Finite Group Databasebeta

← #11782478

Subgroups — #11782478

Order 1152.

421 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 421 conjugacy classes of subgroups — too many to draw. Only its 106 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#10592791C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic
3C3×#5080C211yesmaximal, characteristic
4#10590312C211yesmaximal, characteristic
5#10590303C211yesmaximal, characteristic
6#10590287C211yesmaximal, characteristic
7C3⋊C82C211yesmaximal, characteristic
8#71333—31nomaximal
9#71212—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3756—22no—
12#64078C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C3×#869C2211yescharacteristic
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#810—22no—
17C3×#808—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63576—22no—
21#63573—22no—
22#63566—22no—
23C3×#498—31no—
24C3×#487—31no—
25#5093D311yescharacteristic
26#5092—31no—
27#5092—31no—
28#5092—61no—
29#5080—31no—
30#5080D311yescharacteristic
31#5079—31no—
32#5078—31no—
33#5078—31no—
34#4681—31no—
35#4680—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
45#3756—44no—
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
48C2×C3⋊(C3⋊C8)D412yes—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8D412yes—
54C2×C3×C3⋊C8D412yes—
55#1707—91noSylow
56C3×C4⋊Q8—21no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8—31no—
59C3×C4⋊Q8C2×D311yescharacteristic
60C3×C4⋊Q8C2×D311yescharacteristic
61C2×#216—62no—
62C2×#216—62no—
63C2×#216—64no—
64#869—31no—
65#869—31no—
66#869—61no—
67#869C2×D311yescharacteristic
68#869C2×D311yescharacteristic
69C3×#106—62no—
70C3×#103—62no—
71C3×C4×C8—31no—
72C3×C4×C8—31no—
73#835—62no—
74#817—62no—
75#816—62no—
76#810—22no—
77#808—22no—
78#808—62no—
79#807—62no—
80#807—62no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—31no—
83C4×C3⋊C8—61no—
84C4×C3⋊C8C2×D311yescharacteristic
85C4×C3⋊C8C2×D311yescharacteristic
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—
94C2×C3×Dic3—41no—
95C3×Dic6—42no—
96C3×Dic6—42no—
97C3⋊(C3⋊C8)SD1614yes—
98C3×C3⋊C8—22no—
99C3×C3⋊C8Q1614yescomplemented
100#500—91no—
101#498—31no—
102#498—91no—
103#494—91no—
104#487—31no—
105#487—91no—
106C82—91no—
107C2×C3×Q8—22no—
108C2×C3×Q8—21no—
109C2×C3×Q8—21no—
110C2×C3×Q8—61no—
111C2×C3×Q8—61no—
112C2×Dic6—21no—
113C2×Dic6—21no—
114C2×Dic6—62no—
115C2×Dic6—61no—
116C2×Dic6—61no—
117C2×C3×C8—32no—
118C2×C3×C8—32no—
119C3×C4⋊C4—21no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—41no—
124C3×C4⋊C4—41no—
125C3×C4⋊C4—61no—
126C3×C4⋊C4—61no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4—61no—
129C3×C42—21no—
130C3×C42C22×D311yescharacteristic
131C3×C42C22×D311yescharacteristic
132#216—124no—
133#216—124no—
134#216—128no—
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—121no—
144C4⋊Dic3—121no—
145C2×C3⋊C8—32no—
146C2×C3⋊C8—32no—
147C2×C3⋊C8—62no—
148C2×C3⋊C8#6712yes—
149C2×C3⋊C8#6712yes—
150C22×C32#12711yescharacteristic
151C32×C4—81no—
152C32×C4C2×SD1612yes—
153C32×C4C2×Q1612yes—
154C32×C4#13512yes—
155C3⋊Dic3—81no—
156C3×Dic3—81no—
157C3×Dic3—81no—
158C2×Q16—182no—
159C4⋊Q8—31no—
160C4⋊Q8—31no—
161C4⋊Q8—91no—
162C4⋊Q8D3211yescharacteristic
163#107—182no—
164#106—62no—
165#106—182no—
166#103—62no—
167#103—182no—
168C4×C8—31no—
169C4×C8—31no—
170C4×C8—91no—
171C3×Q8—44no—
172C3×Q8—42no—
173C3×Q8—42no—
174C3×Q8—122no—
175C3×Q8—122no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—42no—
180C2×C3×C4—41no—
181C2×C3×C4—41no—
182C2×C3×C4—121no—
183C2×C3×C4—121no—
184C2×C3×C4D3×D411yescharacteristic
185C2×C3×C4D3×D411yescharacteristic
186C2×C3×C4D3×D411yescharacteristic
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4C2×#6711yescharacteristic
189C2×C3×C4C2×#6711yescharacteristic
190C2×Dic3—41no—
191C2×Dic3—41no—
192C2×Dic3—122no—
193C2×Dic3—121no—
194C2×Dic3—121no—
195Dic6—42no—
196Dic6—42no—
197Dic6—124no—
198Dic6—122no—
199Dic6—122no—
200C3×C8—34no—
201C3×C8—62no—
202C3⋊C8—22no—
203C3⋊C8—34no—
204C3⋊C8—34no—
205C3⋊C8—64no—
206C3⋊C8#21614yescomplemented
207C2×C32#49211yescharacteristic
208C2×C32#49411yescharacteristic
209C2×C32#49511yescharacteristic
210C2×Q8—21no—
211C2×Q8—61no—
212C2×Q8—61no—
213C2×Q8—181no—
214Q16—364no—
215C2×C8—32no—
216C2×C8—32no—
217C2×C8—92no—
218C4⋊C4—21no—
219C4⋊C4—21no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—61no—
224C4⋊C4—181no—
225C4⋊C4—181no—
226C42C2×D3211yescharacteristic
227C22×C3—21no—
228C22×C3#94011yescharacteristic
229C22×C3#94011yescharacteristic
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—22no—
233C3×C4—82no—
234C3×C4—81no—
235C3×C4—81no—
236C3×C4—241no—
237C3×C4—241no—
238C3×C4D3×SD1612yes—
239C3×C4D3×SD1612yes—
240C3×C4#91612yes—
241C3×C4D3×Q1612yes—
242C3×C4C2×#21612yes—
243C3×C4#95012yes—
244Dic3—81no—
245Dic3—81no—
246Dic3—242no—
247Dic3—241no—
248Dic3—241no—
249C32#170711yescharacteristic, complemented, Sylow
250Q8—42no—
251Q8—122no—
252Q8—122no—
253Q8—362no—
254C2×C4—41no—
255C2×C4—121no—
256C2×C4—121no—
257C2×C4—361no—
258C2×C4D3×#6711yescharacteristic
259C2×C4D3×#6711yescharacteristic
260C2×C4#381111yescharacteristic
261C8—34no—
262C8—62no—
263C8—94no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3#505911yescharacteristic
268C2×C3#509211yescharacteristic
269C2×C3#516811yescharacteristic
270C2×C3#517511yescharacteristic
271C2×C3#517511yescharacteristic
272C2×C3#518311yescharacteristic
273C22#6397911yescharacteristic
274C4—81no—
275C4—241no—
276C4—241no—
277C4—721no—
278C4#6393012yes—
279C4D3×#21612yes—
280C4#6394712yes—
281C3—21no—
282C3#7121211yescharacteristic, complemented
283C3#7133311yescharacteristic, complemented
284C2#1059149211yescharacteristic
285C2#1059160611yescharacteristic
286C2#1059162611yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#127
hypercenterC4⋊Q8D32
hypocenterC32#1707
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
99. C3×C3⋊C8Q16semidirect
206. C3⋊C8#216semidirect
249. C32#1707semidirect
282. C3#71212semidirect
283. C3#71333semidirect

Maximal subgroups

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

subgroupindex
#105927912
C3×#50932
C3×#50802
#105903122
#105903032
#105902872
C3⋊C822
#713333
#712123