Finite Group Databasebeta

← #11888581

Subgroups — #11888581

Order 1152.

1182 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596036C211yesmaximal, characteristic, complemented
2#10596022C211yesmaximal, characteristic, complemented
3C32×#435C211yesmaximal, characteristic, complemented
4#10592833C211yesmaximal, characteristic, complemented
5#10592832C211yesmaximal, characteristic, complemented
6#10592813C211yesmaximal, characteristic, complemented
7#10592812C211yesmaximal, characteristic, complemented
8#10592546C211yesmaximal, characteristic, complemented
9#10592540C211yesmaximal, characteristic, complemented
10#10592433C211yesmaximal, characteristic, complemented
11#10592433C211yesmaximal, characteristic, complemented
12#10592422C211yesmaximal, characteristic, complemented
13#10592420C211yesmaximal, characteristic, complemented
14#10592410C211yesmaximal, characteristic, complemented
15#10592402C211yesmaximal, characteristic, complemented
16#79500—34nomaximal
17C2×#3828C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C2×C32×M16C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C32×C4×D4C2211yescharacteristic
22#64148—21no—
23#64147—21no—
24#64139C2211yescharacteristic
25#64139C2211yescharacteristic
26#64135C2211yescharacteristic
27C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
28#64133C2211yescharacteristic
29#64133C2211yescharacteristic
30C2×#3745C2211yescharacteristic
31C2×#3744C2211yescharacteristic
32C2×#3744C2211yescharacteristic
33#64107—21no—
34C4⋊C4×C3⋊D3—21no—
35#64092—21no—
36#64092—21no—
37#64092—21no—
38#64090—21no—
39C4×C4⋊(C3⋊D3)C2211yescharacteristic
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41#64079C2211yescharacteristic
42#64078C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45C32×C22⋊C8C2211yescharacteristic
46C32×#97C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63645C2211yescharacteristic
52#63644C2211yescharacteristic
53#63644C2211yescharacteristic
54#63643C2211yescharacteristic
55#63643C2211yescharacteristic
56#63643C2211yescharacteristic
57#63643C2211yescharacteristic
58#63643C2211yescharacteristic
59#63643C2211yescharacteristic
60#5565—34no—
61#5551—34no—
62C3×#435D314yescomplemented
63#5134—34no—
64#5133—34no—
65#5114—34no—
66#5113—34no—
67#4847—34no—
68#4841—34no—
69#4734—34no—
70#4734—34no—
71#4723—34no—
72#4721—34no—
73#4711—34no—
74#4703—34no—
75C2×C32×D4D411yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C2×#638—21no—
79C2×#638—21no—
80C2×#638—21no—
81C2×#638—21no—
82C22×C3⋊Dic3—21no—
83#3828—22no—
84#3828—22no—
85#3828—41no—
86#3828—41no—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—21no—
93C2×#634C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C32×M16—41no—
96C2×C32×C8—41no—
97C2×C32×C8C2311yescharacteristic
98C2×C32×C8C2311yescharacteristic
99C2×C32×C8C2311yescharacteristic
100C2×C32×C8C2311yescharacteristic
101C32×C4⋊C4D411yescharacteristic
102C32×C22⋊C4D411yescharacteristic
103C32×C22⋊C4D411yescharacteristic
104C32×C42C2311yescharacteristic
105#3757—21no—
106#3757—21no—
107#3757—21no—
108#3752—21no—
109#3752—21no—
110#3752—21no—
111#3752—21no—
112C4⋊(C3⋊Dic3)—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121#3750—21no—
122#3750—21no—
123C4×C3⋊Dic3—21no—
124#3745—22no—
125#3744—41no—
126#3744—41no—
127#3307—91noSylow
128C2×#235—34no—
129C2×#235—34no—
130C2×C3×M16C2×D314yes—
131C22×C3×C8C2×D314yes—
132C3×C4×D4C2×D314yes—
133#939—64no—
134#938—64no—
135#930—34no—
136#930—34no—
137#926—34no—
138C2×C4⋊Dic3—34no—
139#924—34no—
140#924—34no—
141C2×D24—34no—
142C2×#204—34no—
143C2×#204—34no—
144#898—64no—
145D3×C4⋊C4—64no—
146#883—64no—
147#883—64no—
148#883—64no—
149#67⋊C4—64no—
150C4×D12—34no—
151C4×D12—34no—
152#870—34no—
153#869—34no—
154C3×C4⋊C8C2×D314yes—
155C3×C22⋊C8C2×D314yes—
156C3×C22⋊C8C2×D314yes—
157C3×#97C2×D314yes—
158#821—34no—
159#821—34no—
160#821—34no—
161#821—34no—
162#818—34no—
163#817—34no—
164#817—34no—
165#816—34no—
166#816—34no—
167#816—34no—
168#816—34no—
169#816—34no—
170#816—34no—
171C23×C32C2×D411yescharacteristic
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C22×C3⋊D3—21no—
175C32×D4—41no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2411yescharacteristic
185#638—42no—
186#638—42no—
187#638—42no—
188#638—81no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—81no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)—21no—
199C4⋊(C3⋊D3)#4112yes—
200C4×C3⋊D3—42no—
201C4×C3⋊D3—42no—
202C4×C3⋊D3—42no—
203C4×C3⋊D3—81no—
204#634—21no—
205#634—21no—
206#634—21no—
207#634—21no—
208C32×C8—21no—
209C32×C8—21no—
210C32×C8—21no—
211C32×C8—21no—
212#553—91no—
213#547—91no—
214#491—91no—
215#485—91no—
216#483—91no—
217#478—91no—
218#468—91no—
219#465—91no—
220#461—91no—
221#449—91no—
222#449—91no—
223#442—91no—
224#435C3⋊D311yescharacteristic, complemented
225#417—91no—
226#416—91no—
227C2×C3×D4D1214yes—
228C22×C3×C4C22×D314yes—
229C22×C3×C4C22×D314yes—
230C2×#67—64no—
231C2×#67—64no—
232C2×#67—64no—
233C2×#67—64no—
234C22×Dic3—64no—
235#235—68no—
236#235—68no—
237#235—124no—
238#235—124no—
239C2×D12—34no—
240C2×D12—34no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×C4×D3—64no—
244C2×C4×D3—64no—
245C2×Dic6—34no—
246C2×Dic6—34no—
247C3×M16—44no—
248C2×C3×C8—44no—
249C2×C3×C8C22×D314yes—
250C2×C3×C8C22×D314yes—
251C2×C3×C8C22×D314yes—
252C2×C3×C8C22×D314yes—
253C3×C4⋊C4D1214yes—
254C3×C22⋊C4D1214yes—
255C3×C22⋊C4D1214yes—
256C3×C42C22×D314yes—
257#217—64no—
258#217—64no—
259#217—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—64no—
264C4⋊Dic3—34no—
265C4⋊Dic3—34no—
266C4⋊Dic3—34no—
267C4⋊Dic3—34no—
268C4⋊Dic3—64no—
269C4⋊Dic3—64no—
270C4⋊Dic3—64no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—64no—
274Dic3⋊C4—64no—
275C4×Dic3—64no—
276D24—68no—
277#204—124no—
278#204—124no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32C22×D411yescharacteristic
286C2×C3⋊D3—22no—
287C2×C3⋊D3—41no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—21no—
296C32×C4C2×#4111yescharacteristic
297C32×C4H(5,𝔽2)11yescharacteristic
298C3⋊Dic3—41no—
299C3⋊Dic3—41no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C2×#41—91no—
305C2×#41—91no—
306C2×SD16—91no—
307C2×SD16—91no—
308C2×D8—91no—
309C2×M16C2×C3⋊D311yescharacteristic
310C22×C8C2×C3⋊D311yescharacteristic
311C4⋊Q8—91no—
312#126—181no—
313#125—91no—
314#123—181no—
315#123—181no—
316#123—181no—
317C22⋊Q8—91no—
318C22⋊Q8—91no—
319#121—91no—
320#121—91no—
321#121—181no—
322#121—181no—
323C4×D4—91no—
324C4×D4—91no—
325C4×D4—181no—
326C4×D4C2×C3⋊D311yescharacteristic
327#117—91no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4—181no—
330#107—91no—
331#106—91no—
332#106—91no—
333C4⋊C8C2×C3⋊D311yescharacteristic
334#103—91no—
335#103—91no—
336#103—91no—
337#103—91no—
338#103—91no—
339#103—91no—
340#102—91no—
341#102—91no—
342#102—91no—
343#102—91no—
344C22⋊C8C2×C3⋊D311yescharacteristic
345C22⋊C8C2×C3⋊D311yescharacteristic
346#97C2×C3⋊D311yescharacteristic
347C23×C3C2×D1214yes—
348C23×C3C2×D1214yes—
349C22×D3—64no—
350C22×D3—64no—
351C3×D4—44no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4C2×D1214yes—
357C2×C3×C4C2×D1214yes—
358C2×C3×C4C2×D1214yes—
359C2×C3×C4C2×D1214yes—
360C2×C3×C4C23×D314yes—
361#67—128no—
362#67—128no—
363#67—128no—
364#67—244no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—244no—
372D12—38no—
373D12—64no—
374D12—64no—
375D12—64no—
376C4×D3—128no—
377C4×D3—128no—
378C4×D3—128no—
379C4×D3—244no—
380Dic6—64no—
381Dic6—64no—
382Dic6—64no—
383Dic6—64no—
384C3×C8—24no—
385C3×C8—24no—
386C3×C8—24no—
387C3×C8—24no—
388C2×C32—41no—
389C2×C32—41no—
390C2×C32#54611yescharacteristic
391C2×C32#57511yescharacteristic
392C2×C32#57711yescharacteristic
393C3⋊D3—42no—
394C3⋊D3—81no—
395#41—182no—
396#41—182no—
397#41—361no—
398#41—361no—
399C2×Q8—91no—
400C2×Q8—91no—
401C2×D4—91no—
402C2×D4—91no—
403C2×D4—181no—
404C2×D4—181no—
405C2×D4—181no—
406C2×D4—181no—
407C2×D4C4⋊(C3⋊D3)11yescharacteristic
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4C22×C3⋊D311yescharacteristic
414C22×C4C22×C3⋊D311yescharacteristic
415SD16—361no—
416SD16—361no—
417D8—182no—
418M16—41no—
419C2×C8—41no—
420C2×C8C22×C3⋊D311yescharacteristic
421C2×C8C22×C3⋊D311yescharacteristic
422C2×C8C22×C3⋊D311yescharacteristic
423C2×C8C22×C3⋊D311yescharacteristic
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—91no—
427C4⋊C4—91no—
428C4⋊C4—181no—
429C4⋊C4—181no—
430C4⋊C4—181no—
431C4⋊C4—181no—
432C4⋊C4—181no—
433C4⋊C4—181no—
434C4⋊C4—181no—
435C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C22⋊C4—181no—
441C22⋊C4—181no—
442C22⋊C4—181no—
443C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
444C22⋊C4C4⋊(C3⋊D3)11yescharacteristic
445C42—181no—
446C42C22×C3⋊D311yescharacteristic
447C22×C3—24no—
448C22×C3—24no—
449C22×C3—24no—
450C22×C3—24no—
451C22×C3—24no—
452C22×C3—24no—
453C22×C3C22×D1214yes—
454C2×D3—68no—
455C2×D3—124no—
456C2×D3—124no—
457C2×D3—124no—
458C2×D3—124no—
459C2×D3—124no—
460C3×C4—24no—
461C3×C4—24no—
462C3×C4—24no—
463C3×C4—24no—
464C3×C4#100414yes—
465C3×C4D3×#4114yes—
466Dic3—124no—
467Dic3—124no—
468Dic3—124no—
469Dic3—124no—
470Dic3—124no—
471Dic3—124no—
472C32#330711yescharacteristic, complemented, Sylow
473C23—181no—
474C23—181no—
475C23C2×C4⋊(C3⋊D3)11yescharacteristic
476C23C2×C4⋊(C3⋊D3)11yescharacteristic
477Q8—181no—
478Q8—181no—
479Q8—181no—
480Q8—181no—
481D4—41no—
482D4—92no—
483D4—181no—
484D4—181no—
485D4—181no—
486D4—362no—
487D4—362no—
488D4—362no—
489D4—721no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—362no—
501C2×C4—362no—
502C2×C4—362no—
503C2×C4—721no—
504C2×C4—721no—
505C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
506C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
507C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
508C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
509C2×C4C23×C3⋊D311yescharacteristic
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C2×C3—44no—
515C2×C3—44no—
516C2×C3#555414yes—
517C2×C3#574814yes—
518C2×C3#575114yes—
519D3—128no—
520D3—244no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—182no—
528C22—361no—
529C22—361no—
530C22—361no—
531C22—361no—
532C22—361no—
533C22C22×C4⋊(C3⋊D3)11yescharacteristic
534C4—21no—
535C4—21no—
536C4—21no—
537C4—21no—
538C4—361no—
539C4—361no—
540C4—361no—
541C4—361no—
542C4—361no—
543C4—361no—
544C4#6436111yescharacteristic
545C4#41×C3⋊D311yescharacteristic
546C3#7950014yescomplemented
547C2—41no—
548C2—41no—
549C2—362no—
550C2—721no—
551C2#1059602511yescharacteristic
552C2#1059621911yescharacteristic
553C2#1059622211yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#435C2
socleC22×C32C22×D4
hypercenter#435C3⋊D3
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #10596036C2semidirect
2. #10596022C2semidirect
3. C32×#435C2semidirect
4. #10592833C2semidirect
5. #10592832C2semidirect
6. #10592813C2semidirect
7. #10592812C2semidirect
8. #10592546C2semidirect
9. #10592540C2semidirect
10. #10592433C2semidirect
11. #10592433C2semidirect
12. #10592422C2semidirect
13. #10592420C2semidirect
14. #10592410C2semidirect
15. #10592402C2semidirect
62. C3×#435D3semidirect
224. #435C3⋊D3semidirect
472. C32#3307semidirect
546. C3#79500semidirect

Maximal subgroups

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

subgroupindex
#105960362
#105960222
C32×#4352
#105928332
#105928322
#105928132
#105928122
#105925462
#105925402
#105924332
#105924222
#105924202
#105924102
#105924022
#795003