Finite Group Databasebeta

← #11904694

Subgroups — #11904694

Order 1152.

3461 conjugacy classes of subgroups.

The subgroup lattice has 917 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×#64319C211yesmaximal, characteristic, complemented
3#10596047C211yesmaximal, characteristic, complemented
4C3×#5577C211yesmaximal, characteristic, complemented
5C3×#5574C211yesmaximal, characteristic, complemented
6#10595414C211yesmaximal, characteristic, complemented
7#10595410C211yesmaximal, characteristic, complemented
8#10594630C213yesmaximal, complemented
9#10594621C213yesmaximal, complemented
10D3×#895C213yesmaximal, complemented
11#10594522C213yesmaximal, complemented
12#10594004C213yesmaximal, complemented
13#10594003C213yesmaximal, complemented
14#10594000C213yesmaximal, complemented
15#10593997C213yesmaximal, complemented
16#86769—31nomaximal
17#85900—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×#239C2211yescharacteristic, complemented
23#64320—28no—
24#64319—28no—
25C2×#3802C2213yescomplemented
26C2×#3802C2213yescomplemented
27C2×D3×D12C2213yescomplemented
28C2×D3×D12C2213yescomplemented
29C2×D3×D12C2216yescomplemented
30C2×C4×D32C2213yescomplemented
31C2×#3798C2213yescomplemented
32C2×#3795C2213yescomplemented
33C2×#3795C2213yescomplemented
34C32×C4×Q8C2211yescharacteristic, complemented
35#64106C2213yescomplemented
36#64104C2213yescomplemented
37#64084C2213yescomplemented
38C4×C4⋊(C3⋊D3)C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#895C2213yescomplemented
41C3×#895C2213yescomplemented
42C3×#893C2213yescomplemented
43C3×D3×C4⋊C4C2213yescomplemented
44C3×#874C2213yescomplemented
45C3×C4×D12C2213yescomplemented
46C3×C4×D12C2213yescomplemented
47C3×#872C2213yescomplemented
48#63923C2213yescomplemented
49#63922C2216yescomplemented
50#63922C2213yescomplemented
51#63922C2216yescomplemented
52D3×(C2×D3)⋊C4C2216yescomplemented
53#63916C2213yescomplemented
54#63916C2213yescomplemented
55#63911C2213yescomplemented
56#63910C2213yescomplemented
57#63909C2213yescomplemented
58#63908C2216yescomplemented
59#63906C2216yescomplemented
60C4×#626C2213yescomplemented
61C4×#626C2213yescomplemented
62#63895C2211yescharacteristic, complemented
63#63893C2213yescomplemented
64#63891C2213yescomplemented
65#63890C2213yescomplemented
66#63886C2216yescomplemented
67#63886C2213yescomplemented
68#63860C2213yescomplemented
69#63857C2213yescomplemented
70C2×#1009—31no—
71C2×#1009—31no—
72C2×D3×#41—31no—
73C2×D3×#41—31no—
74C3×#550—31no—
75C3×#520—31no—
76#5834—31no—
77#5831—31no—
78#5717—33no—
79#5715—33no—
80#5612—33no—
81#5609—33no—
82#5608—33no—
83D3×#121—33no—
84#5577—31no—
85#5577D311yescharacteristic, complemented
86#5576—31no—
87#5576—31no—
88#5576—31no—
89#5576—61no—
90#5574D311yescharacteristic, complemented
91#5554—33no—
92#5554—33no—
93#5550—33no—
94D4×D12—33no—
95D4×D12—33no—
96#5547—33no—
97#5525—33no—
98#5524—33no—
99#5510—33no—
100C2×#895—33no—
101C22×D32C2313yes—
102C22×D32C2316yes—
103C2×C32×Q8C2311yescharacteristic
104#3832—24no—
105Q8×C3⋊D3—24no—
106C2×C4⋊(C3⋊D3)C2313yes—
107C2×C4⋊(C3⋊D3)C2313yes—
108C2×C4×C3⋊D3C2313yes—
109C2×C4×C3⋊D3C2313yes—
110C2×#634C2313yes—
111C3×#239—24no—
112C3×#239—24no—
113C3×#239D418yescomplemented
114C2×C3×D12C2313yes—
115C2×C3×D12C2313yes—
116C2×C3×D12C2316yes—
117C2×C3×D12C2313yes—
118C2×C3×D12C2313yes—
119C2×C3×C4×D3C2313yes—
120C2×C3×C4×D3C2313yes—
121C2×C3×C4×D3C2316yes—
122C2×C3×C4×D3C2313yes—
123C2×#627C2311yescharacteristic
124C2×#626C2313yes—
125C2×#626C2313yes—
126C2×#626C2313yes—
127C2×#626C2316yes—
128C2×#626C2313yes—
129C2×#625C2316yes—
130C2×#625C2313yes—
131C2×#624C2311yescharacteristic
132C2×D3×Dic3C2313yes—
133C2×D3×Dic3C2313yes—
134#3802—212no—
135#3802—212no—
136D3×D12—212no—
137D3×D12—212no—
138D3×D12—412no—
139C4×D32—212no—
140#3798—212no—
141#3795—212no—
142#3795—212no—
143C32×C4⋊C4C2313yes—
144C32×C42C2313yes—
145#3752C2311yescharacteristic
146#3752C2313yes—
147#3752C2316yes—
148C4⋊(C3⋊Dic3)C2313yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×C4⋊Dic3C2313yes—
154C3×C4⋊Dic3C2311yescharacteristic
155C3×Dic3⋊C4C2313yes—
156C3×Dic3⋊C4C2311yescharacteristic
157C3×C4×Dic3C2313yes—
158Dic3⋊Dic3C2313yes—
159Dic3⋊Dic3C2311yescharacteristic
160#3722C2313yes—
161#3722C2311yescharacteristic
162(C2×D3)⋊Dic3C2316yes—
163(C2×D3)⋊Dic3C2313yes—
164(C2×D3)⋊Dic3C2313yes—
165#3488—91noSylow
166C2×C3×#41—31no—
167C2×C3×#41—31no—
168C2×C3×#41—31no—
169#1009—68no—
170#1009—68no—
171D3×#41—68no—
172D3×#41—68no—
173C2×#239—31no—
174C2×#239—31no—
175C2×#239—61no—
176C2×#239C2×D311yescharacteristic
177C2×#239C2×D311yescharacteristic, complemented
178C2×#239C2×D311yescharacteristic, complemented
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—61no—
182C2×#237—33no—
183C2×#237—33no—
184C2×D3×D4—33no—
185C2×D3×D4—33no—
186C2×D3×D4—33no—
187C2×D3×D4—33no—
188C2×D3×D4—33no—
189C2×D3×D4—33no—
190C2×D3×D4—36no—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235—33no—
194C2×#235—33no—
195C22×D12—33no—
196C22×D12—33no—
197C22×D12—36no—
198C22×C4×D3—33no—
199C22×C4×D3—33no—
200C3×#127—33no—
201C3×#121—33no—
202C3×#121—33no—
203C3×C4×Q8—21no—
204C3×C4×Q8—31no—
205C3×C4×Q8C2×D311yescharacteristic, complemented
206C3×C4×Q8C2×D311yescharacteristic, complemented
207C3×C4×D4—33no—
208C3×C4×D4—33no—
209C3×C4×D4—33no—
210C3×#117—33no—
211C2×C3×C4⋊C4—33no—
212Q8×Dic3C2×D311yescharacteristic, complemented
213#940—33no—
214#939—33no—
215#939—36no—
216#938—36no—
217#938—33no—
218#938—33no—
219#937—36no—
220#937—36no—
221#937—33no—
222#936—33no—
223#930—36no—
224#930—36no—
225#930—33no—
226C4×#67—33no—
227C4×#67—33no—
228C2×(C2×D3)⋊C4—36no—
229#924—33no—
230#897—33no—
231#897—33no—
232#897—33no—
233#897—33no—
234#897—31no—
235#897—63no—
236#896—31no—
237#895—36no—
238#895—33no—
239#895—33no—
240#895—33no—
241#895—33no—
242#895—33no—
243#895—33no—
244#895—33no—
245#895—63no—
246#895C2×D313yescomplemented
247#895C2×D313yescomplemented
248#894—33no—
249#893C2×D313yescomplemented
250D3×C4⋊C4C2×D313yescomplemented
251#886—33no—
252#886—33no—
253#884—36no—
254#884—33no—
255#883—33no—
256#882—33no—
257#882—36no—
258#882—36no—
259#882—33no—
260#882—33no—
261D3×C22⋊C4—36no—
262#878—33no—
263#875—33no—
264#875—33no—
265#875—33no—
266#875—63no—
267#874—33no—
268#874C2×D313yescomplemented
269C4×D12—33no—
270C4×D12—33no—
271C4×D12—33no—
272C4×D12—33no—
273C4×D12—63no—
274C4×D12C2×D313yescomplemented
275C4×D12C2×D313yescomplemented
276#872C2×D313yescomplemented
277C22×C3⋊D3C2413yes—
278C22×C3⋊D3C2411yescharacteristic
279C22×C3×D3C2413yes—
280C22×C3×D3C2413yes—
281C22×C3×D3C2413yes—
282C2×D32—26no—
283C2×D32—26no—
284C2×D32—212no—
285C2×D32—43no—
286C2×D32—46no—
287C2×D32—46no—
288C32×Q8C2×D414yescomplemented
289C2×C32×C4C2411yescharacteristic
290C2×C32×C4C2413yes—
291C2×C32×C4C2413yes—
292C2×C3⋊Dic3C2411yescharacteristic
293C2×C3⋊Dic3C2413yes—
294C4⋊(C3⋊D3)—26no—
295C4⋊(C3⋊D3)—26no—
296C4×C3⋊D3—26no—
297C4×C3⋊D3—26no—
298#634—26no—
299C2×C3×Dic3C2411yescharacteristic
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2411yescharacteristic
304C3×D12—26no—
305C3×D12—26no—
306C3×D12—46no—
307C3×D12—43no—
308C3×D12C2×D4112yescomplemented
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3—46no—
312C3×C4×D3C2×D4112yescomplemented
313#627—22no—
314#626—26no—
315#626—26no—
316#626—26no—
317#626—46no—
318#626—43no—
319#625—212no—
320#625—26no—
321#624—22no—
322D3×Dic3—26no—
323D3×Dic3—26no—
324C2×H(5,𝔽2)—91no—
325C22×#41—91no—
326#550—31no—
327#550—91no—
328#548—91no—
329#548—91no—
330#546—93no—
331#546—93no—
332D42—93no—
333D42—93no—
334#537—93no—
335#535—93no—
336#525—93no—
337C2×#121—93no—
338#520—31no—
339C23×D3—33no—
340C23×D3—33no—
341C23×D3—36no—
342C23×D3—36no—
343C3×#41—38no—
344C3×#41—64no—
345C3×#41—64no—
346C2×C3×Q8—21no—
347C2×C3×Q8C22×D311yescharacteristic
348C2×C3×Q8C22×D311yescharacteristic
349C2×C3×D4—33no—
350C2×C3×D4—33no—
351C2×C3×D4—33no—
352C2×C3×D4—33no—
353C2×C3×D4—36no—
354C22×C3×C4—33no—
355C22×C3×C4—33no—
356C22×C3×C4—33no—
357C22×C3×C4—36no—
358C2×#67—36no—
359C2×#67—33no—
360C2×#67—33no—
361C2×#67—36no—
362C2×#67—33no—
363C2×#67—33no—
364C2×#67—33no—
365C2×#67—33no—
366C2×#67—36no—
367C22×Dic3—33no—
368C22×Dic3—33no—
369#239—24no—
370#239—24no—
371#239—64no—
372#239—64no—
373#239—124no—
374#239D1218yescomplemented
375D3×Q8—64no—
376D3×Q8—64no—
377D3×Q8—124no—
378#237—612no—
379#237—612no—
380D3×D4—612no—
381D3×D4—612no—
382D3×D4—612no—
383D3×D4—612no—
384D3×D4—612no—
385D3×D4—612no—
386D3×D4—1212no—
387#235—612no—
388#235—612no—
389#235—612no—
390#235—612no—
391C2×D12—33no—
392C2×D12—33no—
393C2×D12—33no—
394C2×D12—33no—
395C2×D12—33no—
396C2×D12—33no—
397C2×D12—33no—
398C2×D12—33no—
399C2×D12—36no—
400C2×D12—63no—
401C2×D12—63no—
402C2×D12—612no—
403C2×D12—612no—
404C2×D12—1212no—
405C2×D12C22×D313yes—
406C2×D12C22×D313yes—
407C2×D12C22×D313yes—
408C2×D12C22×D316yes—
409C2×D12C22×D313yes—
410C2×C4×D3—33no—
411C2×C4×D3—33no—
412C2×C4×D3—33no—
413C2×C4×D3—33no—
414C2×C4×D3—33no—
415C2×C4×D3—33no—
416C2×C4×D3—31no—
417C2×C4×D3—31no—
418C2×C4×D3—63no—
419C2×C4×D3—63no—
420C2×C4×D3—612no—
421C2×C4×D3—612no—
422C2×C4×D3C22×D313yes—
423C2×C4×D3C22×D313yes—
424C2×C4×D3C22×D316yes—
425C2×C4×D3C22×D313yes—
426C2×Dic6—33no—
427C2×Dic6—33no—
428C2×Dic6—31no—
429C2×Dic6—31no—
430C2×Dic6—63no—
431C3×C4⋊C4—23no—
432C3×C4⋊C4—31no—
433C3×C4⋊C4—33no—
434C3×C4⋊C4—31no—
435C3×C4⋊C4—33no—
436C3×C4⋊C4C22×D313yes—
437C3×C4⋊C4C22×D313yes—
438C3×C22⋊C4—33no—
439C3×C22⋊C4—33no—
440C3×C22⋊C4—33no—
441C3×C22⋊C4—33no—
442C3×C42—23no—
443C3×C42—33no—
444C3×C42C22×D313yes—
445C3×C42C22×D313yes—
446#217—33no—
447#217—36no—
448#217—33no—
449(C2×D3)⋊C4—33no—
450(C2×D3)⋊C4—33no—
451(C2×D3)⋊C4—36no—
452(C2×D3)⋊C4—31no—
453(C2×D3)⋊C4—31no—
454(C2×D3)⋊C4—33no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—36no—
457(C2×D3)⋊C4—36no—
458(C2×D3)⋊C4—31no—
459(C2×D3)⋊C4—33no—
460(C2×D3)⋊C4—33no—
461(C2×D3)⋊C4—31no—
462(C2×D3)⋊C4—61no—
463(C2×D3)⋊C4—63no—
464(C2×D3)⋊C4—66no—
465(C2×D3)⋊C4C22×D313yes—
466(C2×D3)⋊C4C22×D313yes—
467(C2×D3)⋊C4C22×D313yes—
468(C2×D3)⋊C4C22×D313yes—
469C4⋊Dic3—33no—
470C4⋊Dic3—33no—
471C4⋊Dic3—31no—
472C4⋊Dic3—33no—
473C4⋊Dic3—63no—
474C4⋊Dic3C22×D311yescharacteristic
475C4⋊Dic3C22×D313yes—
476Dic3⋊C4—33no—
477Dic3⋊C4—31no—
478Dic3⋊C4C22×D311yescharacteristic
479Dic3⋊C4C22×D313yes—
480C4×Dic3C22×D313yes—
481C22×C32C2511yescharacteristic
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—23no—
485C2×C3⋊D3—23no—
486C2×C3⋊D3—23no—
487C2×C3⋊D3H(5,𝔽2)12yescomplemented
488C2×C3×D3—23no—
489C2×C3×D3—23no—
490C2×C3×D3—23no—
491C2×C3×D3—23no—
492C2×C3×D3—23no—
493C2×C3×D3—23no—
494C2×C3×D3—23no—
495C2×C3×D3—23no—
496C2×C3×D3C22×D416yes—
497D32—412no—
498D32—812no—
499C32×C4—23no—
500C32×C4—21no—
501C32×C4C22×D416yes—
502C3⋊Dic3—23no—
503C3⋊Dic3—21no—
504C3×Dic3—21no—
505C3×Dic3—21no—
506C3×Dic3—23no—
507C3×Dic3—21no—
508C3×Dic3C22×D412yes—
509H(5,𝔽2)—188no—
510C2×#41—31no—
511C2×#41—31no—
512C2×#41—31no—
513C2×#41—93no—
514C2×#41—93no—
515C2×#41—93no—
516C2×#41—91no—
517C2×#41—188no—
518C22×Q8—91no—
519C22×D4—93no—
520C22×D4—93no—
521C22×D4—96no—
522C22×D4—93no—
523C22×D4—93no—
524C23×C4—93no—
525#127—33no—
526#127—93no—
527#124—93no—
528#124—93no—
529#123—93no—
530#123—93no—
531C22⋊Q8—93no—
532C22⋊Q8—91no—
533C22⋊Q8—93no—
534C22⋊Q8—93no—
535#121—33no—
536#121—33no—
537#121—93no—
538#121—96no—
539#121—93no—
540#121—96no—
541#121—93no—
542#121—93no—
543#121—93no—
544#121—96no—
545#121—93no—
546#120—93no—
547#120—93no—
548#120—96no—
549#120—96no—
550C4×Q8—31no—
551C4×Q8D3211yescharacteristic, complemented
552C4×D4—33no—
553C4×D4—33no—
554C4×D4—33no—
555C4×D4—93no—
556C4×D4—93no—
557C4×D4—93no—
558#117—33no—
559C2×C4⋊C4—33no—
560C2×C22⋊C4—96no—
561C23×C3—33no—
562C23×C3—33no—
563C23×C3—33no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—33no—
567C22×D3—33no—
568C22×D3—61no—
569C22×D3—63no—
570C22×D3—66no—
571C22×D3—66no—
572C22×D3—66no—
573C22×D3—612no—
574C22×D3—66no—
575C22×D3—612no—
576C22×D3—123no—
577C22×D3—123no—
578C22×D3—126no—
579C22×D3—126no—
580C22×D3—126no—
581C22×D3—126no—
582C22×D3C23×D313yes—
583C22×D3C23×D313yes—
584C22×D3C23×D313yes—
585C3×Q8—24no—
586C3×Q8C2×D1214yescomplemented
587C3×Q8D3×D414yescomplemented
588C3×D4—312no—
589C3×D4—66no—
590C3×D4—66no—
591C3×D4—126no—
592C3×D4—123no—
593C2×C3×C4—23no—
594C2×C3×C4—23no—
595C2×C3×C4—21no—
596C2×C3×C4—31no—
597C2×C3×C4—312no—
598C2×C3×C4—31no—
599C2×C3×C4—31no—
600C2×C3×C4—31no—
601C2×C3×C4—33no—
602C2×C3×C4—66no—
603C2×C3×C4—66no—
604C2×C3×C4—126no—
605C2×C3×C4C23×D313yes—
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D313yes—
608C2×C3×C4C23×D311yescharacteristic
609C2×C3×C4C23×D313yes—
610C2×C3×C4C23×D313yes—
611#67—66no—
612#67—66no—
613#67—66no—
614#67—612no—
615#67—66no—
616#67—612no—
617#67—66no—
618#67—126no—
619#67—123no—
620C2×Dic3—31no—
621C2×Dic3—33no—
622C2×Dic3—31no—
623C2×Dic3—33no—
624C2×Dic3—61no—
625C2×Dic3—63no—
626C2×Dic3—66no—
627C2×Dic3—66no—
628C2×Dic3C23×D311yescharacteristic
629C2×Dic3C23×D313yes—
630C2×Dic3C23×D311yescharacteristic
631C2×Dic3C23×D311yescharacteristic
632C2×Dic3C23×D311yescharacteristic
633D12—26no—
634D12—26no—
635D12—46no—
636D12—43no—
637D12—66no—
638D12—66no—
639D12—66no—
640D12—66no—
641D12—66no—
642D12—66no—
643D12—66no—
644D12—126no—
645D12—126no—
646D12—123no—
647D12—126no—
648D12C2×D12112yescomplemented
649C4×D3—26no—
650C4×D3—26no—
651C4×D3—46no—
652C4×D3—62no—
653C4×D3—66no—
654C4×D3—66no—
655C4×D3—66no—
656C4×D3—66no—
657C4×D3—66no—
658C4×D3—66no—
659C4×D3—62no—
660C4×D3—126no—
661C4×D3—126no—
662C4×D3C2×D12112yescomplemented
663Dic6—62no—
664Dic6—66no—
665Dic6—66no—
666Dic6—62no—
667Dic6—126no—
668C2×C32C23×D411yescharacteristic
669C2×C32C2×H(5,𝔽2)11yescharacteristic
670C2×C32#58511yescharacteristic
671C3⋊D3—22no—
672C3⋊D3—43no—
673C3×D3—26no—
674C3×D3—43no—
675C3×D3—43no—
676C24—93no—
677C24—96no—
678#41—38no—
679#41—64no—
680#41—64no—
681#41—1812no—
682#41—1812no—
683#41—1812no—
684#41—184no—
685C2×Q8—91no—
686C2×Q8—93no—
687C2×Q8—184no—
688C2×Q8C2×D3211yescharacteristic
689C2×D4—33no—
690C2×D4—33no—
691C2×D4—33no—
692C2×D4—33no—
693C2×D4—36no—
694C2×D4—93no—
695C2×D4—93no—
696C2×D4—93no—
697C2×D4—93no—
698C2×D4—96no—
699C2×D4—96no—
700C2×D4—93no—
701C2×D4—93no—
702C2×D4—93no—
703C2×D4—1812no—
704C2×D4—1812no—
705C2×D4—1812no—
706C2×D4—1812no—
707C2×D4—3612no—
708C22×C4—33no—
709C22×C4—33no—
710C22×C4—33no—
711C22×C4—36no—
712C22×C4—91no—
713C22×C4—93no—
714C22×C4—93no—
715C22×C4—93no—
716C22×C4—93no—
717C22×C4—1812no—
718C4⋊C4—33no—
719C4⋊C4—33no—
720C4⋊C4—31no—
721C4⋊C4—31no—
722C4⋊C4—91no—
723C4⋊C4—93no—
724C4⋊C4—93no—
725C4⋊C4C2×D3213yes—
726C22⋊C4—33no—
727C22⋊C4—33no—
728C22⋊C4—33no—
729C22⋊C4—33no—
730C22⋊C4—93no—
731C22⋊C4—91no—
732C22⋊C4—96no—
733C22⋊C4—93no—
734C22⋊C4—93no—
735C22⋊C4—96no—
736C22⋊C4—91no—
737C22⋊C4—93no—
738C42—33no—
739C42C2×D3213yes—
740C22×C3—21no—
741C22×C3—36no—
742C22×C3—63no—
743C22×C3—63no—
744C22×C3—63no—
745C22×C3—63no—
746C22×C3—63no—
747C22×C3—63no—
748C22×C3—63no—
749C22×C3—63no—
750C22×C3C24×D311yescharacteristic
751C22×C3C24×D311yescharacteristic
752C2×D3—23no—
753C2×D3—23no—
754C2×D3—23no—
755C2×D3—23no—
756C2×D3—23no—
757C2×D3—23no—
758C2×D3—23no—
759C2×D3—23no—
760C2×D3—32no—
761C2×D3—32no—
762C2×D3—62no—
763C2×D3—61no—
764C2×D3—61no—
765C2×D3—61no—
766C2×D3—61no—
767C2×D3—63no—
768C2×D3—63no—
769C2×D3—63no—
770C2×D3—63no—
771C2×D3—63no—
772C2×D3—63no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—123no—
776C2×D3—123no—
777C2×D3—123no—
778C2×D3—1212no—
779C2×D3—1212no—
780C2×D3—2412no—
781C2×D3—2412no—
782C2×D3C22×D1216yes—
783C3×C4—21no—
784C3×C4—23no—
785C3×C4—23no—
786C3×C4—21no—
787C3×C4—26no—
788C3×C4—32no—
789C3×C4—43no—
790C3×C4—41no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—61no—
794C3×C4—63no—
795C3×C4C22×D1216yes—
796C3×C4C2×D3×D416yes—
797Dic3—21no—
798Dic3—21no—
799Dic3—23no—
800Dic3—21no—
801Dic3—63no—
802Dic3—61no—
803Dic3—63no—
804Dic3—61no—
805Dic3—123no—
806Dic3—121no—
807Dic3C22×D1212yes—
808C32#348811yescharacteristic, complemented, Sylow
809C23—33no—
810C23—33no—
811C23—33no—
812C23—91no—
813C23—93no—
814C23—186no—
815C23—1812no—
816C23—186no—
817C23—363no—
818C23—366no—
819C23—366no—
820Q8—182no—
821Q8—186no—
822Q8D3×D1214yescomplemented
823D4—312no—
824D4—66no—
825D4—66no—
826D4—126no—
827D4—123no—
828D4—186no—
829D4—186no—
830D4—186no—
831D4—186no—
832D4—186no—
833D4—1812no—
834D4—186no—
835D4—366no—
836D4—363no—
837C2×C4—31no—
838C2×C4—312no—
839C2×C4—31no—
840C2×C4—33no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—66no—
844C2×C4—66no—
845C2×C4—93no—
846C2×C4—91no—
847C2×C4—126no—
848C2×C4—182no—
849C2×C4—186no—
850C2×C4—186no—
851C2×C4—186no—
852C2×C4—186no—
853C2×C4C22×D3211yescharacteristic
854C2×C4C22×D3213yes—
855C2×C4C22×D3213yes—
856C2×C3—21no—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—66no—
860C2×C3—123no—
861C2×C3—123no—
862C2×C3C23×D1211yescharacteristic
863C2×C3C22×D3×D411yescharacteristic
864C2×C3#596411yescharacteristic
865C2×C3D3×H(5,𝔽2)11yescharacteristic
866C2×C3D3×H(5,𝔽2)11yescharacteristic
867C2×C3#596811yescharacteristic
868D3—26no—
869D3—43no—
870D3—43no—
871D3—62no—
872D3—62no—
873D3—122no—
874D3—123no—
875D3—123no—
876D3—243no—
877C22—36no—
878C22—63no—
879C22—63no—
880C22—63no—
881C22—63no—
882C22—63no—
883C22—63no—
884C22—63no—
885C22—63no—
886C22—92no—
887C22—181no—
888C22—181no—
889C22—183no—
890C22—183no—
891C22—183no—
892C22—3612no—
893C22—7212no—
894C22C23×D3211yescharacteristic
895C4—21no—
896C4—23no—
897C4—32no—
898C4—61no—
899C4—61no—
900C4—61no—
901C4—63no—
902C4—181no—
903C4—183no—
904C4C2×D3×D1216yes—
905C3—21no—
906C3#8590011yescharacteristic, complemented
907C3#8676911yescharacteristic, complemented
908C2—66no—
909C2—123no—
910C2—123no—
911C2—182no—
912C2—363no—
913C2C22×D3×D1211yescharacteristic
914C2#1059668811yescharacteristic
915C2#1059669211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64320C2semidirect
2. C2×#64319C2semidirect
3. #10596047C2semidirect
4. C3×#5577C2semidirect
5. C3×#5574C2semidirect
6. #10595414C2semidirect
7. #10595410C2semidirect
8. #10594630C2semidirect
9. #10594621C2semidirect
10. D3×#895C2semidirect
11. #10594522C2semidirect
12. #10594004C2semidirect
13. #10594003C2semidirect
14. #10594000C2semidirect
15. #10593997C2semidirect
18. C2×#3832C22semidirect
19. C2×Q8×C3⋊D3C22semidirect
21. C2×C3×#239C22semidirect
22. C2×C3×#239C22semidirect
25. C2×#3802C22semidirect
26. C2×#3802C22semidirect
27. C2×D3×D12C22semidirect
28. C2×D3×D12C22semidirect
29. C2×D3×D12C22semidirect
30. C2×C4×D32C22semidirect
31. C2×#3798C22semidirect
32. C2×#3795C22semidirect
33. C2×#3795C22semidirect
34. C32×C4×Q8C22semidirect
35. #64106C22semidirect
36. #64104C22semidirect
37. #64084C22semidirect
38. C4×C4⋊(C3⋊D3)C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#895C22semidirect
41. C3×#895C22semidirect
42. C3×#893C22semidirect
43. C3×D3×C4⋊C4C22semidirect
44. C3×#874C22semidirect
45. C3×C4×D12C22semidirect
46. C3×C4×D12C22semidirect
47. C3×#872C22semidirect
48. #63923C22semidirect
49. #63922C22semidirect
50. #63922C22semidirect
51. #63922C22semidirect
52. D3×(C2×D3)⋊C4C22semidirect
53. #63916C22semidirect
54. #63916C22semidirect
55. #63911C22semidirect
56. #63910C22semidirect
57. #63909C22semidirect
58. #63908C22semidirect
59. #63906C22semidirect
60. C4×#626C22semidirect
61. C4×#626C22semidirect
62. #63895C22semidirect
63. #63893C22semidirect
64. #63891C22semidirect
65. #63890C22semidirect
66. #63886C22semidirect
67. #63886C22semidirect
68. #63860C22semidirect
69. #63857C22semidirect
85. #5577D3semidirect
90. #5574D3semidirect
113. C3×#239D4semidirect
177. C2×#239C2×D3semidirect
178. C2×#239C2×D3semidirect
205. C3×C4×Q8C2×D3semidirect
206. C3×C4×Q8C2×D3semidirect
212. Q8×Dic3C2×D3semidirect
246. #895C2×D3semidirect
247. #895C2×D3semidirect
249. #893C2×D3semidirect
250. D3×C4⋊C4C2×D3semidirect
268. #874C2×D3semidirect
274. C4×D12C2×D3semidirect
275. C4×D12C2×D3semidirect
276. #872C2×D3semidirect
288. C32×Q8C2×D4semidirect
308. C3×D12C2×D4semidirect
312. C3×C4×D3C2×D4semidirect
374. #239D12semidirect
487. C2×C3⋊D3H(5,𝔽2)semidirect
551. C4×Q8D32semidirect
586. C3×Q8C2×D12semidirect
587. C3×Q8D3×D4semidirect
648. D12C2×D12semidirect
662. C4×D3C2×D12semidirect
808. C32#3488semidirect
822. Q8D3×D12semidirect
906. C3#85900semidirect
907. C3#86769semidirect

Maximal subgroups

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

subgroupindex
C2×#643202
C2×#643192
#105960472
C3×#55772
C3×#55742
#105954142
#105954102
#105946302
#105946212
D3×#8952
#105945222
#105940042
#105940032
#105940002
#105939972
#867693
#859003