Finite Group Databasebeta

← #11782489

Subgroups — #11782489

Order 1152.

409 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 409 conjugacy classes of subgroups — too many to draw. Only its 116 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
2C3×#4681C211yesmaximal, characteristic
3#10590386C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic
5#10590303C211yesmaximal, characteristic
6#10590303C211yesmaximal, characteristic
7C3×C8×C3⋊C8C211yesmaximal, characteristic
8#71212—31nomaximal
9#68063—31nomaximal
10#64078C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3719—22no—
15C32×C4×C8C2211yescharacteristic
16#63643—22no—
17C3×#816—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63575—22no—
21#63573—22no—
22#63573—22no—
23C3×#487—31no—
24#5092—31no—
25#5080—31no—
26#5080—31no—
27#5078—31no—
28#4699—31no—
29#4682—31no—
30#4681—31no—
31#4681—31no—
32#4681—61no—
33#4681D311yescharacteristic
34#4680—31no—
35#4680—31no—
36C3×C82—31no—
37C8×C3⋊C8D311yescharacteristic
38C2×#634—21no—
39C2×#634—21no—
40C2×C3×Dic6—21no—
41C2×C3×Dic6—21no—
42C2×C32×C8D412yes—
43C32×C42C2311yescharacteristic
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
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#3719—44no—
55#1707—91noSylow
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C2×#216—62no—
59C2×Dic12—62no—
60#869—31no—
61#869—31no—
62#869—31no—
63#869—31no—
64#869—61no—
65#869—61no—
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68C3×#103—62no—
69C3×C4×C8—21no—
70C3×C4×C8—31no—
71C3×C4×C8—31no—
72C3×C4×C8C2×D311yescharacteristic
73C3×C4×C8C2×D311yescharacteristic
74#818—62no—
75#817—62no—
76#817—62no—
77#816—22no—
78#816—64no—
79#816—62no—
80#816—62no—
81#808—62no—
82#808—62no—
83#807—62no—
84C4×C3⋊C8C2×D311yescharacteristic
85C4×C3⋊C8C2×D311yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C3⋊Dic3—41no—
90C2×C3⋊Dic3—41no—
91#634—42no—
92#634—42no—
93C2×C3×Dic3—41no—
94C2×C3×Dic3—41no—
95C3×Dic6—42no—
96C3×Dic6—42no—
97C32×C8—22no—
98C3×C3⋊C8SD1614yes—
99C3×C3⋊C8Q1614yescomplemented
100#500—91no—
101#498—91no—
102#498—91no—
103#494—91no—
104#487—31no—
105#487—91no—
106C82—31no—
107C2×C3×Q8—61no—
108C2×C3×Q8—61no—
109C2×Dic6—21no—
110C2×Dic6—21no—
111C2×Dic6—62no—
112C2×Dic6—61no—
113C2×Dic6—61no—
114C2×Dic6—61no—
115C2×Dic6—61no—
116C2×Dic6—121no—
117C2×C3×C8—22no—
118C2×C3×C8—32no—
119C2×C3×C8—32no—
120C2×C3×C8D1212yes—
121C2×C3×C8#6712yes—
122C3×C4⋊C4—61no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—61no—
125C3×C4⋊C4—61no—
126C3×C42—21no—
127C3×C42C22×D311yescharacteristic
128C3×C42C22×D311yescharacteristic
129#216—124no—
130C4⋊Dic3—21no—
131C4⋊Dic3—21no—
132C4⋊Dic3—21no—
133C4⋊Dic3—21no—
134C4⋊Dic3—62no—
135C4⋊Dic3—61no—
136C4⋊Dic3—61no—
137C4⋊Dic3—61no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—121no—
144C4⋊Dic3—121no—
145C4⋊Dic3—121no—
146C2×C3⋊C8D1212yes—
147C2×C3⋊C8D1212yes—
148Dic12—124no—
149C22×C32#12711yescharacteristic
150C32×C4C2×SD1612yes—
151C32×C4C2×Q1612yes—
152C32×C4#13512yes—
153C3⋊Dic3—81no—
154C3⋊Dic3—81no—
155C3×Dic3—81no—
156C3×Dic3—81no—
157C2×Q16—182no—
158C4⋊Q8—31no—
159C4⋊Q8—31no—
160C4⋊Q8—91no—
161C4⋊Q8—91no—
162#107—182no—
163#106—182no—
164#106—182no—
165#103—62no—
166#103—182no—
167C4×C8—31no—
168C4×C8—31no—
169C4×C8D3211yescharacteristic
170C3×Q8—122no—
171C3×Q8—122no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—121no—
176C2×C3×C4—121no—
177C2×C3×C4C2×D1211yescharacteristic
178C2×C3×C4C2×D1211yescharacteristic
179C2×C3×C4C2×D1211yescharacteristic
180C2×C3×C4D3×D411yescharacteristic
181C2×C3×C4D3×D411yescharacteristic
182C2×C3×C4C2×#6711yescharacteristic
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187C2×Dic3—121no—
188C2×Dic3—121no—
189C2×Dic3—121no—
190C2×Dic3—121no—
191Dic6—42no—
192Dic6—42no—
193Dic6—124no—
194Dic6—122no—
195Dic6—122no—
196Dic6—122no—
197Dic6—122no—
198Dic6—242no—
199C3×C8—22no—
200C3×C8—22no—
201C3×C8—34no—
202C3×C8—34no—
203C3×C8—42no—
204C3⋊C8#20414yes—
205C3⋊C8Dic1214yescomplemented
206C2×C32#49211yescharacteristic
207C2×C32#49411yescharacteristic
208C2×C32#49511yescharacteristic
209C2×Q8—61no—
210C2×Q8—61no—
211C2×Q8—181no—
212C2×Q8—181no—
213Q16—364no—
214C2×C8—32no—
215C2×C8—32no—
216C2×C8#62612yes—
217C4⋊C4—61no—
218C4⋊C4—61no—
219C4⋊C4—61no—
220C4⋊C4—61no—
221C4⋊C4—181no—
222C4⋊C4—181no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C42C2×D3211yescharacteristic
226C22×C3—21no—
227C22×C3#87411yescharacteristic
228C22×C3#94011yescharacteristic
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—241no—
233C3×C4—241no—
234C3×C4C2×#20412yes—
235C3×C4#90412yes—
236C3×C4C2×Dic1212yes—
237C3×C4D3×SD1612yes—
238C3×C4D3×Q1612yes—
239C3×C4#95012yes—
240Dic3—81no—
241Dic3—81no—
242Dic3—242no—
243Dic3—242no—
244Dic3—241no—
245Dic3—241no—
246Dic3—241no—
247Dic3—241no—
248C32#170711yescharacteristic, complemented, Sylow
249Q8—122no—
250Q8—122no—
251Q8—362no—
252Q8—362no—
253C2×C4—121no—
254C2×C4—121no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4D3×D1211yescharacteristic
258C2×C4D3×D1211yescharacteristic
259C2×C4C2×#62611yescharacteristic
260C8—22no—
261C8—34no—
262C8—34no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3#469311yescharacteristic
267C2×C3#469611yescharacteristic
268C2×C3#469911yescharacteristic
269C2×C3#505911yescharacteristic
270C2×C3#517511yescharacteristic
271C2×C3#518311yescharacteristic
272C22#6391111yescharacteristic
273C4—241no—
274C4—241no—
275C4—721no—
276C4—721no—
277C4D3×#20412yes—
278C4D3×Dic1212yes—
279C4#6382912yes—
280C3—21no—
281C3#6806311yescharacteristic, complemented
282C3#7121211yescharacteristic, complemented
283C2#1059037011yescharacteristic
284C2#1059087711yescharacteristic
285C2#1059089611yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#127
hypercenterC4×C8D32
hypocenterC32#1707
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
99. C3×C3⋊C8Q16semidirect
205. C3⋊C8Dic12semidirect
248. C32#1707semidirect
281. C3#68063semidirect
282. C3#71212semidirect

Maximal subgroups

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

subgroupindex
#105923802
C3×#46812
#105903862
#105903112
#105903032
C3×C8×C3⋊C82
#712123
#680633