Finite Group Databasebeta

← #11909338

Subgroups — #11909338

Order 1152.

2365 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596151C211yesmaximal, characteristic, complemented
2C3×#5677C212yesmaximal, complemented
3D3×#946C212yesmaximal, complemented
4#10595413C211yesmaximal, characteristic, complemented
5Q8×#625C211yesmaximal, characteristic, complemented
6#10595301C212yesmaximal, complemented
7#10595252C211yesmaximal, characteristic, complemented
8#10595134C211yesmaximal, characteristic, complemented
9#10594300C214yesmaximal, complemented
10#10594276C212yesmaximal, complemented
11#10594224C212yesmaximal, complemented
12#10594168C212yesmaximal, complemented
13#10594114C214yesmaximal, complemented
14#10594051C212yesmaximal, complemented
15C4×#3802C211yesmaximal, characteristic, complemented
16#10593917C212yesmaximal, complemented
17#10593882C211yesmaximal, characteristic, complemented
18#86721—32nomaximal
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#237C2212yescomplemented
21C2×#3805C2212yes—
22C2×#3802C2211yescharacteristic
23C2×C4×D32C2212yes—
24C32×#124C2211yescharacteristic, complemented
25#64155C2211yescharacteristic
26Q8×C3⋊Dic3C2211yescharacteristic, complemented
27#64147C2211yescharacteristic
28D4×C3⋊Dic3C2211yescharacteristic, complemented
29#64092C2212yes—
30#64090C2212yes—
31#64088C2212yescomplemented
32#64086C2212yescomplemented
33C42×C3⋊D3C2211yescharacteristic
34#64079C2211yescharacteristic, complemented
35C3×#946C2212yescomplemented
36C3×#938C2212yescomplemented
37C3×#885C2214yescomplemented
38C3×#884C2214yes—
39C3×#67⋊C4C2214yescomplemented
40C3×#878C2214yescomplemented
41C3×C4×D12C2212yes—
42C3×C4×Dic6C2212yescomplemented
43#63983C2214yes—
44#63982C2212yescomplemented
45#63980C2212yes—
46Dic3×#67C2214yescomplemented
47#63969C2214yescomplemented
48#63969C2214yescomplemented
49C2×#3724C2212yescomplemented
50#63961C2214yescomplemented
51#63952C2214yes—
52#63921C2212yes—
53D3×(C2×D3)⋊C4C2214yes—
54#63919C2211yescharacteristic, complemented
55C4×#627C2212yescomplemented
56#63915C2212yes—
57#63902C2211yescharacteristic
58#63902C2211yescharacteristic
59C4×#625C2212yes—
60C4×#625C2211yescharacteristic
61C4×#625C2211yescharacteristic
62#63900C2211yescharacteristic
63#63898C2212yes—
64D3×C4⋊Dic3C2212yescomplemented
65#63888C2214yes—
66#63887C2214yescomplemented
67#63884C2214yes—
68#63877C2214yescomplemented
69D3×Dic3⋊C4C2214yescomplemented
70#63874C2212yes—
71#63873C2211yescharacteristic, complemented
72#63873C2212yescomplemented
73#63871C2212yes—
74#63870C2212yescomplemented
75#63865C2212yes—
76#63861C2214yescomplemented
77#63859C2214yescomplemented
78#63856C2214yescomplemented
79#63856C2212yescomplemented
80#63856C2212yescomplemented
81#63847C2214yescomplemented
82#63841C2212yescomplemented
83#63838C2212yescomplemented
84C3×#548—32no—
85#5828—32no—
86#5824—32no—
87Q8×#67—32no—
88C2×#946—32no—
89#5680—32no—
90#5680—61no—
91#5679—34no—
92#5677D312yescomplemented
93#5669—34no—
94#5641—32no—
95#5638—34no—
96#5636—34no—
97D3×C22⋊Q8—32no—
98#5611—32no—
99#5610—34no—
100#5606—32no—
101#5602—34no—
102#5581—32no—
103#5578—32no—
104#5556—34no—
105#5546—34no—
106C4×D3×D4—32no—
107#5541—32no—
108C22×D32C2312yes—
109C2×C32×Q8C2311yescharacteristic
110C2×C32×D4C2311yescharacteristic
111C2×#638C2312yes—
112C22×C3⋊Dic3C2312yes—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C4×C3⋊D3C2311yescharacteristic
115C2×C4×C3⋊D3C2311yescharacteristic
116C2×C3×#67C2314yes—
117C2×C3×#67C2314yes—
118C22×C3×Dic3C2314yes—
119C3×D3×Q8—44no—
120C3×#237—44no—
121C2×C3×D12C2312yes—
122C2×C3×C4×D3C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×C4×D3C2314yes—
125C2×C3×Dic6C2312yes—
126C2×C3×Dic6C2314yes—
127C2×#627C2312yes—
128C2×#625C2311yescharacteristic
129C2×#625C2311yescharacteristic
130C2×#624C2312yes—
131#3805—28no—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2312yes—
135#3802—24no—
136C4×D32—44no—
137C32×C22⋊C4C2312yes—
138C32×C22⋊C4C2312yes—
139C32×C42C2311yescharacteristic
140#3757C2312yes—
141#3757C2312yes—
142#3752C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145C4⋊(C3⋊Dic3)C2312yes—
146#3750C2312yes—
147#3750C2312yes—
148#3750C2312yes—
149C4×C3⋊Dic3C2311yescharacteristic
150C4×C3⋊Dic3C2311yescharacteristic
151C4×C3⋊Dic3C2311yescharacteristic
152C4×C3⋊Dic3C2312yes—
153C3×#217C2314yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×C4×Dic3C2314yes—
162#3724C2311yescharacteristic
163#3724C2314yes—
164#3724C2314yes—
165#3724C2312yes—
166#3724C2312yes—
167#3724C2312yes—
168#3724C2311yescharacteristic
169Dic3⋊Dic3C2314yes—
170Dic3⋊Dic3C2314yes—
171#3722C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2312yes—
175(C2×D3)⋊Dic3C2314yes—
176(C2×D3)⋊Dic3C2312yes—
177Dic32C2314yes—
178#3520—91noSylow
179C2×C3×#41—32no—
180C22×C3×Q8—32no—
181C2×D3×Q8C2×D312yescomplemented
182C2×#237—34no—
183C2×#237C2×D312yescomplemented
184C2×D3×D4—32no—
185C22×C4×D3—32no—
186C22×C4×D3—32no—
187C3×#124—21no—
188C3×#124—34no—
189C3×#124C2×D312yescomplemented
190C3×C22⋊Q8—32no—
191C3×C22⋊Q8—34no—
192C3×#121—32no—
193C3×#121—34no—
194C3×C4×Q8—32no—
195C3×C4×D4—34no—
196C3×C4×D4—32no—
197#946—32no—
198#946—34no—
199#946—32no—
200#946—32no—
201#946—34no—
202#946—32no—
203#946—34no—
204#946—61no—
205#946C2×D312yescomplemented
206Q8×Dic3—32no—
207Q8×Dic3—61no—
208#944—34no—
209#944—32no—
210#939—34no—
211#938—32no—
212#938—61no—
213#938C2×D312yescomplemented
214#937—34no—
215#937—34no—
216#935—34no—
217#935—34no—
218#935—34no—
219#935—34no—
220D4×Dic3—32no—
221D4×Dic3—34no—
222D4×Dic3—32no—
223D4×Dic3—61no—
224#929—34no—
225C4×#67—34no—
226C4×#67—32no—
227C4×#67—32no—
228C4×#67—34no—
229C4×#67—34no—
230C2×(C2×D3)⋊C4—34no—
231#926—32no—
232C2×C4⋊Dic3—32no—
233#924—32no—
234#924—32no—
235#924—34no—
236C2×Dic3⋊C4—34no—
237C2×Dic3⋊C4—34no—
238#898—34no—
239#897—32no—
240#896—34no—
241#896—34no—
242#894—34no—
243#893—32no—
244#892—32no—
245D3×C4⋊C4—34no—
246D3×C4⋊C4—32no—
247D3×C4⋊C4—32no—
248#889—34no—
249#889—34no—
250#889—34no—
251#888—32no—
252#887—34no—
253#885—34no—
254#885C2×D314yescomplemented
255#884C2×D314yes—
256#883—34no—
257#883—34no—
258#883—34no—
259#883—62no—
260#67⋊C4—34no—
261#67⋊C4—34no—
262#67⋊C4—32no—
263#67⋊C4—32no—
264#67⋊C4—62no—
265#67⋊C4C2×D314yescomplemented
266D3×C22⋊C4—34no—
267D3×C22⋊C4—32no—
268D3×C22⋊C4—32no—
269#879—34no—
270#879—34no—
271#879—34no—
272#879—62no—
273#878—34no—
274#878—34no—
275#878C2×D314yescomplemented
276#877—34no—
277#877—34no—
278#877—62no—
279#876—34no—
280C4×D12C2×D312yes—
281#872—34no—
282#872—34no—
283C42×D3—32no—
284C42×D3—61no—
285#870—32no—
286#870—61no—
287C4×Dic6—34no—
288C4×Dic6C2×D312yescomplemented
289C23×C32C2412yes—
290C22×C3⋊D3C2411yescharacteristic
291C22×C3×D3C2412yes—
292C22×C3×D3C2412yes—
293C2×D32—24no—
294C2×D32—24no—
295C2×D32—42no—
296C32×Q8—22no—
297C32×D4—22no—
298C2×C32×C4C2411yescharacteristic
299C2×C32×C4C2411yescharacteristic
300C2×C32×C4C2412yes—
301C2×C32×C4C2411yescharacteristic
302#638—24no—
303C2×C3⋊Dic3—24no—
304C2×C3⋊Dic3C2412yes—
305C2×C3⋊Dic3C2411yescharacteristic
306C2×C3⋊Dic3C2412yes—
307C2×C3⋊Dic3C2411yescharacteristic
308C2×C3⋊Dic3C2411yescharacteristic
309C4×C3⋊D3—22no—
310C4×C3⋊D3—22no—
311C4×C3⋊D3—22no—
312C3×#67—28no—
313C3×#67—44no—
314C2×C3×Dic3—44no—
315C2×C3×Dic3C2412yes—
316C2×C3×Dic3C2414yes—
317C2×C3×Dic3C2414yes—
318C2×C3×Dic3C2412yes—
319C3×D12—24no—
320C3×C4×D3—24no—
321C3×C4×D3—24no—
322C3×C4×D3—44no—
323C3×Dic6—24no—
324C3×Dic6—44no—
325#627—24no—
326#625—22no—
327#625#4114yescomplemented
328#624—42no—
329D3×Dic3—28no—
330D3×Dic3—42no—
331D3×Dic3—42no—
332#556—91no—
333#554—92no—
334#552—92no—
335#551—94no—
336D4×Q8—91no—
337#548—32no—
338#547—91no—
339#547—91no—
340#546—92no—
341#542—92no—
342#539—94no—
343#533—91no—
344#529—91no—
345#525—92no—
346C2×C22⋊Q8—92no—
347#520—92no—
348C2×C4×D4—91no—
349C23×D3—32no—
350C23×D3—32no—
351C3×#41—124no—
352C2×C3×Q8—21no—
353C2×C3×Q8—32no—
354C2×C3×Q8—34no—
355C2×C3×Q8—124no—
356C2×C3×Q8C22×D312yes—
357C2×C3×D4—21no—
358C2×C3×D4—34no—
359C2×C3×D4—34no—
360C2×C3×D4—32no—
361C2×C3×D4C22×D312yes—
362C22×C3×C4—34no—
363C22×C3×C4—32no—
364C22×C3×C4—32no—
365C22×C3×C4—34no—
366C2×#67—32no—
367C2×#67—34no—
368C2×#67—32no—
369C2×#67—62no—
370C2×#67C22×D314yes—
371C2×#67C22×D314yes—
372C22×Dic3—34no—
373C22×Dic3—34no—
374C22×Dic3—32no—
375C22×Dic3—32no—
376C22×Dic3—62no—
377C22×Dic3C22×D314yes—
378D3×Q8—44no—
379#237—44no—
380#237—616no—
381D3×D4—68no—
382C2×D12C22×D312yes—
383C2×C4×D3—34no—
384C2×C4×D3—32no—
385C2×C4×D3—32no—
386C2×C4×D3—32no—
387C2×C4×D3—32no—
388C2×C4×D3—32no—
389C2×C4×D3—32no—
390C2×C4×D3—32no—
391C2×C4×D3—61no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—124no—
395C2×C4×D3—124no—
396C2×C4×D3C22×D312yes—
397C2×C4×D3C22×D312yes—
398C2×C4×D3C22×D314yes—
399C2×Dic6—34no—
400C2×Dic6C22×D312yes—
401C2×Dic6C22×D314yes—
402C3×C4⋊C4—34no—
403C3×C4⋊C4—32no—
404C3×C4⋊C4—32no—
405C3×C4⋊C4—34no—
406C3×C22⋊C4—22no—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—32no—
410C3×C22⋊C4—34no—
411C3×C22⋊C4—32no—
412C3×C22⋊C4C22×D314yes—
413C3×C22⋊C4C22×D314yes—
414C3×C42—21no—
415C3×C42—34no—
416C3×C42C22×D312yes—
417#217—34no—
418#217—34no—
419#217—34no—
420#217—34no—
421#217—32no—
422#217—34no—
423#217—32no—
424#217—62no—
425#217—62no—
426#217C22×D314yes—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—32no—
431(C2×D3)⋊C4—32no—
432(C2×D3)⋊C4—34no—
433(C2×D3)⋊C4—34no—
434(C2×D3)⋊C4—34no—
435(C2×D3)⋊C4—62no—
436(C2×D3)⋊C4C22×D312yes—
437(C2×D3)⋊C4C22×D312yes—
438(C2×D3)⋊C4C22×D314yes—
439C4⋊Dic3—32no—
440C4⋊Dic3—32no—
441C4⋊Dic3—34no—
442C4⋊Dic3—34no—
443C4⋊Dic3—34no—
444C4⋊Dic3—61no—
445C4⋊Dic3—61no—
446C4⋊Dic3—62no—
447C4⋊Dic3C22×D312yes—
448C4⋊Dic3C22×D312yes—
449Dic3⋊C4—34no—
450Dic3⋊C4—34no—
451Dic3⋊C4—34no—
452Dic3⋊C4—34no—
453Dic3⋊C4—34no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—34no—
459Dic3⋊C4—34no—
460Dic3⋊C4—32no—
461Dic3⋊C4—34no—
462Dic3⋊C4—32no—
463Dic3⋊C4—62no—
464Dic3⋊C4—62no—
465Dic3⋊C4—62no—
466Dic3⋊C4C22×D314yes—
467Dic3⋊C4C22×D314yes—
468C4×Dic3—32no—
469C4×Dic3—32no—
470C4×Dic3—32no—
471C4×Dic3—34no—
472C4×Dic3—34no—
473C4×Dic3—34no—
474C4×Dic3—61no—
475C4×Dic3—61no—
476C4×Dic3—61no—
477C4×Dic3—62no—
478C4×Dic3C22×D314yes—
479C22×C32—22no—
480C22×C32—22no—
481C22×C32—22no—
482C22×C32C2511yescharacteristic
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D32−1+412yes—
486C2×C3×D3—22no—
487C2×C3×D3—22no—
488C2×C3×D3—22no—
489C2×C3×D3—22no—
490C2×C3×D3—22no—
491C2×C3×D3C2×#4114yes—
492D32—48no—
493C32×C4—21no—
494C32×C4—22no—
495C32×C4—21no—
496C32×C4H(5,𝔽2)12yes—
497C3⋊Dic3—22no—
498C3⋊Dic3—21no—
499C3⋊Dic3—21no—
500C3⋊Dic3—22no—
501C3⋊Dic3C2×#4112yes—
502C3×Dic3—24no—
503C3×Dic3—22no—
504C3×Dic3—22no—
505C3×Dic3—24no—
506C2×#41—32no—
507C2×#41—92no—
508C22×Q8—32no—
509C22×D4—91no—
510C23×C4—92no—
511C4⋊Q8—91no—
512C4⋊Q8—91no—
513C4⋊Q8—92no—
514#126—94no—
515#126—94no—
516#126—92no—
517#125—92no—
518#125—94no—
519#125—91no—
520#124—34no—
521#124—92no—
522#124D3211yescharacteristic, complemented
523#123—94no—
524#123—94no—
525#123—94no—
526#123—94no—
527#123—92no—
528C22⋊Q8—32no—
529C22⋊Q8—34no—
530C22⋊Q8—92no—
531C22⋊Q8—94no—
532C22⋊Q8—92no—
533C22⋊Q8—92no—
534C22⋊Q8—94no—
535C22⋊Q8—92no—
536C22⋊Q8—92no—
537C22⋊Q8—94no—
538C22⋊Q8—91no—
539#121—32no—
540#121—34no—
541#121—92no—
542#121—91no—
543#120—94no—
544C4×Q8—32no—
545C4×Q8—92no—
546C4×Q8—92no—
547C4×Q8—91no—
548C4×D4—34no—
549C4×D4—32no—
550C4×D4—91no—
551C4×D4—91no—
552C4×D4—94no—
553C4×D4—92no—
554C4×D4—91no—
555C4×D4—91no—
556C4×D4—92no—
557C4×D4—94no—
558C4×D4—91no—
559C4×D4—92no—
560#117—92no—
561#117—94no—
562#117—92no—
563#117—92no—
564C2×C4⋊C4—91no—
565C2×C4⋊C4—94no—
566C2×C4⋊C4—92no—
567C2×C4⋊C4—92no—
568C2×C22⋊C4—92no—
569C2×C22⋊C4—94no—
570C2×C42—91no—
571C23×C3—22no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3C23×D314yes—
575C22×D3—32no—
576C22×D3—61no—
577C22×D3—64no—
578C22×D3—64no—
579C22×D3—64no—
580C22×D3—64no—
581C22×D3—122no—
582C22×D3—122no—
583C22×D3C23×D312yes—
584C22×D3C23×D312yes—
585C3×Q8—24no—
586C3×Q8—42no—
587C3×Q8—64no—
588C3×Q8—124no—
589C3×D4—24no—
590C3×D4—42no—
591C3×D4—64no—
592C3×D4—68no—
593C3×D4—124no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—22no—
598C2×C3×C4—32no—
599C2×C3×C4—34no—
600C2×C3×C4—34no—
601C2×C3×C4—32no—
602C2×C3×C4—64no—
603C2×C3×C4—64no—
604C2×C3×C4—124no—
605C2×C3×C4—124no—
606C2×C3×C4C23×D312yes—
607C2×C3×C4C23×D312yes—
608C2×C3×C4C23×D314yes—
609C2×C3×C4C23×D312yes—
610#67—28no—
611#67—38no—
612#67—44no—
613#67—64no—
614#67—68no—
615#67—124no—
616C2×Dic3—32no—
617C2×Dic3—34no—
618C2×Dic3—32no—
619C2×Dic3—32no—
620C2×Dic3—34no—
621C2×Dic3—44no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—62no—
626C2×Dic3—62no—
627C2×Dic3—68no—
628C2×Dic3—68no—
629C2×Dic3—124no—
630C2×Dic3—122no—
631C2×Dic3—122no—
632C2×Dic3C23×D312yes—
633C2×Dic3C23×D314yes—
634C2×Dic3C23×D314yes—
635C2×Dic3C23×D312yes—
636D12—24no—
637C4×D3—24no—
638C4×D3—24no—
639C4×D3—44no—
640C4×D3—64no—
641C4×D3—64no—
642C4×D3—68no—
643C4×D3—64no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—122no—
647C4×D3—122no—
648C4×D3—122no—
649C4×D3—122no—
650C4×D3—122no—
651Dic6—24no—
652Dic6—44no—
653Dic6—68no—
654C2×C32—42no—
655C2×C32C22×#4111yescharacteristic
656C2×C32C2×H(5,𝔽2)11yescharacteristic
657C2×C32C2×2−1+411yescharacteristic
658C3⋊D3—22no—
659C3×D3—24no—
660C3×D3—42no—
661C24—92no—
662#41—124no—
663#41—188no—
664C2×Q8—32no—
665C2×Q8—34no—
666C2×Q8—92no—
667C2×Q8—124no—
668C2×Q8C2×D3211yescharacteristic
669C2×D4—34no—
670C2×D4—34no—
671C2×D4—32no—
672C2×D4—91no—
673C2×D4—91no—
674C2×D4—92no—
675C2×D4—184no—
676C2×D4C2×D3211yescharacteristic
677C22×C4—34no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—34no—
681C22×C4—92no—
682C22×C4—94no—
683C22×C4—92no—
684C22×C4—92no—
685C22×C4—92no—
686C22×C4—91no—
687C22×C4—91no—
688C22×C4—91no—
689C22×C4—364no—
690C4⋊C4—32no—
691C4⋊C4—32no—
692C4⋊C4—34no—
693C4⋊C4—34no—
694C4⋊C4—91no—
695C4⋊C4—94no—
696C4⋊C4—91no—
697C4⋊C4—92no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—92no—
701C4⋊C4—92no—
702C4⋊C4—94no—
703C4⋊C4—92no—
704C4⋊C4—91no—
705C4⋊C4—92no—
706C4⋊C4—91no—
707C4⋊C4—92no—
708C4⋊C4—92no—
709C22⋊C4—34no—
710C22⋊C4—32no—
711C22⋊C4—32no—
712C22⋊C4—34no—
713C22⋊C4—94no—
714C22⋊C4—92no—
715C22⋊C4—92no—
716C22⋊C4—94no—
717C22⋊C4—94no—
718C22⋊C4—94no—
719C22⋊C4—92no—
720C22⋊C4—92no—
721C22⋊C4—92no—
722C22⋊C4C2×D3212yes—
723C22⋊C4C2×D3212yes—
724C42—34no—
725C42—94no—
726C42—91no—
727C42—91no—
728C42—91no—
729C42—92no—
730C42C2×D3211yescharacteristic
731C22×C3—24no—
732C22×C3—24no—
733C22×C3—24no—
734C22×C3—21no—
735C22×C3—34no—
736C22×C3—42no—
737C22×C3—42no—
738C22×C3—42no—
739C22×C3—62no—
740C22×C3—62no—
741C22×C3—62no—
742C22×C3—62no—
743C22×C3—62no—
744C22×C3C24×D312yes—
745C2×D3—22no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—34no—
751C2×D3—62no—
752C2×D3—62no—
753C2×D3—62no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—128no—
757C2×D3—128no—
758C2×D3D3×#4114yes—
759C3×C4—24no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—22no—
763C3×C4—41no—
764C3×C4—41no—
765C3×C4—42no—
766C3×C4—62no—
767C3×C4—62no—
768C3×C4—64no—
769C3×C4—64no—
770C3×C4#100414yes—
771Dic3—24no—
772Dic3—22no—
773Dic3—22no—
774Dic3—24no—
775Dic3—34no—
776Dic3—62no—
777Dic3—62no—
778Dic3—64no—
779Dic3—62no—
780Dic3—64no—
781Dic3—121no—
782Dic3—121no—
783Dic3—122no—
784Dic3—122no—
785C32#352011yescharacteristic, complemented, Sylow
786C23—32no—
787C23—32no—
788C23—91no—
789C23—184no—
790C23—184no—
791C23—362no—
792C23C22×D3212yes—
793Q8—22no—
794Q8—64no—
795Q8—124no—
796Q8—184no—
797D4—22no—
798D4—64no—
799D4—68no—
800D4—94no—
801D4—124no—
802D4—182no—
803D4—184no—
804C2×C4—34no—
805C2×C4—34no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—64no—
809C2×C4—64no—
810C2×C4—91no—
811C2×C4—92no—
812C2×C4—91no—
813C2×C4—91no—
814C2×C4—92no—
815C2×C4—124no—
816C2×C4—124no—
817C2×C4—182no—
818C2×C4—182no—
819C2×C4—188no—
820C2×C4—184no—
821C2×C4—182no—
822C2×C4—362no—
823C2×C4—362no—
824C2×C4—362no—
825C2×C4C22×D3211yescharacteristic
826C2×C4C22×D3211yescharacteristic
827C2×C4C22×D3212yes—
828C2×C4C22×D3211yescharacteristic
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—44no—
833C2×C3—64no—
834C2×C3—82no—
835C2×C3—122no—
836C2×C3C2×#100412yes—
837C2×C3C2×D3×#4112yes—
838C2×C3D3×2−1+412yes—
839D3—24no—
840D3—42no—
841D3—64no—
842D3—122no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—34no—
847C22—62no—
848C22—62no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22—92no—
853C22—181no—
854C22—181no—
855C22—368no—
856C22C23×D3211yescharacteristic
857C4—22no—
858C4—21no—
859C4—21no—
860C4—62no—
861C4—62no—
862C4—64no—
863C4—64no—
864C4—92no—
865C4—181no—
866C4—182no—
867C4—181no—
868C4—182no—
869C4#6431312yes—
870C3—21no—
871C3#8672112yescomplemented
872C2—42no—
873C2—64no—
874C2—122no—
875C2—182no—
876C2C2×#6431311yescharacteristic
877C2D32×#4111yescharacteristic
878C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#124C22
hypercenter#124D32
hypocenterC32#3520
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #10596151C2semidirect
2. C3×#5677C2semidirect
3. D3×#946C2semidirect
4. #10595413C2semidirect
5. Q8×#625C2semidirect
6. #10595301C2semidirect
7. #10595252C2semidirect
8. #10595134C2semidirect
9. #10594300C2semidirect
10. #10594276C2semidirect
11. #10594224C2semidirect
12. #10594168C2semidirect
13. #10594114C2semidirect
14. #10594051C2semidirect
15. C4×#3802C2semidirect
16. #10593917C2semidirect
17. #10593882C2semidirect
19. C2×C3×D3×Q8C22semidirect
20. C2×C3×#237C22semidirect
24. C32×#124C22semidirect
26. Q8×C3⋊Dic3C22semidirect
28. D4×C3⋊Dic3C22semidirect
31. #64088C22semidirect
32. #64086C22semidirect
34. #64079C22semidirect
35. C3×#946C22semidirect
36. C3×#938C22semidirect
37. C3×#885C22semidirect
39. C3×#67⋊C4C22semidirect
40. C3×#878C22semidirect
42. C3×C4×Dic6C22semidirect
44. #63982C22semidirect
46. Dic3×#67C22semidirect
47. #63969C22semidirect
48. #63969C22semidirect
49. C2×#3724C22semidirect
50. #63961C22semidirect
54. #63919C22semidirect
55. C4×#627C22semidirect
64. D3×C4⋊Dic3C22semidirect
66. #63887C22semidirect
68. #63877C22semidirect
69. D3×Dic3⋊C4C22semidirect
71. #63873C22semidirect
72. #63873C22semidirect
74. #63870C22semidirect
76. #63861C22semidirect
77. #63859C22semidirect
78. #63856C22semidirect
79. #63856C22semidirect
80. #63856C22semidirect
81. #63847C22semidirect
82. #63841C22semidirect
83. #63838C22semidirect
92. #5677D3semidirect
181. C2×D3×Q8C2×D3semidirect
183. C2×#237C2×D3semidirect
189. C3×#124C2×D3semidirect
205. #946C2×D3semidirect
213. #938C2×D3semidirect
254. #885C2×D3semidirect
265. #67⋊C4C2×D3semidirect
275. #878C2×D3semidirect
288. C4×Dic6C2×D3semidirect
327. #625#41semidirect
522. #124D32semidirect
785. C32#3520semidirect
871. C3#86721semidirect

Maximal subgroups

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

subgroupindex
#105961512
C3×#56772
D3×#9462
#105954132
Q8×#6252
#105953012
#105952522
#105951342
#105943002
#105942762
#105942242
#105941682
#105941142
#105940512
C4×#38022
#105939172
#105938822
#867213