Finite Group Databasebeta

← #11870359

Subgroups — #11870359

Order 1152.

943 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596298C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic
3C3×#5234C211yesmaximal, characteristic, complemented
4#10591130C211yesmaximal, characteristic, complemented
5#10591127C212yesmaximal, complemented
6#10591126C212yesmaximal, complemented
7C2×#63573C211yesmaximal, characteristic, complemented
8#10591093C212yesmaximal, complemented
9#10591092C212yesmaximal, complemented
10#10591088C211yesmaximal, characteristic, complemented
11#10591084C211yesmaximal, characteristic, complemented
12#83419—31nomaximal
13#78654—31nomaximal
14C2×C32×#41C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16Q8×C3⋊Dic3—21no—
17D4×C3⋊Dic3—21no—
18D4×C3⋊Dic3—22no—
19#64135C2211yescharacteristic
20#64135C2212yes—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2212yes—
23C3×#946—21no—
24C3×#939—22no—
25C3×#938—21no—
26C3×#930C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#924C2212yes—
29C2×C3×#208C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C3×#830C2212yes—
32C3×#830C2212yes—
33#63575C2212yes—
34#63573C2212yes—
35#63573C2212yes—
36#63573C2212yes—
37#63566C2211yescharacteristic
38#63566C2211yescharacteristic
39#63566C2212yes—
40#63563C2211yescharacteristic
41#63563C2211yescharacteristic
42#63563C2212yes—
43C3×#537—31no—
44#5833D311yescharacteristic
45#5827—31no—
46#5827—31no—
47#5827—61no—
48C3×#408—31no—
49#5234D311yescharacteristic, complemented
50#5233—31no—
51#5232—31no—
52#5133—31no—
53#5121—31no—
54#5113—31no—
55C2×#817—31no—
56#5045—32no—
57#5043—32no—
58#5035—32no—
59#5034—32no—
60#4964—31no—
61C2×#808—31no—
62#4737—32no—
63#4735—32no—
64#4723—32no—
65#4721—32no—
66C32×#41—22no—
67C32×#41—22no—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4D411yescharacteristic
70C2×C32×D4D412yes—
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3—22no—
74C22×C3⋊Dic3—21no—
75C2×C3×#67—21no—
76C2×C3×#67—22no—
77C22×C3×Dic3—21no—
78C3×#235—22no—
79C3×#235—22no—
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×Dic6C2311yescharacteristic
83#3757—22no—
84#3757—21no—
85C4⋊(C3⋊Dic3)—22no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4⋊(C3⋊Dic3)C2312yes—
89C4⋊(C3⋊Dic3)C2311yescharacteristic
90C4×C3⋊Dic3—22no—
91C4×C3⋊Dic3—21no—
92C3×#217—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—22no—
97C3×#208—22no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2311yescharacteristic
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102#3099—91noSylow
103C2×C3×#41—21no—
104C2×C3×#41—31no—
105C2×C3×#41C2×D311yescharacteristic
106C2×C3×#41C2×D311yescharacteristic
107C2×#235C2×D311yescharacteristic
108C2×C3×M16—31no—
109C22×C3×C8—31no—
110C3×C22⋊Q8—32no—
111C3×C22⋊Q8—61no—
112C3×#121—32no—
113C3×#121—61no—
114C3×#121—62no—
115C2×C3×C4⋊C4—31no—
116#946—21no—
117Q8×Dic3—62no—
118Q8×Dic3—61no—
119Q8×Dic3—61no—
120#939—22no—
121#938—21no—
122D4×Dic3—62no—
123D4×Dic3—64no—
124D4×Dic3—62no—
125D4×Dic3—61no—
126D4×Dic3—61no—
127D4×Dic3—62no—
128#930C2×D312yes—
129#926—31no—
130#926—31no—
131#926—32no—
132#926—32no—
133#926—61no—
134#926—62no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—31no—
137C2×C4⋊Dic3—32no—
138C2×C4⋊Dic3—32no—
139C2×C4⋊Dic3—61no—
140C2×C4⋊Dic3—62no—
141C2×C4⋊Dic3C2×D311yescharacteristic
142#924C2×D312yes—
143C2×#208C2×D311yescharacteristic
144C22×C3⋊C8C2×D311yescharacteristic
145C3×C22⋊C8—32no—
146C3×C22⋊C8—32no—
147#835—32no—
148#835—31no—
149#835—31no—
150#832—32no—
151#832—31no—
152#832—31no—
153#830C2×D312yes—
154#830C2×D312yes—
155#821—32no—
156#821—31no—
157#821—31no—
158#818—32no—
159#817—32no—
160#817—32no—
161#817—32no—
162#816—32no—
163#816—31no—
164#816—31no—
165#808—32no—
166#808—32no—
167#808—32no—
168#807—32no—
169C23×C32C2×D412yes—
170C23×C32C2×D411yescharacteristic
171C22×C3×D3—21no—
172C32×Q8—22no—
173C32×D4—24no—
174C32×D4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4#4112yes—
180C2×C32×C4#4112yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—81no—
186C2×C3⋊Dic3—82no—
187C3×#67—42no—
188C3×#67—82no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—81no—
192C3×D12—21no—
193C3×D12—21no—
194C3×C4×D3—42no—
195C3×Dic6—21no—
196C3×Dic6—21no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199C3×C3⋊C8—22no—
200#537—31no—
201#520—91no—
202#485—92no—
203#483—92no—
204#482—92no—
205#481—92no—
206#428—91no—
207C2×#106—91no—
208#417—91no—
209#416—91no—
210#408—31no—
211C3×#41—24no—
212C3×#41—24no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—22no—
216C3×#41—22no—
217C3×#41—62no—
218C3×#41—62no—
219C2×C3×Q8—21no—
220C2×C3×Q8—31no—
221C2×C3×Q8D1211yescharacteristic
222C2×C3×Q8#6711yescharacteristic
223C2×C3×D4—21no—
224C2×C3×D4—22no—
225C2×C3×D4—31no—
226C2×C3×D4—61no—
227C2×C3×D4—62no—
228C2×C3×D4D1212yes—
229C2×C3×D4D1211yescharacteristic
230C2×C3×D4#6711yescharacteristic
231C2×C3×D4#6712yes—
232C22×C3×C4—22no—
233C22×C3×C4—21no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D312yes—
237C22×C3×C4C22×D312yes—
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—21no—
241C2×#67—22no—
242C22×Dic3—21no—
243C22×Dic3—64no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—61no—
247C22×Dic3—62no—
248C22×Dic3—61no—
249#235—22no—
250#235—22no—
251C2×D12C22×D311yescharacteristic
252C2×C4×D3—21no—
253C2×Dic6C22×D311yescharacteristic
254C3×M16—62no—
255C2×C3×C8—31no—
256C2×C3×C8—31no—
257C2×C3×C8—32no—
258C2×C3×C8—62no—
259C3×C4⋊C4—32no—
260C3×C4⋊C4—62no—
261C3×C4⋊C4—61no—
262C3×C22⋊C4—62no—
263C3×C22⋊C4—62no—
264#217—22no—
265#217—64no—
266#217—62no—
267#217—62no—
268#217—61no—
269#217—62no—
270#217—61no—
271(C2×D3)⋊C4—22no—
272C4⋊Dic3—21no—
273C4⋊Dic3—31no—
274C4⋊Dic3—32no—
275C4⋊Dic3—31no—
276C4⋊Dic3—32no—
277C4⋊Dic3—31no—
278C4⋊Dic3—31no—
279C4⋊Dic3—61no—
280C4⋊Dic3—62no—
281C4⋊Dic3—61no—
282C4⋊Dic3—64no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3—61no—
286C4⋊Dic3—62no—
287C4⋊Dic3—61no—
288C4⋊Dic3C22×D312yes—
289Dic3⋊C4—22no—
290C4×Dic3—64no—
291C4×Dic3—62no—
292C4×Dic3—62no—
293C4×Dic3—61no—
294C4×Dic3—62no—
295C4×Dic3—61no—
296#208—22no—
297C2×C3⋊C8—22no—
298C2×C3⋊C8C22×D312yes—
299C2×C3⋊C8C22×D311yescharacteristic
300C2×C3⋊C8C22×D311yescharacteristic
301C22×C32—22no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32—22no—
305C22×C32—22no—
306C22×C32#12312yes—
307C22×C32C22×D411yescharacteristic
308C2×C3×D3—41no—
309C2×C3×D3—41no—
310C2×C3×D3—41no—
311C32×C4—22no—
312C32×C4#12312yes—
313C32×C4C2×#4111yescharacteristic
314C32×C4C2×#4111yescharacteristic
315C3⋊Dic3—41no—
316C3⋊Dic3—42no—
317C3⋊Dic3—41no—
318C3×Dic3—41no—
319C3×Dic3—42no—
320C2×#41—31no—
321C2×#41D3211yescharacteristic
322C2×M16—31no—
323C22×C8—31no—
324C22⋊Q8—32no—
325C22⋊Q8—61no—
326#121—32no—
327#121—61no—
328#121—62no—
329C4×Q8—181no—
330C4×D4—182no—
331C4×D4—181no—
332#117—91no—
333#117—92no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—91no—
336C2×C4⋊C4—92no—
337#107—92no—
338#106—92no—
339#106—92no—
340#106—92no—
341#103—91no—
342#103—91no—
343#103—92no—
344#102—91no—
345#102—91no—
346#102—92no—
347C22⋊C8—32no—
348C22⋊C8—32no—
349C23×C3—22no—
350C23×C3—21no—
351C23×C3—61no—
352C23×C3C2×D1212yes—
353C23×C3C2×D1211yescharacteristic
354C23×C3C2×#6712yes—
355C23×C3C2×#6711yescharacteristic
356C22×D3—21no—
357C3×Q8—24no—
358C3×Q8—22no—
359C3×Q8—22no—
360C3×Q8—61no—
361C3×Q8—61no—
362C3×D4—28no—
363C3×D4—24no—
364C3×D4—24no—
365C3×D4—24no—
366C3×D4—22no—
367C3×D4—22no—
368C3×D4—61no—
369C3×D4—61no—
370C3×D4—122no—
371C3×D4—242no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—62no—
384C2×C3×C4—61no—
385C2×C3×C4—122no—
386C2×C3×C4—241no—
387C2×C3×C4C2×D1212yes—
388C2×C3×C4C2×D1211yescharacteristic
389C2×C3×C4#23712yes—
390C2×C3×C4#23712yes—
391C2×C3×C4#23712yes—
392C2×C3×C4#23712yes—
393C2×C3×C4C2×#6712yes—
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—42no—
398#67—82no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—62no—
402C2×Dic3—64no—
403C2×Dic3—62no—
404C2×Dic3—61no—
405C2×Dic3—62no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—81no—
411C2×Dic3—241no—
412C2×Dic3—242no—
413C2×Dic3—241no—
414C2×Dic3—242no—
415C2×Dic3—242no—
416C2×Dic3—244no—
417D12—21no—
418D12—21no—
419C4×D3—42no—
420Dic6—21no—
421Dic6—21no—
422C3×C8—61no—
423C3×C8—61no—
424C3×C8—62no—
425C3⋊C8—21no—
426C3⋊C8—21no—
427C3⋊C8—22no—
428C2×C32—22no—
429C2×C32—42no—
430C2×C32C2×#12311yescharacteristic
431C2×C32#57711yescharacteristic
432C2×C32#57711yescharacteristic
433C3×D3—81no—
434#41—22no—
435#41—22no—
436#41—62no—
437#41—62no—
438C2×Q8—31no—
439C2×Q8#62611yescharacteristic
440C2×D4—31no—
441C2×D4—61no—
442C2×D4—62no—
443C2×D4#62612yes—
444C2×D4#62611yescharacteristic
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—182no—
448C22×C4—181no—
449C22×C4C2×D3212yes—
450C22×C4C2×D3211yescharacteristic
451M16—62no—
452C2×C8—31no—
453C2×C8—31no—
454C2×C8—32no—
455C2×C8—62no—
456C4⋊C4—32no—
457C4⋊C4—61no—
458C4⋊C4—62no—
459C4⋊C4—91no—
460C4⋊C4—92no—
461C4⋊C4—91no—
462C4⋊C4—182no—
463C4⋊C4—181no—
464C22⋊C4—62no—
465C22⋊C4—62no—
466C22⋊C4—182no—
467C22⋊C4—181no—
468C42—182no—
469C42—181no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—24no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—21no—
482C22×C3—22no—
483C22×C3—41no—
484C22×C3—42no—
485C22×C3—41no—
486C22×C3—42no—
487C22×C3—121no—
488C22×C3—121no—
489C22×C3—121no—
490C22×C3#88612yes—
491C22×C3#93512yes—
492C22×C3C22×D1211yescharacteristic
493C22×C3C22×#6711yescharacteristic
494C2×D3—41no—
495C2×D3—41no—
496C2×D3—41no—
497C3×C4—24no—
498C3×C4—22no—
499C3×C4—22no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—22no—
503C3×C4—121no—
504C3×C4—122no—
505C3×C4#88612yes—
506C3×C4#93512yes—
507C3×C4C2×#23711yescharacteristic
508C3×C4C2×#23711yescharacteristic
509C3×C4C2×#23711yescharacteristic
510C3×C4C2×#23711yescharacteristic
511Dic3—41no—
512Dic3—42no—
513Dic3—124no—
514Dic3—122no—
515Dic3—122no—
516Dic3—122no—
517Dic3—121no—
518Dic3—121no—
519Dic3—121no—
520Dic3—122no—
521Dic3—121no—
522C32#309911yescharacteristic, complemented, Sylow
523C23—61no—
524C23C2×#62612yes—
525C23C2×#62611yescharacteristic
526Q8—22no—
527Q8—61no—
528Q8—61no—
529D4—24no—
530D4—22no—
531D4—61no—
532D4—61no—
533D4—122no—
534D4—242no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—62no—
538C2×C4—61no—
539C2×C4—122no—
540C2×C4—181no—
541C2×C4—182no—
542C2×C4—181no—
543C2×C4—241no—
544C2×C4—721no—
545C2×C4—722no—
546C2×C4#380512yes—
547C2×C4#380512yes—
548C2×C4C2×#62612yes—
549C2×C4C2×#62611yescharacteristic
550C2×C4C22×D3211yescharacteristic
551C8—61no—
552C8—61no—
553C8—62no—
554C2×C3—22no—
555C2×C3—22no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—42no—
560C2×C3—44no—
561C2×C3—42no—
562C2×C3—42no—
563C2×C3—241no—
564C2×C3C2×#88611yescharacteristic
565C2×C3#575111yescharacteristic
566C2×C3#575111yescharacteristic
567C2×C3C2×#93511yescharacteristic
568C2×C3#583611yescharacteristic
569C2×C3#583711yescharacteristic
570D3—81no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—121no—
577C22—121no—
578C22—121no—
579C22#6396212yes—
580C22C22×#62611yescharacteristic
581C4—22no—
582C4—122no—
583C4—121no—
584C4—361no—
585C4—362no—
586C4—361no—
587C4#6396212yes—
588C4C2×#380511yescharacteristic
589C4C2×#380511yescharacteristic
590C3—21no—
591C3#7865411yescharacteristic, complemented
592C3#8341911yescharacteristic, complemented
593C2—22no—
594C2—42no—
595C2—241no—
596C2#1059544711yescharacteristic
597C2#1059544811yescharacteristic
598C2C2×#6396211yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5833C2
hypercenterC2×#41D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596298C2semidirect
3. C3×#5234C2semidirect
4. #10591130C2semidirect
5. #10591127C2semidirect
6. #10591126C2semidirect
7. C2×#63573C2semidirect
8. #10591093C2semidirect
9. #10591092C2semidirect
10. #10591088C2semidirect
11. #10591084C2semidirect
49. #5234D3semidirect
522. C32#3099semidirect
591. C3#78654semidirect
592. C3#83419semidirect

Maximal subgroups

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

subgroupindex
#105962982
C3×#58332
C3×#52342
#105911302
#105911272
#105911262
C2×#635732
#105910932
#105910922
#105910882
#105910842
#834193
#786543