Finite Group Databasebeta

← #11782560

Subgroups — #11782560

Order 1152.

385 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 385 conjugacy classes of subgroups — too many to draw. Only its 98 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#10592777C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic
3C3×#5079C211yesmaximal, characteristic
4#10590312C211yesmaximal, characteristic
5#10590288C211yesmaximal, characteristic
6#10590287C211yesmaximal, characteristic
7C3⋊C82C211yesmaximal, characteristic
8#71214—31nomaximal
9#71214—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63634—22no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#835—22no—
17C3×#810—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63576—22no—
21#63567—22no—
22#63566—22no—
23C3×#487—31no—
24C3×#487—31no—
25#5093—31no—
26#5093D311yescharacteristic
27#5079—31no—
28#5079D311yescharacteristic
29#5078—31no—
30#5078—31no—
31#5078—31no—
32#5078—31no—
33#5078—61no—
34#4681—31no—
35#4681—31no—
36C8×C3⋊C8—31no—
37C8×C3⋊C8—31no—
38C2×C32×Q8—21no—
39C2×#634—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C42C2311yescharacteristic
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C2×C3⋊(C3⋊C8)D412yes—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54#1710—91noSylow
55C3×C4⋊Q8—21no—
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×C4⋊Q8C2×D311yescharacteristic
60#869—31no—
61#869—31no—
62#869—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C3×#103—62no—
66C3×#103—62no—
67C3×C4×C8—31no—
68C3×C4×C8—31no—
69#835—22no—
70#835—62no—
71#816—62no—
72#816—62no—
73#810—22no—
74#810—62no—
75#807—62no—
76#807—62no—
77#807—62no—
78#807—62no—
79#807—64no—
80C4×C3⋊C8—31no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—61no—
83C4×C3⋊C8C2×D311yescharacteristic
84C4×C3⋊C8C2×D311yescharacteristic
85C32×Q8—42no—
86C2×C32×C4—41no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—41no—
91#634—42no—
92C2×C3×Dic3—41no—
93C2×C3×Dic3—41no—
94C3×Dic6—42no—
95C3×Dic6—42no—
96C3⋊(C3⋊C8)Q1614yes—
97C3×C3⋊C8—22no—
98C3×C3⋊C8—22no—
99#500—91no—
100#500—91no—
101#487—31no—
102#487—31no—
103#487—91no—
104#487—91no—
105C82—91no—
106C2×C3×Q8—21no—
107C2×C3×Q8—21no—
108C2×C3×Q8—41no—
109C2×C3×Q8—61no—
110C2×C3×Q8—61no—
111C2×Dic6—21no—
112C2×Dic6—21no—
113C2×Dic6—61no—
114C2×Dic6—61no—
115C2×Dic6—121no—
116C2×C3×C8—32no—
117C2×C3×C8—32no—
118C3×C4⋊C4—22no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—41no—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C42—21no—
129C3×C42C22×D311yescharacteristic
130C3×C42C22×D311yescharacteristic
131C4⋊Dic3—21no—
132C4⋊Dic3—21no—
133C4⋊Dic3—21no—
134C4⋊Dic3—21no—
135C4⋊Dic3—62no—
136C4⋊Dic3—61no—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140C4⋊Dic3—121no—
141C2×C3⋊C8—32no—
142C2×C3⋊C8—32no—
143C2×C3⋊C8—62no—
144C2×C3⋊C8#6712yes—
145C2×C3⋊C8#6712yes—
146C22×C32#12711yescharacteristic
147C32×C4—81no—
148C32×C4C2×Q1612yes—
149C32×C4#13512yes—
150C32×C4#13512yes—
151C3⋊Dic3—81no—
152C3×Dic3—81no—
153C3×Dic3—81no—
154C4⋊Q8—31no—
155C4⋊Q8—31no—
156C4⋊Q8—91no—
157C4⋊Q8D3211yescharacteristic
158#107—182no—
159#107—182no—
160#103—62no—
161#103—62no—
162#103—182no—
163#103—182no—
164C4×C8—31no—
165C4×C8—31no—
166C4×C8—91no—
167C3×Q8—42no—
168C3×Q8—42no—
169C3×Q8—82no—
170C3×Q8—122no—
171C3×Q8—122no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—42no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4—121no—
179C2×C3×C4—121no—
180C2×C3×C4D3×D411yescharacteristic
181C2×C3×C4D3×D411yescharacteristic
182C2×C3×C4D3×D411yescharacteristic
183C2×C3×C4D3×D411yescharacteristic
184C2×C3×C4C2×#6711yescharacteristic
185C2×C3×C4C2×#6711yescharacteristic
186C2×Dic3—41no—
187C2×Dic3—41no—
188C2×Dic3—122no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191Dic6—42no—
192Dic6—42no—
193Dic6—122no—
194Dic6—122no—
195Dic6—242no—
196C3×C8—62no—
197C3×C8—62no—
198C3⋊C8—22no—
199C3⋊C8—22no—
200C3⋊C8—34no—
201C3⋊C8—34no—
202C3⋊C8—64no—
203C2×C32#49411yescharacteristic
204C2×C32#49511yescharacteristic
205C2×C32#49511yescharacteristic
206C2×Q8—21no—
207C2×Q8—61no—
208C2×Q8—61no—
209C2×Q8—181no—
210C2×C8—32no—
211C2×C8—32no—
212C2×C8—92no—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—61no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C4⋊C4—61no—
219C4⋊C4—181no—
220C4⋊C4—181no—
221C42C2×D3211yescharacteristic
222C22×C3—21no—
223C22×C3#94011yescharacteristic
224C22×C3#94011yescharacteristic
225C3×C4—22no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—82no—
229C3×C4—81no—
230C3×C4—81no—
231C3×C4—241no—
232C3×C4—241no—
233C3×C4#91612yes—
234C3×C4#91612yes—
235C3×C4D3×Q1612yes—
236C3×C4D3×Q1612yes—
237C3×C4#95012yes—
238C3×C4#95012yes—
239Dic3—81no—
240Dic3—81no—
241Dic3—242no—
242Dic3—241no—
243Dic3—241no—
244C32#171011yescharacteristic, complemented, Sylow
245Q8—42no—
246Q8—122no—
247Q8—122no—
248Q8—362no—
249C2×C4—41no—
250C2×C4—121no—
251C2×C4—121no—
252C2×C4—361no—
253C2×C4D3×#6711yescharacteristic
254C2×C4D3×#6711yescharacteristic
255C2×C4#381111yescharacteristic
256C8—62no—
257C8—62no—
258C8—94no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3#505911yescharacteristic
263C2×C3#505911yescharacteristic
264C2×C3#516811yescharacteristic
265C2×C3#516811yescharacteristic
266C2×C3#518311yescharacteristic
267C2×C3#518311yescharacteristic
268C22#6397911yescharacteristic
269C4—81no—
270C4—241no—
271C4—241no—
272C4—721no—
273C4#6393512yes—
274C4#6394412yes—
275C4#6394712yes—
276C3—21no—
277C3#7121411yescharacteristic, complemented
278C3#7121411yescharacteristic, complemented
279C2#1059147311yescharacteristic
280C2#1059160611yescharacteristic
281C2#1059162811yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#127
hypercenterC4⋊Q8D32
hypocenterC32#1710
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
244. C32#1710semidirect
277. C3#71214semidirect
278. C3#71214semidirect

Maximal subgroups

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

subgroupindex
#105927772
C3×#50932
C3×#50792
#105903122
#105902882
#105902872
C3⋊C822
#712143