
611C4⋊C4C2×D4×C4312yes—
612C4⋊C4C2×D4×C4311yescharacteristic
613C4⋊C4C2×D4×C4312yes—
614C4⋊C4C2×D4×C4311yescharacteristic
615C4⋊C4C2×D4×C4312yes—
616C4⋊C4C24×C4312yes—
617C4⋊C4C24×C4312yes—
618C4⋊C4C24×C4314yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4C2×D4×C4312yes—
624C22⋊C4C2×D4×C4312yes—
625C22⋊C4C2×D4×C4312yes—
626C22⋊C4C2×D4×C4312yes—
627C22⋊C4C2×D4×C4312yes—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—24no—
633C42—24no—
634C42—24no—
635C42—24no—
636C42C2×D4×C4311yescharacteristic
637C42C2×D4×C4311yescharacteristic
638C42C24×C4311yescharacteristic
639C42C24×C4311yescharacteristic
640C42C24×C4312yes—
641C23C22×D4×C4312yes—
642C23C22×D4×C4311yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—22no—
646Q8—24no—
647Q8—24no—
648Q8—22no—
649Q8—44no—
650Q8—48no—
651Q8—44no—
652Q8C2×#41×C4314yes—
653D4—24no—
654D4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—44no—
668C2×C4—48no—
669C2×C4—44no—
670C2×C4C22×D4×C4311yescharacteristic
671C2×C4C22×D4×C4311yescharacteristic
672C2×C4C22×D4×C4312yes—
673C2×C4C22×D4×C4312yes—
674C2×C4C22×D4×C4312yes—
675C2×C4C22×D4×C4311yescharacteristic
676C2×C4C22×D4×C4311yescharacteristic
677C2×C4C22×D4×C4311yescharacteristic
678C2×C4C25×C4311yescharacteristic
679C8—21no—
680C8—22no—
681C8—21no—
682C8—21no—
683C8—22no—
684C8C2×#41×C4312yes—
685C22—21no—
686C22—21no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22C43×#57812yes—
691C22C23×D4×C4311yescharacteristic
692C4—21no—
693C4—22no—
694C4—24no—
695C4—21no—
696C4—21no—
697C4—21no—
698C4—22no—
699C4—22no—
700C4—42no—
701C4—44no—
702C4—42no—
703C4—42no—
704C4—44no—
705C4C43×#57812yes—
706C4C22×#41×C4311yescharacteristic
707C4C43×#58511yescharacteristic
708C2—22no—
709C2—42no—
710C2D4×#41×C4311yescharacteristic
711C2C2×C43×#57811yescharacteristic
712C2C2×C43×#57811yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
prime radical#121×C43D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C43×#529 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#3395C2semidirect
3. C43×#3383C2semidirect
4. C43×#3374C2semidirect
5. C43×#3342C2semidirect
6. C43×#3336C2semidirect
7. C43×#3328C2semidirect
8. C43×#3312C2semidirect
9. D4×Q16×C43C2semidirect
10. D4×Q16×C43C2semidirect
11. C43×#3177C2semidirect
12. C43×#3170C2semidirect
13. C43×#3127C2semidirect
14. C43×#3113C2semidirect
16. C43×#2950C2semidirect
17. C2×C4×Q16×C43C2semidirect
328. #61484C43direct (N × H)
353. #3395C2×C43semidirect
354. #3383C2×C43semidirect
355. #3374C2×C43semidirect
356. #3342C2×C43semidirect
357. #3336C2×C43semidirect
358. #3328C2×C43semidirect
359. #3312C2×C43semidirect
360. D4×Q16C2×C43semidirect
361. D4×Q16C2×C43semidirect
362. #3177C2×C43semidirect
363. #3170C2×C43semidirect
364. #3127C2×C43semidirect
365. #3113C2×C43semidirect
367. #2950C2×C43semidirect
368. C2×C4×Q16C2×C43semidirect
445. C43#61484direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35232
C43×#33952
C43×#33832
C43×#33742
C43×#33422
C43×#33362
C43×#33282
C43×#33122
D4×Q16×C432
C43×#31772
C43×#31702
C43×#31272
C43×#31132
C43×#29662
C43×#29502
C2×C4×Q16×C432
#6148443