Finite Group Databasebeta

← #11901953

Subgroups — #11901953

Order 1152.

2103 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic, complemented
2C3×D3×#117C211yesmaximal, characteristic
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595050C211yesmaximal, characteristic, complemented
5#10595049C211yesmaximal, characteristic, complemented
6D3×#926C211yesmaximal, characteristic
7C2×#63855C211yesmaximal, characteristic
8#10594505C212yesmaximal, complemented
9#10594502C212yesmaximal, complemented
10#10594344C212yesmaximal, complemented
11#10594342C212yesmaximal, complemented
12#10594170C214yesmaximal
13#10594035C214yesmaximal, complemented
14#10593926C214yesmaximal, complemented
15#10593873C214yesmaximal, complemented
16#86274—31nomaximal
17#85725—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C32×#117C2211yescharacteristic
20#64135C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64099C2212yescomplemented
23#64097C2212yescomplemented
24#64087C2214yes—
25C4×#634C2214yescomplemented
26C3×#926C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×#892C2212yes—
30C3×D3×C4⋊C4C2212yes—
31C3×#890C2212yescomplemented
32C3×#888C2212yescomplemented
33C3×D3×C22⋊C4C2212yes—
34C3×#878C2214yes—
35C3×#877C2212yes—
36C3×#872C2212yes—
37C3×C42×D3C2212yes—
38C3×C4×Dic6C2214yescomplemented
39#63982C2214yes—
40D3×#217C2212yes—
41C2×Dic3⋊Dic3C2212yes—
42#63964C2214yes—
43C2×(C2×D3)⋊Dic3C2212yes—
44#63955C2212yes—
45#63919C2212yescomplemented
46#63918C2212yescomplemented
47#63918C2214yescomplemented
48C4×#627C2214yescomplemented
49C4×#627C2214yescomplemented
50#63899C2214yes—
51#63896C2214yes—
52#63893C2214yes—
53D3×C4⋊Dic3C2212yes—
54#63887C2214yes—
55C4×D3×Dic3C2212yes—
56#63872C2212yescomplemented
57#63869C2212yescomplemented
58#63867C2214yescomplemented
59#63867C2214yescomplemented
60#63866C2214yescomplemented
61#63857C2214yes—
62#63856C2214yes—
63#63855C2211yescharacteristic
64#63855C2211yescharacteristic
65#63855C2212yes—
66#63855C2212yes—
67#63855C2211yescharacteristic
68#63855C2211yescharacteristic
69#63855C2212yes—
70#63851C2214yes—
71#63851C2214yes—
72#63846C2214yescomplemented
73#63845C2214yescomplemented
74#63841C2212yes—
75#63840C2214yescomplemented
76#63839C2214yescomplemented
77C3×#533—31no—
78C2×C3×#117—31no—
79C2×#926—31no—
80C2×#926—31no—
81#5729—32no—
82#5729—32no—
83#5689—32no—
84#5689—32no—
85#5634—34no—
86#5623—34no—
87#5578—34no—
88#5578—34no—
89D3×#117—31no—
90D3×#117D311yescharacteristic
91#5519—32no—
92#5519—32no—
93#5519—34no—
94#5517—31no—
95#5517—31no—
96#5517—31no—
97#5517—31no—
98#5517—31no—
99#5517—34no—
100#5517—61no—
101#5517D311yescharacteristic, complemented
102#5500—32no—
103#5500—32no—
104#5483—34no—
105C2×#872—31no—
106#5470—31no—
107#5470—34no—
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2312yes—
111C2×#634C2314yes—
112C22×C3×Dic3C2312yes—
113C22×C3×Dic3C2311yescharacteristic
114C2×C3×C4×D3Q818yescomplemented
115C2×C3×C4×D3C2314yes—
116C2×C3×C4×D3C2311yescharacteristic
117C2×C3×C4×D3C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119C2×C3×C4×D3C2311yescharacteristic
120C2×C3×Dic6C2314yes—
121C2×#627C2314yes—
122C2×#627C2314yes—
123C2×D3×Dic3C2314yes—
124C32×C4⋊C4C2312yes—
125C32×C22⋊C4C2312yes—
126C32×C42C2312yes—
127#3757C2312yes—
128C4⋊(C3⋊Dic3)C2314yes—
129C4⋊(C3⋊Dic3)C2312yes—
130#3750C2314yes—
131#3750C2314yes—
132C4×C3⋊Dic3C2312yes—
133C4×C3⋊Dic3C2312yes—
134C4×C3⋊Dic3C2311yescharacteristic
135C4×C3⋊Dic3C2311yescharacteristic
136C3×#217C2312yes—
137C3×#217C2312yes—
138C3×(C2×D3)⋊C4C2314yes—
139C3×C4⋊Dic3C2314yes—
140C3×C4⋊Dic3C2312yes—
141C3×C4⋊Dic3C2312yes—
142C3×Dic3⋊C4C2314yes—
143C3×Dic3⋊C4C2314yes—
144C3×Dic3⋊C4C2314yes—
145C3×C4×Dic3C2314yes—
146C3×C4×Dic3C2311yescharacteristic
147C3×C4×Dic3C2311yescharacteristic
148C3×C4×Dic3C2312yes—
149C3×C4×Dic3C2312yes—
150C3×C4×Dic3C2312yes—
151#3724C2314yes—
152#3724C2314yes—
153Dic3⋊Dic3C2312yes—
154Dic3⋊Dic3C2312yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2314yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2314yes—
159Dic3⋊Dic3C2312yes—
160Dic3⋊Dic3C2312yes—
161Dic3⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2312yes—
164(C2×D3)⋊Dic3C2312yes—
165(C2×D3)⋊Dic3C2312yes—
166(C2×D3)⋊Dic3C2312yes—
167Dic32C2314yes—
168#3458—91noSylow
169C23×C3×C4—31no—
170C22×C4×D3C2×D311yescharacteristic
171C3×C4⋊Q8—32no—
172C3×#125—32no—
173C3×C22⋊Q8—34no—
174C3×C4×Q8—34no—
175C3×#117—21no—
176C3×#117—31no—
177C3×#117—31no—
178C3×#117—32no—
179C3×#117—32no—
180C3×#117—32no—
181C3×#117C2×D311yescharacteristic
182C3×#117C2×D311yescharacteristic
183C2×C3×C4⋊C4—32no—
184C2×C3×C22⋊C4—32no—
185C2×C3×C42—31no—
186C2×C3×C42—32no—
187C2×#217—32no—
188C2×#217—32no—
189#946—34no—
190#946—34no—
191#944—34no—
192#944—34no—
193C2×(C2×D3)⋊C4—32no—
194#926—31no—
195#926—31no—
196#926—32no—
197#926—32no—
198#926—32no—
199#926—32no—
200#926—31no—
201#926—31no—
202#926—32no—
203#926—31no—
204#926—31no—
205#926—61no—
206#926C2×D311yescharacteristic
207#926C2×D311yescharacteristic
208C2×C4⋊Dic3—32no—
209C2×C4⋊Dic3—32no—
210#924—34no—
211#924—34no—
212#924—34no—
213#924—34no—
214#924—34no—
215C2×Dic3⋊C4—32no—
216C2×C4×Dic3—31no—
217C2×C4×Dic3—31no—
218C2×C4×Dic3—32no—
219C2×C4×Dic3—61no—
220C2×C4×Dic3C2×D311yescharacteristic
221#897—34no—
222#897—34no—
223#896—34no—
224#896—34no—
225#896—34no—
226#896—34no—
227#892—32no—
228#892C2×D312yes—
229D3×C4⋊C4—32no—
230D3×C4⋊C4C2×D312yes—
231#890—32no—
232#890—32no—
233#890—32no—
234#890—34no—
235#890—32no—
236#890—34no—
237#890—32no—
238#890—62no—
239#890C2×D312yescomplemented
240#889—34no—
241#889—34no—
242#889—34no—
243#889—34no—
244#888—34no—
245#888—32no—
246#888—32no—
247#888—32no—
248#888—32no—
249#888—34no—
250#888—34no—
251#888—34no—
252#888—32no—
253#888—62no—
254#888C2×D312yescomplemented
255D3×C22⋊C4—32no—
256D3×C22⋊C4C2×D312yes—
257#878—34no—
258#878—34no—
259#878—34no—
260#878—34no—
261#878—34no—
262#878—34no—
263#878—34no—
264#878—34no—
265#878—34no—
266#878—64no—
267#878C2×D314yes—
268#877—32no—
269#877C2×D312yes—
270#872—31no—
271#872—31no—
272#872—31no—
273#872—31no—
274#872—32no—
275#872—32no—
276#872—32no—
277#872C2×D312yes—
278C42×D3—32no—
279C42×D3C2×D312yes—
280#870—32no—
281#870—34no—
282#870—34no—
283#869—34no—
284#869—32no—
285#869—34no—
286C4×Dic6—34no—
287C4×Dic6—34no—
288C4×Dic6—34no—
289C4×Dic6—34no—
290C4×Dic6—34no—
291C4×Dic6—34no—
292C4×Dic6—64no—
293C4×Dic6C2×D314yescomplemented
294C23×C32C2411yescharacteristic
295C22×C3×D3—42no—
296C22×C3×D3C2×Q814yes—
297C22×C3×D3C2411yescharacteristic
298C22×C3×D3C2411yescharacteristic
299C2×C32×C4C2×Q814yes—
300C2×C32×C4C2414yes—
301C2×C32×C4C2411yescharacteristic
302C2×C32×C4C2411yescharacteristic
303C2×C3⋊Dic3—42no—
304C2×C3⋊Dic3C2414yes—
305C2×C3⋊Dic3C2412yes—
306C2×C3⋊Dic3C2412yes—
307#634—44no—
308C2×C3×Dic3—42no—
309C2×C3×Dic3C2×Q814yes—
310C2×C3×Dic3C2414yes—
311C2×C3×Dic3C2412yes—
312C2×C3×Dic3C2412yes—
313C2×C3×Dic3C2414yes—
314C2×C3×Dic3C2411yescharacteristic
315C2×C3×Dic3C2411yescharacteristic
316C3×C4×D3—44no—
317C3×C4×D3C2×Q814yes—
318C3×C4×D3C2×Q814yes—
319C3×C4×D3C2×Q814yes—
320C3×C4×D3C2×Q814yes—
321C3×Dic6—44no—
322#627—44no—
323#627—44no—
324D3×Dic3—44no—
325#544—92no—
326#544—92no—
327#544—94no—
328#544—92no—
329#544—92no—
330#543—94no—
331#533—31no—
332#533—91no—
333#533—94no—
334#533—91no—
335#533—94no—
336#533—91no—
337C2×#117—31no—
338C2×#117—91no—
339C2×#117—91no—
340C24×C3—31no—
341C23×D3C22×D311yescharacteristic
342C2×C3×Q8—34no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—38no—
346C22×C3×C4—31no—
347C22×C3×C4—31no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—32no—
351C22×C3×C4—34no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×Dic3—32no—
355C22×Dic3—32no—
356C22×Dic3—34no—
357C22×Dic3—62no—
358C22×Dic3C22×D312yes—
359C22×Dic3C22×D311yescharacteristic
360C2×C4×D3—34no—
361C2×C4×D3Dic618yescomplemented
362C2×C4×D3C22×D314yes—
363C2×C4×D3C22×D311yescharacteristic
364C2×C4×D3C22×D311yescharacteristic
365C2×C4×D3C22×D311yescharacteristic
366C2×C4×D3C22×D311yescharacteristic
367C2×Dic6—34no—
368C2×Dic6—34no—
369C2×Dic6—34no—
370C2×Dic6—34no—
371C2×Dic6—34no—
372C2×Dic6—34no—
373C2×Dic6—64no—
374C2×Dic6C22×D314yes—
375C3×C4⋊C4—22no—
376C3×C4⋊C4—34no—
377C3×C4⋊C4—32no—
378C3×C4⋊C4—34no—
379C3×C4⋊C4—34no—
380C3×C4⋊C4—32no—
381C3×C4⋊C4—34no—
382C3×C4⋊C4C22×D312yes—
383C3×C4⋊C4C22×D312yes—
384C3×C22⋊C4—22no—
385C3×C22⋊C4—32no—
386C3×C22⋊C4—32no—
387C3×C22⋊C4—34no—
388C3×C22⋊C4C22×D312yes—
389C3×C22⋊C4C22×D312yes—
390C3×C42—22no—
391C3×C42—32no—
392C3×C42—32no—
393C3×C42—32no—
394C3×C42—34no—
395C3×C42—31no—
396C3×C42—31no—
397C3×C42C22×D312yes—
398C3×C42C22×D312yes—
399#217—32no—
400#217—32no—
401#217—32no—
402#217—32no—
403#217—34no—
404#217—32no—
405#217—32no—
406#217—62no—
407#217C22×D312yes—
408#217C22×D312yes—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—32no—
411(C2×D3)⋊C4—32no—
412(C2×D3)⋊C4—32no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4C22×D314yes—
415C4⋊Dic3—34no—
416C4⋊Dic3—34no—
417C4⋊Dic3—32no—
418C4⋊Dic3—32no—
419C4⋊Dic3—34no—
420C4⋊Dic3—34no—
421C4⋊Dic3—34no—
422C4⋊Dic3—34no—
423C4⋊Dic3—34no—
424C4⋊Dic3—32no—
425C4⋊Dic3—32no—
426C4⋊Dic3—32no—
427C4⋊Dic3—32no—
428C4⋊Dic3—64no—
429C4⋊Dic3—62no—
430C4⋊Dic3C22×D314yes—
431C4⋊Dic3C22×D312yes—
432C4⋊Dic3C22×D312yes—
433Dic3⋊C4—34no—
434Dic3⋊C4—34no—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—32no—
446Dic3⋊C4—32no—
447Dic3⋊C4—32no—
448Dic3⋊C4—32no—
449Dic3⋊C4—34no—
450Dic3⋊C4—64no—
451Dic3⋊C4—64no—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D314yes—
454Dic3⋊C4C22×D314yes—
455C4×Dic3—32no—
456C4×Dic3—32no—
457C4×Dic3—32no—
458C4×Dic3—32no—
459C4×Dic3—31no—
460C4×Dic3—31no—
461C4×Dic3—31no—
462C4×Dic3—31no—
463C4×Dic3—34no—
464C4×Dic3—34no—
465C4×Dic3—62no—
466C4×Dic3—62no—
467C4×Dic3—61no—
468C4×Dic3—61no—
469C4×Dic3C22×D312yes—
470C4×Dic3C22×D312yes—
471C4×Dic3C22×D312yes—
472C4×Dic3C22×D314yes—
473C4×Dic3C22×D311yescharacteristic
474C4×Dic3C22×D311yescharacteristic
475C22×C32—22no—
476C22×C32C22×Q812yes—
477C22×C32C2511yescharacteristic
478C2×C3×D3—22no—
479C2×C3×D3—22no—
480C2×C3×D3—44no—
481C2×C3×D3C22×Q812yes—
482C2×C3×D3C22×Q812yes—
483C32×C4—24no—
484C32×C4C22×Q812yes—
485C32×C4C22×Q812yes—
486C3⋊Dic3—22no—
487C3⋊Dic3—24no—
488C3⋊Dic3—22no—
489C3×Dic3—24no—
490C3×Dic3—24no—
491C3×Dic3—22no—
492C3×Dic3—22no—
493C3×Dic3C22×Q812yes—
494C3×Dic3C22×Q812yes—
495C23×C4—31no—
496C4⋊Q8—32no—
497C4⋊Q8—94no—
498C4⋊Q8—92no—
499C4⋊Q8—94no—
500C4⋊Q8—94no—
501C4⋊Q8—92no—
502C4⋊Q8—94no—
503C4⋊Q8—92no—
504#125—32no—
505#125—94no—
506#125—94no—
507#125—92no—
508#125—94no—
509#125—94no—
510#125—92no—
511#125—92no—
512C22⋊Q8—34no—
513C22⋊Q8—94no—
514C22⋊Q8—94no—
515C22⋊Q8—94no—
516C22⋊Q8—94no—
517C22⋊Q8—94no—
518C22⋊Q8—94no—
519C22⋊Q8—94no—
520C22⋊Q8—94no—
521C22⋊Q8—94no—
522C22⋊Q8—94no—
523C22⋊Q8—94no—
524C4×Q8—34no—
525C4×Q8—94no—
526C4×Q8—94no—
527C4×Q8—94no—
528#117—31no—
529#117—31no—
530#117—32no—
531#117—32no—
532#117—32no—
533#117—92no—
534#117—92no—
535#117—92no—
536#117—91no—
537#117—91no—
538#117—91no—
539#117—91no—
540#117—92no—
541#117—92no—
542#117—91no—
543#117D3211yescharacteristic
544C2×C4⋊C4—32no—
545C2×C4⋊C4—92no—
546C2×C4⋊C4—92no—
547C2×C22⋊C4—32no—
548C2×C22⋊C4—92no—
549C2×C22⋊C4—92no—
550C2×C42—31no—
551C2×C42—32no—
552C2×C42—92no—
553C2×C42—91no—
554C23×C3—21no—
555C23×C3—31no—
556C23×C3—31no—
557C23×C3—34no—
558C23×C3—122no—
559C23×C3C23×D311yescharacteristic
560C23×C3C23×D311yescharacteristic
561C22×D3—42no—
562C22×D3C2×Dic614yes—
563C22×D3C23×D311yescharacteristic
564C22×D3C23×D311yescharacteristic
565C3×Q8—124no—
566C2×C3×C4—21no—
567C2×C3×C4—24no—
568C2×C3×C4—21no—
569C2×C3×C4—24no—
570C2×C3×C4—34no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—34no—
574C2×C3×C4—34no—
575C2×C3×C4—34no—
576C2×C3×C4—34no—
577C2×C3×C4—34no—
578C2×C3×C4—32no—
579C2×C3×C4—34no—
580C2×C3×C4—32no—
581C2×C3×C4—124no—
582C2×C3×C4—122no—
583C2×C3×C4C2×Dic614yes—
584C2×C3×C4D3×Q814yes—
585C2×C3×C4C23×D314yes—
586C2×C3×C4C23×D314yes—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—34no—
594C2×Dic3—34no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—42no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—64no—
601C2×Dic3—124no—
602C2×Dic3—122no—
603C2×Dic3—122no—
604C2×Dic3—124no—
605C2×Dic3C2×Dic614yes—
606C2×Dic3C23×D314yes—
607C2×Dic3C23×D314yes—
608C2×Dic3C23×D312yes—
609C2×Dic3C23×D312yes—
610C2×Dic3C23×D311yescharacteristic
611C2×Dic3C23×D311yescharacteristic
612C4×D3—44no—
613C4×D3—124no—
614C4×D3C2×Dic614yes—
615C4×D3C2×Dic614yes—
616C4×D3C2×Dic614yes—
617C4×D3C2×Dic614yes—
618Dic6—44no—
619Dic6—124no—
620Dic6—124no—
621Dic6—124no—
622Dic6—124no—
623Dic6—124no—
624Dic6—124no—
625Dic6—128no—
626C2×C32—22no—
627C2×C32C23×Q811yescharacteristic
628C2×C32#58512yes—
629C3×D3—22no—
630C3×D3—22no—
631C24—31no—
632C2×Q8—34no—
633C2×Q8—94no—
634C2×Q8—94no—
635C2×Q8—94no—
636C22×C4—31no—
637C22×C4—31no—
638C22×C4—31no—
639C22×C4—31no—
640C22×C4—31no—
641C22×C4—38no—
642C22×C4—32no—
643C22×C4—34no—
644C22×C4—94no—
645C22×C4—92no—
646C22×C4C2×D3211yescharacteristic
647C4⋊C4—34no—
648C4⋊C4—32no—
649C4⋊C4—32no—
650C4⋊C4—34no—
651C4⋊C4—34no—
652C4⋊C4—34no—
653C4⋊C4—92no—
654C4⋊C4—92no—
655C4⋊C4—94no—
656C4⋊C4—92no—
657C4⋊C4—92no—
658C4⋊C4—94no—
659C4⋊C4—94no—
660C4⋊C4—94no—
661C4⋊C4—94no—
662C4⋊C4—94no—
663C4⋊C4—94no—
664C4⋊C4—92no—
665C4⋊C4—94no—
666C4⋊C4—94no—
667C4⋊C4—94no—
668C4⋊C4C2×D3212yes—
669C22⋊C4—32no—
670C22⋊C4—32no—
671C22⋊C4—34no—
672C22⋊C4—92no—
673C22⋊C4—92no—
674C22⋊C4—92no—
675C22⋊C4—92no—
676C22⋊C4—94no—
677C22⋊C4—92no—
678C22⋊C4C2×D3212yes—
679C42—34no—
680C42—31no—
681C42—31no—
682C42—32no—
683C42—32no—
684C42—32no—
685C42—94no—
686C42—91no—
687C42—91no—
688C42—92no—
689C42—92no—
690C42C2×D3212yes—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—21no—
695C22×C3—32no—
696C22×C3—32no—
697C22×C3—42no—
698C22×C3—62no—
699C22×C3—62no—
700C22×C3—124no—
701C22×C3C22×Dic612yes—
702C22×C3C2×D3×Q812yes—
703C22×C3C24×D311yescharacteristic
704C22×C3C24×D311yescharacteristic
705C2×D3—22no—
706C2×D3—22no—
707C2×D3—44no—
708C2×D3C22×Dic612yes—
709C2×D3C22×Dic612yes—
710C3×C4—24no—
711C3×C4—24no—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—32no—
715C3×C4—32no—
716C3×C4—44no—
717C3×C4—64no—
718C3×C4—62no—
719C3×C4—64no—
720C3×C4—62no—
721C3×C4C22×Dic612yes—
722C3×C4C22×Dic612yes—
723C3×C4C2×D3×Q812yes—
724C3×C4C2×D3×Q812yes—
725Dic3—22no—
726Dic3—24no—
727Dic3—24no—
728Dic3—22no—
729Dic3—64no—
730Dic3—64no—
731Dic3—62no—
732Dic3—62no—
733Dic3—62no—
734Dic3—64no—
735Dic3—62no—
736Dic3—124no—
737Dic3—122no—
738Dic3C22×Dic612yes—
739Dic3C22×Dic612yes—
740C32#345811yescharacteristic, complemented, Sylow
741C23—31no—
742C23—31no—
743C23—34no—
744C23—122no—
745C23C22×D3211yescharacteristic
746Q8—124no—
747Q8—364no—
748Q8—364no—
749Q8—364no—
750C2×C4—34no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—34no—
754C2×C4—34no—
755C2×C4—34no—
756C2×C4—34no—
757C2×C4—34no—
758C2×C4—32no—
759C2×C4—32no—
760C2×C4—34no—
761C2×C4—92no—
762C2×C4—94no—
763C2×C4—92no—
764C2×C4—124no—
765C2×C4—122no—
766C2×C4—364no—
767C2×C4—362no—
768C2×C4D3×Dic614yes—
769C2×C4C22×D3214yes—
770C2×C4C22×D3211yescharacteristic
771C2×C4C22×D3211yescharacteristic
772C2×C3—22no—
773C2×C3—22no—
774C2×C3—21no—
775C2×C3—22no—
776C2×C3—42no—
777C2×C3—62no—
778C2×C3—62no—
779C2×C3C23×Dic611yescharacteristic
780C2×C3C22×D3×Q811yescharacteristic
781C2×C3#596412yes—
782C2×C3#596412yes—
783D3—22no—
784D3—22no—
785C22—22no—
786C22—32no—
787C22—32no—
788C22—62no—
789C22—62no—
790C22—124no—
791C22C2×D3×Dic612yes—
792C22C23×D3211yescharacteristic
793C4—24no—
794C4—32no—
795C4—32no—
796C4—62no—
797C4—64no—
798C4—62no—
799C4—64no—
800C4—182no—
801C4—184no—
802C4—182no—
803C4C2×D3×Dic612yes—
804C4C2×D3×Dic612yes—
805C3—21no—
806C3#8572511yescharacteristic, complemented
807C3#8627411yescharacteristic, complemented
808C2—22no—
809C2—62no—
810C2—62no—
811C2C22×D3×Dic611yescharacteristic
812C2#1059669512yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
prime radicalC23×C3×D3C23
hypercenter#117D32
hypocenterC32#3458
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595988C2semidirect
3. C3×#5517C2semidirect
4. #10595050C2semidirect
5. #10595049C2semidirect
8. #10594505C2semidirect
9. #10594502C2semidirect
10. #10594344C2semidirect
11. #10594342C2semidirect
13. #10594035C2semidirect
14. #10593926C2semidirect
15. #10593873C2semidirect
22. #64099C22semidirect
23. #64097C22semidirect
25. C4×#634C22semidirect
31. C3×#890C22semidirect
32. C3×#888C22semidirect
38. C3×C4×Dic6C22semidirect
45. #63919C22semidirect
46. #63918C22semidirect
47. #63918C22semidirect
48. C4×#627C22semidirect
49. C4×#627C22semidirect
56. #63872C22semidirect
57. #63869C22semidirect
58. #63867C22semidirect
59. #63867C22semidirect
60. #63866C22semidirect
72. #63846C22semidirect
73. #63845C22semidirect
75. #63840C22semidirect
76. #63839C22semidirect
101. #5517D3semidirect
114. C2×C3×C4×D3Q8semidirect
239. #890C2×D3semidirect
254. #888C2×D3semidirect
293. C4×Dic6C2×D3semidirect
361. C2×C4×D3Dic6semidirect
740. C32#3458semidirect
806. C3#85725semidirect
807. C3#86274semidirect

Maximal subgroups

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

subgroupindex
#105959882
C3×D3×#1172
C3×#55172
#105950502
#105950492
D3×#9262
C2×#638552
#105945052
#105945022
#105943442
#105943422
#105941702
#105940352
#105939262
#105938732
#862743
#857253