Finite Group Databasebeta

← #11904695

Subgroups — #11904695

Order 1152.

3463 conjugacy classes of subgroups.

The subgroup lattice has 911 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64320C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3#10596045C211yesmaximal, characteristic, complemented
4C3×#5577C211yesmaximal, characteristic, complemented
5C3×#5576C211yesmaximal, characteristic, complemented
6#10595412C211yesmaximal, characteristic, complemented
7#10595409C211yesmaximal, characteristic, complemented
8#10594633C213yesmaximal, complemented
9#10594618C213yesmaximal, complemented
10#10594612C213yesmaximal, complemented
11#10594528C213yesmaximal, complemented
12#10594010C213yesmaximal, complemented
13#10594007C213yesmaximal, complemented
14#10594006C213yesmaximal, complemented
15#10594004C213yesmaximal, complemented
16#86769—31nomaximal
17#86713—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic, complemented
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23#64320—28no—
24D3×#239—28no—
25C2×#3802C2213yescomplemented
26C2×#3802C2216yescomplemented
27C2×D3×D12C2213yescomplemented
28C2×D3×D12C2213yescomplemented
29C2×D3×D12C2213yescomplemented
30C2×C4×D32C2213yescomplemented
31C2×#3799C2213yescomplemented
32C2×#3798C2213yescomplemented
33C2×#3796C2213yescomplemented
34C32×C4×Q8C2211yescharacteristic, complemented
35Q8×C3⋊Dic3C2211yescharacteristic, complemented
36#64102C2213yescomplemented
37C4⋊C4×C3⋊D3C2213yescomplemented
38C4×C4⋊(C3⋊D3)C2213yescomplemented
39#64081C2213yescomplemented
40C3×#897C2213yescomplemented
41C3×#895C2213yescomplemented
42C3×#895C2213yescomplemented
43C3×#895C2213yescomplemented
44C3×#875C2213yescomplemented
45C3×#874C2213yescomplemented
46C3×C4×D12C2213yescomplemented
47C3×C4×D12C2213yescomplemented
48#63922C2213yescomplemented
49#63922C2216yescomplemented
50#63922C2213yescomplemented
51#63922C2216yescomplemented
52#63921C2216yescomplemented
53#63916C2216yescomplemented
54#63914C2213yescomplemented
55#63912C2216yescomplemented
56#63908C2213yescomplemented
57#63908C2213yescomplemented
58#63908C2213yescomplemented
59C4×#625C2213yescomplemented
60C4×#625C2213yescomplemented
61#63899C2211yescharacteristic, complemented
62#63899C2213yescomplemented
63#63885C2213yescomplemented
64#63885C2216yescomplemented
65#63885C2213yescomplemented
66#63863C2213yescomplemented
67#63856C2213yescomplemented
68#63854C2213yescomplemented
69#63854C2213yescomplemented
70C2×#1009—31no—
71C2×#1009—31no—
72C2×D3×#41—31no—
73C22×#239—31no—
74C3×#550—31no—
75C3×#548—31no—
76#5834—31no—
77#5834—31no—
78#5831—31no—
79#5817—31no—
80#5717—33no—
81#5715—33no—
82#5676—33no—
83#5674—33no—
84#5630—33no—
85#5629—33no—
86#5612—33no—
87#5609—33no—
88#5609—33no—
89#5608—33no—
90D3×#121—33no—
91D3×#121—33no—
92#5577D311yescharacteristic, complemented
93#5576D311yescharacteristic, complemented
94#5574—31no—
95#5574—31no—
96#5574—61no—
97#5550—33no—
98D4×D12—33no—
99#5547—33no—
100#5547—33no—
101C22×D32C2313yes—
102C22×D32C2316yes—
103C2×C32×Q8C2311yescharacteristic
104#3832D418yescomplemented
105C2×C4⋊(C3⋊D3)C2313yes—
106C2×C4×C3⋊D3C2316yes—
107C2×C4×C3⋊D3C2313yes—
108C3×#239—24no—
109C3×#239—24no—
110C3×#239—24no—
111C3×D3×Q8—24no—
112C2×C3×D12C2313yes—
113C2×C3×D12C2313yes—
114C2×C3×D12C2313yes—
115C2×C3×D12C2313yes—
116C2×C3×D12C2316yes—
117C2×C3×D12C2313yes—
118C2×C3×C4×D3C2313yes—
119C2×C3×C4×D3C2313yes—
120C2×C3×C4×D3C2313yes—
121C2×C3×C4×D3C2313yes—
122C2×C3×Dic6C2313yes—
123C2×#627C2311yescharacteristic
124C2×#626C2316yes—
125C2×#626C2313yes—
126C2×#626C2313yes—
127C2×#625C2313yes—
128C2×#625C2313yes—
129C2×#625C2316yes—
130C2×#625C2313yes—
131C2×#624C2313yes—
132C2×D3×Dic3C2313yes—
133C2×D3×Dic3C2311yescharacteristic
134#3802—212no—
135#3802—412no—
136D3×D12—212no—
137D3×D12—212no—
138D3×D12—212no—
139C4×D32—212no—
140#3799—212no—
141#3798—212no—
142#3796—212no—
143C32×C4⋊C4C2313yes—
144C32×C42C2313yes—
145#3752C2313yes—
146#3752C2313yes—
147C4⋊(C3⋊Dic3)C2313yes—
148#3750C2311yescharacteristic
149#3750C2313yes—
150C4×C3⋊Dic3C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2316yes—
154C3×(C2×D3)⋊C4C2313yes—
155C3×(C2×D3)⋊C4C2311yescharacteristic
156C3×C4⋊Dic3C2313yes—
157C3×C4⋊Dic3C2311yescharacteristic
158#3724C2311yescharacteristic
159#3724C2313yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2316yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164(C2×D3)⋊Dic3C2313yes—
165#3488—91noSylow
166C2×C3×#41—31no—
167C2×C3×#41—31no—
168C2×C3×#41—31no—
169C22×C3×Q8—31no—
170#1009—68no—
171#1009—68no—
172D3×#41—68no—
173C2×#239—31no—
174C2×#239—31no—
175C2×#239—33no—
176C2×#239—33no—
177C2×#239—61no—
178C2×#239—68no—
179C2×#239C2×D311yescharacteristic, complemented
180C2×#239C2×D311yescharacteristic, complemented
181C2×#239C2×D311yescharacteristic, complemented
182C2×D3×Q8C2×D311yescharacteristic, complemented
183C2×#237—33no—
184C2×D3×D4—33no—
185C2×D3×D4—33no—
186C2×D3×D4—36no—
187C2×D3×D4—36no—
188C2×D3×D4—33no—
189C2×D3×D4—33no—
190C2×D3×D4—33no—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235—33no—
194C22×D12—33no—
195C22×D12—33no—
196C22×D12—33no—
197C22×C4×D3—33no—
198C22×C4×D3—33no—
199C3×#127—33no—
200C3×#124—33no—
201C3×C22⋊Q8—33no—
202C3×#121—33no—
203C3×#121—33no—
204C3×#121—33no—
205C3×C4×Q8—21no—
206C3×C4×Q8C2×D311yescharacteristic, complemented
207C3×C4×Q8C2×D311yescharacteristic, complemented
208C3×C4×D4—33no—
209C3×C4×D4—33no—
210#947—33no—
211#946—33no—
212Q8×Dic3—31no—
213Q8×Dic3—31no—
214Q8×Dic3—61no—
215#940—33no—
216#940—33no—
217#939—33no—
218#939—36no—
219#939—33no—
220#938—33no—
221#938—33no—
222#938—33no—
223#938—36no—
224#937—36no—
225#937—36no—
226#937—33no—
227#937—33no—
228#936—33no—
229#930—33no—
230#930—33no—
231#930—33no—
232C4×#67—33no—
233C4×#67—33no—
234C4×#67—33no—
235C4×#67—33no—
236#924—33no—
237#897C2×D313yescomplemented
238#896—31no—
239#896—33no—
240#895—36no—
241#895C2×D313yescomplemented
242#895C2×D313yescomplemented
243#895C2×D313yescomplemented
244#894—33no—
245#894—33no—
246#893—33no—
247#893—33no—
248#893—63no—
249D3×C4⋊C4—33no—
250D3×C4⋊C4—33no—
251D3×C4⋊C4—63no—
252#884—33no—
253#884—36no—
254#884—33no—
255#884—36no—
256#884—36no—
257#883—33no—
258#883—33no—
259#882—36no—
260#882—36no—
261#882—33no—
262#882—33no—
263D3×C22⋊C4—36no—
264D3×C22⋊C4—36no—
265#878—31no—
266#878—33no—
267#875C2×D313yescomplemented
268#874C2×D313yescomplemented
269C4×D12—33no—
270C4×D12—33no—
271C4×D12—63no—
272C4×D12C2×D313yescomplemented
273C4×D12C2×D313yescomplemented
274#872—33no—
275#872—33no—
276#872—63no—
277C22×C3⋊D3C2413yes—
278C22×C3×D3C2413yes—
279C22×C3×D3C2413yes—
280C22×C3×D3C2413yes—
281C22×C3×D3C2411yescharacteristic
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—
294C2×C3⋊Dic3C2411yescharacteristic
295C4⋊(C3⋊D3)C2×D4112yescomplemented
296C4×C3⋊D3—46no—
297C4×C3⋊D3C2×D4112yescomplemented
298C2×C3×Dic3C2411yescharacteristic
299C2×C3×Dic3C2411yescharacteristic
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2411yescharacteristic
302C3×D12—26no—
303C3×D12—26no—
304C3×D12—26no—
305C3×D12—26no—
306C3×D12—46no—
307C3×D12—43no—
308C3×C4×D3—26no—
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3—26no—
312C3×Dic6—26no—
313#627—22no—
314#626—212no—
315#626—26no—
316#626—26no—
317#625—26no—
318#625—26no—
319#625—46no—
320#625—43no—
321#624—26no—
322D3×Dic3—26no—
323D3×Dic3—22no—
324C2×H(5,𝔽2)—91no—
325C22×#41—91no—
326#550—31no—
327#550—91no—
328#548—31no—
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—91no—
339C23×D3—33no—
340C23×D3—33no—
341C23×D3—36no—
342C23×D3—36no—
343C3×#41—64no—
344C3×#41—64no—
345C3×#41—64no—
346C2×C3×Q8—21no—
347C2×C3×Q8—33no—
348C2×C3×Q8—64no—
349C2×C3×Q8C22×D311yescharacteristic
350C2×C3×Q8C22×D311yescharacteristic
351C2×C3×D4—33no—
352C2×C3×D4—33no—
353C2×C3×D4—33no—
354C2×C3×D4—33no—
355C2×C3×D4—33no—
356C2×C3×D4—36no—
357C22×C3×C4—33no—
358C22×C3×C4—33no—
359C22×C3×C4—33no—
360C22×C3×C4—33no—
361C2×#67—33no—
362C2×#67—33no—
363C2×#67—33no—
364C2×#67—33no—
365C2×#67—33no—
366C2×#67—36no—
367C2×#67—33no—
368C2×#67—36no—
369C2×#67—33no—
370C2×#67—33no—
371C2×#67—36no—
372C22×Dic3—31no—
373C22×Dic3—33no—
374#239—24no—
375#239—24no—
376#239—24no—
377#239—38no—
378#239—38no—
379#239—68no—
380#239—612no—
381#239—612no—
382D3×Q8—24no—
383#237—612no—
384D3×D4—612no—
385D3×D4—612no—
386D3×D4—612no—
387D3×D4—612no—
388D3×D4—612no—
389D3×D4—1212no—
390D3×D4—1212no—
391#235—612no—
392#235—612no—
393#235—612no—
394C2×D12—33no—
395C2×D12—33no—
396C2×D12—36no—
397C2×D12—33no—
398C2×D12—33no—
399C2×D12—63no—
400C2×D12—612no—
401C2×D12—612no—
402C2×D12—612no—
403C2×D12C22×D313yes—
404C2×D12C22×D313yes—
405C2×D12C22×D313yes—
406C2×D12C22×D313yes—
407C2×D12C22×D313yes—
408C2×D12C22×D316yes—
409C2×C4×D3—33no—
410C2×C4×D3—33no—
411C2×C4×D3—31no—
412C2×C4×D3—33no—
413C2×C4×D3—33no—
414C2×C4×D3—33no—
415C2×C4×D3—36no—
416C2×C4×D3—36no—
417C2×C4×D3—63no—
418C2×C4×D3—66no—
419C2×C4×D3—612no—
420C2×C4×D3—612no—
421C2×C4×D3C22×D313yes—
422C2×C4×D3C22×D313yes—
423C2×C4×D3C22×D313yes—
424C2×C4×D3C22×D313yes—
425C2×Dic6—31no—
426C2×Dic6—31no—
427C2×Dic6C22×D313yes—
428C3×C4⋊C4—23no—
429C3×C4⋊C4—31no—
430C3×C4⋊C4—33no—
431C3×C4⋊C4C22×D313yes—
432C3×C4⋊C4C22×D313yes—
433C3×C22⋊C4—31no—
434C3×C22⋊C4—33no—
435C3×C22⋊C4—33no—
436C3×C22⋊C4—36no—
437C3×C22⋊C4—33no—
438C3×C42—23no—
439C3×C42C22×D313yes—
440C3×C42C22×D313yes—
441#217—31no—
442#217—33no—
443#217—33no—
444#217—36no—
445#217—33no—
446(C2×D3)⋊C4—33no—
447(C2×D3)⋊C4—36no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—33no—
450(C2×D3)⋊C4—33no—
451(C2×D3)⋊C4—33no—
452(C2×D3)⋊C4—33no—
453(C2×D3)⋊C4—33no—
454(C2×D3)⋊C4—33no—
455(C2×D3)⋊C4—63no—
456(C2×D3)⋊C4—63no—
457(C2×D3)⋊C4C22×D311yescharacteristic
458(C2×D3)⋊C4C22×D313yes—
459(C2×D3)⋊C4C22×D313yes—
460(C2×D3)⋊C4C22×D313yes—
461(C2×D3)⋊C4C22×D316yes—
462C4⋊Dic3—33no—
463C4⋊Dic3—33no—
464C4⋊Dic3—63no—
465C4⋊Dic3C22×D311yescharacteristic
466C4⋊Dic3C22×D313yes—
467Dic3⋊C4—31no—
468Dic3⋊C4—31no—
469Dic3⋊C4—33no—
470Dic3⋊C4—33no—
471Dic3⋊C4—33no—
472Dic3⋊C4—31no—
473Dic3⋊C4—31no—
474Dic3⋊C4—33no—
475Dic3⋊C4—61no—
476Dic3⋊C4—63no—
477C4×Dic3—33no—
478C4×Dic3—33no—
479C4×Dic3—63no—
480C22×C32C2511yescharacteristic
481C2×C3⋊D3—23no—
482C2×C3⋊D3—23no—
483C2×C3⋊D3C22×D416yes—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—23no—
487C2×C3×D3—23no—
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×D3H(5,𝔽2)12yescomplemented
496D32—412no—
497D32—812no—
498C32×C4—23no—
499C32×C4—21no—
500C32×C4C22×D416yes—
501C3⋊Dic3—23no—
502C3⋊Dic3—21no—
503C3⋊Dic3C22×D412yes—
504C3×Dic3—21no—
505C3×Dic3—23no—
506C3×Dic3—21no—
507C3×Dic3—21no—
508H(5,𝔽2)—188no—
509C2×#41—31no—
510C2×#41—31no—
511C2×#41—31no—
512C2×#41—93no—
513C2×#41—93no—
514C2×#41—93no—
515C2×#41—91no—
516C2×#41—188no—
517C22×Q8—31no—
518C22×D4—93no—
519C22×D4—93no—
520C22×D4—93no—
521C22×D4—93no—
522C22×D4—96no—
523C23×C4—93no—
524#127—33no—
525#127—93no—
526#124—33no—
527#124—93no—
528#123—93no—
529#123—93no—
530C22⋊Q8—33no—
531C22⋊Q8—91no—
532C22⋊Q8—93no—
533C22⋊Q8—93no—
534#121—33no—
535#121—33no—
536#121—33no—
537#121—96no—
538#121—93no—
539#121—96no—
540#121—93no—
541#121—96no—
542#121—93no—
543#121—93no—
544#121—93no—
545#120—93no—
546#120—93no—
547#120—96no—
548#120—96no—
549C4×Q8—91no—
550C4×Q8D3211yescharacteristic, complemented
551C4×D4—33no—
552C4×D4—33no—
553C4×D4—93no—
554C4×D4—93no—
555C4×D4—93no—
556C4×D4—93no—
557#117—93no—
558C2×C4⋊C4—93no—
559C2×C22⋊C4—96no—
560C23×C3—31no—
561C23×C3—33no—
562C23×C3—33no—
563C23×C3—33no—
564C22×D3—33no—
565C22×D3—33no—
566C22×D3—63no—
567C22×D3—66no—
568C22×D3—66no—
569C22×D3—612no—
570C22×D3—612no—
571C22×D3—66no—
572C22×D3—66no—
573C22×D3—123no—
574C22×D3—123no—
575C22×D3—126no—
576C22×D3—126no—
577C22×D3—126no—
578C22×D3—126no—
579C22×D3C23×D313yes—
580C22×D3C23×D313yes—
581C22×D3C23×D313yes—
582C22×D3C23×D311yescharacteristic
583C3×Q8—24no—
584C3×Q8—66no—
585C3×Q8D3×D414yescomplemented
586C3×Q8D3×D414yescomplemented
587C3×D4—66no—
588C3×D4—66no—
589C3×D4—66no—
590C3×D4—66no—
591C3×D4—126no—
592C3×D4—123no—
593C2×C3×C4—23no—
594C2×C3×C4—21no—
595C2×C3×C4—23no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—33no—
599C2×C3×C4—31no—
600C2×C3×C4—66no—
601C2×C3×C4—66no—
602C2×C3×C4—66no—
603C2×C3×C4—66no—
604C2×C3×C4C23×D311yescharacteristic
605C2×C3×C4C23×D313yes—
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D313yes—
608C2×C3×C4C23×D313yes—
609C2×C3×C4C23×D313yes—
610#67—66no—
611#67—66no—
612#67—612no—
613#67—66no—
614#67—66no—
615#67—66no—
616#67—66no—
617#67—126no—
618#67—126no—
619#67—123no—
620#67—123no—
621C2×Dic3—31no—
622C2×Dic3—31no—
623C2×Dic3—31no—
624C2×Dic3—31no—
625C2×Dic3—33no—
626C2×Dic3—33no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—63no—
630C2×Dic3—62no—
631C2×Dic3—66no—
632C2×Dic3C23×D311yescharacteristic
633C2×Dic3C23×D311yescharacteristic
634C2×Dic3C23×D313yes—
635C2×Dic3C23×D311yescharacteristic
636D12—26no—
637D12—26no—
638D12—26no—
639D12—26no—
640D12—312no—
641D12—312no—
642D12—43no—
643D12—46no—
644D12—612no—
645D12—66no—
646D12—66no—
647D12—612no—
648C4×D3—26no—
649C4×D3—26no—
650C4×D3—26no—
651C4×D3—26no—
652C4×D3—312no—
653C4×D3—312no—
654C4×D3—612no—
655C4×D3—66no—
656C4×D3—66no—
657C4×D3—62no—
658C4×D3—66no—
659C4×D3—126no—
660C4×D3—126no—
661C4×D3—246no—
662Dic6—26no—
663Dic6—62no—
664Dic6—62no—
665C2×C32C23×D411yescharacteristic
666C2×C32C2×H(5,𝔽2)11yescharacteristic
667C2×C32#58511yescharacteristic
668C3⋊D3—26no—
669C3×D3—22no—
670C3×D3—43no—
671C3×D3—43no—
672C3×D3—43no—
673C24—93no—
674C24—96no—
675#41—64no—
676#41—64no—
677#41—64no—
678#41—98no—
679#41—1812no—
680#41—1812no—
681#41—1812no—
682C2×Q8—33no—
683C2×Q8—64no—
684C2×Q8—91no—
685C2×Q8C2×D3211yescharacteristic
686C2×D4—33no—
687C2×D4—33no—
688C2×D4—33no—
689C2×D4—33no—
690C2×D4—33no—
691C2×D4—36no—
692C2×D4—96no—
693C2×D4—93no—
694C2×D4—93no—
695C2×D4—93no—
696C2×D4—93no—
697C2×D4—93no—
698C2×D4—96no—
699C2×D4—93no—
700C2×D4—1812no—
701C2×D4—1812no—
702C2×D4—1812no—
703C2×D4—1812no—
704C2×D4—3612no—
705C22×C4—33no—
706C22×C4—33no—
707C22×C4—33no—
708C22×C4—33no—
709C22×C4—93no—
710C22×C4—91no—
711C22×C4—93no—
712C22×C4—93no—
713C22×C4—96no—
714C22×C4—1812no—
715C4⋊C4—31no—
716C4⋊C4—33no—
717C4⋊C4—91no—
718C4⋊C4—93no—
719C4⋊C4—93no—
720C4⋊C4—93no—
721C4⋊C4—91no—
722C4⋊C4C2×D3213yes—
723C22⋊C4—33no—
724C22⋊C4—36no—
725C22⋊C4—31no—
726C22⋊C4—33no—
727C22⋊C4—33no—
728C22⋊C4—93no—
729C22⋊C4—96no—
730C22⋊C4—91no—
731C22⋊C4—93no—
732C22⋊C4—93no—
733C22⋊C4—93no—
734C22⋊C4—93no—
735C42—93no—
736C42C2×D3213yes—
737C22×C3—21no—
738C22×C3—32no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—63no—
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—21no—
753C2×D3—21no—
754C2×D3—23no—
755C2×D3—23no—
756C2×D3—23no—
757C2×D3—23no—
758C2×D3—23no—
759C2×D3—23no—
760C2×D3—23no—
761C2×D3—23no—
762C2×D3—23no—
763C2×D3—36no—
764C2×D3—36no—
765C2×D3—66no—
766C2×D3—63no—
767C2×D3—63no—
768C2×D3—63no—
769C2×D3—63no—
770C2×D3—123no—
771C2×D3—123no—
772C2×D3—1212no—
773C2×D3—1212no—
774C2×D3—2412no—
775C2×D3—2412no—
776C2×D3#100912yescomplemented
777C3×C4—23no—
778C3×C4—21no—
779C3×C4—23no—
780C3×C4—21no—
781C3×C4—26no—
782C3×C4—43no—
783C3×C4—41no—
784C3×C4—61no—
785C3×C4—61no—
786C3×C4—61no—
787C3×C4—63no—
788C3×C4C2×D3×D416yes—
789C3×C4C2×D3×D416yes—
790Dic3—23no—
791Dic3—21no—
792Dic3—21no—
793Dic3—21no—
794Dic3—32no—
795Dic3—32no—
796Dic3—62no—
797Dic3—63no—
798Dic3—61no—
799Dic3—63no—
800Dic3—61no—
801Dic3—123no—
802Dic3—121no—
803C32#348811yescharacteristic, complemented, Sylow
804C23—31no—
805C23—33no—
806C23—33no—
807C23—33no—
808C23—93no—
809C23—186no—
810C23—186no—
811C23—1812no—
812C23—363no—
813C23—366no—
814C23—366no—
815Q8—66no—
816Q8—182no—
817Q8#380214yescomplemented
818D4—66no—
819D4—66no—
820D4—66no—
821D4—66no—
822D4—912no—
823D4—126no—
824D4—123no—
825D4—186no—
826D4—186no—
827D4—1812no—
828D4—186no—
829D4—186no—
830D4—366no—
831D4—363no—
832C2×C4—31no—
833C2×C4—33no—
834C2×C4—31no—
835C2×C4—31no—
836C2×C4—66no—
837C2×C4—66no—
838C2×C4—66no—
839C2×C4—66no—
840C2×C4—91no—
841C2×C4—912no—
842C2×C4—91no—
843C2×C4—93no—
844C2×C4—186no—
845C2×C4—182no—
846C2×C4—186no—
847C2×C4—366no—
848C2×C4C22×D3211yescharacteristic
849C2×C4C22×D3213yes—
850C2×C4C22×D3213yes—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—21no—
854C2×C3—62no—
855C2×C3—123no—
856C2×C3—123no—
857C2×C3—123no—
858C2×C3C22×D3×D411yescharacteristic
859C2×C3C22×D3×D411yescharacteristic
860C2×C3C2×#100911yescharacteristic
861C2×C3#596411yescharacteristic
862C2×C3D3×H(5,𝔽2)11yescharacteristic
863C2×C3#596811yescharacteristic
864D3—22no—
865D3—43no—
866D3—43no—
867D3—43no—
868D3—66no—
869D3—66no—
870D3—126no—
871C22—32no—
872C22—61no—
873C22—61no—
874C22—63no—
875C22—63no—
876C22—63no—
877C22—63no—
878C22—63no—
879C22—63no—
880C22—63no—
881C22—63no—
882C22—63no—
883C22—96no—
884C22—183no—
885C22—183no—
886C22—3612no—
887C22—7212no—
888C22C23×D3211yescharacteristic
889C4—21no—
890C4—23no—
891C4—61no—
892C4—61no—
893C4—61no—
894C4—63no—
895C4—92no—
896C4—181no—
897C4—183no—
898C4C2×#380216yes—
899C3—21no—
900C3#8671311yescharacteristic, complemented
901C3#8676911yescharacteristic, complemented
902C2—62no—
903C2—123no—
904C2—123no—
905C2—123no—
906C2—186no—
907C2C22×#380211yescharacteristic
908C2#1059668811yescharacteristic
909C2D3×#100911yescharacteristic
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×D3×#239C2semidirect
3. #10596045C2semidirect
4. C3×#5577C2semidirect
5. C3×#5576C2semidirect
6. #10595412C2semidirect
7. #10595409C2semidirect
8. #10594633C2semidirect
9. #10594618C2semidirect
10. #10594612C2semidirect
11. #10594528C2semidirect
12. #10594010C2semidirect
13. #10594007C2semidirect
14. #10594006C2semidirect
15. #10594004C2semidirect
19. C2×C3×#239C22semidirect
20. C2×C3×#239C22semidirect
21. C2×C3×#239C22semidirect
22. C2×C3×D3×Q8C22semidirect
25. C2×#3802C22semidirect
26. C2×#3802C22semidirect
27. C2×D3×D12C22semidirect
28. C2×D3×D12C22semidirect
29. C2×D3×D12C22semidirect
30. C2×C4×D32C22semidirect
31. C2×#3799C22semidirect
32. C2×#3798C22semidirect
33. C2×#3796C22semidirect
34. C32×C4×Q8C22semidirect
35. Q8×C3⋊Dic3C22semidirect
36. #64102C22semidirect
37. C4⋊C4×C3⋊D3C22semidirect
38. C4×C4⋊(C3⋊D3)C22semidirect
39. #64081C22semidirect
40. C3×#897C22semidirect
41. C3×#895C22semidirect
42. C3×#895C22semidirect
43. C3×#895C22semidirect
44. C3×#875C22semidirect
45. C3×#874C22semidirect
46. C3×C4×D12C22semidirect
47. C3×C4×D12C22semidirect
48. #63922C22semidirect
49. #63922C22semidirect
50. #63922C22semidirect
51. #63922C22semidirect
52. #63921C22semidirect
53. #63916C22semidirect
54. #63914C22semidirect
55. #63912C22semidirect
56. #63908C22semidirect
57. #63908C22semidirect
58. #63908C22semidirect
59. C4×#625C22semidirect
60. C4×#625C22semidirect
61. #63899C22semidirect
62. #63899C22semidirect
63. #63885C22semidirect
64. #63885C22semidirect
65. #63885C22semidirect
66. #63863C22semidirect
67. #63856C22semidirect
68. #63854C22semidirect
69. #63854C22semidirect
92. #5577D3semidirect
93. #5576D3semidirect
104. #3832D4semidirect
179. C2×#239C2×D3semidirect
180. C2×#239C2×D3semidirect
181. C2×#239C2×D3semidirect
182. C2×D3×Q8C2×D3semidirect
206. C3×C4×Q8C2×D3semidirect
207. C3×C4×Q8C2×D3semidirect
237. #897C2×D3semidirect
241. #895C2×D3semidirect
242. #895C2×D3semidirect
243. #895C2×D3semidirect
267. #875C2×D3semidirect
268. #874C2×D3semidirect
272. C4×D12C2×D3semidirect
273. C4×D12C2×D3semidirect
288. C32×Q8C2×D4semidirect
295. C4⋊(C3⋊D3)C2×D4semidirect
297. C4×C3⋊D3C2×D4semidirect
495. C2×C3×D3H(5,𝔽2)semidirect
550. C4×Q8D32semidirect
585. C3×Q8D3×D4semidirect
586. C3×Q8D3×D4semidirect
776. C2×D3#1009semidirect
803. C32#3488semidirect
817. Q8#3802semidirect
900. C3#86713semidirect
901. 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×D3×#2392
#105960452
C3×#55772
C3×#55762
#105954122
#105954092
#105946332
#105946182
#105946122
#105945282
#105940102
#105940072
#105940062
#105940042
#867693
#867133