Finite Group Databasebeta

← C43×#61478 #24981495

Subgroups — C43×#61478 #24981495

Order 11008.

1768 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3518C212yesmaximal, complemented
2C43×#3393C211yesmaximal, characteristic, complemented
3Q8×Q16×C43C211yesmaximal, characteristic, complemented
4C43×#3369C212yesmaximal, complemented
5C43×#3342C212yesmaximal, complemented
6C43×#3341C211yesmaximal, characteristic, complemented
7C43×#3329C212yesmaximal, complemented
8C43×#3313C214yesmaximal, complemented
9D4×Q16×C43C211yesmaximal, characteristic, complemented
10C43×#3285C212yesmaximal, complemented
11C43×#3175C212yesmaximal, complemented
12C43×#3170C211yesmaximal, characteristic, complemented
13C43×#3121C214yesmaximal, complemented
14C43×#3116C212yesmaximal, complemented
15C43×#2966C211yesmaximal, characteristic, complemented
16C43×#2950C212yesmaximal, complemented
17C4×#135×C43C211yesmaximal, characteristic, complemented
18C2×#135×C43C2211yescharacteristic
19C22×Q16×C43C2212yes—
20Q82×C43C2212yes—
21C43×#556—24no—
22C43×#556—22no—
23C43×#556C2212yes—
24C43×#556C2214yes—
25C43×#555—22no—
26C43×#555C2212yes—
27D4×Q8×C43C2212yes—
28C43×#548C2214yes—
29C43×#542—24no—
30C43×#542C2214yes—
31C43×#533—22no—
32C43×#533C2212yes—
33C43×#529—22no—
34C43×#529C2211yescharacteristic
35C43×#519C2214yes—
36C4×#41×C43C2212yes—
37C43×#500C2211yescharacteristic
38C43×#500C2212yes—
39C43×#495C2212yes—
40C43×#494C2211yescharacteristic
41C43×#489C2214yes—
42C43×#487C2212yes—
43C43×#485C2214yes—
44C43×#485C2214yes—
45C43×#482C2214yes—
46C43×#477C2212yes—
47C43×#477C2214yes—
48C43×#476C2212yes—
49C43×#475C2214yes—
50C43×#468C2214yes—
51C43×#467C2212yes—
52C43×#467C2212yes—
53C43×#467C2212yes—
54C43×#466C2212yes—
55C43×#464C2214yes—
56C43×#464C2214yes—
57C43×#462C2212yes—
58C43×#461C2212yes—
59C43×#452C2214yes—
60C43×#451C2214yes—
61C43×#448C2214yes—
62C43×#446C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#441C2214yes—
65C43×#441C2214yes—
66C43×#440C2214yes—
67C4×Q16×C43C2212yes—
68C4×Q16×C43C2211yescharacteristic
69C4×Q16×C43C2212yes—
70C4×Q16×C43C2212yes—
71C4×Q16×C43C2212yes—
72C4×Q16×C43C2211yescharacteristic
73C4×SD16×C43C2212yes—
74C4×SD16×C43C2212yes—
75C4×D8×C43C2211yescharacteristic
76C4×D8×C43C2211yescharacteristic
77C43×#436C2211yescharacteristic
78C43×#435C2212yes—
79C8×D4×C43C2212yes—
80C8×D4×C43C2211yescharacteristic
81C43×#433C2212yes—
82C43×#432C2211yescharacteristic
83C43×#427C2211yescharacteristic
84C43×#427C2212yes—
85C43×#419C2214yes—
86C43×#416C2212yes—
87C43×#405C2212yes—
88C2×C4×C8×C43C2211yescharacteristic
89C2×#41×C43C2312yes—
90C22×Q8×C43C2314yes—
91#135×C43—24no—
92C2×Q16×C43—28no—
93C2×Q16×C43C2312yes—
94C2×Q16×C43C2314yes—
95C2×Q16×C43C2312yes—
96C2×Q16×C43C2311yescharacteristic
97C2×SD16×C43C2312yes—
98C2×SD16×C43C2314yes—
99C2×D8×C43C2311yescharacteristic
100C2×M16×C43C2312yes—
101C22×C8×C43C2312yes—
102C22×C8×C43C2311yescharacteristic
103C22×C8×C43C2311yescharacteristic
104C4⋊Q8×C43—22no—
105C4⋊Q8×C43—22no—
106C4⋊Q8×C43—24no—
107C4⋊Q8×C43C2312yes—
108C4⋊Q8×C43C2312yes—
109C4⋊Q8×C43C2314yes—
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×C43D411yescharacteristic
117#124×C43—24no—
118#124×C43—24no—
119#124×C43—24no—
120#124×C43—24no—
121#124×C43D411yescharacteristic
122#124×C43C2314yes—
123#123×C43—24no—
124#123×C43D412yes—
125C22⋊Q8×C43—22no—
126C22⋊Q8×C43—22no—
127C22⋊Q8×C43—24no—
128C22⋊Q8×C43—24no—
129C22⋊Q8×C43—24no—
130C22⋊Q8×C43D411yescharacteristic
131C22⋊Q8×C43C2314yes—
132C22⋊Q8×C43C2314yes—
133#121×C43—22no—
134#121×C43—24no—
135#121×C43D411yescharacteristic
136#121×C43C2314yes—
137C4×Q8×C43—22no—
138C4×Q8×C43—24no—
139C4×Q8×C43—24no—
140C4×Q8×C43—24no—
141C4×Q8×C43—22no—
142C4×Q8×C43C2312yes—
143C4×Q8×C43C2312yes—
144C4×Q8×C43C2314yes—
145C4×Q8×C43C2314yes—
146C4×Q8×C43C2314yes—
147C4×Q8×C43C2311yescharacteristic
148C4×D4×C43—22no—
149C4×D4×C43—22no—
150C4×D4×C43—22no—
151C4×D4×C43—24no—
152C4×D4×C43C2312yes—
153C4×D4×C43C2312yes—
154C4×D4×C43C2312yes—
155C4×D4×C43C2311yescharacteristic
156#117×C43—22no—
157#117×C43—22no—
158#117×C43—22no—
159#117×C43—24no—
160#117×C43—24no—
161#117×C43—22no—
162#117×C43C2312yes—
163#117×C43C2314yes—
164#117×C43C2312yes—
165C2×C42×C43—22no—
166C2×C42×C43C2311yescharacteristic
167#107×C43C2311yescharacteristic
168#107×C43C2312yes—
169#107×C43C2312yes—
170#107×C43C2314yes—
171#107×C43C2311yescharacteristic
172#106×C43C2312yes—
173#106×C43C2314yes—
174C4⋊C8×C43C2311yescharacteristic
175C4⋊C8×C43C2311yescharacteristic
176C4⋊C8×C43C2312yes—
177C4⋊C8×C43C2312yes—
178#103×C43C2312yes—
179#103×C43C2312yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#103×C43C2314yes—
185#102×C43C2312yes—
186#102×C43C2312yes—
187#102×C43C2314yes—
188C22⋊C8×C43C2312yes—
189C22⋊C8×C43C2312yes—
190C22⋊C8×C43C2312yes—
191#97×C43C2312yes—
192#97×C43C2312yes—
193C4×C8×C43C2311yescharacteristic
194C4×C8×C43C2312yes—
195C4×C8×C43C2311yescharacteristic
196C4×C8×C43C2311yescharacteristic
197C4×C8×C43C2311yescharacteristic
198#41×C43—24no—
199#41×C43—42no—
200C2×Q8×C43—24no—
201C2×Q8×C43—22no—
202C2×Q8×C43—24no—
203C2×Q8×C43—28no—
204C2×Q8×C43—44no—
205C2×Q8×C43C2×D411yescharacteristic
206C2×Q8×C43C2414yes—
207C2×Q8×C43C2412yes—
208C2×D4×C43—22no—
209C2×D4×C43—24no—
210C2×D4×C43C2×D411yescharacteristic
211C2×D4×C43C2×D412yes—
212C2×D4×C43C2412yes—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43—22no—
216C22×C4×C43—24no—
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2411yescharacteristic
220C22×C4×C43C2412yes—
221Q16×C43—28no—
222Q16×C43—24no—
223Q16×C43—42no—
224Q16×C43#4114yes—
225SD16×C43—24no—
226SD16×C43—44no—
227D8×C43—22no—
228M16×C43—42no—
229C2×C8×C43—24no—
230C2×C8×C43—22no—
231C2×C8×C43—41no—
232C2×C8×C43C2411yescharacteristic
233C2×C8×C43C2411yescharacteristic
234C2×C8×C43C2411yescharacteristic
235C2×C8×C43C2412yes—
236C2×C8×C43C2412yes—
237C2×C8×C43C2411yescharacteristic
238C4⋊C4×C43—22no—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—22no—
241C4⋊C4×C43—22no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—24no—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—22no—
247C4⋊C4×C43—24no—
248C4⋊C4×C43—24no—
249C4⋊C4×C43C2×D411yescharacteristic
250C4⋊C4×C43C2×D411yescharacteristic
251C4⋊C4×C43C2×D412yes—
252C4⋊C4×C43C2×D412yes—
253C4⋊C4×C43C2×D412yes—
254C4⋊C4×C43C2×D412yes—
255C4⋊C4×C43C2412yes—
256C4⋊C4×C43C2412yes—
257C4⋊C4×C43C2414yes—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C22⋊C4×C43—24no—
263C22⋊C4×C43—24no—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—22no—
266C22⋊C4×C43—24no—
267C22⋊C4×C43C2×D412yes—
268C22⋊C4×C43C2×D412yes—
269C22⋊C4×C43C2×D412yes—
270C22⋊C4×C43C2×D412yes—
271C22⋊C4×C43C2×D412yes—
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×C43—22no—
285C23×C43C22×D411yescharacteristic
286C23×C43C22×D412yes—
287Q8×C43—22no—
288Q8×C43—22no—
289Q8×C43—24no—
290Q8×C43—24no—
291Q8×C43—48no—
292Q8×C43—82no—
293Q8×C43—84no—
294Q8×C43C2×#4114yes—
295D4×C43—22no—
296D4×C43—22no—
297D4×C43—22no—
298D4×C43—42no—
299D4×C43—44no—
300D4×C43—84no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—24no—
309C2×C4×C43—24no—
310C2×C4×C43—22no—
311C2×C4×C43—41no—
312C2×C4×C43—44no—
313C2×C4×C43—48no—
314C2×C4×C43—44no—
315C2×C4×C43—82no—
316C2×C4×C43C22×D411yescharacteristic
317C2×C4×C43C22×D411yescharacteristic
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D412yes—
320C2×C4×C43C22×D412yes—
321C2×C4×C43C22×D412yes—
322C2×C4×C43C22×D411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C2511yescharacteristic
325C8×C43—21no—
326C8×C43—22no—
327C8×C43—21no—
328C8×C43—21no—
329C8×C43—22no—
330C8×C43C2×#4112yes—
331#61478C4311yesmaximal, characteristic, direct product factor, Sylow
332C22×C43—21no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—21no—
336C22×C43—21no—
337C22×C43—22no—
338C22×C43—42no—
339C22×C43—42no—
340C22×C43—42no—
341C22×C43C23×D411yescharacteristic
342C4×C43—21no—
343C4×C43—21no—
344C4×C43—22no—
345C4×C43—21no—
346C4×C43—22no—
347C4×C43—24no—
348C4×C43—21no—
349C4×C43—22no—
350C4×C43—42no—
351C4×C43—44no—
352C4×C43—44no—
353C4×C43—42no—
354C4×C43#57812yes—
355C4×C43C22×#4111yescharacteristic
356C4×C43#58511yescharacteristic
357#3518C2×C4312yescomplemented
358#3393C2×C4311yescharacteristic, complemented
359Q8×Q16C2×C4311yescharacteristic, complemented
360#3369C2×C4312yescomplemented
361#3342C2×C4312yescomplemented
362#3341C2×C4311yescharacteristic, complemented
363#3329C2×C4312yescomplemented
364#3313C2×C4314yescomplemented
365D4×Q16C2×C4311yescharacteristic, complemented
366#3285C2×C4312yescomplemented
367#3175C2×C4312yescomplemented
368#3170C2×C4311yescharacteristic, complemented
369#3121C2×C4314yescomplemented
370#3116C2×C4312yescomplemented
371#2966C2×C4311yescharacteristic, complemented
372#2950C2×C4312yescomplemented
373C4×#135C2×C4311yescharacteristic, complemented
374C2×C43—41no—
375C2×C43—42no—
376C2×C43—82no—
377C2×C43D4×#4111yescharacteristic
378C2×C43C2×#57811yescharacteristic
379C2×C43#358411yescharacteristic
380C2×#135C22×C4311yescharacteristic
381C22×Q16C22×C4312yes—
382Q82C22×C4312yes—
383#556—24no—
384#556—22no—
385#556C22×C4312yes—
386#556C22×C4314yes—
387#555—22no—
388#555C22×C4312yes—
389D4×Q8C22×C4312yes—
390#548C22×C4314yes—
391#542—24no—
392#542C22×C4314yes—
393#533—22no—
394#533C22×C4312yes—
395#529—22no—
396#529C22×C4311yescharacteristic
397#519C22×C4314yes—
398C4×#41C22×C4312yes—
399#500C22×C4311yescharacteristic
400#500C22×C4312yes—
401#495C22×C4312yes—
402#494C22×C4311yescharacteristic
403#489C22×C4314yes—
404#487C22×C4312yes—
405#485C22×C4314yes—
406#485C22×C4314yes—
407#482C22×C4314yes—
408#477C22×C4312yes—
409#477C22×C4314yes—
410#476C22×C4312yes—
411#475C22×C4314yes—
412#468C22×C4314yes—
413#467C22×C4312yes—
414#467C22×C4312yes—
415#467C22×C4312yes—
416#466C22×C4312yes—
417#464C22×C4314yes—
418#464C22×C4314yes—
419#462C22×C4312yes—
420#461C22×C4312yes—
421#452C22×C4314yes—
422#451C22×C4314yes—
423#448C22×C4314yes—
424#446C22×C4311yescharacteristic
425C8×Q8C22×C4311yescharacteristic
426#441C22×C4314yes—
427#441C22×C4314yes—
428#440C22×C4314yes—
429C4×Q16C22×C4312yes—
430C4×Q16C22×C4312yes—
431C4×Q16C22×C4311yescharacteristic
432C4×Q16C22×C4312yes—
433C4×Q16C22×C4312yes—
434C4×Q16C22×C4311yescharacteristic
435C4×SD16C22×C4312yes—
436C4×SD16C22×C4312yes—
437C4×D8C22×C4311yescharacteristic
438C4×D8C22×C4311yescharacteristic
439#436C22×C4311yescharacteristic
440#435C22×C4312yes—
441C8×D4C22×C4311yescharacteristic
442C8×D4C22×C4312yes—
443#433C22×C4312yes—
444#432C22×C4311yescharacteristic
445#427C22×C4312yes—
446#427C22×C4311yescharacteristic
447#419C22×C4314yes—
448#416C22×C4312yes—
449#405C22×C4312yes—
450C2×C4×C8C22×C4311yescharacteristic
451C43#6147811yescharacteristic, direct product factor, Sylow
452C2×#41C23×C4312yes—
453C22×Q8C23×C4314yes—
454#135—24no—
455C2×Q16—28no—
456C2×Q16C23×C4312yes—
457C2×Q16C23×C4314yes—
458C2×Q16C23×C4312yes—
459C2×Q16C23×C4311yescharacteristic
460C2×SD16C23×C4312yes—
461C2×SD16C23×C4314yes—
462C2×D8C23×C4311yescharacteristic
463C2×M16C23×C4312yes—
464C22×C8C23×C4312yes—
465C22×C8C23×C4311yescharacteristic
466C22×C8C23×C4311yescharacteristic
467C4⋊Q8—22no—
468C4⋊Q8—22no—
469C4⋊Q8—24no—
470C4⋊Q8C23×C4312yes—
471C4⋊Q8C23×C4312yes—
472C4⋊Q8C23×C4314yes—
473#126—24no—
474#126—24no—
475#126—24no—
476#126—24no—
477#126D4×C4312yes—
478#125—22no—
479#125D4×C4311yescharacteristic
480#124—24no—
481#124—24no—
482#124—24no—
483#124—24no—
484#124D4×C4311yescharacteristic
485#124C23×C4314yes—
486#123—24no—
487#123D4×C4312yes—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—24no—
491C22⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8D4×C4311yescharacteristic
494C22⋊Q8C23×C4314yes—
495C22⋊Q8C23×C4314yes—
496#121—22no—
497#121—24no—
498#121D4×C4311yescharacteristic
499#121C23×C4314yes—
500C4×Q8—22no—
501C4×Q8—24no—
502C4×Q8—24no—
503C4×Q8—24no—
504C4×Q8—22no—
505C4×Q8C23×C4312yes—
506C4×Q8C23×C4312yes—
507C4×Q8C23×C4314yes—
508C4×Q8C23×C4314yes—
509C4×Q8C23×C4314yes—
510C4×Q8C23×C4311yescharacteristic
511C4×D4—22no—
512C4×D4—22no—
513C4×D4—22no—
514C4×D4—24no—
515C4×D4C23×C4312yes—
516C4×D4C23×C4312yes—
517C4×D4C23×C4312yes—
518C4×D4C23×C4311yescharacteristic
519#117—22no—
520#117—22no—
521#117—22no—
522#117—24no—
523#117—24no—
524#117—22no—
525#117C23×C4312yes—
526#117C23×C4314yes—
527#117C23×C4312yes—
528C2×C42—22no—
529C2×C42C23×C4311yescharacteristic
530#107C23×C4311yescharacteristic
531#107C23×C4311yescharacteristic
532#107C23×C4312yes—
533#107C23×C4312yes—
534#107C23×C4314yes—
535#106C23×C4312yes—
536#106C23×C4314yes—
537C4⋊C8C23×C4311yescharacteristic
538C4⋊C8C23×C4311yescharacteristic
539C4⋊C8C23×C4312yes—
540C4⋊C8C23×C4312yes—
541#103C23×C4312yes—
542#103C23×C4312yes—
543#103C23×C4314yes—
544#103C23×C4314yes—
545#103C23×C4314yes—
546#103C23×C4314yes—
547#103C23×C4314yes—
548#102C23×C4312yes—
549#102C23×C4312yes—
550#102C23×C4314yes—
551C22⋊C8C23×C4312yes—
552C22⋊C8C23×C4312yes—
553C22⋊C8C23×C4312yes—
554#97C23×C4312yes—
555#97C23×C4312yes—
556C4×C8C23×C4311yescharacteristic
557C4×C8C23×C4311yescharacteristic
558C4×C8C23×C4311yescharacteristic
559C4×C8C23×C4311yescharacteristic
560C4×C8C23×C4312yes—
561#41—24no—
562#41—42no—
563C2×Q8—24no—
564C2×Q8—22no—
565C2×Q8—24no—
566C2×Q8—28no—
567C2×Q8—44no—
568C2×Q8C2×D4×C4311yescharacteristic
569C2×Q8C24×C4314yes—
570C2×Q8C24×C4312yes—
571C2×D4—22no—
572C2×D4—24no—
573C2×D4C2×D4×C4311yescharacteristic
574C2×D4C2×D4×C4312yes—
575C2×D4C24×C4312yes—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4C2×D4×C4311yescharacteristic
581C22×C4C2×D4×C4311yescharacteristic
582C22×C4C24×C4311yescharacteristic
583C22×C4C24×C4312yes—
584Q16—28no—
585Q16—24no—
586Q16—42no—
587Q16#41×C4314yes—
588SD16—24no—
589SD16—44no—
590D8—22no—
591M16—42no—
592C2×C8—24no—
593C2×C8—22no—
594C2×C8—41no—
595C2×C8C24×C4311yescharacteristic
596C2×C8C24×C4311yescharacteristic
597C2×C8C24×C4311yescharacteristic
598C2×C8C24×C4312yes—
599C2×C8C24×C4312yes—
600C2×C8C24×C4311yescharacteristic
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4C2×D4×C4311yescharacteristic
613C4⋊C4C2×D4×C4311yescharacteristic
614C4⋊C4C2×D4×C4312yes—
615C4⋊C4C2×D4×C4312yes—
616C4⋊C4C2×D4×C4312yes—
617C4⋊C4C2×D4×C4312yes—
618C4⋊C4C24×C4312yes—
619C4⋊C4C24×C4312yes—
620C4⋊C4C24×C4314yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—24no—
628C22⋊C4—24no—
629C22⋊C4—24no—
630C22⋊C4C2×D4×C4312yes—
631C22⋊C4C2×D4×C4312yes—
632C22⋊C4C2×D4×C4312yes—
633C22⋊C4C2×D4×C4312yes—
634C22⋊C4C2×D4×C4312yes—
635C42—22no—
636C42—22no—
637C42—22no—
638C42—24no—
639C42—24no—
640C42—24no—
641C42—24no—
642C42C2×D4×C4311yescharacteristic
643C42C2×D4×C4311yescharacteristic
644C42C24×C4311yescharacteristic
645C42C24×C4311yescharacteristic
646C42C24×C4312yes—
647C23—22no—
648C23C22×D4×C4311yescharacteristic
649C23C22×D4×C4312yes—
650Q8—22no—
651Q8—22no—
652Q8—24no—
653Q8—24no—
654Q8—48no—
655Q8—82no—
656Q8—84no—
657Q8C2×#41×C4314yes—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—42no—
662D4—44no—
663D4—84no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—44no—
676C2×C4—48no—
677C2×C4—44no—
678C2×C4—82no—
679C2×C4C22×D4×C4311yescharacteristic
680C2×C4C22×D4×C4311yescharacteristic
681C2×C4C22×D4×C4311yescharacteristic
682C2×C4C22×D4×C4312yes—
683C2×C4C22×D4×C4312yes—
684C2×C4C22×D4×C4312yes—
685C2×C4C22×D4×C4311yescharacteristic
686C2×C4C22×D4×C4311yescharacteristic
687C2×C4C25×C4311yescharacteristic
688C8—21no—
689C8—22no—
690C8—21no—
691C8—21no—
692C8—22no—
693C8C2×#41×C4312yes—
694C22—22no—
695C22—21no—
696C22—21no—
697C22—22no—
698C22—21no—
699C22—22no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22C23×D4×C4311yescharacteristic
704C4—21no—
705C4—22no—
706C4—24no—
707C4—21no—
708C4—22no—
709C4—21no—
710C4—21no—
711C4—22no—
712C4—44no—
713C4—42no—
714C4—42no—
715C4—44no—
716C4C43×#57812yes—
717C4C22×#41×C4311yescharacteristic
718C4C43×#58511yescharacteristic
719C2—42no—
720C2—41no—
721C2—82no—
722C2D4×#41×C4311yescharacteristic
723C2C2×C43×#57811yescharacteristic
724C2C43×#358411yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
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
1. C43×#3518C2semidirect
2. C43×#3393C2semidirect
3. Q8×Q16×C43C2semidirect
4. C43×#3369C2semidirect
5. C43×#3342C2semidirect
6. C43×#3341C2semidirect
7. C43×#3329C2semidirect
8. C43×#3313C2semidirect
9. D4×Q16×C43C2semidirect
10. C43×#3285C2semidirect
11. C43×#3175C2semidirect
12. C43×#3170C2semidirect
13. C43×#3121C2semidirect
14. C43×#3116C2semidirect
15. C43×#2966C2semidirect
16. C43×#2950C2semidirect
17. C4×#135×C43C2semidirect
331. #61478C43direct (N × H)
357. #3518C2×C43semidirect
358. #3393C2×C43semidirect
359. Q8×Q16C2×C43semidirect
360. #3369C2×C43semidirect
361. #3342C2×C43semidirect
362. #3341C2×C43semidirect
363. #3329C2×C43semidirect
364. #3313C2×C43semidirect
365. D4×Q16C2×C43semidirect
366. #3285C2×C43semidirect
367. #3175C2×C43semidirect
368. #3170C2×C43semidirect
369. #3121C2×C43semidirect
370. #3116C2×C43semidirect
371. #2966C2×C43semidirect
372. #2950C2×C43semidirect
373. C4×#135C2×C43semidirect
451. C43#61478direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35182
C43×#33932
Q8×Q16×C432
C43×#33692
C43×#33422
C43×#33412
C43×#33292
C43×#33132
D4×Q16×C432
C43×#32852
C43×#31752
C43×#31702
C43×#31212
C43×#31162
C43×#29662
C43×#29502
C4×#135×C432
#6147843