Finite Group Databasebeta

← #11872690

Subgroups — #11872690

Order 1152.

793 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594352C211yesmaximal, characteristic
2#10594347C211yesmaximal, characteristic, complemented
3#10592584C211yesmaximal, characteristic
4C3×#4875C211yesmaximal, characteristic, complemented
5C3×#4873C211yesmaximal, characteristic, complemented
6#10590950C211yesmaximal, characteristic, complemented
7#10590801C211yesmaximal, characteristic, complemented
8#10590792C211yesmaximal, characteristic, complemented
9#10590648C211yesmaximal, characteristic, complemented
10#10590606C211yesmaximal, characteristic
11#10590536C211yesmaximal, characteristic, complemented
12#10590526C211yesmaximal, characteristic, complemented
13#10590486C211yesmaximal, characteristic, complemented
14#10590477C211yesmaximal, characteristic, complemented
15#10590457C211yesmaximal, characteristic, complemented
16#81096—31nomaximal
17#79750—31nomaximal
18C2×#3797C2211yescharacteristic
19#64104C2211yescharacteristic
20#64101C2211yescharacteristic
21C2×C3×Dic12C2211yescharacteristic
22C3×#888C2211yescharacteristic
23C3×#887C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26C4×#627—21no—
27#63897—21no—
28#63894C2211yescharacteristic
29#63888—21no—
30#63874C2211yescharacteristic
31#63871C2211yescharacteristic
32#63868—21no—
33#63864—21no—
34#63864C2211yescharacteristic
35Dic3×Dic6C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37#63838—21no—
38#63836—21no—
39#63836—21no—
40C2×#3718C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C32×#107C2211yescharacteristic
44#63648C2211yescharacteristic
45#63647C2211yescharacteristic
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#816C2211yescharacteristic
49C3×Dic3⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#810C2211yescharacteristic
54C3×#807C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59#63557C2211yescharacteristic
60#63554C2211yescharacteristic
61#5733—31no—
62#5582—31no—
63#5572—31no—
64#5572—31no—
65C3×#477—31no—
66C3×C4×Q16—31no—
67#5186—31no—
68#5185—31no—
69#5094—31no—
70#5030—31no—
71#5028—31no—
72#5026—31no—
73#4889—31no—
74#4888—31no—
75#4885—31no—
76#4885—31no—
77#4885—61no—
78#4875D311yescharacteristic, complemented
79#4873D311yescharacteristic, complemented
80#4845—31no—
81#4840—31no—
82#4815—31no—
83#4809—31no—
84#4806—31no—
85#4806—31no—
86#4798—31no—
87#4791—31no—
88#4789—31no—
89#4788—31no—
90C4×#204—31no—
91#4690—31no—
92C2×C4⋊(C3⋊D3)—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×Dic6—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#624—21no—
101C2×#624—21no—
102#3797—22no—
103#3797—22no—
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3752—21no—
108#3752—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4×C3⋊Dic3—21no—
111C2×C3⋊(C3⋊C8)C2311yescharacteristic
112C3×C4⋊Dic3C2311yescharacteristic
113C3×Dic3⋊C4—21no—
114C3×Dic3⋊C4—21no—
115C3×Dic3⋊C4—21no—
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×Dic12—22no—
125#3724D411yescharacteristic
126#3724D411yescharacteristic
127Dic3⋊Dic3—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130#3722—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134#3722D411yescharacteristic
135#3722D411yescharacteristic
136Dic32—21no—
137Dic32—21no—
138#3718—22no—
139#3717—22no—
140#3717—22no—
141#3121—91noSylow
142C2×D3×Q8—31no—
143C2×D3×Q8—31no—
144C2×C3×Q16—31no—
145C3×C4⋊Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149#947—31no—
150#947—61no—
151#946—31no—
152#946—61no—
153Q8×Dic3—31no—
154Q8×Dic3—31no—
155C2×#216—31no—
156C2×#216—31no—
157C2×#215—31no—
158C2×#215—31no—
159C2×Dic12C2×D311yescharacteristic
160C2×#204—31no—
161C2×#204—31no—
162#898—61no—
163#897—31no—
164#896—61no—
165#895—31no—
166#895—31no—
167#895—61no—
168#894—61no—
169#894—61no—
170#893—31no—
171#892—31no—
172#892—31no—
173#892—61no—
174#892—61no—
175#892—61no—
176#888C2×D311yescharacteristic
177#887—61no—
178#887—61no—
179#887C2×D311yescharacteristic
180#887C2×D311yescharacteristic
181#887C2×D311yescharacteristic
182#876—61no—
183#875—31no—
184#875—61no—
185C4×D12—31no—
186#872—31no—
187#872—31no—
188#872—61no—
189#872—61no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—61no—
193C4×Dic6—61no—
194C3×#107—21no—
195C3×#107—31no—
196C3×#107C2×D311yescharacteristic
197C3×#107C2×D311yescharacteristic
198C3×C4⋊C8—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×C4×C8—31no—
204#835—31no—
205#835—31no—
206#821—31no—
207#821—31no—
208#821—61no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—61no—
214#817—31no—
215#816—31no—
216#816C2×D311yescharacteristic
217#815—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8C2×D311yescharacteristic
220C8×Dic3C2×D311yescharacteristic
221#810—31no—
222#810C2×D311yescharacteristic
223#810C2×D311yescharacteristic
224#810C2×D311yescharacteristic
225#809—31no—
226#809—31no—
227#809—61no—
228#808—31no—
229#808—31no—
230#808—31no—
231#808—61no—
232#807C2×D311yescharacteristic
233C4⋊(C3⋊C8)—31no—
234#803—31no—
235C22×C3⋊D3—21no—
236C22×C3⋊D3C2×D411yescharacteristic
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4C2411yescharacteristic
240C2×C3⋊Dic3—21no—
241C2×C3⋊Dic3C2×D411yescharacteristic
242C4⋊(C3⋊D3)—21no—
243C4⋊(C3⋊D3)—21no—
244C4⋊(C3⋊D3)—81no—
245C4×C3⋊D3—21no—
246C4×C3⋊D3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3C2×D411yescharacteristic
252C2×C3×Dic3C2×D411yescharacteristic
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6—81no—
260C3×Dic6#4112yes—
261C3×Dic6#4112yes—
262#627—24no—
263#624—24no—
264#624—81no—
265C32×C8—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—91no—
270#519—91no—
271#485—91no—
272#482—91no—
273#477—31no—
274#475—91no—
275#464—91no—
276#464—91no—
277#451—91no—
278#448—91no—
279#441—91no—
280#440—91no—
281C4×Q16—31no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—31no—
285C2×C3×Q8—31no—
286C2×C3×Q8—31no—
287C2×C3×Q8—61no—
288D3×Q8—62no—
289D3×Q8—62no—
290D3×Q8—62no—
291D3×Q8—62no—
292C2×D12—31no—
293C2×D12—31no—
294C2×D12—61no—
295C2×D12—61no—
296C2×D12—61no—
297C2×D12—121no—
298C2×C4×D3—31no—
299C2×C4×D3—31no—
300C2×C4×D3—61no—
301C2×C4×D3—61no—
302C2×C4×D3—61no—
303C2×C4×D3—61no—
304C2×C4×D3—61no—
305C2×Dic6—21no—
306C2×Dic6—61no—
307C2×Dic6—61no—
308C2×Dic6C22×D311yescharacteristic
309C2×Dic6C22×D311yescharacteristic
310C2×Dic6C22×D311yescharacteristic
311C3×Q16—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—21no—
319C3×C4⋊C4—31no—
320C3×C4⋊C4—61no—
321C3×C4⋊C4—61no—
322C3×C4⋊C4—61no—
323C3×C4⋊C4—61no—
324C3×C4⋊C4C22×D311yescharacteristic
325C3×C4⋊C4C22×D311yescharacteristic
326C3×C4⋊C4C22×D311yescharacteristic
327C3×C4⋊C4C22×D311yescharacteristic
328C3×C42—31no—
329C3×C42—31no—
330C3×C42—61no—
331C3×C42—61no—
332C3×C42—61no—
333#216—62no—
334#216—62no—
335#215—62no—
336#215—62no—
337(C2×D3)⋊C4—31no—
338(C2×D3)⋊C4—31no—
339(C2×D3)⋊C4—31no—
340(C2×D3)⋊C4—31no—
341(C2×D3)⋊C4—61no—
342(C2×D3)⋊C4—61no—
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—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—121no—
354(C2×D3)⋊C4—121no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—61no—
358C4⋊Dic3—61no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3C22×D311yescharacteristic
362Dic3⋊C4—21no—
363Dic3⋊C4—21no—
364Dic3⋊C4—21no—
365Dic3⋊C4—21no—
366Dic3⋊C4—31no—
367Dic3⋊C4—31no—
368Dic3⋊C4—31no—
369Dic3⋊C4—31no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373C4×Dic3—21no—
374C4×Dic3—21no—
375C4×Dic3—21no—
376C4×Dic3—61no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—121no—
383C4×Dic3C22×D311yescharacteristic
384C4×Dic3C22×D311yescharacteristic
385C2×C3⋊C8—31no—
386C2×C3⋊C8—31no—
387C2×C3⋊C8—61no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—22no—
391#204—62no—
392#204—62no—
393C22×C32C22×D411yescharacteristic
394C2×C3⋊D3—21no—
395C2×C3⋊D3—21no—
396C2×C3⋊D3—21no—
397C2×C3⋊D3—41no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4C2×#4111yescharacteristic
403C32×C4C2×#4111yescharacteristic
404C3⋊Dic3—21no—
405C3⋊Dic3—41no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—21no—
409C3×Dic3—21no—
410C3×Dic3—21no—
411C3×Dic3—21no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C22×Q8—91no—
415C2×Q16—31no—
416C2×Q16—91no—
417C2×SD16—91no—
418C2×SD16—91no—
419C4⋊Q8—31no—
420#126—181no—
421#124—91no—
422#124—181no—
423#123—181no—
424C22⋊Q8—91no—
425C22⋊Q8—181no—
426#121—91no—
427C4×Q8—31no—
428C4×Q8—31no—
429C4×Q8—31no—
430C4×Q8—91no—
431C4×Q8—91no—
432C4×Q8—181no—
433C4×Q8—181no—
434C4×D4—91no—
435#117—91no—
436#117—91no—
437#117—181no—
438#117—181no—
439#107—31no—
440#107D3211yescharacteristic
441#106—91no—
442#106—91no—
443C4⋊C8—31no—
444C4⋊C8—91no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#103—91no—
450#103—91no—
451#102—91no—
452#102—91no—
453C22⋊C8—91no—
454C22⋊C8—91no—
455#97—91no—
456C4×C8—31no—
457C22×D3—31no—
458C22×D3—31no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—121no—
463C3×Q8—32no—
464C3×Q8—32no—
465C3×Q8—61no—
466C3×Q8—61no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×Q8—241no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—31no—
476C2×C3×C4—31no—
477C2×C3×C4—31no—
478C2×C3×C4—31no—
479C2×C3×C4—41no—
480C2×C3×C4—41no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4C23×D311yescharacteristic
486C2×C3×C4C23×D311yescharacteristic
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—31no—
492C2×Dic3—31no—
493C2×Dic3—61no—
494C2×Dic3—61no—
495C2×Dic3—61no—
496C2×Dic3—121no—
497C2×Dic3D3×D411yescharacteristic
498C2×Dic3D3×D411yescharacteristic
499C2×Dic3D3×D411yescharacteristic
500C2×Dic3D3×D411yescharacteristic
501D12—61no—
502D12—61no—
503D12—61no—
504D12—61no—
505D12—121no—
506D12—121no—
507D12—241no—
508D12—241no—
509D12—242no—
510C4×D3—64no—
511C4×D3—64no—
512C4×D3—61no—
513C4×D3—61no—
514C4×D3—61no—
515C4×D3—61no—
516C4×D3—121no—
517C4×D3—121no—
518C4×D3—241no—
519C4×D3—241no—
520Dic6—21no—
521Dic6—21no—
522Dic6—21no—
523Dic6—21no—
524Dic6—64no—
525Dic6—64no—
526Dic6—81no—
527Dic6#23512yes—
528Dic6#23912yes—
529C3×C8—21no—
530C3×C8—21no—
531C3×C8—41no—
532C3×C8—61no—
533C3×C8—61no—
534C3⋊C8—21no—
535C3⋊C8—21no—
536C3⋊C8—61no—
537C3⋊C8—61no—
538C3⋊C8—121no—
539C2×C32#52511yescharacteristic
540C2×C32#57711yescharacteristic
541C2×C32#57811yescharacteristic
542C3⋊D3—41no—
543C3⋊D3—81no—
544C2×Q8—31no—
545C2×Q8—31no—
546C2×Q8—31no—
547C2×Q8—61no—
548C2×Q8—181no—
549C2×Q8—182no—
550C2×Q8—182no—
551C2×D4—91no—
552C2×D4—181no—
553C22×C4—91no—
554C22×C4—181no—
555C22×C4—181no—
556Q16—62no—
557Q16—182no—
558SD16—182no—
559SD16—182no—
560C2×C8—31no—
561C2×C8—31no—
562C2×C8—91no—
563C2×C8C2×D3211yescharacteristic
564C4⋊C4—31no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—61no—
568C4⋊C4—61no—
569C4⋊C4—91no—
570C4⋊C4—91no—
571C4⋊C4—91no—
572C4⋊C4—181no—
573C4⋊C4—181no—
574C4⋊C4—181no—
575C4⋊C4C2×D3211yescharacteristic
576C4⋊C4C2×D3211yescharacteristic
577C22⋊C4—91no—
578C22⋊C4—91no—
579C22⋊C4—181no—
580C22⋊C4—181no—
581C22⋊C4—181no—
582C22⋊C4—181no—
583C22⋊C4—181no—
584C22⋊C4—181no—
585C42—31no—
586C42—31no—
587C42—61no—
588C42—61no—
589C42—61no—
590C42—181no—
591C42—181no—
592C42—181no—
593C22×C3—21no—
594C22×C3C2×D3×D411yescharacteristic
595C22×C3C2×D3×D411yescharacteristic
596C2×D3—61no—
597C2×D3—61no—
598C2×D3—61no—
599C2×D3—61no—
600C2×D3—61no—
601C2×D3—61no—
602C2×D3—121no—
603C2×D3—121no—
604C2×D3—121no—
605C2×D3—121no—
606C2×D3—121no—
607C2×D3—121no—
608C2×D3—121no—
609C2×D3—121no—
610C2×D3—121no—
611C2×D3—241no—
612C2×D3—241no—
613C2×D3—241no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—41no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—61no—
621C3×C4—61no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—81no—
627C3×C4—81no—
628C3×C4—121no—
629C3×C4—121no—
630C3×C4C2×#23511yescharacteristic
631C3×C4C2×#23911yescharacteristic
632C3×C4D3×#4111yescharacteristic
633C3×C4D3×#4111yescharacteristic
634Dic3—21no—
635Dic3—21no—
636Dic3—21no—
637Dic3—21no—
638Dic3—22no—
639Dic3—22no—
640Dic3—41no—
641Dic3—41no—
642Dic3—61no—
643Dic3—61no—
644Dic3—121no—
645Dic3—121no—
646Dic3—121no—
647Dic3—241no—
648C32#312111yescharacteristic, complemented, Sylow
649C23—91no—
650C23—181no—
651Q8—32no—
652Q8—32no—
653Q8—61no—
654Q8—61no—
655Q8—61no—
656Q8—61no—
657Q8—184no—
658Q8—241no—
659D4—181no—
660D4—181no—
661D4—721no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—31no—
665C2×C4—31no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—91no—
673C2×C4—184no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—721no—
678C2×C4C22×D3211yescharacteristic
679C8—21no—
680C8—61no—
681C8—61no—
682C8—181no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3#554711yescharacteristic
687C2×C3#562711yescharacteristic
688C2×C3#576611yescharacteristic
689C2×C3#576611yescharacteristic
690C2×C3#577011yescharacteristic
691C2×C3#577511yescharacteristic
692D3—121no—
693D3—121no—
694D3—241no—
695D3—241no—
696D3—241no—
697D3—481no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—361no—
702C22—361no—
703C22—361no—
704C22D32×D411yescharacteristic
705C4—41no—
706C4—41no—
707C4—62no—
708C4—62no—
709C4—61no—
710C4—61no—
711C4—61no—
712C4—61no—
713C4—121no—
714C4—121no—
715C4—181no—
716C4—361no—
717C4D3×#23511yescharacteristic
718C4D3×#23911yescharacteristic
719C3—21no—
720C3#7975011yescharacteristic, complemented
721C3#8109611yescharacteristic, complemented
722C2—361no—
723C2—721no—
724C2#1059462311yescharacteristic
725C2#1059473611yescharacteristic
726C2#1059476511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radical#64104C22
hypercenter#107D32
hypocenterC32#3121
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594347C2semidirect
4. C3×#4875C2semidirect
5. C3×#4873C2semidirect
6. #10590950C2semidirect
7. #10590801C2semidirect
8. #10590792C2semidirect
9. #10590648C2semidirect
11. #10590536C2semidirect
12. #10590526C2semidirect
13. #10590486C2semidirect
14. #10590477C2semidirect
15. #10590457C2semidirect
78. #4875D3semidirect
79. #4873D3semidirect
648. C32#3121semidirect
720. C3#79750semidirect
721. C3#81096semidirect

Maximal subgroups

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

subgroupindex
#105943522
#105943472
#105925842
C3×#48752
C3×#48732
#105909502
#105908012
#105907922
#105906482
#105906062
#105905362
#105905262
#105904862
#105904772
#105904572
#810963
#797503