Finite Group Databasebeta

← #11858180

Subgroups — #11858180

Order 1152.

2214 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596756C211yesmaximal, characteristic
2#10596216C211yesmaximal, characteristic, complemented
3#10595993C211yesmaximal, characteristic, complemented
4C32×#421C211yesmaximal, characteristic, complemented
5C2×#63664C211yesmaximal, characteristic, complemented
6C2×#63652C211yesmaximal, characteristic, complemented
7#10592704C211yesmaximal, characteristic, complemented
8#10592520C214yesmaximal, complemented
9C3⋊D3×#104C214yesmaximal, complemented
10#78992—34nomaximal
11C2×C32×#41C2211yescharacteristic
12#64367—21no—
13#64367C412yescomplemented
14#64366—21no—
15#64366C412yescomplemented
16#41×C3⋊D3—22no—
17#41×C3⋊D3C2214yes—
18#64364C412yescomplemented
19#64361—22no—
20#64361C412yescomplemented
21C2×#3828—22no—
22C2×#3828C2211yescharacteristic
23C2×#3828C2211yescharacteristic
24C2×C32×M16C2211yescharacteristic, complemented
25C32×#117C2211yescharacteristic, complemented
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C2×#3748C2211yescharacteristic, complemented
28#64116—22no—
29M16×C3⋊D3C2214yescomplemented
30#64110—22no—
31#64102—21no—
32#64096—21no—
33#64090—22no—
34#64081C2212yescomplemented
35C42×C3⋊D3C2212yescomplemented
36C32×#104C2214yescomplemented
37#63664C2212yescomplemented
38#63664C2212yescomplemented
39#63652C2212yescomplemented
40#63652C2212yescomplemented
41#63632C2214yescomplemented
42#5964—34no—
43#5745—34no—
44#5522—34no—
45C3×#421D314yescomplemented
46C2×#837—34no—
47C2×#825—34no—
48#5005—34no—
49#4821—316no—
50D3×#104—316no—
51C32×#41—21no—
52C32×#41—21no—
53C32×#41C2×C412yescomplemented
54C32×#41C2312yes—
55C2×C32×Q8C2×C411yescharacteristic, complemented
56C2×C32×D4—21no—
57C2×C32×D4C2×C411yescharacteristic, complemented
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61C2×#638—24no—
62C2×#638D412yes—
63C22×C3⋊Dic3—21no—
64#3832—22no—
65#3832C2×C414yescomplemented
66Q8×C3⋊D3—22no—
67Q8×C3⋊D3C2×C414yescomplemented
68#3830—24no—
69#3830—24no—
70#3830—22no—
71#3830C2×C414yescomplemented
72D4×C3⋊D3—24no—
73D4×C3⋊D3—24no—
74D4×C3⋊D3—22no—
75D4×C3⋊D3C2×C414yescomplemented
76#3828—21no—
77#3828—21no—
78#3828—24no—
79#3828—22no—
80#3828—24no—
81#3828—22no—
82#3828C2×C412yes—
83#3828C2×C412yes—
84#3828C2×C412yescomplemented
85#3828D412yes—
86#3828D412yes—
87#3828C2312yes—
88C2×C4⋊(C3⋊D3)—22no—
89C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
90C2×C4⋊(C3⋊D3)D411yescharacteristic
91C2×C4×C3⋊D3—21no—
92C2×C4×C3⋊D3—24no—
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3C2312yes—
95C2×#634—22no—
96C2×#634C2×C411yescharacteristic, complemented
97C2×#634D411yescharacteristic
98C32×M16—21no—
99C32×M16C2312yes—
100C2×C32×C8—21no—
101C32×C4⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C42C2312yes—
104#3752—22no—
105#3750—22no—
106C4×C3⋊Dic3—21no—
107C4×C3⋊Dic3—22no—
108C4×C3⋊Dic3C2311yescharacteristic
109C4×C3⋊Dic3C2311yescharacteristic
110#3748—21no—
111#3748C2312yes—
112C2×C3⋊(C3⋊C8)—21no—
113#3743—24no—
114C8×C3⋊D3—24no—
115#2901—91noSylow
116C2×C3×#41C2×D314yes—
117#1010—38no—
118#1010—64no—
119#1009—38no—
120#1009—64no—
121D3×#41—316no—
122D3×#41—68no—
123#1007—38no—
124#1004—38no—
125#1004—68no—
126C2×#235—34no—
127C2×#235—34no—
128C2×#235—68no—
129C2×C3×M16C2×D314yescomplemented
130C3×#117C2×D314yescomplemented
131C2×C4×Dic3—34no—
132C2×#208—34no—
133#907—68no—
134D3×M16—316no—
135#901—68no—
136#893—64no—
137#887—64no—
138#67⋊C4—68no—
139#872—38no—
140C42×D3—38no—
141C3×#104C2×D3116yescomplemented
142#837—38no—
143#837—38no—
144#825—38no—
145#825—38no—
146#805—316no—
147C23×C32—21no—
148C23×C32C2×D411yescharacteristic
149C22×C3⋊D3—21no—
150C22×C3⋊D3—24no—
151C22×C3⋊D3C2×D412yes—
152C32×Q8—21no—
153C32×Q8C22×C412yes—
154C32×D4—22no—
155C32×D4—22no—
156C32×D4—21no—
157C32×D4C22×C412yes—
158C2×C32×C4—21no—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4C22×C411yescharacteristic
163C2×C32×C4C22×C411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168#638—22no—
169#638—22no—
170#638—24no—
171#638—24no—
172#638C22⋊C414yes—
173#638C22⋊C414yes—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—24no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—42no—
179C2×C3⋊Dic3C2×D412yes—
180C4⋊(C3⋊D3)—24no—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)C22⋊C412yes—
183C4⋊(C3⋊D3)C22⋊C412yes—
184C4⋊(C3⋊D3)C22×C412yes—
185C4×C3⋊D3—24no—
186C4×C3⋊D3—22no—
187C4×C3⋊D3—22no—
188C4×C3⋊D3—24no—
189C4×C3⋊D3—44no—
190C4×C3⋊D3C22×C414yes—
191C4×C3⋊D3C2×D414yes—
192#634—21no—
193#634—24no—
194#634C22⋊C412yes—
195#634C22⋊C412yes—
196#634C22×C412yes—
197C32×C8—22no—
198C3⋊(C3⋊C8)—22no—
199#585—91no—
200#568—91no—
201C4×#41—91no—
202#421—91no—
203#421—94no—
204#421C3⋊D311yescharacteristic, complemented
205C2×#104—91no—
206C2×#104—91no—
207C2×#104—94no—
208C3×#41—24no—
209C3×#41—24no—
210C3×#41C4×D318yescomplemented
211C3×#41C22×D318yes—
212C2×C3×Q8C4×D314yescomplemented
213C2×C3×D4—24no—
214C2×C3×D4C4×D314yescomplemented
215C22×C3×C4—24no—
216C22×C3×C4C22×D314yes—
217C2×#67—38no—
218C2×#67—616no—
219C2×#67—64no—
220C22×Dic3—64no—
221#239—316no—
222#239—68no—
223D3×Q8—316no—
224D3×Q8—68no—
225#237—316no—
226#237—68no—
227#237—616no—
228#237—616no—
229D3×D4—316no—
230D3×D4—68no—
231D3×D4—616no—
232D3×D4—616no—
233#235—38no—
234#235—38no—
235#235—38no—
236#235—38no—
237#235—38no—
238#235—38no—
239#235—68no—
240#235—616no—
241#235—68no—
242#235—616no—
243#235—64no—
244#235—64no—
245C2×D12—34no—
246C2×D12—34no—
247C2×D12—68no—
248C2×C4×D3—38no—
249C2×C4×D3—616no—
250C2×C4×D3—64no—
251C2×C4×D3—68no—
252C2×Dic6—34no—
253C2×Dic6—34no—
254C2×Dic6—68no—
255C3×M16—24no—
256C3×M16C22×D318yes—
257C2×C3×C8—24no—
258C3×C4⋊C4—24no—
259C3×C22⋊C4—24no—
260C3×C42C22×D318yes—
261(C2×D3)⋊C4—68no—
262Dic3⋊C4—68no—
263C4×Dic3—34no—
264C4×Dic3—34no—
265C4×Dic3—68no—
266C4×Dic3—64no—
267#208—38no—
268#208—64no—
269C2×C3⋊C8—64no—
270ΓL(1,𝔽25)—616no—
271D3×C8—616no—
272C22×C32—22no—
273C22×C32—41no—
274C22×C32—81no—
275C22×C32C2×C22⋊C411yescharacteristic
276C22×C32C2×C22⋊C411yescharacteristic
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—22no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—84no—
281C2×C3⋊D3—81no—
282C2×C3⋊D3C2×C22⋊C414yes—
283C32×C4—22no—
284C32×C4—42no—
285C32×C4C2×C22⋊C411yescharacteristic
286C32×C4C2×C22⋊C411yescharacteristic
287C32×C4C23×C411yescharacteristic
288C32×C4C22×D411yescharacteristic
289C3⋊Dic3—22no—
290C3⋊Dic3—22no—
291C3⋊Dic3—41no—
292C3⋊Dic3C2×C22⋊C414yes—
2932−1+4—92no—
2942−1+4—92no—
2952−1+4—181no—
296H(5,𝔽2)—92no—
297H(5,𝔽2)—92no—
298H(5,𝔽2)—182no—
299H(5,𝔽2)—181no—
300C2×#41—91no—
301C2×#41—94no—
302C2×#41—91no—
303C2×#41—182no—
304C2×#41—182no—
305C2×#41C2×C3⋊D311yescharacteristic
306#131—182no—
307#131—182no—
308C2×M16—91no—
309C2×M16—94no—
310C2×M16C2×C3⋊D311yescharacteristic, complemented
311C4×Q8—181no—
312C4×D4—182no—
313C4×D4—181no—
314#117—92no—
315#117C2×C3⋊D311yescharacteristic, complemented
316C2×C42—91no—
317C2×C42—92no—
318#104—92no—
319#104—92no—
320#104—92no—
321#104—92no—
322#104—94no—
323#104C2×C3⋊D314yescomplemented
324C23×C3—24no—
325C23×C3D3×D414yes—
326C22×D3—38no—
327C22×D3—616no—
328C22×D3—64no—
329C3×Q8—24no—
330C3×Q8C2×C4×D318yes—
331C3×D4—28no—
332C3×D4—28no—
333C3×D4—24no—
334C3×D4C2×C4×D318yes—
335C2×C3×C4—24no—
336C2×C3×C4—28no—
337C2×C3×C4—28no—
338C2×C3×C4—28no—
339C2×C3×C4C2×C4×D314yes—
340C2×C3×C4C2×C4×D314yes—
341C2×C3×C4D3×D414yes—
342C2×C3×C4D3×D414yes—
343C2×C3×C4D3×D414yes—
344C2×C3×C4C23×D314yes—
345#67—316no—
346#67—316no—
347#67—616no—
348#67—616no—
349#67—68no—
350#67—68no—
351C2×Dic3—38no—
352C2×Dic3—616no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—64no—
356C2×Dic3—128no—
357D12—38no—
358D12—38no—
359D12—38no—
360D12—616no—
361D12—64no—
362C4×D3—316no—
363C4×D3—316no—
364C4×D3—616no—
365C4×D3—616no—
366C4×D3—68no—
367C4×D3—68no—
368C4×D3—1216no—
369Dic6—38no—
370Dic6—38no—
371Dic6—38no—
372Dic6—616no—
373Dic6—64no—
374C3×C8—28no—
375C3⋊C8—68no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32—42no—
380C2×C32C22×C22⋊C411yescharacteristic
381C3⋊D3—24no—
382C3⋊D3—42no—
383#41—21no—
384#41—21no—
385#41—92no—
386#41—92no—
387#41—92no—
388#41—92no—
389#41—94no—
390#41—94no—
391#41—92no—
392#41—92no—
393#41—184no—
394#41—184no—
395#41—182no—
396#41—182no—
397#41—184no—
398#41—184no—
399#41—182no—
400#41—182no—
401#41—181no—
402#41—181no—
403#41C4×C3⋊D312yescomplemented
404#41C22×C3⋊D312yes—
405C2×Q8—91no—
406C2×Q8—94no—
407C2×Q8—91no—
408C2×Q8—182no—
409C2×Q8—182no—
410C2×Q8C4×C3⋊D311yescharacteristic, complemented
411C2×D4—21no—
412C2×D4—92no—
413C2×D4—94no—
414C2×D4—91no—
415C2×D4—91no—
416C2×D4—182no—
417C2×D4—184no—
418C2×D4—182no—
419C2×D4—184no—
420C2×D4—184no—
421C2×D4—181no—
422C2×D4C4×C3⋊D311yescharacteristic, complemented
423C22×C4—21no—
424C22×C4—92no—
425C22×C4—184no—
426C22×C4—182no—
427C22×C4—181no—
428C22×C4—181no—
429C22×C4C22×C3⋊D311yescharacteristic
430M16—21no—
431M16—92no—
432M16—184no—
433M16—181no—
434M16C22×C3⋊D312yes—
435C2×C8—21no—
436C2×C8—184no—
437C2×C8—181no—
438C4⋊C4—21no—
439C4⋊C4—182no—
440C22⋊C4—21no—
441C22⋊C4—182no—
442C42—91no—
443C42—91no—
444C42—182no—
445C42—181no—
446C42C22×C3⋊D312yes—
447C22×C3—28no—
448C22×C3—44no—
449C22×C3—84no—
450C22×C3D3×C22⋊C414yes—
451C22×C3D3×C22⋊C414yes—
452C22×C3C2×D3×D414yes—
453C2×D3—316no—
454C2×D3—68no—
455C2×D3—128no—
456C2×D3—2416no—
457C2×D3—244no—
458C3×C4—28no—
459C3×C4—48no—
460C3×C4D3×C22⋊C414yes—
461C3×C4D3×C22⋊C414yes—
462C3×C4C22×C4×D314yes—
463C3×C4C2×D3×D414yes—
464Dic3—316no—
465Dic3—68no—
466Dic3—68no—
467Dic3—124no—
468C32#290111yescharacteristic, complemented, Sylow
469C23—21no—
470C23—92no—
471C23—184no—
472C23—181no—
473C23D4×C3⋊D311yescharacteristic
474Q8—21no—
475Q8—92no—
476Q8—92no—
477Q8—92no—
478Q8—184no—
479Q8—181no—
480Q8C2×C4×C3⋊D312yes—
481D4—22no—
482D4—22no—
483D4—21no—
484D4—94no—
485D4—94no—
486D4—92no—
487D4—92no—
488D4—92no—
489D4—184no—
490D4—184no—
491D4—184no—
492D4—182no—
493D4—182no—
494D4—181no—
495D4C2×C4×C3⋊D312yes—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—92no—
501C2×C4—94no—
502C2×C4—94no—
503C2×C4—184no—
504C2×C4—184no—
505C2×C4—184no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—182no—
509C2×C4—182no—
510C2×C4—181no—
511C2×C4—364no—
512C2×C4—362no—
513C2×C4C2×C4×C3⋊D311yescharacteristic
514C2×C4C2×C4×C3⋊D311yescharacteristic
515C2×C4D4×C3⋊D311yescharacteristic
516C2×C4D4×C3⋊D311yescharacteristic
517C2×C4D4×C3⋊D311yescharacteristic
518C2×C4C23×C3⋊D311yescharacteristic
519C8—22no—
520C8—182no—
521C2×C3—24no—
522C2×C3—24no—
523C2×C3—24no—
524C2×C3—48no—
525C2×C3C2×D3×C22⋊C414yes—
526D3—616no—
527D3—128no—
528C22—22no—
529C22—41no—
530C22—81no—
531C22—94no—
532C22—182no—
533C22—362no—
534C22—721no—
535C22—724no—
536C22C22⋊C4×C3⋊D311yescharacteristic
537C22C22⋊C4×C3⋊D311yescharacteristic
538C22C2×D4×C3⋊D311yescharacteristic
539C4—22no—
540C4—42no—
541C4—94no—
542C4—182no—
543C4—182no—
544C4—361no—
545C4C22⋊C4×C3⋊D311yescharacteristic
546C4C22⋊C4×C3⋊D311yescharacteristic
547C4C22×C4×C3⋊D311yescharacteristic
548C4C2×D4×C3⋊D311yescharacteristic
549C3#7899214yescomplemented
550C2—21no—
551C2—21no—
552C2—21no—
553C2—42no—
554C2—184no—
555C2—362no—
556C2C2×C22⋊C4×C3⋊D311yescharacteristic
subgroupG/H
centerC4C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×#421C2
socleC2×C32C22×C22⋊C4
prime radical#10596756C2
cosocleC2×C32×C4C24
hypercenter#421C3⋊D3
hypocenterC32#2901
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #10596216C2semidirect
3. #10595993C2semidirect
4. C32×#421C2semidirect
5. C2×#63664C2semidirect
6. C2×#63652C2semidirect
7. #10592704C2semidirect
8. #10592520C2semidirect
9. C3⋊D3×#104C2semidirect
13. #64367C4semidirect
15. #64366C4semidirect
18. #64364C4semidirect
20. #64361C4semidirect
24. C2×C32×M16C22semidirect
25. C32×#117C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
27. C2×#3748C22semidirect
29. M16×C3⋊D3C22semidirect
34. #64081C22semidirect
35. C42×C3⋊D3C22semidirect
36. C32×#104C22semidirect
37. #63664C22semidirect
38. #63664C22semidirect
39. #63652C22semidirect
40. #63652C22semidirect
41. #63632C22semidirect
45. C3×#421D3semidirect
53. C32×#41C2×C4semidirect
55. C2×C32×Q8C2×C4semidirect
57. C2×C32×D4C2×C4semidirect
65. #3832C2×C4semidirect
67. Q8×C3⋊D3C2×C4semidirect
71. #3830C2×C4semidirect
75. D4×C3⋊D3C2×C4semidirect
84. #3828C2×C4semidirect
89. C2×C4⋊(C3⋊D3)C2×C4semidirect
96. C2×#634C2×C4semidirect
129. C2×C3×M16C2×D3semidirect
130. C3×#117C2×D3semidirect
141. C3×#104C2×D3semidirect
204. #421C3⋊D3semidirect
210. C3×#41C4×D3semidirect
212. C2×C3×Q8C4×D3semidirect
214. C2×C3×D4C4×D3semidirect
310. C2×M16C2×C3⋊D3semidirect
315. #117C2×C3⋊D3semidirect
323. #104C2×C3⋊D3semidirect
403. #41C4×C3⋊D3semidirect
410. C2×Q8C4×C3⋊D3semidirect
422. C2×D4C4×C3⋊D3semidirect
468. C32#2901semidirect
549. C3#78992semidirect

Maximal subgroups

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

subgroupindex
#105967562
#105962162
#105959932
C32×#4212
C2×#636642
C2×#636522
#105927042
#105925202
C3⋊D3×#1042
#789923