Finite Group Databasebeta

← #11782581

Subgroups — #11782581

Order 1152.

405 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 405 conjugacy classes of subgroups — too many to draw. Only its 94 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#10592778C211yesmaximal, characteristic, complemented
2C3×#5093C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic
4#10590288C211yesmaximal, characteristic, complemented
5#10590277C211yesmaximal, characteristic
6#10590273C211yesmaximal, characteristic
7C3⋊C82C211yesmaximal, characteristic, complemented
8#71215—31nomaximal
9#71183—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63662—22no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#810—22no—
17C3×#809—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63567—22no—
21#63563—22no—
22#63562—22no—
23C3×#487—31no—
24C3×#486—31no—
25#5093—31no—
26#5093D311yescharacteristic, complemented
27#5088—31no—
28#5088D311yescharacteristic
29#5079—31no—
30#5079—31no—
31#5079—61no—
32#5070—31no—
33#5070—31no—
34#4694—31no—
35#4681—31no—
36C8×C3⋊C8—31no—
37C8×C3⋊C8—31no—
38C2×C32×Q8—21no—
39C2×#634—21no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)D412yes—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54#1711—91noSylow
55C3×C4⋊Q8—21no—
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8C2×D311yescharacteristic
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×#127—31no—
60#874C2×D311yescharacteristic
61#869—31no—
62#869—31no—
63#869—61no—
64#869C2×D311yescharacteristic
65C3×#103—62no—
66C3×#102—62no—
67C3×C4×C8—31no—
68C3×C4×C8—31no—
69#835—62no—
70#835—62no—
71#835—64no—
72#832—62no—
73#832—62no—
74#821—62no—
75#816—62no—
76#810—22no—
77#810—62no—
78#809—22no—
79#809—62no—
80C4×C3⋊C8—31no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—61no—
83C4×C3⋊C8C2×D311yescharacteristic
84C4×C3⋊C8C2×D311yescharacteristic
85C22×C3×D3—41no—
86C32×Q8—42no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—41no—
92#634—42no—
93C2×C3×Dic3—41no—
94C3×D12—42no—
95C3×D12—42no—
96C3×D12—42no—
97C3×Dic6—42no—
98C3⋊(C3⋊C8)—22no—
99C3×C3⋊C8—22no—
100C3×C3⋊C8—22no—
101#487—31no—
102#487—91no—
103#487—91no—
104#486—31no—
105#486—91no—
106#486—91no—
107C82—91no—
108C2×C3×Q8—22no—
109C2×C3×Q8—21no—
110C2×C3×Q8—21no—
111C2×C3×Q8—61no—
112C2×C3×D4—61no—
113C2×C3×D4—61no—
114C2×C3×D4—61no—
115C2×D12—21no—
116C2×D12—21no—
117C2×D12—21no—
118C2×Dic6—21no—
119C2×Dic6—61no—
120C2×Dic6—61no—
121C2×Dic6—121no—
122C2×C3×C8—32no—
123C2×C3×C8—32no—
124C3×C4⋊C4—21no—
125C3×C4⋊C4—21no—
126C3×C4⋊C4—21no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—41no—
129C3×C4⋊C4—41no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C42—21no—
133C3×C42C22×D311yescharacteristic
134C3×C42C22×D311yescharacteristic
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—62no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—121no—
143C2×C3⋊C8—32no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—62no—
146C2×C3⋊C8#6712yes—
147C2×C3⋊C8#6712yes—
148C22×C32#12711yescharacteristic
149C2×C3×D3—81no—
150C2×C3×D3—81no—
151C2×C3×D3—81no—
152C32×C4—81no—
153C32×C4#13512yes—
154C32×C4#13512yes—
155C32×C4#13512yes—
156C3⋊Dic3—81no—
157C3×Dic3—81no—
158C4⋊Q8—31no—
159C4⋊Q8—91no—
160C4⋊Q8D3211yescharacteristic
161#127—31no—
162#103—62no—
163#103—182no—
164#103—182no—
165#102—62no—
166#102—182no—
167#102—182no—
168C4×C8—31no—
169C4×C8—31no—
170C4×C8—91no—
171C23×C3—121no—
172C22×D3—41no—
173C3×Q8—44no—
174C3×Q8—42no—
175C3×Q8—42no—
176C3×Q8—122no—
177C3×D4—122no—
178C3×D4—122no—
179C3×D4—122no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—42no—
184C2×C3×C4—41no—
185C2×C3×C4—41no—
186C2×C3×C4—121no—
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×C3×C4C2×#6711yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—122no—
195C2×Dic3—121no—
196C2×Dic3—121no—
197D12—42no—
198D12—42no—
199D12—42no—
200Dic6—42no—
201Dic6—122no—
202Dic6—122no—
203Dic6—242no—
204C3×C8—62no—
205C3×C8—62no—
206C3⋊C8—22no—
207C3⋊C8—22no—
208C3⋊C8—62no—
209C3⋊C8—62no—
210C3⋊C8—122no—
211C2×C32#49511yescharacteristic
212C2×C32#49511yescharacteristic
213C2×C32#49511yescharacteristic
214C3×D3—161no—
215C2×Q8—21no—
216C2×Q8—61no—
217C2×Q8—181no—
218C2×D4—61no—
219C2×D4—61no—
220C2×D4—61no—
221C2×C8—32no—
222C2×C8—32no—
223C2×C8—92no—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—181no—
229C4⋊C4—181no—
230C42C2×D3211yescharacteristic
231C22×C3—21no—
232C22×C3—241no—
233C22×C3—241no—
234C22×C3—241no—
235C22×C3#94011yescharacteristic
236C22×C3#94011yescharacteristic
237C2×D3—81no—
238C2×D3—81no—
239C2×D3—81no—
240C3×C4—22no—
241C3×C4—22no—
242C3×C4—22no—
243C3×C4—82no—
244C3×C4—81no—
245C3×C4—81no—
246C3×C4—241no—
247C3×C4#91212yes—
248C3×C4#91612yes—
249C3×C4#91612yes—
250C3×C4#91912yes—
251C3×C4#95012yes—
252C3×C4#95012yes—
253Dic3—81no—
254Dic3—242no—
255Dic3—241no—
256Dic3—241no—
257C32#171111yescharacteristic, complemented, Sylow
258C23—121no—
259Q8—42no—
260Q8—122no—
261Q8—362no—
262D4—122no—
263D4—122no—
264D4—122no—
265C2×C4—41no—
266C2×C4—121no—
267C2×C4—361no—
268C2×C4D3×#6711yescharacteristic
269C2×C4D3×#6711yescharacteristic
270C2×C4#381111yescharacteristic
271C8—62no—
272C8—62no—
273C8—182no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—481no—
278C2×C3#505911yescharacteristic
279C2×C3#505911yescharacteristic
280C2×C3#515511yescharacteristic
281C2×C3#516811yescharacteristic
282C2×C3#516811yescharacteristic
283C2×C3#519111yescharacteristic
284D3—161no—
285C22—241no—
286C22—241no—
287C22—241no—
288C22#6397911yescharacteristic
289C4—81no—
290C4—241no—
291C4—721no—
292C4#6393612yes—
293C4#6394712yes—
294C4#6394912yes—
295C3—21no—
296C3#7118311yescharacteristic, complemented
297C3#7121511yescharacteristic, complemented
298C2—481no—
299C2#1059147411yescharacteristic
300C2#1059160611yescharacteristic
301C2#1059160911yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#127
prime radicalC3×#874C22
hypercenterC4⋊Q8D32
hypocenterC32#1711
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
1. #10592778C2semidirect
2. C3×#5093C2semidirect
4. #10590288C2semidirect
7. C3⋊C82C2semidirect
26. #5093D3semidirect
257. C32#1711semidirect
296. C3#71183semidirect
297. C3#71215semidirect

Maximal subgroups

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

subgroupindex
#105927782
C3×#50932
C3×#50882
#105902882
#105902772
#105902732
C3⋊C822
#712153
#711833