Finite Group Databasebeta

← #11780715

Subgroups — #11780715

Order 1152.

389 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 389 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593868C211yesmaximal, characteristic
2#10592780C211yesmaximal, characteristic
3C3×#5082C211yesmaximal, characteristic
4C3×#5081C211yesmaximal, characteristic
5#10589089C211yesmaximal, characteristic
6#10589088C211yesmaximal, characteristic
7#10589088C211yesmaximal, characteristic
8#71393—31nomaximal
9#71252—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64079C2211yescharacteristic
12C3×#870C2211yescharacteristic
13C3×#870C2211yescharacteristic
14#63847—21no—
15#63847—21no—
16#63846—21no—
17#63846—21no—
18#63845—21no—
19#63845—21no—
20#63635—21no—
21#63634—21no—
22#63630C2211yescharacteristic
23C3×#835—21no—
24C3×#835—21no—
25C3×#808—21no—
26C3×#807—21no—
27C3×#803C2211yescharacteristic
28C3×#803C2211yescharacteristic
29C3⋊#564—31no—
30C3⋊#564—31no—
31C3×#501—31no—
32C3×#491—31no—
33#5082D311yescharacteristic
34#5081—31no—
35#5081—31no—
36#5081—61no—
37#5081D311yescharacteristic
38#4543—31no—
39#4543—31no—
40#4465—31no—
41#4465—31no—
42#4465—31no—
43#4465—31no—
44C2×C32×Q8—21no—
45C32×C4⋊C4—21no—
46C32×C4⋊C4—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)D411yescharacteristic
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—21no—
51#3750—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×C4⋊Dic3D411yescharacteristic
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×Dic3⋊C4—21no—
59C3×Dic3⋊C4—21no—
60C3×Dic3⋊C4—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63#3724—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68Dic3⋊Dic3—21no—
69Dic32—21no—
70Dic32—21no—
71#1663—91noSylow
72C3×C4⋊Q8—21no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C2×D311yescharacteristic
75C3×#125—31no—
76C3×#125—31no—
77#890—61no—
78#890—61no—
79#890—61no—
80#890—61no—
81#889—61no—
82#889—61no—
83#889—61no—
84#889—61no—
85#889—61no—
86#889—61no—
87#889—61no—
88#889—61no—
89#870—31no—
90#870—31no—
91#870—61no—
92#870C2×D311yescharacteristic
93#870C2×D311yescharacteristic
94C3×#107—61no—
95C3×#106—61no—
96C3×#103—61no—
97C3×#103—61no—
98C3×#97—31no—
99C3×#97—31no—
100#835—21no—
101#835—21no—
102#808—21no—
103#808—61no—
104#808—61no—
105#808—62no—
106#807—21no—
107#807—61no—
108#807—61no—
109#807—62no—
110#803—31no—
111#803—31no—
112#803—61no—
113#803C2×D311yescharacteristic
114#803C2×D311yescharacteristic
115C32×Q8—42no—
116C2×C32×C4—41no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C3⋊(C3⋊C8)—22no—
127C3×C3⋊C8—22no—
128C3×C3⋊C8—41no—
129#564—91no—
130#501—31no—
131#501—91no—
132#491—31no—
133#330—91no—
134#330—91no—
135#330—91no—
136C2×C3×Q8—21no—
137C2×C3×Q8—21no—
138C2×C3×Q8—41no—
139C2×C3×C8—61no—
140C2×C3×C8—61no—
141C3×C4⋊C4—22no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—31no—
147C3×C4⋊C4—31no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—31no—
150C3×C4⋊C4—41no—
151C3×C4⋊C4—61no—
152C3×C4⋊C4—61no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C42—21no—
156C3×C42C22×D311yescharacteristic
157C3×C42C22×D311yescharacteristic
158C4⋊Dic3—31no—
159C4⋊Dic3—31no—
160C4⋊Dic3—31no—
161C4⋊Dic3—31no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—61no—
165C4⋊Dic3—61no—
166C4⋊Dic3—61no—
167C4⋊Dic3—61no—
168C4⋊Dic3#6711yescharacteristic
169C4⋊Dic3#6711yescharacteristic
170C4⋊Dic3#6711yescharacteristic
171C4⋊Dic3#6711yescharacteristic
172Dic3⋊C4—21no—
173Dic3⋊C4—21no—
174Dic3⋊C4—21no—
175Dic3⋊C4—21no—
176Dic3⋊C4—61no—
177Dic3⋊C4—61no—
178Dic3⋊C4—61no—
179Dic3⋊C4—61no—
180Dic3⋊C4—61no—
181Dic3⋊C4—61no—
182Dic3⋊C4—61no—
183Dic3⋊C4—61no—
184Dic3⋊C4—61no—
185Dic3⋊C4—61no—
186Dic3⋊C4—61no—
187Dic3⋊C4—61no—
188Dic3⋊C4—121no—
189Dic3⋊C4—121no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C4×Dic3—61no—
193C4×Dic3—61no—
194C2×C3⋊C8—21no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—62no—
197C2×C3⋊C8—61no—
198C2×C3⋊C8—61no—
199C22×C32#12011yescharacteristic
200C32×C4—21no—
201C32×C4—21no—
202C32×C4—21no—
203C32×C4—81no—
204C3⋊Dic3—41no—
205C3⋊Dic3—41no—
206C3×Dic3—41no—
207C3×Dic3—41no—
208C3×Dic3—41no—
209C3×Dic3—41no—
210C4⋊Q8D3211yescharacteristic
211#125—31no—
212#125—31no—
213#125—91no—
214#125—181no—
215#125—181no—
216#125—181no—
217#125—181no—
218#125—181no—
219#125—181no—
220#107—61no—
221#107—181no—
222#106—61no—
223#106—181no—
224#103—61no—
225#103—61no—
226#97—31no—
227#97—31no—
228#97—91no—
229C3×Q8—42no—
230C3×Q8—42no—
231C3×Q8—82no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—42no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—61no—
239C2×C3×C4—61no—
240C2×C3×C4—61no—
241C2×C3×C4—61no—
242C2×C3×C4D3×D411yescharacteristic
243C2×C3×C4D3×D411yescharacteristic
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—61no—
253C2×Dic3—61no—
254C2×Dic3—61no—
255C2×Dic3—61no—
256C2×Dic3—121no—
257C2×Dic3—121no—
258C3×C8—62no—
259C3×C8—121no—
260C3⋊C8—22no—
261C3⋊C8—41no—
262C3⋊C8—64no—
263C3⋊C8—62no—
264C3⋊C8—62no—
265C2×C32#45411yescharacteristic
266C2×C32#45611yescharacteristic
267C2×C32#45611yescharacteristic
268C2×Q8—21no—
269C2×C8—61no—
270C2×C8—61no—
271C2×C8—181no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—31no—
275C4⋊C4—31no—
276C4⋊C4—31no—
277C4⋊C4—31no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C4⋊C4—61no—
281C4⋊C4—61no—
282C4⋊C4—91no—
283C4⋊C4—91no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C4⋊C4—181no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C42—181no—
293C42—181no—
294C42C2×D3211yescharacteristic
295C22×C3—21no—
296C22×C3#93711yescharacteristic
297C22×C3#93711yescharacteristic
298C3×C4—22no—
299C3×C4—21no—
300C3×C4—21no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—41no—
306C3×C4—41no—
307C3×C4—82no—
308C3×C4—81no—
309C3×C4—81no—
310C3×C4—121no—
311C3×C4—121no—
312C3×C4—121no—
313C3×C4—121no—
314Dic3—41no—
315Dic3—41no—
316Dic3—41no—
317Dic3—41no—
318Dic3—121no—
319Dic3—121no—
320Dic3—121no—
321Dic3—121no—
322Dic3—241no—
323Dic3—241no—
324C32#166311yescharacteristic, complemented, Sylow
325Q8—42no—
326C2×C4—41no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—181no—
332C2×C4—181no—
333C2×C4D3×#6711yescharacteristic
334C2×C4D3×#6711yescharacteristic
335C2×C4#381111yescharacteristic
336C8—62no—
337C8—121no—
338C8—182no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—21no—
342C2×C3#506211yescharacteristic
343C2×C3#509511yescharacteristic
344C2×C3#520111yescharacteristic
345C2×C3#520511yescharacteristic
346C2×C3#520511yescharacteristic
347C2×C3#520511yescharacteristic
348C22#6398311yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—81no—
353C4—121no—
354C4—121no—
355C4—121no—
356C4—121no—
357C4—361no—
358C4—361no—
359C3—21no—
360C3#7125211yescharacteristic, complemented
361C3#7139311yescharacteristic, complemented
362C2#1059152511yescharacteristic
363C2#1059166011yescharacteristic
364C2#1059166111yescharacteristic
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊Q8D32
hypocenterC32#1663
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
324. C32#1663semidirect
360. C3#71252semidirect
361. C3#71393semidirect

Maximal subgroups

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

subgroupindex
#105938682
#105927802
C3×#50822
C3×#50812
#105890892
#105890882
#713933
#712523