Finite Group Databasebeta

← #11882258

Subgroups — #11882258

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic, complemented
3C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10591177C214yesmaximal, complemented
5#10590379C212yesmaximal, complemented
6#10590367C212yesmaximal, complemented
7#10590301C212yesmaximal, complemented
8#10590300C212yesmaximal, complemented
9#83363—31nomaximal
10#79027—31nomaximal
11C2×#3828—21no—
12C2×C32×C42C2211yescharacteristic
13#64139—21no—
14#64139C2212yes—
15#64084—21no—
16#64083C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—21no—
18C4×C4⋊(C3⋊D3)C2212yes—
19#64078C2211yescharacteristic
20C3×#926—21no—
21C3×#924—21no—
22C3×#924C2212yes—
23C22×C3×C3⋊C8C2212yes—
24C3×#870—21no—
25C3×#869C2211yescharacteristic
26C3×#869C2211yescharacteristic
27C3×C4×Dic6—21no—
28C3×C4×Dic6C2212yes—
29C2×#3717C2214yes—
30C3×C4⋊(C3⋊C8)C2212yes—
31C3×C4⋊(C3⋊C8)C2212yes—
32#63573C2214yes—
33#63566C2214yes—
34#63564C2214yes—
35C3×#533—31no—
36#5477—31no—
37#5477—31no—
38#5477—61no—
39#5470D311yescharacteristic, complemented
40C2×C3×C4⋊C8—31no—
41#5114—34no—
42#5084—32no—
43#5083—32no—
44#5048—34no—
45#5027—32no—
46#5020—32no—
47C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
48#4851—32no—
49#4848—32no—
50#4842—32no—
51#4841—32no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C2×#638—22no—
56#3828—44no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—22no—
61C2×#634—21no—
62C2×C3×Dic6—21no—
63C2×C3×Dic6C2312yes—
64C32×C42D411yescharacteristic
65C32×C42D411yescharacteristic
66C32×C42C2311yescharacteristic
67C32×C42C2311yescharacteristic
68#3752—22no—
69#3752—22no—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72C3×#217—22no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3C2312yes—
77C3×Dic3⋊C4—22no—
78C3×Dic3⋊C4—22no—
79C3×C4×Dic3—22no—
80C2×C3×C3⋊C8—42no—
81C2×C3×C3⋊C8C2314yes—
82#3717—44no—
83#3246—91noSylow
84C2×#235—62no—
85C2×#235—61no—
86C2×#235—61no—
87C22×C3×C8—32no—
88C3×C4⋊Q8—31no—
89C3×C4⋊Q8—31no—
90C3×#125—61no—
91C3×C22⋊Q8—32no—
92C3×C22⋊Q8—61no—
93C3×C4×Q8—32no—
94C3×C4×Q8—61no—
95C3×#117—61no—
96C2×C3×C42—21no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99C2×#215—34no—
100#930—32no—
101#930—32no—
102#930—62no—
103#930—62no—
104#930—61no—
105#930—61no—
106#926—21no—
107#924—21no—
108#924C2×D312yes—
109C22×C3⋊C8C2×D312yes—
110C2×#204—34no—
111#875—62no—
112#875—61no—
113#875—61no—
114#874—31no—
115#874—31no—
116#874—61no—
117C4×D12—32no—
118C4×D12—32no—
119C4×D12—62no—
120C4×D12—62no—
121C4×D12—61no—
122C4×D12—61no—
123#870—21no—
124#869—31no—
125#869—31no—
126#869—61no—
127#869C2×D311yescharacteristic
128#869C2×D311yescharacteristic
129C4×Dic6—21no—
130C4×Dic6C2×D312yes—
131C3×C4⋊C8—32no—
132C3×C4⋊C8—32no—
133#835—34no—
134#821—34no—
135#817—34no—
136#816—34no—
137#809—34no—
138#808—34no—
139C4⋊(C3⋊C8)C2×D312yes—
140C4⋊(C3⋊C8)C2×D312yes—
141C23×C32C2×D411yescharacteristic
142C22×C3⋊D3—22no—
143C2×C32×C4—21no—
144C2×C32×C4—21no—
145C2×C32×C4—41no—
146C2×C32×C4SD1614yescomplemented
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2411yescharacteristic
153#638—44no—
154C2×C3⋊Dic3—22no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—42no—
158C4⋊(C3⋊D3)—42no—
159C4×C3⋊D3—44no—
160#634—42no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C3×Dic6—22no—
164C3×Dic6—22no—
165C3×Dic6—42no—
166C3×C3⋊C8—24no—
167#533—31no—
168#532—91no—
169#476—92no—
170#475—92no—
171#465—94no—
172#461—92no—
173#460—92no—
174C2×C4⋊C8—31no—
175C2×C3×Q8—32no—
176C2×C3×Q8—61no—
177C22×C3×C4—21no—
178C22×C3×C4—21no—
179C22×C3×C4—21no—
180C22×C3×C4D1211yescharacteristic
181C22×C3×C4D1211yescharacteristic
182C22×C3×C4#6711yescharacteristic
183C22×C3×C4#6711yescharacteristic
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—64no—
187C2×#67—62no—
188C2×#67—62no—
189#235—128no—
190#235—124no—
191#235—124no—
192C2×D12—32no—
193C2×D12—32no—
194C2×D12—62no—
195C2×D12—62no—
196C2×D12—62no—
197C2×D12—61no—
198C2×D12—61no—
199C2×D12—61no—
200C2×D12—61no—
201C2×C4×D3—64no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×Dic6—21no—
205C2×Dic6—62no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6C22×D312yes—
209C2×C3×C8—34no—
210C2×C3×C8—122no—
211C3×C4⋊C4—32no—
212C3×C4⋊C4—62no—
213C3×C4⋊C4—62no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216C3×C4⋊C4—61no—
217C3×C22⋊C4—62no—
218C3×C42—21no—
219C3×C42—21no—
220C3×C42—21no—
221C3×C42—21no—
222C3×C42—62no—
223C3×C42D1211yescharacteristic
224C3×C42D1211yescharacteristic
225C3×C42#6711yescharacteristic
226C3×C42#6711yescharacteristic
227C3×C42C22×D311yescharacteristic
228C3×C42C22×D311yescharacteristic
229C3×C42C22×D311yescharacteristic
230C3×C42C22×D311yescharacteristic
231#217—22no—
232#215—124no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—62no—
236(C2×D3)⋊C4—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—62no—
239C4⋊Dic3—21no—
240C4⋊Dic3—21no—
241C4⋊Dic3—21no—
242C4⋊Dic3—32no—
243C4⋊Dic3—32no—
244C4⋊Dic3—62no—
245C4⋊Dic3—62no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248C4⋊Dic3C22×D312yes—
249Dic3⋊C4—22no—
250Dic3⋊C4—22no—
251C4×Dic3—22no—
252C2×C3⋊C8—42no—
253C2×C3⋊C8C22×D314yes—
254#204—124no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32C2×SD1612yes—
258C22×C32C22×D411yescharacteristic
259C2×C3⋊D3—42no—
260C2×C3⋊D3—42no—
261C2×C3⋊D3—42no—
262C32×C4—21no—
263C32×C4—21no—
264C32×C4—21no—
265C32×C4C2×SD1612yes—
266C32×C4C2×SD1612yes—
267C32×C4H(5,𝔽2)11yescharacteristic
268C32×C42−1+411yescharacteristic
269C3⋊Dic3—42no—
270C3×Dic3—42no—
271C3×Dic3—42no—
272C2×#41—181no—
273C2×SD16—94no—
274C22×C8—32no—
275C4⋊Q8—31no—
276C4⋊Q8—31no—
277C4⋊Q8—91no—
278#127—91no—
279#125—61no—
280#124—181no—
281C22⋊Q8—32no—
282C22⋊Q8—61no—
283#121—92no—
284#121—181no—
285C4×Q8—32no—
286C4×Q8—61no—
287C4×D4—92no—
288C4×D4—181no—
289#117—61no—
290C2×C42D3211yescharacteristic
291#106—94no—
292C4⋊C8—32no—
293C4⋊C8—32no—
294#103—94no—
295#102—94no—
296C23×C3—21no—
297C23×C3C2×D1211yescharacteristic
298C23×C3C2×#6711yescharacteristic
299C22×D3—64no—
300C22×D3—62no—
301C22×D3—62no—
302C3×Q8—62no—
303C3×Q8—62no—
304C3×Q8—122no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—24no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—42no—
321C2×C3×C4—62no—
322C2×C3×C4—62no—
323C2×C3×C4#20414yescomplemented
324C2×C3×C4#21514yescomplemented
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4C2×D1211yescharacteristic
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4C2×D1211yescharacteristic
329C2×C3×C4C2×D1211yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337#67—128no—
338#67—124no—
339#67—124no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—64no—
343C2×Dic3—62no—
344C2×Dic3—62no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—62no—
349D12—122no—
350D12—122no—
351D12—124no—
352D12—122no—
353D12—122no—
354D12—124no—
355D12—122no—
356D12—122no—
357C4×D3—128no—
358C4×D3—124no—
359C4×D3—124no—
360Dic6—22no—
361Dic6—22no—
362Dic6—42no—
363Dic6—124no—
364Dic6—122no—
365Dic6—122no—
366C3×C8—64no—
367C3⋊C8—24no—
368C2×C32—22no—
369C2×C32#53711yescharacteristic
370C2×C32C22×SD1611yescharacteristic
371C2×C32#57511yescharacteristic
372C3⋊D3—82no—
373#41—364no—
374C2×Q8—32no—
375C2×Q8—61no—
376C2×Q8—181no—
377C2×D4—92no—
378C2×D4—182no—
379C2×D4—181no—
380C2×D4—181no—
381C22×C4—182no—
382C22×C4#62611yescharacteristic
383C22×C4#62611yescharacteristic
384C22×C4C2×D3211yescharacteristic
385SD16—364no—
386C2×C8—34no—
387C2×C8—122no—
388C4⋊C4—32no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—62no—
392C4⋊C4—62no—
393C4⋊C4—61no—
394C4⋊C4—92no—
395C4⋊C4—181no—
396C22⋊C4—62no—
397C22⋊C4—182no—
398C22⋊C4—182no—
399C42—62no—
400C42#62611yescharacteristic
401C42#62611yescharacteristic
402C42C2×D3211yescharacteristic
403C42C2×D3211yescharacteristic
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—22no—
410C22×C3—41no—
411C22×C3—41no—
412C22×C3C2×#20412yes—
413C22×C3C2×#21512yes—
414C22×C3C22×D1211yescharacteristic
415C22×C3C22×#6711yescharacteristic
416C2×D3—124no—
417C2×D3—124no—
418C2×D3—124no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—122no—
425C3×C4—22no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—22no—
435C3×C4—22no—
436C3×C4—41no—
437C3×C4—41no—
438C3×C4—122no—
439C3×C4—122no—
440C3×C4C2×#20412yes—
441C3×C4C2×#20412yes—
442C3×C4C2×#21512yes—
443C3×C4C2×#21512yes—
444C3×C4#100411yescharacteristic
445C3×C4#100711yescharacteristic
446C3×C4#100911yescharacteristic
447C3×C4#101011yescharacteristic
448Dic3—42no—
449Dic3—42no—
450Dic3—124no—
451Dic3—122no—
452Dic3—122no—
453C32#324611yescharacteristic, complemented, Sylow
454C23—182no—
455C23C2×#62611yescharacteristic
456Q8—62no—
457Q8—62no—
458Q8—122no—
459Q8—362no—
460D4—182no—
461D4—182no—
462D4—362no—
463D4—364no—
464D4—362no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—41no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—182no—
471C2×C4—364no—
472C2×C4#371714yescomplemented
473C2×C4C2×#62611yescharacteristic
474C2×C4C2×#62611yescharacteristic
475C2×C4C2×#62611yescharacteristic
476C2×C4C2×#62611yescharacteristic
477C2×C4C2×#62611yescharacteristic
478C2×C4C22×D3211yescharacteristic
479C8—64no—
480C2×C3—22no—
481C2×C3—22no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—42no—
486C2×C3#551011yescharacteristic
487C2×C3C22×#20411yescharacteristic
488C2×C3#574811yescharacteristic
489C2×C3C22×#21511yescharacteristic
490C2×C3#582211yescharacteristic
491C2×C3#583311yescharacteristic
492D3—244no—
493D3—242no—
494D3—242no—
495C22—21no—
496C22—21no—
497C22—362no—
498C22—362no—
499C22—362no—
500C22C2×#371712yes—
501C22C22×#62611yescharacteristic
502C4—21no—
503C4—21no—
504C4—21no—
505C4—122no—
506C4—122no—
507C4—362no—
508C4C2×#371712yes—
509C4C2×#371712yes—
510C4#6429711yescharacteristic
511C4#6430711yescharacteristic
512C3—21no—
513C3#7902711yescharacteristic, complemented
514C3#8336311yescharacteristic, complemented
515C2—22no—
516C2—722no—
517C2#1059479511yescharacteristic
518C2C22×#371711yescharacteristic
519C2#1059504311yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radical#10595948C2
hypercenterC2×C42D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
3. C2×C3×C4⋊(C3⋊C8)C2semidirect
4. #10591177C2semidirect
5. #10590379C2semidirect
6. #10590367C2semidirect
7. #10590301C2semidirect
8. #10590300C2semidirect
39. #5470D3semidirect
47. C2×C4⋊(C3⋊C8)D3semidirect
146. C2×C32×C4SD16semidirect
323. C2×C3×C4#204semidirect
324. C2×C3×C4#215semidirect
453. C32#3246semidirect
472. C2×C4#3717semidirect
513. C3#79027semidirect
514. C3#83363semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#54702
C2×C3×C4⋊(C3⋊C8)2
#105911772
#105903792
#105903672
#105903012
#105903002
#833633
#790273