Finite Group Databasebeta

← #11895695

Subgroups — #11895695

Order 1152.

744 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5685C211yesmaximal, characteristic, complemented
2#10593978C211yesmaximal, characteristic
3#10592767C211yesmaximal, characteristic, complemented
4C3×#5066C211yesmaximal, characteristic, complemented
5#10590549C211yesmaximal, characteristic
6#10590548C211yesmaximal, characteristic
7#10590533C211yesmaximal, characteristic, complemented
8#10590532C211yesmaximal, characteristic, complemented
9#10590487C211yesmaximal, characteristic, complemented
10#10590481C211yesmaximal, characteristic, complemented
11#10590468C211yesmaximal, characteristic, complemented
12#10590458C211yesmaximal, characteristic, complemented
13#10590368C211yesmaximal, characteristic, complemented
14C4×#3715C211yesmaximal, characteristic, complemented
15#10590250C211yesmaximal, characteristic, complemented
16#83697—31nomaximal
17#81151—31nomaximal
18C32×#125C2211yescharacteristic
19#64084C2211yescharacteristic
20C3×#890C2211yescharacteristic
21C3×#889—21no—
22C3×#889—21no—
23C3×#888—21no—
24C3×#888C2211yescharacteristic
25C3×#887—21no—
26C3×#887C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×C4×D12C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31#63911C2211yescharacteristic
32#63907—21no—
33#63904—21no—
34#63894C2211yescharacteristic
35#63860C2211yescharacteristic
36#63854—21no—
37#63850—21no—
38#63844C2211yescharacteristic
39C2×#3719C2211yescharacteristic
40C2×#3717C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42#63637C2211yescharacteristic
43#63637C2211yescharacteristic
44#63636C2211yescharacteristic
45#63636C2211yescharacteristic
46C4×C3⋊(C3⋊C8)C2211yescharacteristic
47C3×#809C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51C3×C4⋊(C3⋊C8)C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#557—31no—
62#5685D311yescharacteristic, complemented
63#5585—31no—
64#5559—31no—
65C3×#478—31no—
66#5094—31no—
67#5088—31no—
68#5068—31no—
69#5068—31no—
70#5068—31no—
71#5068—61no—
72#5066—31no—
73#5066D311yescharacteristic, complemented
74C4×#216—31no—
75#5028—31no—
76#5028—31no—
77#5027—31no—
78C4×#215—31no—
79C4×#215—31no—
80Q8×C3⋊C8—31no—
81C4×#214—31no—
82#4891—31no—
83#4873—31no—
84#4854—31no—
85#4852—31no—
86#4845—31no—
87#4830—31no—
88#4768—31no—
89#4767—31no—
90#4762—31no—
91#4760—31no—
92C2×C4⋊(C3⋊D3)C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6—21no—
97C2×C3×Dic6D411yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#626—21no—
100C2×#626—21no—
101C2×#624—21no—
102C32×C4⋊C4—21no—
103C32×C4⋊C4—21no—
104C32×C4⋊C4C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C42C2311yescharacteristic
107#3752—21no—
108#3752—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×(C2×D3)⋊C4—21no—
112C3×C4⋊Dic3—21no—
113C3×C4⋊Dic3D411yescharacteristic
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4D411yescharacteristic
122C3×Dic3⋊C4D411yescharacteristic
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3722—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134Dic32—21no—
135#3719—22no—
136#3717—22no—
137#3715—22no—
138#3365—91noSylow
139C3×C4⋊Q8—31no—
140C3×C4⋊Q8—61no—
141C3×#125—21no—
142C3×#125—31no—
143C3×#125—61no—
144C3×#125—61no—
145C3×#125C2×D311yescharacteristic
146C3×#125C2×D311yescharacteristic
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×Q8—31no—
150C3×C4×Q8—31no—
151C3×C4×Q8—61no—
152C3×C4×D4—31no—
153#947—61no—
154C2×#216—31no—
155C2×#215—31no—
156C2×#215—31no—
157#940—31no—
158#936—31no—
159C2×#214—31no—
160#929—61no—
161C4×#67—61no—
162C2×Dic12—31no—
163C2×#204—31no—
164#894—61no—
165#894—61no—
166#893—31no—
167#893—61no—
168#890C2×D311yescharacteristic
169#889—21no—
170#889—21no—
171#888—21no—
172#888C2×D311yescharacteristic
173#887—21no—
174#887—31no—
175#887C2×D311yescharacteristic
176#887C2×D311yescharacteristic
177#885—61no—
178#883—61no—
179#875—31no—
180#875—31no—
181#875—31no—
182#875—61no—
183#874—31no—
184C4×D12—31no—
185C4×D12C2×D311yescharacteristic
186C4×Dic6—31no—
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×#107—31no—
190C3×#106—31no—
191C3×C4⋊C8—31no—
192C3×#102—31no—
193C3×#102—31no—
194#835—31no—
195#832—31no—
196#821—31no—
197#816—31no—
198Dic3⋊C8—31no—
199Dic3⋊C8—31no—
200C8×Dic3—31no—
201C8×Dic3—31no—
202#810—31no—
203#810—31no—
204#810—31no—
205#810—31no—
206#810—31no—
207#810—31no—
208#810—61no—
209#810—61no—
210#809—31no—
211#809—31no—
212#809—31no—
213#809—31no—
214#809—31no—
215#809—31no—
216#809—61no—
217#809—61no—
218#809C2×D311yescharacteristic
219#809C2×D311yescharacteristic
220#808—31no—
221#808—31no—
222#808C2×D311yescharacteristic
223#807C2×D311yescharacteristic
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)C2×D311yescharacteristic
227C4×C3⋊C8—31no—
228C4×C3⋊C8—31no—
229C4×C3⋊C8—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8—61no—
232C22×C3⋊D3—21no—
233C22×C3×D3—21no—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2×D411yescharacteristic
237C2×C32×C4C2×D411yescharacteristic
238C2×C32×C4C2411yescharacteristic
239C2×C3⋊Dic3—21no—
240C4⋊(C3⋊D3)—21no—
241C4⋊(C3⋊D3)—21no—
242#634—21no—
243#634—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3C2×D411yescharacteristic
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C3×D12—21no—
252C3×D12—21no—
253C3×C4×D3—81no—
254C3×Dic6—21no—
255C3×Dic6—22no—
256C3×Dic6—42no—
257C3×Dic6#4112yes—
258#626—42no—
259#626—81no—
260#624—81no—
261C3⋊(C3⋊C8)—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—91no—
266#557—31no—
267#488—91no—
268#488—91no—
269#486—91no—
270#478—31no—
271#478—91no—
272#475—91no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—91no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283C2×C3×D4—31no—
284C22×C3×C4—61no—
285C2×#67—61no—
286C2×#67—61no—
287C2×D12—31no—
288C2×D12—31no—
289C2×D12—61no—
290C2×D12—61no—
291C2×D12—61no—
292C2×D12C22×D311yescharacteristic
293C2×C4×D3—21no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×Dic6—21no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—61no—
300C2×Dic6#6711yescharacteristic
301C2×Dic6C22×D311yescharacteristic
302C2×C3×C8—31no—
303C2×C3×C8—31no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—21no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—31no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—41no—
316C3×C4⋊C4—41no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C22⋊C4—61no—
328C3×C42—21no—
329C3×C42—31no—
330C3×C42—31no—
331C3×C42—61no—
332C3×C42—61no—
333C3×C42—61no—
334C3×C42C22×D311yescharacteristic
335C3×C42C22×D311yescharacteristic
336#217—61no—
337#217—61no—
338#216—62no—
339#215—62no—
340#215—62no—
341#214—62no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—121no—
352(C2×D3)⋊C4—121no—
353C4⋊Dic3—21no—
354C4⋊Dic3#6711yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356C4⋊Dic3C22×D311yescharacteristic
357Dic3⋊C4—21no—
358Dic3⋊C4—21no—
359Dic3⋊C4—21no—
360Dic3⋊C4—21no—
361Dic3⋊C4—21no—
362Dic3⋊C4—61no—
363Dic3⋊C4—61no—
364Dic3⋊C4#6711yescharacteristic
365Dic3⋊C4#6711yescharacteristic
366C4×Dic3—21no—
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3C22×D311yescharacteristic
372C4×Dic3C22×D311yescharacteristic
373C2×C3⋊C8—31no—
374C2×C3⋊C8—31no—
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—61no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381Dic12—62no—
382#204—62no—
383C22×C32C22×D411yescharacteristic
384C2×C3⋊D3—41no—
385C2×C3⋊D3—41no—
386C2×C3⋊D3—41no—
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—41no—
393C32×C4—41no—
394C32×C4C2×#4111yescharacteristic
395C32×C42−1+411yescharacteristic
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×Q16—91no—
405C2×SD16—91no—
406C2×SD16—91no—
407C4⋊Q8—31no—
408C4⋊Q8—61no—
409#127—91no—
410#125—31no—
411#125—61no—
412#125—61no—
413#125D3211yescharacteristic
414#124—91no—
415#124—91no—
416#124—181no—
417#123—181no—
418#123—181no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—31no—
423C4×Q8—61no—
424C4×Q8—91no—
425C4×D4—31no—
426C4×D4—91no—
427C4×D4—181no—
428#107—31no—
429#106—31no—
430#106—91no—
431C4⋊C8—31no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—91no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—31no—
440#102—91no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—91no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—61no—
448C22×D3—21no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—121no—
452C3×Q8—32no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—122no—
456C3×D4—61no—
457C3×D4—61no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—31no—
468C2×C3×C4—31no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—241no—
475C2×C3×C4D3×D411yescharacteristic
476C2×C3×C4D3×D411yescharacteristic
477C2×C3×C4C2×#6711yescharacteristic
478C2×C3×C4C2×#6711yescharacteristic
479C2×C3×C4C23×D311yescharacteristic
480C2×C3×C4C23×D311yescharacteristic
481#67—122no—
482#67—241no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—61no—
487C2×Dic3—61no—
488C2×Dic3—121no—
489C2×Dic3C2×#6711yescharacteristic
490C2×Dic3C2×#6711yescharacteristic
491C2×Dic3C2×#6711yescharacteristic
492C2×Dic3C2×#6711yescharacteristic
493D12—21no—
494D12—21no—
495D12—61no—
496D12—61no—
497D12—61no—
498D12—61no—
499D12—121no—
500D12—121no—
501D12—122no—
502D12—241no—
503C4×D3—81no—
504C4×D3—241no—
505C4×D3—241no—
506Dic6—21no—
507Dic6—22no—
508Dic6—42no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—61no—
513Dic6—121no—
514Dic6—121no—
515Dic6#23912yes—
516C3×C8—61no—
517C3×C8—61no—
518C3⋊C8—21no—
519C3⋊C8—21no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C3⋊C8—121no—
525C3⋊C8—121no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13511yescharacteristic
528C2×C32#57711yescharacteristic
529C3⋊D3—81no—
530C3×D3—81no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—61no—
534C2×Q8—91no—
535C2×D4—31no—
536C2×D4—91no—
537C2×D4—181no—
538C2×D4—181no—
539C22×C4—61no—
540C22×C4—181no—
541Q16—182no—
542SD16—182no—
543SD16—182no—
544C2×C8—31no—
545C2×C8—31no—
546C2×C8—91no—
547C2×C8—91no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—31no—
551C4⋊C4—31no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—61no—
556C4⋊C4—61no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—181no—
562C4⋊C4C2×D3211yescharacteristic
563C4⋊C4C2×D3211yescharacteristic
564C22⋊C4—61no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C22⋊C4—181no—
570C42—31no—
571C42—31no—
572C42—61no—
573C42—61no—
574C42—61no—
575C42—181no—
576C42C2×D3211yescharacteristic
577C22×C3—21no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3C2×D3×D411yescharacteristic
582C22×C3C22×#6711yescharacteristic
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—41no—
586C2×D3—121no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
591C2×D3—121no—
592C2×D3—241no—
593C2×D3—241no—
594C2×D3—241no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—21no—
601C3×C4—32no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—62no—
609C3×C4—61no—
610C3×C4—61no—
611C3×C4—61no—
612C3×C4—81no—
613C3×C4—81no—
614C3×C4—121no—
615C3×C4—121no—
616C3×C4C2×#23911yescharacteristic
617C3×C4#100711yescharacteristic
618C3×C4#100711yescharacteristic
619C3×C4D3×#4111yescharacteristic
620Dic3—22no—
621Dic3—21no—
622Dic3—21no—
623Dic3—21no—
624Dic3—41no—
625Dic3—41no—
626Dic3—121no—
627Dic3—121no—
628Dic3—241no—
629Dic3#95012yes—
630C32#336511yescharacteristic, complemented, Sylow
631C23—61no—
632C23—181no—
633Q8—32no—
634Q8—62no—
635Q8—61no—
636Q8—122no—
637Q8—181no—
638Q8—181no—
639D4—61no—
640D4—61no—
641D4—181no—
642D4—181no—
643D4—362no—
644D4—721no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—31no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—181no—
655C2×C4—241no—
656C2×C4—721no—
657C2×C4D3×#6711yescharacteristic
658C2×C4D3×#6711yescharacteristic
659C2×C4C22×D3211yescharacteristic
660C8—61no—
661C8—61no—
662C8—181no—
663C8—181no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—241no—
668C2×C3#563311yescharacteristic
669C2×C3D3×#13511yescharacteristic
670C2×C3#577511yescharacteristic
671C2×C3#581711yescharacteristic
672C2×C3C2×#95011yescharacteristic
673C2×C3#583711yescharacteristic
674D3—81no—
675D3—241no—
676D3—241no—
677D3—481no—
678C22—121no—
679C22—121no—
680C22—121no—
681C22—361no—
682C22—361no—
683C22—361no—
684C22C2×D3×#6711yescharacteristic
685C4—21no—
686C4—21no—
687C4—32no—
688C4—41no—
689C4—41no—
690C4—62no—
691C4—61no—
692C4—61no—
693C4—61no—
694C4—121no—
695C4—121no—
696C4—361no—
697C4#6431611yescharacteristic
698C4D3×#23911yescharacteristic
699C3—21no—
700C3#8115111yescharacteristic, complemented
701C3#8369711yescharacteristic, complemented
702C2—241no—
703C2—721no—
704C2#1059540211yescharacteristic
705C2D3×#95011yescharacteristic
706C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#125C22
socleC22×C32C22×D4
prime radical#63911C22
hypercenter#125D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×#5685C2semidirect
3. #10592767C2semidirect
4. C3×#5066C2semidirect
7. #10590533C2semidirect
8. #10590532C2semidirect
9. #10590487C2semidirect
10. #10590481C2semidirect
11. #10590468C2semidirect
12. #10590458C2semidirect
13. #10590368C2semidirect
14. C4×#3715C2semidirect
15. #10590250C2semidirect
62. #5685D3semidirect
73. #5066D3semidirect
630. C32#3365semidirect
700. C3#81151semidirect
701. C3#83697semidirect

Maximal subgroups

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

subgroupindex
C3×#56852
#105939782
#105927672
C3×#50662
#105905492
#105905482
#105905332
#105905322
#105904872
#105904812
#105904682
#105904582
#105903682
C4×#37152
#105902502
#836973
#811513