Finite Group Databasebeta

← #11903783

Subgroups — #11903783

Order 1152.

2285 conjugacy classes of subgroups.

The subgroup lattice has 821 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5578C212yesmaximal, complemented
3#10595407C211yesmaximal, characteristic, complemented
4#10595361C212yesmaximal, complemented
5#10595338C211yesmaximal, characteristic, complemented
6#10594597C212yesmaximal, complemented
7#10594534C212yesmaximal, complemented
8#10594526C211yesmaximal, characteristic, complemented
9#10594394C214yesmaximal, complemented
10#10594393C212yesmaximal, complemented
11#10594313C211yesmaximal, characteristic, complemented
12#10593966C212yesmaximal
13C4×#3798C211yesmaximal, characteristic
14#10593926C214yesmaximal, complemented
15C4×D3×Dic6C212yesmaximal, complemented
16#10593882C211yesmaximal, characteristic, complemented
17#10593882C212yesmaximal, complemented
18#86277—32nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3798C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C32×C4×Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24C4⋊C4×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2212yes—
26#64096C2211yescharacteristic
27#64096C2212yes—
28C42×C3⋊D3C2211yescharacteristic
29C42×C3⋊D3C2212yes—
30C4×#634C2211yescharacteristic
31C4×#634C2212yes—
32C3×#946C2212yes—
33C3×#944C2212yes—
34C3×#897C2212yes—
35C3×#896C2214yes—
36C3×#889C2214yes—
37C3×#888C2212yes—
38C3×#872C2214yes—
39C3×C42×D3C2212yes—
40C3×C4×Dic6C2212yes—
41C3×C4×Dic6C2214yes—
42#63919C2211yescharacteristic
43#63919C2212yes—
44C4×#627C2211yescharacteristic
45C4×#627C2211yescharacteristic
46C4×#627C2214yes—
47C4×#627C2212yes—
48C4×#626C2212yes—
49C4×#626C2212yes—
50#63902C2212yes—
51#63902C2212yes—
52C4×#625C2211yescharacteristic
53C4×#625C2211yescharacteristic
54#63899C2214yes—
55#63896C2214yes—
56#63893C2214yes—
57D3×C4⋊Dic3C2212yes—
58#63887C2214yes—
59#63881C2214yes—
60#63881C2214yes—
61D3×Dic3⋊C4C2214yes—
62C4×D3×Dic3C2214yes—
63#63874C2211yescharacteristic
64#63874C2212yes—
65#63873C2212yes—
66#63873C2211yescharacteristic
67#63871C2212yes—
68#63871C2214yes—
69#63870C2212yes—
70#63870C2212yes—
71#63870C2212yes—
72#63865C2214yes—
73#63865C2212yes—
74#63855C2212yes—
75#63846C2214yes—
76#63845C2214yes—
77#63844C2212yes—
78Dic3×Dic6C2212yes—
79#63840C2214yes—
80#63839C2214yes—
81#63838C2212yes—
82#63838C2212yes—
83#63837C2214yes—
84C3×#533—32no—
85#5730—32no—
86#5727—32no—
87#5722—32no—
88#5721—32no—
89#5690—34no—
90#5685—34no—
91#5636—34no—
92#5636—34no—
93#5635—32no—
94#5635—32no—
95#5632—32no—
96#5632—32no—
97#5578—34no—
98#5578—34no—
99#5578—32no—
100#5578D312yescomplemented
101C4×D3×Q8—32no—
102C4×D3×Q8—32no—
103C4×D3×Q8—61no—
104#5522—34no—
105#5517—34no—
106C4×#235—32no—
107C2×C4×Dic6—32no—
108C2×C32×Q8C2311yescharacteristic
109Q8×C3⋊D3—24no—
110C2×C4×C3⋊D3C2312yes—
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2312yes—
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×#634C2312yes—
116C2×#634C2311yescharacteristic
117C2×C3×C4×D3C2312yes—
118C2×C3×C4×D3C2312yes—
119C2×C3×C4×D3C2312yes—
120C2×C3×Dic6C2312yes—
121C2×C3×Dic6C2314yes—
122C2×#627C2314yes—
123C2×#627C2312yes—
124C2×#627C2311yescharacteristic
125C2×#626C2312yes—
126C2×#625C2311yescharacteristic
127C2×D3×Dic3C2314yes—
128C2×D3×Dic3C2314yes—
129#3798Q818yescomplemented
130D3×Dic6—28no—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2312yes—
133C32×C42C2311yescharacteristic
134C32×C42C2312yes—
135C4⋊(C3⋊Dic3)C2311yescharacteristic
136C4⋊(C3⋊Dic3)C2312yes—
137#3750C2312yes—
138#3750C2312yes—
139#3750C2312yes—
140C4×C3⋊Dic3C2311yescharacteristic
141C4×C3⋊Dic3C2312yes—
142C4×C3⋊Dic3C2312yes—
143C4×C3⋊Dic3C2312yes—
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×C4⋊Dic3C2312yes—
149C3×C4⋊Dic3C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×Dic3⋊C4C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2312yes—
158C3×C4×Dic3C2314yes—
159#3724C2312yes—
160#3724C2312yes—
161#3724C2314yes—
162#3724C2312yes—
163#3724C2311yescharacteristic
164#3724C2311yescharacteristic
165Dic3⋊Dic3C2314yes—
166Dic3⋊Dic3C2312yes—
167Dic3⋊Dic3C2312yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2314yes—
170#3722C2314yes—
171#3722C2312yes—
172(C2×D3)⋊Dic3C2312yes—
173(C2×D3)⋊Dic3C2312yes—
174Dic32C2314yes—
175Dic32C2314yes—
176Q8×#41—91noSylow
177C2×D3×Q8—32no—
178C2×D3×Q8—32no—
179C2×D3×Q8—61no—
180C2×#235—32no—
181C22×Dic6—32no—
182C3×C4⋊Q8—32no—
183C3×C4⋊Q8—32no—
184C3×#125—34no—
185C3×C22⋊Q8—32no—
186C3×C22⋊Q8—32no—
187C3×C22⋊Q8—34no—
188C3×C4×Q8—21no—
189C3×C4×Q8—32no—
190C3×C4×Q8—34no—
191C3×C4×Q8C2×D312yes—
192C3×#117—34no—
193C2×C3×C42—32no—
194#946—34no—
195#946—32no—
196#946—34no—
197#946C2×D312yes—
198Q8×Dic3—32no—
199Q8×Dic3—32no—
200Q8×Dic3—61no—
201#944—32no—
202#944—34no—
203#944—34no—
204#944C2×D312yes—
205C4×#67—32no—
206C4×#67—32no—
207C4×#67—32no—
208C4×#67—32no—
209#926—32no—
210C2×C4⋊Dic3—32no—
211C2×Dic3⋊C4—34no—
212C2×C4×Dic3—34no—
213#897—32no—
214#897—34no—
215#897—34no—
216#897C2×D312yes—
217#896—34no—
218#896—34no—
219#896—34no—
220#896—34no—
221#896—34no—
222#896C2×D314yes—
223#893—34no—
224#893—34no—
225D3×C4⋊C4—32no—
226D3×C4⋊C4—34no—
227D3×C4⋊C4—32no—
228D3×C4⋊C4—34no—
229D3×C4⋊C4—61no—
230D3×C4⋊C4—62no—
231#890—34no—
232#890—34no—
233#889—34no—
234#889—34no—
235#889—34no—
236#889—34no—
237#889—34no—
238#889C2×D314yes—
239#888—34no—
240#888—34no—
241#888—32no—
242#888—34no—
243#888—34no—
244#888C2×D312yes—
245#887—32no—
246#887—34no—
247#887—34no—
248#887—34no—
249#887—32no—
250#887—34no—
251#887—61no—
252#887—62no—
253#67⋊C4—34no—
254#67⋊C4—34no—
255#67⋊C4—34no—
256#67⋊C4—34no—
257#878—34no—
258#878—34no—
259#878—34no—
260#878—34no—
261C4×D12—32no—
262C4×D12—32no—
263#872—32no—
264#872—32no—
265#872—34no—
266#872C2×D314yes—
267C42×D3—34no—
268C42×D3—32no—
269C42×D3—34no—
270C42×D3—61no—
271C42×D3—62no—
272C42×D3C2×D312yes—
273C4×Dic6—32no—
274C4×Dic6—32no—
275C4×Dic6—34no—
276C4×Dic6—32no—
277C4×Dic6—34no—
278C4×Dic6—32no—
279C4×Dic6—32no—
280C4×Dic6—34no—
281C4×Dic6—34no—
282C4×Dic6—34no—
283C4×Dic6—61no—
284C4×Dic6—62no—
285C4×Dic6C2×D312yes—
286C4×Dic6C2×D314yes—
287C22×C3⋊D3C2411yescharacteristic
288C22×C3×D3C2412yes—
289C32×Q8—22no—
290C2×C32×C4C2411yescharacteristic
291C2×C32×C4C2412yes—
292C2×C32×C4C2412yes—
293C2×C32×C4C2411yescharacteristic
294C2×C32×C4C2411yescharacteristic
295C2×C3⋊Dic3C2412yes—
296C2×C3⋊Dic3C2411yescharacteristic
297C2×C3⋊Dic3C2411yescharacteristic
298C2×C3⋊Dic3C2411yescharacteristic
299C2×C3⋊Dic3C2412yes—
300C4×C3⋊D3—22no—
301C4×C3⋊D3—24no—
302C4×C3⋊D3—42no—
303C4×C3⋊D3—41no—
304C4×C3⋊D3C2×Q814yescomplemented
305#634—24no—
306#634#4114yescomplemented
307C2×C3×Dic3C2414yes—
308C2×C3×Dic3C2414yes—
309C2×C3×Dic3C2412yes—
310C2×C3×Dic3C2412yes—
311C2×C3×Dic3C2412yes—
312C3×C4×D3—24no—
313C3×C4×D3—42no—
314C3×C4×D3C2×Q818yescomplemented
315C3×Dic6—24no—
316C3×Dic6—44no—
317#627—28no—
318#627—42no—
319#627C2×Q814yescomplemented
320#626C2×Q818yescomplemented
321#625C2×Q814yescomplemented
322D3×Dic3—28no—
323D3×Dic3—44no—
324Q82—91no—
325#557—92no—
326#557—91no—
327#554—91no—
328#554—92no—
329#554—94no—
330#554—92no—
331D4×Q8—91no—
332D4×Q8—92no—
333#533—32no—
334#533—94no—
335#533—91no—
336#533—92no—
337C4×#41—91no—
338C4×#41—92no—
339C2×C4×Q8—92no—
340C2×C4×Q8—91no—
341C2×C3×Q8—21no—
342C2×C3×Q8—32no—
343C2×C3×Q8—34no—
344C2×C3×Q8C22×D312yes—
345C22×C3×C4—32no—
346C22×C3×C4—32no—
347C22×C3×C4—32no—
348C2×#67—32no—
349C2×#67—32no—
350C22×Dic3—34no—
351C22×Dic3—34no—
352D3×Q8—68no—
353D3×Q8—68no—
354D3×Q8—68no—
355#235—316no—
356C2×D12—32no—
357C2×C4×D3—32no—
358C2×C4×D3—34no—
359C2×C4×D3—32no—
360C2×C4×D3—34no—
361C2×C4×D3—34no—
362C2×C4×D3—32no—
363C2×C4×D3—34no—
364C2×C4×D3—61no—
365C2×C4×D3—62no—
366C2×C4×D3—61no—
367C2×C4×D3—61no—
368C2×C4×D3—62no—
369C2×C4×D3C22×D312yes—
370C2×C4×D3C22×D312yes—
371C2×C4×D3C22×D312yes—
372C2×Dic6—32no—
373C2×Dic6—32no—
374C2×Dic6—34no—
375C2×Dic6—34no—
376C2×Dic6—34no—
377C2×Dic6—34no—
378C2×Dic6—61no—
379C2×Dic6—62no—
380C2×Dic6—68no—
381C2×Dic6C22×D312yes—
382C2×Dic6C22×D314yes—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—34no—
386C3×C4⋊C4—34no—
387C3×C4⋊C4—32no—
388C3×C4⋊C4—34no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—34no—
391C3×C4⋊C4—34no—
392C3×C4⋊C4C22×D312yes—
393C3×C4⋊C4C22×D314yes—
394C3×C22⋊C4—34no—
395C3×C22⋊C4—34no—
396C3×C42—21no—
397C3×C42—22no—
398C3×C42—32no—
399C3×C42—32no—
400C3×C42—34no—
401C3×C42—32no—
402C3×C42C22×D312yes—
403C3×C42C22×D314yes—
404#217—32no—
405#217—32no—
406(C2×D3)⋊C4—32no—
407(C2×D3)⋊C4—32no—
408(C2×D3)⋊C4—32no—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4C22×D314yes—
413(C2×D3)⋊C4C22×D314yes—
414C4⋊Dic3—32no—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—32no—
418C4⋊Dic3—32no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—61no—
422C4⋊Dic3—62no—
423C4⋊Dic3C22×D312yes—
424C4⋊Dic3C22×D314yes—
425Dic3⋊C4—34no—
426Dic3⋊C4—34no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—32no—
431Dic3⋊C4—32no—
432Dic3⋊C4—32no—
433Dic3⋊C4—32no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—62no—
441Dic3⋊C4—62no—
442Dic3⋊C4—62no—
443Dic3⋊C4C22×D314yes—
444Dic3⋊C4C22×D314yes—
445Dic3⋊C4C22×D314yes—
446Dic3⋊C4C22×D314yes—
447Dic3⋊C4C22×D314yes—
448C4×Dic3—34no—
449C4×Dic3—32no—
450C4×Dic3—32no—
451C4×Dic3—32no—
452C4×Dic3—34no—
453C4×Dic3—34no—
454C4×Dic3—34no—
455C4×Dic3—34no—
456C4×Dic3—34no—
457C4×Dic3—34no—
458C4×Dic3—62no—
459C4×Dic3—61no—
460C4×Dic3—61no—
461C4×Dic3—62no—
462C4×Dic3—62no—
463C4×Dic3—61no—
464C4×Dic3C22×D312yes—
465C4×Dic3C22×D314yes—
466C4×Dic3C22×D312yes—
467C4×Dic3C22×D312yes—
468C22×C32C2511yescharacteristic
469C2×C3⋊D3—21no—
470C2×C3⋊D3—21no—
471C2×C3⋊D3C22×Q812yes—
472C2×C3×D3—22no—
473C2×C3×D3—22no—
474C2×C3×D3C22×Q814yes—
475C32×C4—22no—
476C32×C4—22no—
477C32×C4—21no—
478C32×C4C22×Q812yes—
479C32×C4C2×#4112yes—
480C3⋊Dic3—21no—
481C3⋊Dic3—22no—
482C3⋊Dic3—21no—
483C3⋊Dic3C22×Q812yes—
484C3⋊Dic3C2×#4114yes—
485C3×Dic3—24no—
486C3×Dic3—22no—
487C3×Dic3—24no—
488C3×Dic3—22no—
489C3×Dic3C22×Q814yes—
490C2×#41—91no—
491C22×Q8—92no—
492C22×Q8—91no—
493C4⋊Q8—32no—
494C4⋊Q8—32no—
495C4⋊Q8—94no—
496C4⋊Q8—92no—
497C4⋊Q8—91no—
498C4⋊Q8—94no—
499C4⋊Q8—91no—
500C4⋊Q8—92no—
501#125—34no—
502#125—92no—
503#125—92no—
504#125—92no—
505#125—94no—
506#125—94no—
507C22⋊Q8—32no—
508C22⋊Q8—32no—
509C22⋊Q8—34no—
510C22⋊Q8—94no—
511C22⋊Q8—94no—
512C22⋊Q8—94no—
513C22⋊Q8—94no—
514C22⋊Q8—94no—
515C22⋊Q8—92no—
516C22⋊Q8—92no—
517C22⋊Q8—94no—
518C4×Q8—32no—
519C4×Q8—34no—
520C4×Q8—94no—
521C4×Q8—91no—
522C4×Q8—91no—
523C4×Q8—92no—
524C4×Q8—92no—
525C4×Q8—94no—
526C4×Q8—92no—
527C4×Q8—92no—
528C4×Q8—92no—
529C4×Q8—91no—
530C4×Q8—91no—
531C4×Q8—92no—
532C4×Q8—91no—
533C4×Q8—92no—
534C4×Q8D3211yescharacteristic
535C4×D4—92no—
536C4×D4—92no—
537C4×D4—92no—
538C4×D4—92no—
539C4×D4—94no—
540C4×D4—94no—
541C4×D4—91no—
542C4×D4—91no—
543#117—34no—
544#117—91no—
545#117—92no—
546#117—92no—
547C2×C4⋊C4—94no—
548C2×C4⋊C4—92no—
549C2×C4⋊C4—92no—
550C2×C4⋊C4—91no—
551C2×C42—32no—
552C2×C42—94no—
553C2×C42—92no—
554C2×C42—91no—
555C23×C3—32no—
556C22×D3—32no—
557C22×D3—61no—
558C22×D3C23×D312yes—
559C3×Q8—24no—
560C3×Q8—24no—
561C3×Q8—64no—
562C3×Q8—124no—
563C2×C3×C4—22no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—22no—
567C2×C3×C4—21no—
568C2×C3×C4—32no—
569C2×C3×C4—38no—
570C2×C3×C4—34no—
571C2×C3×C4—34no—
572C2×C3×C4—32no—
573C2×C3×C4—32no—
574C2×C3×C4—64no—
575C2×C3×C4—122no—
576C2×C3×C4C23×D312yes—
577C2×C3×C4C23×D314yes—
578C2×C3×C4C23×D314yes—
579C2×C3×C4C23×D312yes—
580C2×C3×C4C23×D312yes—
581#67—38no—
582#67—38no—
583C2×Dic3—32no—
584C2×Dic3—34no—
585C2×Dic3—34no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—61no—
589C2×Dic3—62no—
590C2×Dic3—61no—
591C2×Dic3—62no—
592C2×Dic3—61no—
593C2×Dic3—68no—
594C2×Dic3—124no—
595C2×Dic3C23×D314yes—
596C2×Dic3C23×D314yes—
597C2×Dic3C23×D312yes—
598C2×Dic3C23×D312yes—
599C2×Dic3C23×D312yes—
600D12—38no—
601C4×D3—24no—
602C4×D3—38no—
603C4×D3—42no—
604C4×D3—64no—
605C4×D3—68no—
606C4×D3—68no—
607C4×D3—68no—
608C4×D3—64no—
609C4×D3—64no—
610C4×D3—122no—
611C4×D3—124no—
612C4×D3—124no—
613C4×D3—122no—
614C4×D3—124no—
615C4×D3D3×Q818yescomplemented
616Dic6—24no—
617Dic6—38no—
618Dic6—38no—
619Dic6—44no—
620Dic6—64no—
621Dic6—68no—
622Dic6—68no—
623Dic6—68no—
624Dic6—68no—
625Dic6—124no—
626C2×C32C23×Q811yescharacteristic
627C2×C32C22×#4111yescharacteristic
628C2×C32#58511yescharacteristic
629C3⋊D3—22no—
630C3×D3—24no—
631#41—98no—
632C2×Q8—32no—
633C2×Q8—34no—
634C2×Q8—91no—
635C2×Q8—94no—
636C2×Q8—92no—
637C2×Q8—91no—
638C2×Q8—92no—
639C2×Q8—188no—
640C2×Q8—184no—
641C2×Q8C2×D3211yescharacteristic
642C2×D4—92no—
643C2×D4—91no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—32no—
647C22×C4—94no—
648C22×C4—94no—
649C22×C4—91no—
650C22×C4—92no—
651C22×C4—91no—
652C22×C4—92no—
653C22×C4—91no—
654C4⋊C4—34no—
655C4⋊C4—32no—
656C4⋊C4—34no—
657C4⋊C4—34no—
658C4⋊C4—34no—
659C4⋊C4—34no—
660C4⋊C4—34no—
661C4⋊C4—94no—
662C4⋊C4—94no—
663C4⋊C4—94no—
664C4⋊C4—91no—
665C4⋊C4—91no—
666C4⋊C4—92no—
667C4⋊C4—92no—
668C4⋊C4—92no—
669C4⋊C4—92no—
670C4⋊C4—92no—
671C4⋊C4—94no—
672C4⋊C4—92no—
673C4⋊C4—91no—
674C4⋊C4—92no—
675C4⋊C4—92no—
676C4⋊C4—92no—
677C4⋊C4C2×D3212yes—
678C4⋊C4C2×D3211yescharacteristic
679C22⋊C4—34no—
680C22⋊C4—34no—
681C22⋊C4—92no—
682C22⋊C4—94no—
683C22⋊C4—92no—
684C22⋊C4—92no—
685C42—32no—
686C42—32no—
687C42—32no—
688C42—34no—
689C42—94no—
690C42—94no—
691C42—92no—
692C42—91no—
693C42—92no—
694C42—91no—
695C42—92no—
696C42—91no—
697C42C2×D3211yescharacteristic
698C42C2×D3212yes—
699C22×C3—21no—
700C22×C3—34no—
701C22×C3—62no—
702C22×C3—62no—
703C22×C3C24×D312yes—
704C2×D3—22no—
705C2×D3—22no—
706C2×D3—34no—
707C2×D3—62no—
708C2×D3—62no—
709C2×D3—62no—
710C2×D3—62no—
711C2×D3—62no—
712C2×D3C2×D3×Q814yes—
713C3×C4—24no—
714C3×C4—24no—
715C3×C4—24no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—34no—
720C3×C4—41no—
721C3×C4—42no—
722C3×C4—62no—
723C3×C4—64no—
724C3×C4—64no—
725C3×C4—62no—
726C3×C4C2×D3×Q814yes—
727C3×C4D3×#4114yes—
728Dic3—24no—
729Dic3—22no—
730Dic3—22no—
731Dic3—24no—
732Dic3—34no—
733Dic3—38no—
734Dic3—64no—
735Dic3—62no—
736Dic3—62no—
737Dic3—62no—
738Dic3—62no—
739Dic3—64no—
740Dic3—122no—
741Dic3—121no—
742Dic3C2×D3×Q814yes—
743C32Q8×#4111yescharacteristic, complemented, Sylow
744C23—32no—
745C23—91no—
746Q8—22no—
747Q8—64no—
748Q8—94no—
749Q8—94no—
750Q8—124no—
751Q8—184no—
752Q8—188no—
753Q8—362no—
754D4—98no—
755D4—94no—
756C2×C4—32no—
757C2×C4—38no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—34no—
761C2×C4—34no—
762C2×C4—64no—
763C2×C4—91no—
764C2×C4—92no—
765C2×C4—94no—
766C2×C4—92no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—122no—
770C2×C4—184no—
771C2×C4—188no—
772C2×C4—182no—
773C2×C4—361no—
774C2×C4—362no—
775C2×C4—364no—
776C2×C4C22×D3211yescharacteristic
777C2×C4C22×D3212yes—
778C2×C4C22×D3212yes—
779C2×C4C22×D3211yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C2×C3—21no—
782C2×C3—21no—
783C2×C3—21no—
784C2×C3—64no—
785C2×C3C22×D3×Q812yes—
786C2×C3C2×D3×#4112yes—
787C2×C3#596412yes—
788D3—24no—
789D3—64no—
790D3—64no—
791C22—34no—
792C22—62no—
793C22—62no—
794C22—92no—
795C22—181no—
796C22—181no—
797C22C23×D3211yescharacteristic
798C4—22no—
799C4—21no—
800C4—22no—
801C4—34no—
802C4—62no—
803C4—64no—
804C4—62no—
805C4—64no—
806C4—94no—
807C4—92no—
808C4—181no—
809C4—182no—
810C4—181no—
811C4#6430612yes—
812C4D32×Q812yes—
813C3—21no—
814C3#8627712yescomplemented
815C2—64no—
816C2—182no—
817C2C2×#6430611yescharacteristic
818C2C2×D32×Q811yescharacteristic
819C2#1059669511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×C4×Q8C22
prime radicalC2×#3798C22
hypercenterC4×Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5578C2semidirect
3. #10595407C2semidirect
4. #10595361C2semidirect
5. #10595338C2semidirect
6. #10594597C2semidirect
7. #10594534C2semidirect
8. #10594526C2semidirect
9. #10594394C2semidirect
10. #10594393C2semidirect
11. #10594313C2semidirect
14. #10593926C2semidirect
15. C4×D3×Dic6C2semidirect
16. #10593882C2semidirect
17. #10593882C2semidirect
100. #5578D3semidirect
129. #3798Q8semidirect
304. C4×C3⋊D3C2×Q8semidirect
306. #634#41semidirect
314. C3×C4×D3C2×Q8semidirect
319. #627C2×Q8semidirect
320. #626C2×Q8semidirect
321. #625C2×Q8semidirect
615. C4×D3D3×Q8semidirect
743. C32Q8×#41semidirect
814. C3#86277semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55782
#105954072
#105953612
#105953382
#105945972
#105945342
#105945262
#105943942
#105943932
#105943132
#105939662
C4×#37982
#105939262
C4×D3×Dic62
#105938822
#862773