Finite Group Databasebeta

← #11868761

Subgroups — #11868761

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594448C211yesmaximal, characteristic
2#10594363C211yesmaximal, characteristic
3#10592560C211yesmaximal, characteristic
4C3×#4857C211yesmaximal, characteristic, complemented
5C3×#4854C211yesmaximal, characteristic, complemented
6#10590811C211yesmaximal, characteristic, complemented
7#10590804C211yesmaximal, characteristic, complemented
8#10590691C211yesmaximal, characteristic
9#10590666C211yesmaximal, characteristic
10#10590602C211yesmaximal, characteristic
11#10590583C211yesmaximal, characteristic
12#10590557C211yesmaximal, characteristic, complemented
13#10590543C211yesmaximal, characteristic, complemented
14#10590491C211yesmaximal, characteristic, complemented
15#10590486C211yesmaximal, characteristic, complemented
16#81230—31nomaximal
17#81011—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×#3743C2211yescharacteristic
20#64101C2211yescharacteristic
21C4⋊C4×C3⋊D3C2211yescharacteristic
22C3×#890C2211yescharacteristic
23C3×#888C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#887C2211yescharacteristic
26#63918C2211yescharacteristic
27#63895—21no—
28#63888—21no—
29#63883—21no—
30C4×#624—21no—
31C4×#624C2211yescharacteristic
32#63869C2211yescharacteristic
33#63849C2211yescharacteristic
34#63843—21no—
35Dic3×Dic6C2211yescharacteristic
36Dic3×Dic6C2211yescharacteristic
37#63838—21no—
38#63837—21no—
39#63837—21no—
40C2×#3712C2211yescharacteristic
41C32×#106C2211yescharacteristic
42#63645C2211yescharacteristic
43#63635C2211yescharacteristic
44#63634C2211yescharacteristic
45C3×#816C2211yescharacteristic
46C3×#816C2211yescharacteristic
47C3×Dic3⋊C8C2211yescharacteristic
48C3×Dic3⋊C8C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#807C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#5728—31no—
62#5688—31no—
63C4×D3×Q8—31no—
64C4×D3×Q8—31no—
65C3×#479—31no—
66C3×#475—31no—
67#5094—31no—
68#5063—31no—
69#5022—31no—
70#5021—31no—
71#4881—31no—
72#4875—31no—
73#4861—31no—
74#4861—31no—
75#4861—31no—
76#4861—61no—
77#4857—31no—
78#4857D311yescharacteristic, complemented
79#4854D311yescharacteristic, complemented
80#4850—31no—
81#4837—31no—
82#4837—31no—
83#4829—31no—
84#4802—31no—
85#4802—31no—
86#4802—31no—
87#4802—31no—
88#4796—31no—
89#4796—31no—
90#4793—31no—
91#4791—31no—
92C2×C4×C3⋊D3—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C3×Dic6—21no—
95C2×C3×Dic6C2311yescharacteristic
96C2×C3×Dic6C2311yescharacteristic
97C2×#627—21no—
98C2×#627—21no—
99C2×#624—21no—
100C2×#624D411yescharacteristic
101C2×#624D411yescharacteristic
102#3797—22no—
103#3797Q814yescomplemented
104C2×C32×C8C2311yescharacteristic
105C32×C4⋊C4C2311yescharacteristic
106C32×C4⋊C4C2311yescharacteristic
107#3752—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111C4×C3⋊Dic3—21no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113#3743—22no—
114C3×C4⋊Dic3—21no—
115C3×C4⋊Dic3C2311yescharacteristic
116C3×C4⋊Dic3C2311yescharacteristic
117C3×Dic3⋊C4—21no—
118C3×Dic3⋊C4—21no—
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×C4×Dic3—21no—
122C3×C4×Dic3—21no—
123C3×C4×Dic3C2311yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132#3722—21no—
133Dic32—21no—
134Dic32—21no—
135Dic32—21no—
136Dic32D411yescharacteristic
137Dic32D411yescharacteristic
138#3712—22no—
139#3078—91noSylow
140C2×D3×Q8—31no—
141C2×D3×Q8—31no—
142C3×C4⋊Q8—31no—
143C3×#125—31no—
144C3×C4×Q8—31no—
145C3×C4×Q8—31no—
146#946—61no—
147Q8×Dic3—31no—
148Q8×Dic3—31no—
149Q8×Dic3—61no—
150C2×ΓL(1,𝔽25)—31no—
151C2×ΓL(1,𝔽25)—31no—
152C2×ΓL(1,𝔽25)—31no—
153C2×ΓL(1,𝔽25)—31no—
154C2×ΓL(1,𝔽25)—61no—
155#897—61no—
156#896—61no—
157#896—61no—
158#892—31no—
159#892—31no—
160#892—31no—
161#892—31no—
162#892—61no—
163D3×C4⋊C4—31no—
164D3×C4⋊C4—31no—
165D3×C4⋊C4—61no—
166D3×C4⋊C4—61no—
167D3×C4⋊C4—61no—
168#890—31no—
169#890C2×D311yescharacteristic
170#888—31no—
171#888C2×D311yescharacteristic
172#887—61no—
173#887—61no—
174#887—61no—
175#887—61no—
176#887—61no—
177#887C2×D311yescharacteristic
178#887C2×D311yescharacteristic
179C42×D3—31no—
180C42×D3—31no—
181C42×D3—61no—
182C42×D3—61no—
183#870—31no—
184#869—31no—
185C4×Dic6—31no—
186C4×Dic6—31no—
187C4×Dic6—61no—
188C4×Dic6—61no—
189C3×#107—31no—
190C3×#106—21no—
191C3×#106—31no—
192C3×#106C2×D311yescharacteristic
193C3×#106C2×D311yescharacteristic
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#103—31no—
197C3×#103—31no—
198C3×#103—31no—
199C3×#103—31no—
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#818—31no—
205#818—31no—
206#818—31no—
207#818—61no—
208#817—31no—
209#816—31no—
210#816—31no—
211#816C2×D311yescharacteristic
212#816C2×D311yescharacteristic
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8C2×D311yescharacteristic
216Dic3⋊C8C2×D311yescharacteristic
217#810—31no—
218#810—31no—
219#810C2×D311yescharacteristic
220#810C2×D311yescharacteristic
221#808—31no—
222#808—31no—
223#808—31no—
224#808—61no—
225#808C2×D311yescharacteristic
226#807—31no—
227#807—31no—
228#807—31no—
229#807—61no—
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233C22×C3⋊D3C2×D411yescharacteristic
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4C2411yescharacteristic
237C2×C3⋊Dic3—21no—
238C2×C3⋊Dic3—21no—
239C2×C3⋊Dic3C2×D411yescharacteristic
240C4×C3⋊D3—42no—
241C4×C3⋊D3C2×Q812yes—
242C4×C3⋊D3#4112yes—
243C2×C3×Dic3—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×Dic6—21no—
252C3×Dic6—21no—
253C3×Dic6—42no—
254C3×Dic6C2×Q812yes—
255C3×Dic6C2×Q812yes—
256#627—24no—
257#627—42no—
258#624—24no—
259#624—22no—
260#624—41no—
261C32×C8—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#533—91no—
266C2×C4×Q8—91no—
267#479—31no—
268#479—91no—
269#479—91no—
270#479—91no—
271#477—91no—
272#477—91no—
273#475—31no—
274#475—91no—
275#428—91no—
276#428—91no—
277#423—91no—
278#419—91no—
279#419—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—61no—
283D3×Q8—34no—
284D3×Q8—34no—
285D3×Q8—62no—
286D3×Q8—62no—
287C2×C4×D3—31no—
288C2×C4×D3—31no—
289C2×C4×D3—31no—
290C2×C4×D3—31no—
291C2×C4×D3—31no—
292C2×C4×D3—31no—
293C2×C4×D3—61no—
294C2×C4×D3—61no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×C4×D3—61no—
298C2×C4×D3—121no—
299C2×Dic6—21no—
300C2×Dic6—61no—
301C2×Dic6—61no—
302C2×Dic6—61no—
303C2×Dic6—61no—
304C2×Dic6C22×D311yescharacteristic
305C2×Dic6C22×D311yescharacteristic
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8C22×D311yescharacteristic
310C2×C3×C8C22×D311yescharacteristic
311C3×C4⋊C4—21no—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—31no—
314C3×C4⋊C4—31no—
315C3×C4⋊C4—61no—
316C3×C4⋊C4—61no—
317C3×C4⋊C4—61no—
318C3×C4⋊C4—61no—
319C3×C4⋊C4—61no—
320C3×C4⋊C4C22×D311yescharacteristic
321C3×C4⋊C4C22×D311yescharacteristic
322C3×C4⋊C4C22×D311yescharacteristic
323C3×C4⋊C4C22×D311yescharacteristic
324C3×C42—31no—
325C3×C42—31no—
326C3×C42—61no—
327C3×C42—61no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—121no—
333C4⋊Dic3—21no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—31no—
337C4⋊Dic3—31no—
338C4⋊Dic3—61no—
339C4⋊Dic3—61no—
340C4⋊Dic3—61no—
341C4⋊Dic3—61no—
342C4⋊Dic3—61no—
343C4⋊Dic3—61no—
344C4⋊Dic3C22×D311yescharacteristic
345C4⋊Dic3C22×D311yescharacteristic
346Dic3⋊C4—21no—
347Dic3⋊C4—21no—
348Dic3⋊C4—21no—
349Dic3⋊C4—21no—
350Dic3⋊C4—61no—
351Dic3⋊C4—61no—
352Dic3⋊C4—61no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—121no—
359C4×Dic3—21no—
360C4×Dic3—21no—
361C4×Dic3—31no—
362C4×Dic3—31no—
363C4×Dic3—31no—
364C4×Dic3—31no—
365C4×Dic3—61no—
366C4×Dic3—61no—
367C4×Dic3—61no—
368C4×Dic3—61no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3—121no—
374C4×Dic3C22×D311yescharacteristic
375C4×Dic3C22×D311yescharacteristic
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—61no—
379C2×C3⋊C8C22×D311yescharacteristic
380C2×C3⋊C8C22×D311yescharacteristic
381ΓL(1,𝔽25)—62no—
382ΓL(1,𝔽25)—62no—
383ΓL(1,𝔽25)—62no—
384ΓL(1,𝔽25)—62no—
385ΓL(1,𝔽25)—64no—
386C22×C32C22×D411yescharacteristic
387C2×C3⋊D3—21no—
388C2×C3⋊D3—21no—
389C2×C3⋊D3C22⋊Q812yes—
390C32×C4—41no—
391C32×C4—41no—
392C32×C4C22×Q811yescharacteristic
393C32×C4C2×#4111yescharacteristic
394C3⋊Dic3—41no—
395C3⋊Dic3—41no—
396C3⋊Dic3C22⋊Q812yes—
397C3×Dic3—22no—
398C3×Dic3—22no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—21no—
402C3×Dic3—41no—
403C3×Dic3—41no—
404C3×Dic3#13712yes—
405C22×Q8—91no—
406C2×M16—91no—
407C2×M16—91no—
408C4⋊Q8—31no—
409C4⋊Q8—91no—
410#125—31no—
411#125—91no—
412C22⋊Q8—181no—
413C22⋊Q8—181no—
414C4×Q8—31no—
415C4×Q8—31no—
416C4×Q8—91no—
417C4×Q8—91no—
418C4×Q8—181no—
419C4×Q8—181no—
420C4×Q8—181no—
421C4×Q8—181no—
422#117—91no—
423#117—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—181no—
426C2×C42—91no—
427C2×C42—181no—
428#107—31no—
429#107—91no—
430#107—91no—
431#107—91no—
432#106—31no—
433#106—91no—
434#106—91no—
435#106D3211yescharacteristic
436C4⋊C8—31no—
437C4⋊C8—31no—
438C4⋊C8—91no—
439C4⋊C8—91no—
440#103—31no—
441#103—31no—
442#103—31no—
443#103—31no—
444#103—91no—
445#103—91no—
446#103—91no—
447#103—91no—
448C22×D3—31no—
449C22×D3—31no—
450C22×D3—61no—
451C3×Q8—32no—
452C3×Q8—32no—
453C3×Q8—61no—
454C3×Q8—61no—
455C3×Q8—122no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—31no—
462C2×C3×C4—31no—
463C2×C3×C4—31no—
464C2×C3×C4—31no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4C23×D311yescharacteristic
472C2×C3×C4C23×D311yescharacteristic
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—31no—
478C2×Dic3—31no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C2×Dic3—121no—
485C2×Dic3—121no—
486C2×Dic3D3×D411yescharacteristic
487C2×Dic3D3×D411yescharacteristic
488C2×Dic3D3×D411yescharacteristic
489C2×Dic3D3×D411yescharacteristic
490C4×D3—32no—
491C4×D3—32no—
492C4×D3—32no—
493C4×D3—32no—
494C4×D3—62no—
495C4×D3—62no—
496C4×D3—62no—
497C4×D3—64no—
498C4×D3—64no—
499C4×D3—62no—
500C4×D3—121no—
501C4×D3—121no—
502C4×D3—122no—
503C4×D3—122no—
504C4×D3—242no—
505Dic6—21no—
506Dic6—21no—
507Dic6—42no—
508Dic6—64no—
509Dic6—64no—
510Dic6—122no—
511Dic6—122no—
512Dic6D3×Q812yes—
513Dic6D3×Q812yes—
514C3×C8—22no—
515C3×C8—21no—
516C3×C8—21no—
517C3×C8—61no—
518C3×C8—61no—
519C3⋊C8—21no—
520C3⋊C8—21no—
521C3⋊C8—62no—
522C3⋊C8—61no—
523C3⋊C8—61no—
524C2×C32C2×C22⋊Q811yescharacteristic
525C2×C32C2×#13711yescharacteristic
526C2×C32#57511yescharacteristic
527C3⋊D3—22no—
528C2×Q8—31no—
529C2×Q8—31no—
530C2×Q8—61no—
531C2×Q8—94no—
532C2×Q8—181no—
533C2×Q8—181no—
534C2×Q8—182no—
535C22×C4—91no—
536C22×C4—91no—
537C22×C4—91no—
538C22×C4—181no—
539C22×C4—181no—
540M16—182no—
541M16—182no—
542C2×C8—31no—
543C2×C8—31no—
544C2×C8—91no—
545C2×C8C2×D3211yescharacteristic
546C4⋊C4—31no—
547C4⋊C4—31no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4C2×D3211yescharacteristic
562C4⋊C4C2×D3211yescharacteristic
563C22⋊C4—181no—
564C22⋊C4—181no—
565C42—31no—
566C42—31no—
567C42—61no—
568C42—61no—
569C42—91no—
570C42—91no—
571C42—181no—
572C42—181no—
573C42—181no—
574C42—181no—
575C22×C3—21no—
576C22×C3C2×D3×D411yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C2×D3—32no—
579C2×D3—32no—
580C2×D3—62no—
581C2×D3—61no—
582C2×D3—61no—
583C2×D3—61no—
584C2×D3—61no—
585C2×D3—121no—
586C2×D3—121no—
587C3×C4—21no—
588C3×C4—21no—
589C3×C4—32no—
590C3×C4—41no—
591C3×C4—41no—
592C3×C4—41no—
593C3×C4—41no—
594C3×C4—61no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—62no—
598C3×C4—62no—
599C3×C4—81no—
600C3×C4—81no—
601C3×C4—121no—
602C3×C4—121no—
603C3×C4C2×D3×Q811yescharacteristic
604C3×C4C2×D3×Q811yescharacteristic
605C3×C4D3×#4111yescharacteristic
606C3×C4D3×#4111yescharacteristic
607Dic3—21no—
608Dic3—21no—
609Dic3—21no—
610Dic3—22no—
611Dic3—22no—
612Dic3—32no—
613Dic3—32no—
614Dic3—41no—
615Dic3—41no—
616Dic3—62no—
617Dic3—121no—
618Dic3—121no—
619Dic3—121no—
620Dic3—121no—
621Dic3—241no—
622Dic3—241no—
623Dic3#91512yes—
624C32#307811yescharacteristic, complemented, Sylow
625C23—91no—
626Q8—32no—
627Q8—32no—
628Q8—61no—
629Q8—61no—
630Q8—122no—
631Q8—184no—
632Q8—362no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—31no—
636C2×C4—31no—
637C2×C4—31no—
638C2×C4—31no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—61no—
643C2×C4—91no—
644C2×C4—92no—
645C2×C4—92no—
646C2×C4—182no—
647C2×C4—184no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4—362no—
651C2×C4—361no—
652C2×C4C22×D3211yescharacteristic
653C8—21no—
654C8—61no—
655C8—61no—
656C8—181no—
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3D3×C22⋊Q811yescharacteristic
661C2×C3D3×C22⋊Q811yescharacteristic
662C2×C3C2×#91511yescharacteristic
663C2×C3#576811yescharacteristic
664C2×C3D3×#13711yescharacteristic
665C2×C3#577711yescharacteristic
666D3—62no—
667D3—62no—
668D3—122no—
669C22—92no—
670C22—181no—
671C22—181no—
672C22D32×D411yescharacteristic
673C4—32no—
674C4—41no—
675C4—41no—
676C4—62no—
677C4—62no—
678C4—61no—
679C4—61no—
680C4—61no—
681C4—92no—
682C4—121no—
683C4—121no—
684C4—361no—
685C4—361no—
686C4#6430611yescharacteristic
687C4D32×Q811yescharacteristic
688C3—21no—
689C3#8101111yescharacteristic, complemented
690C3#8123011yescharacteristic, complemented
691C2—182no—
692C2#1059462411yescharacteristic
693C2D3×#91511yescharacteristic
694C2#1059474611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#106D32
hypocenterC32#3078
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
4. C3×#4857C2semidirect
5. C3×#4854C2semidirect
6. #10590811C2semidirect
7. #10590804C2semidirect
12. #10590557C2semidirect
13. #10590543C2semidirect
14. #10590491C2semidirect
15. #10590486C2semidirect
78. #4857D3semidirect
79. #4854D3semidirect
103. #3797Q8semidirect
624. C32#3078semidirect
689. C3#81011semidirect
690. C3#81230semidirect

Maximal subgroups

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

subgroupindex
#105944482
#105943632
#105925602
C3×#48572
C3×#48542
#105908112
#105908042
#105906912
#105906662
#105906022
#105905832
#105905572
#105905432
#105904912
#105904862
#812303
#810113