Finite Group Databasebeta

← #11906277

Subgroups — #11906277

Order 1152.

2061 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596043C211yesmaximal, characteristic
2C3×#5570C211yesmaximal, characteristic, complemented
3C3×#5569C211yesmaximal, characteristic, complemented
4#10595422C211yesmaximal, characteristic, complemented
5Q8×#627C211yesmaximal, characteristic, complemented
6Q8×#624C211yesmaximal, characteristic
7#10595339C211yesmaximal, characteristic
8#10594508C213yesmaximal
9#10594448C213yesmaximal
10#10594324C213yesmaximal, complemented
11#10594318C213yesmaximal, complemented
12#10593935C213yesmaximal
13#10593856C213yesmaximal, complemented
14#10593855C213yesmaximal
15#10593852C213yesmaximal, complemented
16#87032—31nomaximal
17#87031—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20Q8×C3⋊Dic3C2211yescharacteristic
21#64101C2213yes—
22#64096C2213yes—
23#64081C2213yes—
24C4×#634C2213yes—
25C3×Q8×Dic3C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×Q8×Dic3C2211yescharacteristic
28C3×Q8×Dic3C2211yescharacteristic
29C3×#890C2213yes—
30C3×#890C2213yes—
31C3×#890C2213yes—
32C3×#888C2213yes—
33C3×#870C2213yes—
34C3×#869C2213yes—
35C3×C4×Dic6C2213yes—
36C3×C4×Dic6C2213yes—
37#63919C2213yes—
38#63919C2216yes—
39#63918C2213yes—
40#63918C2213yes—
41#63918C2213yes—
42C4×#627C2213yes—
43C4×#627C2213yes—
44#63900C2213yes—
45#63895C2216yes—
46#63895C2211yescharacteristic
47#63895C2213yes—
48#63888C2213yes—
49#63888C2213yes—
50C4×#624C2213yes—
51#63874C2213yes—
52#63872C2213yes—
53#63870C2216yes—
54#63869C2213yes—
55#63849C2213yes—
56#63847C2216yes—
57#63847C2213yes—
58#63847C2213yes—
59#63844C2213yes—
60#63844C2213yes—
61#63844C2213yes—
62#63844C2213yes—
63#63843C2216yes—
64#63839C2213yes—
65#63839C2216yes—
66#63839C2213yes—
67#63838C2216yes—
68C3×#557—31no—
69C3×#557—31no—
70#5729—33no—
71#5728—33no—
72#5722—33no—
73#5721—33no—
74#5689—33no—
75#5689—33no—
76#5689—33no—
77#5688—33no—
78#5685—33no—
79#5685—33no—
80#5685—33no—
81#5685—33no—
82#5578—33no—
83#5578—33no—
84#5572—31no—
85#5572—31no—
86#5572—31no—
87#5572—31no—
88#5572—61no—
89C4×D3×Q8—31no—
90C4×D3×Q8—31no—
91#5570—31no—
92#5570D311yescharacteristic, complemented
93#5569—31no—
94#5569D311yescharacteristic, complemented
95#5567—33no—
96Q8×Dic6—31no—
97Q8×Dic6—31no—
98Q8×Dic6—33no—
99C2×C32×Q8C2311yescharacteristic
100Q8×C3⋊D3Q818yescomplemented
101C2×C4×C3⋊D3C2313yes—
102C2×#634C2313yes—
103C2×C3×Dic6C2313yes—
104C2×C3×Dic6C2313yes—
105C2×#627C2311yescharacteristic
106C2×#627C2316yes—
107C2×#627C2313yes—
108C2×#624C2311yescharacteristic
109C2×#624C2313yes—
110C32×C4⋊C4C2313yes—
111C32×C42C2313yes—
112#3752C2311yescharacteristic
113#3752C2313yes—
114C4⋊(C3⋊Dic3)C2313yes—
115#3750C2313yes—
116#3750C2313yes—
117C4×C3⋊Dic3C2316yes—
118C4×C3⋊Dic3C2313yes—
119C3×C4⋊Dic3C2313yes—
120C3×C4⋊Dic3C2316yes—
121C3×C4⋊Dic3C2313yes—
122C3×C4⋊Dic3C2313yes—
123C3×C4⋊Dic3C2313yes—
124C3×C4⋊Dic3C2313yes—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4C2316yes—
127C3×Dic3⋊C4C2313yes—
128C3×Dic3⋊C4C2313yes—
129C3×Dic3⋊C4C2311yescharacteristic
130C3×Dic3⋊C4C2313yes—
131C3×C4×Dic3C2313yes—
132C3×C4×Dic3C2313yes—
133C3×C4×Dic3C2313yes—
134C3×C4×Dic3C2313yes—
135#3724C2313yes—
136#3724C2313yes—
137#3724C2316yes—
138#3724C2313yes—
139#3724C2313yes—
140Dic3⋊Dic3C2313yes—
141Dic3⋊Dic3C2316yes—
142Dic3⋊Dic3C2313yes—
143Dic3⋊Dic3C2311yescharacteristic
144Dic3⋊Dic3C2313yes—
145#3722C2313yes—
146#3722C2311yescharacteristic
147Dic32C2313yes—
148Dic32C2316yes—
149Dic32C2313yes—
150#3502—91noSylow
151C2×D3×Q8—31no—
152C2×D3×Q8—31no—
153C2×D3×Q8—61no—
154C3×C4⋊Q8—33no—
155C3×C4⋊Q8—33no—
156C3×#125—33no—
157C3×#125—33no—
158C3×#125—33no—
159C3×#125—33no—
160C3×C4×Q8—21no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×Q8—33no—
166C3×C4×Q8—33no—
167C3×C4×Q8C2×D311yescharacteristic
168C3×C4×Q8C2×D311yescharacteristic
169#946—33no—
170#946—33no—
171Q8×Dic3—31no—
172Q8×Dic3—31no—
173Q8×Dic3—36no—
174Q8×Dic3—61no—
175Q8×Dic3C2×D311yescharacteristic
176Q8×Dic3C2×D311yescharacteristic
177Q8×Dic3C2×D311yescharacteristic
178Q8×Dic3C2×D311yescharacteristic
179#944—33no—
180#944—33no—
181#944—36no—
182#897—36no—
183#897—33no—
184#897—31no—
185#896—33no—
186#896—33no—
187#896—36no—
188#896—33no—
189#896—31no—
190#892—33no—
191#892—33no—
192#892—33no—
193#892—33no—
194#892—63no—
195D3×C4⋊C4—33no—
196D3×C4⋊C4—33no—
197#890—33no—
198#890—33no—
199#890—33no—
200#890C2×D313yes—
201#890C2×D313yes—
202#890C2×D313yes—
203#889—33no—
204#889—33no—
205#889—36no—
206#889—36no—
207#889—33no—
208#889—36no—
209#889—36no—
210#889—33no—
211#888—33no—
212#888—36no—
213#888—33no—
214#888—36no—
215#888—33no—
216#888—36no—
217#888—33no—
218#888—33no—
219#888—33no—
220#888—33no—
221#888C2×D313yes—
222#887—36no—
223#887—33no—
224#887—33no—
225#887—36no—
226#887—36no—
227#887—33no—
228#887—33no—
229#887—33no—
230#887—33no—
231#887—63no—
232#872—33no—
233#872—33no—
234#872—33no—
235#872—33no—
236#872—63no—
237C42×D3—33no—
238C42×D3—33no—
239#870—33no—
240#870C2×D313yes—
241#869—33no—
242#869—33no—
243#869—33no—
244#869C2×D313yes—
245C4×Dic6—33no—
246C4×Dic6—33no—
247C4×Dic6—33no—
248C4×Dic6—33no—
249C4×Dic6—33no—
250C4×Dic6—33no—
251C4×Dic6—33no—
252C4×Dic6—33no—
253C4×Dic6—33no—
254C4×Dic6—33no—
255C4×Dic6—63no—
256C4×Dic6C2×D313yes—
257C4×Dic6C2×D313yes—
258C22×C3⋊D3C2411yescharacteristic
259C32×Q8C2×Q814yes—
260C2×C32×C4C2413yes—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2413yes—
263C2×C3⋊Dic3C2411yescharacteristic
264C2×C3⋊Dic3C2413yes—
265C2×C3⋊Dic3C2413yes—
266C4×C3⋊D3C2×Q8112yes—
267#634C2×Q8112yes—
268C2×C3×Dic3C2411yescharacteristic
269C2×C3×Dic3C2413yes—
270C2×C3×Dic3C2413yes—
271C2×C3×Dic3C2413yes—
272C2×C3×Dic3C2413yes—
273C2×C3×Dic3C2411yescharacteristic
274C2×C3×Dic3C2411yescharacteristic
275C2×C3×Dic3C2411yescharacteristic
276C3×Dic6—26no—
277C3×Dic6—43no—
278#627—22no—
279#627—46no—
280#627—43no—
281#624—22no—
282#624—43no—
283Q82—91no—
284Q82—93no—
285#557—31no—
286#557—31no—
287#557—91no—
288#557—93no—
289#557—93no—
290#557—93no—
291#544—93no—
292#544—93no—
293#533—93no—
294#533—93no—
295#519—91no—
296#519—91no—
297C2×C4×Q8—91no—
298C2×C3×Q8—21no—
299C2×C3×Q8—33no—
300C2×C3×Q8—33no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303D3×Q8—38no—
304D3×Q8—38no—
305D3×Q8—68no—
306C2×C4×D3—33no—
307C2×C4×D3—33no—
308C2×C4×D3—31no—
309C2×C4×D3—31no—
310C2×C4×D3—33no—
311C2×C4×D3—33no—
312C2×C4×D3—63no—
313C2×Dic6—33no—
314C2×Dic6—33no—
315C2×Dic6—31no—
316C2×Dic6—31no—
317C2×Dic6—33no—
318C2×Dic6—33no—
319C2×Dic6—36no—
320C2×Dic6—36no—
321C2×Dic6—63no—
322C2×Dic6C22×D313yes—
323C2×Dic6C22×D313yes—
324C3×C4⋊C4—23no—
325C3×C4⋊C4—33no—
326C3×C4⋊C4—33no—
327C3×C4⋊C4—33no—
328C3×C4⋊C4—36no—
329C3×C4⋊C4—33no—
330C3×C4⋊C4—36no—
331C3×C4⋊C4—33no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—33no—
334C3×C4⋊C4—33no—
335C3×C4⋊C4—33no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4C22×D313yes—
338C3×C4⋊C4C22×D313yes—
339C3×C42—23no—
340C3×C42—33no—
341C3×C42—33no—
342C3×C42—33no—
343C3×C42—33no—
344C3×C42C22×D313yes—
345C3×C42C22×D313yes—
346(C2×D3)⋊C4—31no—
347(C2×D3)⋊C4—31no—
348(C2×D3)⋊C4—33no—
349(C2×D3)⋊C4—33no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—33no—
353(C2×D3)⋊C4—33no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—63no—
356C4⋊Dic3—33no—
357C4⋊Dic3—33no—
358C4⋊Dic3—31no—
359C4⋊Dic3—33no—
360C4⋊Dic3—33no—
361C4⋊Dic3—33no—
362C4⋊Dic3—36no—
363C4⋊Dic3—63no—
364C4⋊Dic3C22×D313yes—
365C4⋊Dic3C22×D313yes—
366C4⋊Dic3C22×D313yes—
367C4⋊Dic3C22×D313yes—
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D313yes—
370C4⋊Dic3C22×D316yes—
371Dic3⋊C4—33no—
372Dic3⋊C4—33no—
373Dic3⋊C4—33no—
374Dic3⋊C4—33no—
375Dic3⋊C4—31no—
376Dic3⋊C4—33no—
377Dic3⋊C4—33no—
378Dic3⋊C4—33no—
379Dic3⋊C4—33no—
380Dic3⋊C4—33no—
381Dic3⋊C4—36no—
382Dic3⋊C4—36no—
383Dic3⋊C4—33no—
384Dic3⋊C4—33no—
385Dic3⋊C4—33no—
386Dic3⋊C4—33no—
387Dic3⋊C4—36no—
388Dic3⋊C4—33no—
389Dic3⋊C4—33no—
390Dic3⋊C4—63no—
391Dic3⋊C4—63no—
392Dic3⋊C4C22×D311yescharacteristic
393Dic3⋊C4C22×D313yes—
394Dic3⋊C4C22×D313yes—
395Dic3⋊C4C22×D313yes—
396Dic3⋊C4C22×D316yes—
397C4×Dic3—33no—
398C4×Dic3—33no—
399C4×Dic3—36no—
400C4×Dic3—36no—
401C4×Dic3—33no—
402C4×Dic3—33no—
403C4×Dic3—36no—
404C4×Dic3—36no—
405C4×Dic3—33no—
406C4×Dic3—33no—
407C4×Dic3—66no—
408C4×Dic3—63no—
409C4×Dic3C22×D313yes—
410C4×Dic3C22×D313yes—
411C4×Dic3C22×D313yes—
412C4×Dic3C22×D313yes—
413C22×C32C2511yescharacteristic
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3C22×Q812yes—
417C32×C4—23no—
418C32×C4—21no—
419C32×C4C22×Q816yes—
420C3⋊Dic3—21no—
421C3⋊Dic3—23no—
422C3⋊Dic3C22×Q816yes—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—23no—
426C3×Dic3—23no—
427C3×Dic3—23no—
428C3×Dic3—21no—
429C3×Dic3—23no—
430C3×Dic32−1+412yes—
431C22×Q8—91no—
432C4⋊Q8—33no—
433C4⋊Q8—33no—
434C4⋊Q8—93no—
435C4⋊Q8—93no—
436C4⋊Q8—93no—
437C4⋊Q8—93no—
438C4⋊Q8—96no—
439C4⋊Q8—93no—
440C4⋊Q8—93no—
441C4⋊Q8—96no—
442#125—33no—
443#125—33no—
444#125—33no—
445#125—33no—
446#125—93no—
447#125—93no—
448#125—93no—
449#125—96no—
450#125—96no—
451#125—93no—
452C22⋊Q8—91no—
453C22⋊Q8—93no—
454C22⋊Q8—96no—
455C22⋊Q8—93no—
456C22⋊Q8—93no—
457C4×Q8—31no—
458C4×Q8—31no—
459C4×Q8—31no—
460C4×Q8—31no—
461C4×Q8—33no—
462C4×Q8—33no—
463C4×Q8—93no—
464C4×Q8—93no—
465C4×Q8—93no—
466C4×Q8—93no—
467C4×Q8—93no—
468C4×Q8—93no—
469C4×Q8—96no—
470C4×Q8—96no—
471C4×Q8—91no—
472C4×Q8—93no—
473C4×Q8—93no—
474C4×Q8D3211yescharacteristic
475#117—93no—
476#117—93no—
477#117—93no—
478#117—93no—
479C2×C4⋊C4—93no—
480C2×C42—93no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C3×Q8—24no—
485C3×Q8—66no—
486C3×Q8—123no—
487C3×Q8D3×Q814yes—
488C3×Q8D3×Q814yes—
489C2×C3×C4—23no—
490C2×C3×C4—23no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—33no—
495C2×C3×C4—33no—
496C2×C3×C4—33no—
497C2×C3×C4—33no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4C23×D313yes—
501C2×C3×C4C23×D313yes—
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D313yes—
505C2×C3×C4C23×D313yes—
506C2×Dic3—33no—
507C2×Dic3—33no—
508C2×Dic3—31no—
509C2×Dic3—31no—
510C2×Dic3—33no—
511C2×Dic3—33no—
512C2×Dic3—63no—
513C2×Dic3—61no—
514C2×Dic3—63no—
515C2×Dic3C23×D311yescharacteristic
516C2×Dic3C23×D313yes—
517C2×Dic3C23×D313yes—
518C2×Dic3C23×D313yes—
519C2×Dic3C23×D313yes—
520C2×Dic3C23×D311yescharacteristic
521C2×Dic3C23×D311yescharacteristic
522C2×Dic3C23×D311yescharacteristic
523C4×D3—312no—
524C4×D3—312no—
525C4×D3—612no—
526C4×D3—62no—
527C4×D3—62no—
528C4×D3—123no—
529C4×D3—123no—
530Dic6—26no—
531Dic6—312no—
532Dic6—312no—
533Dic6—43no—
534Dic6—612no—
535Dic6—62no—
536Dic6—62no—
537Dic6—126no—
538Dic6—123no—
539Dic6—123no—
540Dic6—126no—
541C2×C32C23×Q811yescharacteristic
542C2×C32C2×2−1+411yescharacteristic
543C2×C32#58511yescharacteristic
544C3⋊D3—22no—
545C2×Q8—33no—
546C2×Q8—33no—
547C2×Q8—91no—
548C2×Q8—93no—
549C2×Q8—96no—
550C2×Q8—98no—
551C2×Q8—93no—
552C2×Q8C2×D3211yescharacteristic
553C22×C4—91no—
554C22×C4—93no—
555C22×C4—93no—
556C4⋊C4—33no—
557C4⋊C4—33no—
558C4⋊C4—33no—
559C4⋊C4—33no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—33no—
563C4⋊C4—33no—
564C4⋊C4—33no—
565C4⋊C4—33no—
566C4⋊C4—36no—
567C4⋊C4—36no—
568C4⋊C4—96no—
569C4⋊C4—93no—
570C4⋊C4—93no—
571C4⋊C4—93no—
572C4⋊C4—91no—
573C4⋊C4—93no—
574C4⋊C4—93no—
575C4⋊C4—93no—
576C4⋊C4—93no—
577C4⋊C4—96no—
578C4⋊C4—93no—
579C4⋊C4—93no—
580C4⋊C4—93no—
581C4⋊C4C2×D3213yes—
582C22⋊C4—91no—
583C22⋊C4—93no—
584C22⋊C4—91no—
585C22⋊C4—93no—
586C42—33no—
587C42—33no—
588C42—33no—
589C42—33no—
590C42—93no—
591C42—93no—
592C42—96no—
593C42—96no—
594C42—93no—
595C42C2×D3213yes—
596C22×C3—21no—
597C22×C3C24×D311yescharacteristic
598C22×C3C24×D311yescharacteristic
599C2×D3—32no—
600C2×D3—32no—
601C2×D3—62no—
602C2×D3—61no—
603C2×D3—61no—
604C2×D3—61no—
605C2×D3—61no—
606C2×D3—121no—
607C2×D3—121no—
608C3×C4—23no—
609C3×C4—21no—
610C3×C4—23no—
611C3×C4—21no—
612C3×C4—26no—
613C3×C4—32no—
614C3×C4—41no—
615C3×C4—43no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—63no—
620C3×C4—63no—
621C3×C4—63no—
622C3×C4—63no—
623C3×C4C2×D3×Q816yes—
624C3×C4C2×D3×Q816yes—
625Dic3—23no—
626Dic3—23no—
627Dic3—23no—
628Dic3—21no—
629Dic3—21no—
630Dic3—21no—
631Dic3—23no—
632Dic3—36no—
633Dic3—36no—
634Dic3—66no—
635Dic3—61no—
636Dic3—63no—
637Dic3—61no—
638Dic3—63no—
639Dic3—123no—
640Dic3—121no—
641Dic3#101012yes—
642C32#350211yescharacteristic, complemented, Sylow
643C23—91no—
644Q8—66no—
645Q8—912no—
646Q8—123no—
647Q8—182no—
648Q8—363no—
649Q8—366no—
650Q8#379714yes—
651C2×C4—31no—
652C2×C4—31no—
653C2×C4—31no—
654C2×C4—31no—
655C2×C4—33no—
656C2×C4—33no—
657C2×C4—33no—
658C2×C4—33no—
659C2×C4—93no—
660C2×C4—912no—
661C2×C4—91no—
662C2×C4—93no—
663C2×C4—182no—
664C2×C4—363no—
665C2×C4C22×D3213yes—
666C2×C4C22×D3211yescharacteristic
667C2×C4C22×D3213yes—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3C22×D3×Q811yescharacteristic
672C2×C3C22×D3×Q811yescharacteristic
673C2×C3C2×#101011yescharacteristic
674C2×C3#596411yescharacteristic
675C2×C3D3×2−1+411yescharacteristic
676C2×C3#596811yescharacteristic
677D3—62no—
678D3—62no—
679D3—122no—
680C22—92no—
681C22—181no—
682C22—181no—
683C22C23×D3211yescharacteristic
684C4—21no—
685C4—23no—
686C4—32no—
687C4—63no—
688C4—63no—
689C4—63no—
690C4—61no—
691C4—61no—
692C4—63no—
693C4—61no—
694C4—96no—
695C4—183no—
696C4—181no—
697C4C2×#379716yes—
698C3—21no—
699C3#8703111yescharacteristic, complemented
700C3#8703211yescharacteristic, complemented
701C2—182no—
702C2C22×#379711yescharacteristic
703C2#1059668811yescharacteristic
704C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC22×C3⋊D3C24
hypercenterC4×Q8D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5570C2semidirect
3. C3×#5569C2semidirect
4. #10595422C2semidirect
5. Q8×#627C2semidirect
10. #10594324C2semidirect
11. #10594318C2semidirect
13. #10593856C2semidirect
15. #10593852C2semidirect
92. #5570D3semidirect
94. #5569D3semidirect
100. Q8×C3⋊D3Q8semidirect
642. C32#3502semidirect
699. C3#87031semidirect
700. C3#87032semidirect

Maximal subgroups

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

subgroupindex
#105960432
C3×#55702
C3×#55692
#105954222
Q8×#6272
Q8×#6242
#105953392
#105945082
#105944482
#105943242
#105943182
#105939352
#105938562
#105938552
#105938522
#870323
#870313