Finite Group Databasebeta

← #11781532

Subgroups — #11781532

Order 1152.

369 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 369 conjugacy classes of subgroups — too many to draw. Only its 92 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#10592380C211yesmaximal, characteristic, complemented
2C3×C8×D12C211yesmaximal, characteristic
3#10590272C211yesmaximal, characteristic
4#10590268C211yesmaximal, characteristic
5C3×#4458C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#70855—31nomaximal
9#68581—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×D3×C8—21no—
13C3×C4×D12C2211yescharacteristic
14C32×C4×C8C2211yescharacteristic
15#63643—21no—
16#63643—21no—
17C3×(C2×D3)⋊C8—21no—
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21#63575—21no—
22#63573—21no—
23#63563—21no—
24#63563—21no—
25C3×C8×D4—31no—
26#5008—31no—
27#5007—31no—
28#4846—31no—
29#4842—31no—
30C8×D12D311yescharacteristic
31#4681—31no—
32#4681—31no—
33#4681—61no—
34C3×#335—31no—
35#4486—31no—
36#4482—31no—
37#4481—31no—
38#4481—31no—
39#4458D311yescharacteristic, complemented
40C2×#634—21no—
41C2×#634—21no—
42C2×C3×D12D411yescharacteristic
43C2×C3×C4×D3—21no—
44C2×C32×C8D411yescharacteristic
45C2×C32×C8D411yescharacteristic
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C3×D3×C8—42no—
57#1683—91noSylow
58C22×C3×C8—61no—
59C3×C4×D4—31no—
60C2×D3×C8—21no—
61C4×D12C2×D311yescharacteristic
62#869—31no—
63#869—31no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869—61no—
68C3×C4⋊C8—31no—
69C3×C4⋊C8—31no—
70C3×C4⋊C8—31no—
71C3×C22⋊C8—61no—
72C3×C4×C8—21no—
73C3×C4×C8C2×D311yescharacteristic
74C3×C4×C8C2×D311yescharacteristic
75#832—61no—
76#832—61no—
77#821—61no—
78#821—61no—
79(C2×D3)⋊C8—21no—
80#818—61no—
81#817—61no—
82#816—62no—
83#816—62no—
84#816—61no—
85#816—61no—
86#816—61no—
87#816—61no—
88#808—61no—
89#807—61no—
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C22×C3×D3—21no—
94C2×C32×C4C2×D411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4#4111yescharacteristic
97C2×C3⋊Dic3—41no—
98C2×C3⋊Dic3—41no—
99#634—41no—
100#634—41no—
101#634—81no—
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12Q1612yes—
105C3×C4×D3—41no—
106C3×C4×D3—41no—
107C32×C8—21no—
108C32×C8—21no—
109C3×C3⋊C8—41no—
110C3×C3⋊C8—41no—
111C3×C3⋊C8—41no—
112#487—91no—
113#476—91no—
114#474—91no—
115C8×D4—31no—
116#335—31no—
117#333—91no—
118#332—91no—
119C2×C3×D4—31no—
120C22×C3×C4—61no—
121C2×D12D1211yescharacteristic
122C2×C4×D3—21no—
123C2×Dic6—62no—
124C2×Dic6—61no—
125C2×Dic6—61no—
126C2×Dic6—61no—
127C2×Dic6—61no—
128C2×Dic6—121no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—61no—
132C2×C3×C8—61no—
133C2×C3×C8—61no—
134C2×C3×C8—122no—
135C2×C3×C8D1211yescharacteristic
136C2×C3×C8D1211yescharacteristic
137C2×C3×C8#6711yescharacteristic
138C2×C3×C8#6711yescharacteristic
139C3×C4⋊C4—31no—
140C3×C22⋊C4—61no—
141C3×C42—21no—
142C3×C42C22×D311yescharacteristic
143C3×C42C22×D311yescharacteristic
144(C2×D3)⋊C4—21no—
145C4⋊Dic3—62no—
146C4⋊Dic3—61no—
147C4⋊Dic3—61no—
148C4⋊Dic3—61no—
149C4⋊Dic3—61no—
150C4⋊Dic3—61no—
151C4⋊Dic3—61no—
152C4⋊Dic3—61no—
153C4⋊Dic3—61no—
154C4⋊Dic3—121no—
155C4⋊Dic3—121no—
156C4⋊Dic3—121no—
157C4⋊Dic3D1211yescharacteristic
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—21no—
161D3×C8—42no—
162C22×C32#12111yescharacteristic
163C2×C3×D3—22no—
164C2×C3×D3—41no—
165C2×C3×D3—41no—
166C32×C4—21no—
167C32×C4C2×Q1611yescharacteristic
168C32×C4#13511yescharacteristic
169C32×C4#13511yescharacteristic
170C32×C4AGL(1,ℤ/8)11yescharacteristic
171C3⋊Dic3—81no—
172C3⋊Dic3—81no—
173C3×Dic3—41no—
174C22×C8—61no—
175C4⋊Q8—91no—
176C4⋊Q8—91no—
177C4×D4—31no—
178#107—181no—
179#106—181no—
180C4⋊C8—31no—
181C4⋊C8—31no—
182C4⋊C8—31no—
183#103—181no—
184#103—181no—
185#102—181no—
186#102—181no—
187C22⋊C8—61no—
188C4×C8D3211yescharacteristic
189C23×C3—61no—
190C22×D3—21no—
191C3×D4—32no—
192C3×D4—61no—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—61no—
197C2×C3×C4—121no—
198C2×C3×C4—121no—
199C2×C3×C4C2×D1211yescharacteristic
200C2×C3×C4C2×D1211yescharacteristic
201C2×C3×C4#23511yescharacteristic
202C2×C3×C4D3×D411yescharacteristic
203C2×C3×C4#23911yescharacteristic
204C2×C3×C4C2×#6711yescharacteristic
205C2×Dic3—21no—
206C2×Dic3—122no—
207C2×Dic3—122no—
208C2×Dic3—121no—
209C2×Dic3—121no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212D12—21no—
213D12Dic1212yes—
214C4×D3—41no—
215C4×D3—41no—
216Dic6—122no—
217Dic6—122no—
218Dic6—121no—
219Dic6—121no—
220Dic6—121no—
221Dic6—121no—
222Dic6—242no—
223Dic6—241no—
224Dic6—241no—
225C3×C8—21no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—21no—
229C3×C8—41no—
230C3×C8—41no—
231C3×C8—121no—
232C3×C8—121no—
233C3×C8—121no—
234C3⋊C8—41no—
235C3⋊C8—41no—
236C3⋊C8—41no—
237C2×C32#46311yescharacteristic
238C2×C32#46711yescharacteristic
239C2×C32#47111yescharacteristic
240C3×D3—42no—
241C2×Q8—181no—
242C2×Q8—181no—
243C2×D4—31no—
244C22×C4—61no—
245C2×C8—61no—
246C2×C8—61no—
247C2×C8—61no—
248C2×C8—122no—
249C2×C8#62611yescharacteristic
250C2×C8#62611yescharacteristic
251C4⋊C4—31no—
252C4⋊C4—181no—
253C4⋊C4—181no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C22⋊C4—61no—
257C42C2×D3211yescharacteristic
258C22×C3—21no—
259C22×C3—62no—
260C22×C3—121no—
261C22×C3—121no—
262C22×C3#89511yescharacteristic
263C22×C3#93011yescharacteristic
264C2×D3—22no—
265C2×D3—41no—
266C2×D3—41no—
267C3×C4—22no—
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—121no—
275C3×C4#90411yescharacteristic
276C3×C4#90411yescharacteristic
277C3×C4C2×Dic1211yescharacteristic
278C3×C4#90811yescharacteristic
279C3×C4#91211yescharacteristic
280C3×C4D3×Q1611yescharacteristic
281C3×C4#93211yescharacteristic
282C3×C4#95011yescharacteristic
283Dic3—41no—
284Dic3—242no—
285Dic3—242no—
286Dic3—241no—
287Dic3—241no—
288Dic3—241no—
289Dic3—241no—
290C32#168311yescharacteristic, complemented, Sylow
291C23—61no—
292Q8—361no—
293Q8—361no—
294Q8—721no—
295D4—32no—
296D4—61no—
297C2×C4—61no—
298C2×C4—121no—
299C2×C4—121no—
300C2×C4—361no—
301C2×C4—361no—
302C2×C4#379911yescharacteristic
303C2×C4D3×D1211yescharacteristic
304C2×C4C2×#62611yescharacteristic
305C8—21no—
306C8—21no—
307C8—121no—
308C8—121no—
309C8—121no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3—122no—
314C2×C3#484411yescharacteristic
315C2×C3#488711yescharacteristic
316C2×C3#489811yescharacteristic
317C2×C3#501611yescharacteristic
318C2×C3#511611yescharacteristic
319C2×C3#514111yescharacteristic
320D3—42no—
321C22—62no—
322C22—121no—
323C22—121no—
324C22#6390911yescharacteristic
325C4—21no—
326C4—121no—
327C4—721no—
328C4—721no—
329C4D3×Dic1211yescharacteristic
330C4#6380711yescharacteristic
331C4#6382911yescharacteristic
332C4#6383011yescharacteristic
333C3—21no—
334C3#6858111yescharacteristic, complemented
335C3#7085511yescharacteristic, complemented
336C2—122no—
337C2#1059036611yescharacteristic
338C2#1059085211yescharacteristic
339C2#1059093111yescharacteristic
subgroupG/H
centerC22#63909
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#121
prime radicalC2×C3×D12D4
hypercenterC4×C8D32
hypocenterC32#1683
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10592380C2semidirect
5. C3×#4458C2semidirect
6. #10589096C2semidirect
7. #10589094C2semidirect
39. #4458D3semidirect
290. C32#1683semidirect
334. C3#68581semidirect
335. C3#70855semidirect

Maximal subgroups

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

subgroupindex
#105923802
C3×C8×D122
#105902722
#105902682
C3×#44582
#105890962
#105890942
#708553
#685813