Finite Group Databasebeta

← #11895162

Subgroups — #11895162

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 519 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593903C211yesmaximal, characteristic
2#10593860C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic
4C3×#4851C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590890C212yesmaximal, complemented
7#10590802C212yesmaximal, complemented
8#10590760C212yesmaximal
9#10590758C212yesmaximal
10C4×#3717C211yesmaximal, characteristic
11#10590288C211yesmaximal, characteristic, complemented
12#81037—31nomaximal
13#79925—31nomaximal
14C2×#3797—21no—
15C2×#3744C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63895—22no—
23#63894C2212yes—
24#63871—21no—
25#63869—21no—
26#63866C2212yes—
27#63845—22no—
28#63844C2212yes—
29Dic3×Dic6—21no—
30C2×#3717C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63643C2212yes—
33C3×#817C2212yes—
34C3×#816C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63567C2212yes—
40#63567C2212yes—
41#63566C2211yescharacteristic
42#63564C2211yescharacteristic
43#5727—31no—
44Q8×D12—31no—
45#5570—31no—
46#5567—31no—
47C3×#475—31no—
48C3×C8×Q8—31no—
49#5093—31no—
50C4×#215—31no—
51#4854—32no—
52#4852—32no—
53#4851—32no—
54#4851D311yescharacteristic, complemented
55#4841—31no—
56#4841—31no—
57#4841—32no—
58#4841—61no—
59#4830D311yescharacteristic, complemented
60#4818—32no—
61#4792—32no—
62C4×#204—31no—
63C4×#204—32no—
64#4681—31no—
65#4681—32no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2312yes—
69C2×C3×Dic6—21no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2311yescharacteristic
72C2×#627—22no—
73C2×#624—22no—
74#3797—44no—
75C2×C32×C8C2312yes—
76C32×C42C2311yescharacteristic
77#3752—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3744—24no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4—21no—
87C3×Dic3⋊C4D412yes—
88C3×C4×Dic3—21no—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92#3724—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97Dic32—22no—
98#3717—22no—
99#3359—91noSylow
100C2×D3×Q8—61no—
101C2×D3×Q8—61no—
102C3×C4⋊Q8—31no—
103C3×C4×Q8—31no—
104C3×C4×Q8—31no—
105#946—61no—
106Q8×Dic3—61no—
107#944—32no—
108C2×#215—31no—
109C2×#204—31no—
110C2×#204—32no—
111C2×#204—32no—
112C2×#204—62no—
113#897—62no—
114#897—61no—
115#896—62no—
116#893—32no—
117#890—61no—
118#890—62no—
119#889—62no—
120#888—32no—
121#887—32no—
122C4×D12—31no—
123C4×D12—31no—
124C4×D12—32no—
125C4×D12—61no—
126#870—61no—
127#869—32no—
128#869—32no—
129#869—31no—
130#869—31no—
131#869—61no—
132#869C2×D311yescharacteristic
133C4×Dic6—32no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#106—32no—
138C3×C4⋊C8—21no—
139C3×C4⋊C8—32no—
140C3×C4⋊C8C2×D311yescharacteristic
141C3×C4⋊C8C2×D311yescharacteristic
142C3×#103—32no—
143C3×C4×C8—32no—
144C3×C4×C8—31no—
145#835—31no—
146#821—31no—
147#817—31no—
148#817C2×D312yes—
149#816—31no—
150#816—32no—
151#816—32no—
152#816—32no—
153#816—32no—
154#816—62no—
155#816C2×D312yes—
156Dic3⋊C8C2×D312yes—
157C8×Dic3C2×D312yes—
158#810—32no—
159#810—32no—
160#809—31no—
161#808—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)#4112yes—
171C4×C3⋊D3—42no—
172#634—22no—
173#634—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3C2×D412yes—
178C2×C3×Dic3C2×D412yes—
179C3×Dic6—21no—
180C3×Dic6—21no—
181C3×Dic6—42no—
182C3×Dic6SD1614yescomplemented
183#627—44no—
184#624—44no—
185C32×C8—22no—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—21no—
188#557—91no—
189D4×Q8—91no—
190#487—92no—
191#487—91no—
192#475—31no—
193#475—92no—
194#461—92no—
195#461—91no—
196C8×Q8—31no—
197C4×SD16—92no—
198C4×SD16—91no—
199C2×C3×Q8—31no—
200C2×C3×Q8—31no—
201C2×C3×Q8—61no—
202D3×Q8—124no—
203D3×Q8—124no—
204C2×D12—31no—
205C2×D12—31no—
206C2×D12—61no—
207C2×C4×D3—62no—
208C2×C4×D3—61no—
209C2×C4×D3—61no—
210C2×C4×D3—62no—
211C2×C4×D3—121no—
212C2×Dic6—21no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6D1211yescharacteristic
219C2×Dic6C22×D311yescharacteristic
220C2×C3×C8—22no—
221C2×C3×C8—31no—
222C2×C3×C8—31no—
223C2×C3×C8C22×D312yes—
224C2×C3×C8C22×D312yes—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—31no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C42—21no—
232C3×C42—32no—
233C3×C42—61no—
234C3×C42C22×D311yescharacteristic
235C3×C42C22×D311yescharacteristic
236#215—62no—
237(C2×D3)⋊C4—62no—
238(C2×D3)⋊C4—61no—
239(C2×D3)⋊C4—61no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—121no—
242C4⋊Dic3—21no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—61no—
246C4⋊Dic3—62no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4⋊Dic3—61no—
252C4⋊Dic3—61no—
253C4⋊Dic3—121no—
254C4⋊Dic3—121no—
255C4⋊Dic3D1211yescharacteristic
256C4⋊Dic3C22×D312yes—
257C4⋊Dic3C22×D311yescharacteristic
258Dic3⋊C4—21no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4D1212yes—
265C4×Dic3—21no—
266C4×Dic3—62no—
267C4×Dic3—62no—
268C4×Dic3C22×D312yes—
269C2×C3⋊C8C22×D311yescharacteristic
270C2×C3⋊C8C22×D311yescharacteristic
271#204—64no—
272#204—64no—
273#204—62no—
274#204—124no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—22no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C32×C4—21no—
280C32×C4C2×SD1612yes—
281C32×C4C2×#4111yescharacteristic
282C32×C42−1+411yescharacteristic
283C3⋊Dic3—42no—
284C3⋊Dic3—41no—
285C3×Dic3—22no—
286C3×Dic3—41no—
287C3×Dic3—42no—
288C3×Dic3—41no—
289C3×Dic3C2×SD1614yes—
290C22×Q8—181no—
291C2×SD16—91no—
292C2×SD16—92no—
293C4⋊Q8—31no—
294C4⋊Q8—92no—
295C4⋊Q8—92no—
296C4⋊Q8—91no—
297#125—181no—
298#125—182no—
299C22⋊Q8—182no—
300C22⋊Q8—181no—
301C4×Q8—31no—
302C4×Q8—31no—
303C4×Q8—92no—
304C4×Q8—181no—
305C4×D4—92no—
306C4×D4—91no—
307#106—32no—
308#106—91no—
309C4⋊C8—32no—
310C4⋊C8D3211yescharacteristic
311#103—32no—
312#103—92no—
313#103—92no—
314#103—91no—
315#103—92no—
316#102—91no—
317C4×C8—32no—
318C4×C8—31no—
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—121no—
322C3×Q8—34no—
323C3×Q8—61no—
324C3×Q8—61no—
325C3×Q8—122no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—22no—
343C2×Dic3—62no—
344C2×Dic3—61no—
345C2×Dic3—62no—
346C2×Dic3—61no—
347C2×Dic3—121no—
348C2×Dic3—122no—
349C2×Dic3C2×D1212yes—
350C2×Dic3C2×D1212yes—
351D12—32no—
352D12—32no—
353D12—62no—
354D12—61no—
355D12—61no—
356D12—121no—
357C4×D3—124no—
358C4×D3—122no—
359C4×D3—122no—
360C4×D3—124no—
361C4×D3—242no—
362Dic6—21no—
363Dic6—21no—
364Dic6—42no—
365Dic6—62no—
366Dic6—62no—
367Dic6—62no—
368Dic6—62no—
369Dic6—122no—
370Dic6—122no—
371Dic6—124no—
372Dic6—124no—
373Dic6#20414yescomplemented
374C3×C8—22no—
375C3×C8—22no—
376C3×C8—42no—
377C3×C8—61no—
378C3×C8—61no—
379C3⋊C8—21no—
380C3⋊C8—21no—
381C2×C32#54811yescharacteristic
382C2×C32C22×SD1611yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—42no—
385C2×Q8—31no—
386C2×Q8—31no—
387C2×Q8—61no—
388C2×Q8—92no—
389C2×Q8—182no—
390C2×Q8—364no—
391C2×D4—91no—
392C22×C4—182no—
393C22×C4—181no—
394SD16—184no—
395SD16—182no—
396C2×C8—31no—
397C2×C8—31no—
398C2×C8C2×D3212yes—
399C4⋊C4—32no—
400C4⋊C4—31no—
401C4⋊C4—31no—
402C4⋊C4—32no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C4⋊C4—91no—
406C4⋊C4—182no—
407C4⋊C4—182no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C22⋊C4—182no—
413C22⋊C4—181no—
414C42—32no—
415C42—61no—
416C42—182no—
417C42C2×D3211yescharacteristic
418C22×C3—21no—
419C22×C3C22×D1211yescharacteristic
420C22×C3C2×D3×D411yescharacteristic
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—122no—
424C2×D3—121no—
425C2×D3—121no—
426C2×D3—121no—
427C2×D3—121no—
428C2×D3—241no—
429C2×D3—241no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—22no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—34no—
436C3×C4—41no—
437C3×C4—62no—
438C3×C4—122no—
439C3×C4—121no—
440C3×C4—121no—
441C3×C4C2×#20412yes—
442C3×C4D3×SD1612yes—
443C3×C4#100711yescharacteristic
444C3×C4#100711yescharacteristic
445C3×C4D3×#4111yescharacteristic
446C3×C4D3×#4111yescharacteristic
447Dic3—22no—
448Dic3—41no—
449Dic3—42no—
450Dic3—41no—
451Dic3—122no—
452Dic3—121no—
453Dic3—121no—
454Dic3—122no—
455Dic3—242no—
456Dic3—241no—
457Dic3C2×#20414yes—
458C32#335911yescharacteristic, complemented, Sylow
459C23—181no—
460Q8—34no—
461Q8—61no—
462Q8—61no—
463Q8—122no—
464Q8—182no—
465Q8—182no—
466Q8—364no—
467D4—92no—
468D4—181no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—62no—
474C2×C4—182no—
475C2×C4—181no—
476C2×C4—364no—
477C2×C4—362no—
478C2×C4D3×D1211yescharacteristic
479C2×C4D3×D1211yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—22no—
482C8—61no—
483C8—61no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3#557611yescharacteristic
488C2×C3#563311yescharacteristic
489C2×C3C22×#20411yescharacteristic
490C2×C3#575311yescharacteristic
491C2×C3C2×D3×SD1611yescharacteristic
492C2×C3#577911yescharacteristic
493D3—122no—
494D3—122no—
495D3—242no—
496C22—182no—
497C22—361no—
498C22—361no—
499C22C2×D3×D1211yescharacteristic
500C4—21no—
501C4—34no—
502C4—62no—
503C4—121no—
504C4—122no—
505C4—121no—
506C4—362no—
507C4—361no—
508C4D3×#20412yes—
509C4#6431211yescharacteristic
510C4#6431611yescharacteristic
511C3—21no—
512C3#7992511yescharacteristic, complemented
513C3#8103711yescharacteristic, complemented
514C2—362no—
515C2#1059432911yescharacteristic
516C2C2×D3×#20411yescharacteristic
517C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)C23
hypercenterC4⋊C8D32
hypocenterC32#3359
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593860C2semidirect
4. C3×#4851C2semidirect
5. C3×#4830C2semidirect
6. #10590890C2semidirect
7. #10590802C2semidirect
11. #10590288C2semidirect
54. #4851D3semidirect
59. #4830D3semidirect
182. C3×Dic6SD16semidirect
373. Dic6#204semidirect
458. C32#3359semidirect
512. C3#79925semidirect
513. C3#81037semidirect

Maximal subgroups

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

subgroupindex
#105939032
#105938602
#105925402
C3×#48512
C3×#48302
#105908902
#105908022
#105907602
#105907582
C4×#37172
#105902882
#810373
#799253