Finite Group Databasebeta

← #11876936

Subgroups — #11876936

Order 1152.

788 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595172C211yesmaximal, characteristic, complemented
2#10594426C211yesmaximal, characteristic, complemented
3#10592467C211yesmaximal, characteristic, complemented
4C3×#4782C211yesmaximal, characteristic
5C3×#4757C211yesmaximal, characteristic, complemented
6#10591502C211yesmaximal, characteristic, complemented
7#10591474C211yesmaximal, characteristic, complemented
8#10591430C211yesmaximal, characteristic, complemented
9#10590868C211yesmaximal, characteristic, complemented
10#10590849C211yesmaximal, characteristic, complemented
11#10590747C211yesmaximal, characteristic, complemented
12#10590667C211yesmaximal, characteristic, complemented
13#10590588C211yesmaximal, characteristic, complemented
14#10590480C211yesmaximal, characteristic, complemented
15#10590417C211yesmaximal, characteristic, complemented
16#80852—31nomaximal
17#79793—31nomaximal
18#64145C2211yescharacteristic
19#64099C2211yescharacteristic
20C3×#938C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#887C2211yescharacteristic
27Dic3×#67—21no—
28#63969—21no—
29#63956—21no—
30#63955—21no—
31Dic3×D12—21no—
32Dic3×D12C2211yescharacteristic
33#63884—21no—
34#63877—21no—
35C4×D3×Dic3C2211yescharacteristic
36#63872C2211yescharacteristic
37#63863C2211yescharacteristic
38#63861—21no—
39#63857C2211yescharacteristic
40#63856C2211yescharacteristic
41#63844C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3711C2211yescharacteristic
45C32×#102C2211yescharacteristic
46#63659C2211yescharacteristic
47#63643C2211yescharacteristic
48C8×C3⋊Dic3C2211yescharacteristic
49#63637C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×#808C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63575C2211yescharacteristic
56#63573C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60#63553C2211yescharacteristic
61#5600—31no—
62#5600—31no—
63#5580—31no—
64#5557—31no—
65C3×#469—31no—
66C3×#440—31no—
67#5174—31no—
68#5168—31no—
69#5155—31no—
70#5152—31no—
71#5137—31no—
72Dic3×M16—31no—
73#5042—31no—
74#5042—31no—
75#5030—31no—
76#5014—31no—
77#4886—31no—
78#4878—31no—
79#4858—31no—
80#4853—31no—
81#4816—31no—
82#4800—31no—
83#4782D311yescharacteristic
84#4768—31no—
85#4768—31no—
86#4768—31no—
87#4768—61no—
88#4757—31no—
89#4757D311yescharacteristic, complemented
90#4710—31no—
91#4707—31no—
92C2×C32×D4C2311yescharacteristic
93C2×#634C2311yescharacteristic
94C2×C3×#67—21no—
95C22×C3×Dic3—21no—
96C2×C3×D12—21no—
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×D3×Dic3—21no—
101C2×D3×Dic3D411yescharacteristic
102C2×D3×Dic3D411yescharacteristic
103C2×C32×C8C2311yescharacteristic
104C32×C4⋊C4C2311yescharacteristic
105#3757—21no—
106#3757—21no—
107C4⋊(C3⋊Dic3)—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109#3750—21no—
110C4×C3⋊Dic3C2311yescharacteristic
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×#217—21no—
113C3×#217—21no—
114C3×#214—22no—
115C3×#213—22no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3C2311yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×C4×Dic3—21no—
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×ΓL(1,𝔽25)—22no—
125#3724—21no—
126#3724—21no—
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130(C2×D3)⋊Dic3—21no—
131(C2×D3)⋊Dic3—21no—
132(C2×D3)⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3719—22no—
139#3716—22no—
140#3711—22no—
141#3183—91noSylow
142C2×C3×SD16—31no—
143C2×C3×D8—31no—
144C2×C3×M16—31no—
145C3×#121—31no—
146C3×#121—31no—
147C3×C4×Q8—31no—
148C3×C4×D4—31no—
149#947—31no—
150#946—31no—
151C2×#216—31no—
152#938C2×D311yescharacteristic
153#936—31no—
154#936—31no—
155#936—31no—
156#936—61no—
157#935—61no—
158#935—61no—
159D4×Dic3—31no—
160D4×Dic3—61no—
161D4×Dic3—61no—
162D4×Dic3C2×D311yescharacteristic
163C2×#214—31no—
164C2×#214C2×D311yescharacteristic
165C2×#213C2×D311yescharacteristic
166C4×#67—61no—
167#926—61no—
168#924—31no—
169#924—31no—
170C2×C4×Dic3—31no—
171C2×#208—31no—
172C2×Dic12—31no—
173C2×#204—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×ΓL(1,𝔽25)C2×D311yescharacteristic
176#898—61no—
177#897—31no—
178#895C2×D311yescharacteristic
179#894—61no—
180#890—31no—
181#890—31no—
182#890—31no—
183#890—31no—
184#890—61no—
185#887—31no—
186#887C2×D311yescharacteristic
187#883—61no—
188#879—61no—
189#879—61no—
190#879—61no—
191#877—61no—
192#877—61no—
193C4×D12—31no—
194C4×D12—61no—
195#872—61no—
196C42×D3—31no—
197C4×Dic6—31no—
198C3×#107—31no—
199C3×#106—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102C2×D311yescharacteristic
204C3×#102C2×D311yescharacteristic
205C3×#97—31no—
206#835—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—61no—
211#821C2×D311yescharacteristic
212#818—31no—
213#817—31no—
214#816—31no—
215#816—31no—
216#816—61no—
217#816C2×D311yescharacteristic
218#815—31no—
219#815C2×D311yescharacteristic
220C8×Dic3—31no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—61no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#809—31no—
230#808—31no—
231#808C2×D311yescharacteristic
232#807—31no—
233#807C2×D311yescharacteristic
234#803—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×D4—21no—
239C32×D4—21no—
240C2×C32×C4—21no—
241C2×C32×C4C2411yescharacteristic
242C2×C3⋊Dic3—21no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3C2×D411yescharacteristic
245C2×C3⋊Dic3C2×D411yescharacteristic
246#634—21no—
247#634—21no—
248C3×#67—42no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—42no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—42no—
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263D3×Dic3—41no—
264D3×Dic3—41no—
265D3×Dic3—42no—
266C32×C8—21no—
267C3⋊(C3⋊C8)—21no—
268C3×C3⋊C8#4112yes—
269C3×C3⋊C8#4112yes—
270#529—91no—
271#529—91no—
272#499—91no—
273#495—91no—
274#488—91no—
275#488—91no—
276#470—91no—
277#469—31no—
278#468—91no—
279#468—91no—
280#442—91no—
281#441—91no—
282#440—31no—
283#440—91no—
284C4×M16—91no—
285C2×C3×Q8—31no—
286C2×C3×D4—21no—
287C2×C3×D4—31no—
288C2×C3×D4—61no—
289C2×C3×D4—61no—
290C2×C3×D4C22×D311yescharacteristic
291C2×C3×D4C22×D311yescharacteristic
292C22×C3×C4—31no—
293C22×C3×C4—61no—
294C2×#67—21no—
295C22×Dic3—21no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—61no—
299C2×D12—21no—
300C2×D12C22×D311yescharacteristic
301C2×C4×D3—31no—
302C2×C4×D3—31no—
303C2×C4×D3—61no—
304C2×C4×D3C22×D311yescharacteristic
305C2×Dic6—31no—
306C2×Dic6—31no—
307C2×Dic6—61no—
308C2×Dic6C22×D311yescharacteristic
309C3×SD16—62no—
310C3×D8—62no—
311C3×M16—62no—
312C2×C3×C8—21no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8C22×D311yescharacteristic
316C2×C3×C8C22×D311yescharacteristic
317C3×C4⋊C4—21no—
318C3×C4⋊C4—31no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C22⋊C4—61no—
324C3×C22⋊C4—61no—
325C3×C22⋊C4—61no—
326C3×C42—31no—
327C3×C42—61no—
328#217—21no—
329#217—21no—
330#217—61no—
331#217—61no—
332#217—61no—
333#217—61no—
334#217—61no—
335#217—61no—
336#217—61no—
337#217—61no—
338#217—61no—
339#217—121no—
340#217—121no—
341#216—62no—
342#214—22no—
343#214—62no—
344#213—22no—
345(C2×D3)⋊C4—21no—
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—
351C4⋊Dic3—31no—
352C4⋊Dic3—31no—
353C4⋊Dic3—61no—
354C4⋊Dic3—61no—
355C4⋊Dic3—61no—
356C4⋊Dic3—61no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—121no—
360C4⋊Dic3C22×D311yescharacteristic
361C4⋊Dic3C22×D311yescharacteristic
362Dic3⋊C4—21no—
363Dic3⋊C4—61no—
364Dic3⋊C4—61no—
365Dic3⋊C4—61no—
366Dic3⋊C4—61no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—121no—
373C4×Dic3—21no—
374C4×Dic3—31no—
375C4×Dic3—31no—
376C4×Dic3—31no—
377C4×Dic3—31no—
378C4×Dic3—31no—
379C4×Dic3—31no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3C22×D311yescharacteristic
384#208—62no—
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—62no—
391#204—62no—
392ΓL(1,𝔽25)—22no—
393ΓL(1,𝔽25)—62no—
394C22×C32—41no—
395C22×C32—41no—
396C22×C32—41no—
397C22×C32C22×D411yescharacteristic
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C32×C4—41no—
405C32×C4C2×#4111yescharacteristic
406C32×C4C2×#4111yescharacteristic
407C3⋊Dic3—21no—
408C3⋊Dic3—21no—
409C3⋊Dic3—41no—
410C3⋊Dic3—41no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C2×Q16—91no—
418C2×SD16—31no—
419C2×SD16—91no—
420C2×D8—31no—
421C2×M16—31no—
422C2×M16—91no—
423#126—181no—
424#126—181no—
425#125—91no—
426#125—91no—
427#124—91no—
428#124—91no—
429#123—181no—
430#123—181no—
431C22⋊Q8—91no—
432C22⋊Q8—91no—
433#121—31no—
434#121—31no—
435C4×Q8—31no—
436C4×Q8—91no—
437C4×D4—31no—
438C4×D4—91no—
439C4×D4—181no—
440C4×D4—181no—
441#117—181no—
442#117—181no—
443C2×C42—91no—
444#107—31no—
445#107—91no—
446#106—31no—
447#106—91no—
448#103—31no—
449#103—91no—
450#103—91no—
451#103—91no—
452#102—31no—
453#102—91no—
454#102—91no—
455#102D3211yescharacteristic
456#97—31no—
457#97—91no—
458C4×C8—91no—
459C4×C8—91no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—31no—
463C23×C3—41no—
464C23×C3—61no—
465C22×D3—21no—
466C22×D3D3×D411yescharacteristic
467C3×Q8—61no—
468C3×Q8—61no—
469C3×D4—21no—
470C3×D4—21no—
471C3×D4—21no—
472C3×D4—21no—
473C3×D4—41no—
474C3×D4—41no—
475C3×D4—61no—
476C3×D4—61no—
477C3×D4—122no—
478C3×D4—122no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—41no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—122no—
492C2×C3×C4C23×D311yescharacteristic
493C2×C3×C4C23×D311yescharacteristic
494#67—42no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—31no—
502C2×Dic3—42no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—121no—
510C2×Dic3—121no—
511C2×Dic3—121no—
512C2×Dic3—121no—
513C2×Dic3—122no—
514C2×Dic3D3×D411yescharacteristic
515C2×Dic3D3×D411yescharacteristic
516C2×Dic3D3×D411yescharacteristic
517D12—21no—
518D12—21no—
519D12—42no—
520C4×D3—21no—
521C4×D3—21no—
522C4×D3—121no—
523C4×D3—121no—
524C4×D3—122no—
525Dic6—21no—
526Dic6—21no—
527Dic6—61no—
528Dic6—61no—
529Dic6—61no—
530Dic6—61no—
531Dic6—121no—
532Dic6—121no—
533C3×C8—21no—
534C3×C8—21no—
535C3×C8—32no—
536C3×C8—32no—
537C3×C8—41no—
538C3⋊C8—61no—
539C3⋊C8—61no—
540C3⋊C8—121no—
541C3⋊C8#23512yes—
542C3⋊C8#23712yes—
543C2×C32—81no—
544C2×C32#53211yescharacteristic
545C2×C32#57511yescharacteristic
546C2×C32#57511yescharacteristic
547C3×D3—41no—
548C3×D3—81no—
549C2×Q8—31no—
550C2×Q8—91no—
551C2×D4—31no—
552C2×D4—61no—
553C2×D4—61no—
554C2×D4C2×D3211yescharacteristic
555C22×C4—31no—
556C22×C4—61no—
557C22×C4—91no—
558C22×C4—91no—
559C22×C4—181no—
560Q16—182no—
561SD16—62no—
562SD16—182no—
563D8—62no—
564M16—62no—
565M16—182no—
566C2×C8—31no—
567C2×C8—31no—
568C2×C8—91no—
569C2×C8C2×D3211yescharacteristic
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—61no—
573C4⋊C4—91no—
574C4⋊C4—181no—
575C4⋊C4—181no—
576C4⋊C4—181no—
577C4⋊C4—181no—
578C4⋊C4—181no—
579C4⋊C4—181no—
580C4⋊C4—181no—
581C4⋊C4C2×D3211yescharacteristic
582C22⋊C4—61no—
583C22⋊C4—61no—
584C22⋊C4—61no—
585C22⋊C4—181no—
586C22⋊C4—181no—
587C22⋊C4—181no—
588C22⋊C4—181no—
589C22⋊C4—181no—
590C22⋊C4—181no—
591C22⋊C4—181no—
592C42—31no—
593C42—61no—
594C42—91no—
595C42—91no—
596C42—91no—
597C42—181no—
598C22×C3—21no—
599C22×C3—41no—
600C22×C3—41no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—41no—
604C22×C3—41no—
605C22×C3—61no—
606C22×C3—61no—
607C22×C3—61no—
608C22×C3—81no—
609C22×C3—81no—
610C22×C3—81no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3C2×D3×D411yescharacteristic
615C22×C3C2×D3×D411yescharacteristic
616C2×D3—21no—
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—41no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—61no—
627C3×C4—61no—
628C3×C4—61no—
629C3×C4—81no—
630C3×C4—121no—
631C3×C4—121no—
632C3×C4—121no—
633C3×C4C2×#23511yescharacteristic
634C3×C4C2×#23711yescharacteristic
635C3×C4D3×#4111yescharacteristic
636C3×C4D3×#4111yescharacteristic
637Dic3—21no—
638Dic3—21no—
639Dic3—21no—
640Dic3—41no—
641Dic3—41no—
642Dic3—41no—
643Dic3—61no—
644Dic3—61no—
645Dic3—61no—
646Dic3—61no—
647Dic3—121no—
648Dic3—121no—
649Dic3—121no—
650Dic3—121no—
651Dic3—121no—
652Dic3—121no—
653Dic3—241no—
654Dic3—241no—
655C32#318311yescharacteristic, complemented, Sylow
656C23—21no—
657C23—31no—
658C23—61no—
659Q8—61no—
660Q8—61no—
661Q8—181no—
662Q8—181no—
663D4—21no—
664D4—21no—
665D4—61no—
666D4—61no—
667D4—122no—
668D4—122no—
669C2×C4—21no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—31no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—91no—
679C2×C4—91no—
680C2×C4—122no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—361no—
684C2×C4—361no—
685C2×C4—362no—
686C2×C4C22×D3211yescharacteristic
687C8—21no—
688C8—32no—
689C8—32no—
690C8—181no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—81no—
695C2×C3—81no—
696C2×C3—121no—
697C2×C3—161no—
698C2×C3—241no—
699C2×C3#554811yescharacteristic
700C2×C3#559611yescharacteristic
701C2×C3#577311yescharacteristic
702C2×C3#577311yescharacteristic
703C2×C3#577311yescharacteristic
704C2×C3#577711yescharacteristic
705D3—41no—
706D3—81no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—61no—
711C22—61no—
712C22—61no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22D32×D411yescharacteristic
717C4—41no—
718C4—61no—
719C4—61no—
720C4—61no—
721C4—121no—
722C4—121no—
723C4—121no—
724C4—181no—
725C4—181no—
726C4—361no—
727C4—361no—
728C4D3×#23511yescharacteristic
729C4D3×#23711yescharacteristic
730C3—21no—
731C3#7979311yescharacteristic, complemented
732C3#8085211yescharacteristic, complemented
733C2—81no—
734C2—121no—
735C2—241no—
736C2#1059405811yescharacteristic
737C2#1059472811yescharacteristic
738C2#1059474411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC3×#4782C2
hypercenter#102D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595172C2semidirect
2. #10594426C2semidirect
3. #10592467C2semidirect
5. C3×#4757C2semidirect
6. #10591502C2semidirect
7. #10591474C2semidirect
8. #10591430C2semidirect
9. #10590868C2semidirect
10. #10590849C2semidirect
11. #10590747C2semidirect
12. #10590667C2semidirect
13. #10590588C2semidirect
14. #10590480C2semidirect
15. #10590417C2semidirect
89. #4757D3semidirect
655. C32#3183semidirect
731. C3#79793semidirect
732. C3#80852semidirect

Maximal subgroups

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

subgroupindex
#105951722
#105944262
#105924672
C3×#47822
C3×#47572
#105915022
#105914742
#105914302
#105908682
#105908492
#105907472
#105906672
#105905882
#105904802
#105904172
#808523
#797933