Finite Group Databasebeta

← #11782713

Subgroups — #11782713

Order 1152.

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

normal subgroups only

This group has 401 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#10592779C211yesmaximal, characteristic
2C3×#5080C211yesmaximal, characteristic
3C3×#5079C211yesmaximal, characteristic
4#10590387C211yesmaximal, characteristic
5#10590303C211yesmaximal, characteristic
6#10590288C211yesmaximal, characteristic
7#10589079C211yesmaximal, characteristic
8#71337—31nomaximal
9#71217—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3718—22no—
15#63635—22no—
16C4×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#835—22no—
18C3×#808—22no—
19C3×C4×C3⋊C8C2211yescharacteristic
20C3×C4×C3⋊C8C2211yescharacteristic
21#63573—22no—
22#63567—22no—
23C3×#498—31no—
24C3×#487—31no—
25#5093—31no—
26#5092—31no—
27#5092—31no—
28#5080—31no—
29#5080—31no—
30#5080—31no—
31#5080—61no—
32#5080D311yescharacteristic
33#5079D311yescharacteristic
34#4681—31no—
35#4680—31no—
36#4454—31no—
37#4454—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#3718—44no—
55#1716—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—
63#869—31no—
64#869—31no—
65#869—61no—
66#869C2×D311yescharacteristic
67#869C2×D311yescharacteristic
68C3×#106—62no—
69C3×#103—62no—
70C3×C4×C8—31no—
71C3×C4×C8—31no—
72#835—22no—
73#817—62no—
74#816—62no—
75#810—62no—
76#808—22no—
77#808—62no—
78#808—62no—
79#808—64no—
80#808—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⋊C8—22no—
100#498—31no—
101#498—91no—
102#498—91no—
103#494—91no—
104#487—31no—
105#487—91no—
106#322—91no—
107C2×C3×Q8—21no—
108C2×C3×Q8—21no—
109C2×C3×Q8—41no—
110C2×C3×Q8—61no—
111C2×C3×Q8—61no—
112C2×Dic6—21no—
113C2×Dic6—21no—
114C2×Dic6—61no—
115C2×Dic6—61no—
116C2×Dic6—121no—
117C2×C3×C8—32no—
118C2×C3×C8—32no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—21no—
123C3×C4⋊C4—21no—
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—
134C4⋊Dic3—21no—
135C4⋊Dic3—21no—
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—62no—
139C4⋊Dic3—61no—
140C4⋊Dic3—61no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—121no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—32no—
146C2×C3⋊C8—62no—
147C2×C3⋊C8#6712yes—
148C2×C3⋊C8#6712yes—
149C22×C32#12711yescharacteristic
150C32×C4—81no—
151C32×C4C2×SD1612yes—
152C32×C4#13712yes—
153C32×C4#13712yes—
154C3⋊Dic3—81no—
155C3×Dic3—81no—
156C3×Dic3—81no—
157C2×Q16—182no—
158C4⋊Q8—31no—
159C4⋊Q8—31no—
160C4⋊Q8—91no—
161C4⋊Q8D3211yescharacteristic
162#106—62no—
163#106—182no—
164#106—182no—
165#103—62no—
166#103—182no—
167C4×C8—31no—
168C4×C8—31no—
169C4×C8—91no—
170C3×Q8—42no—
171C3×Q8—42no—
172C3×Q8—82no—
173C3×Q8—122no—
174C3×Q8—122no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4—41no—
180C2×C3×C4—41no—
181C2×C3×C4—121no—
182C2×C3×C4—121no—
183C2×C3×C4D3×D411yescharacteristic
184C2×C3×C4D3×D411yescharacteristic
185C2×C3×C4D3×D411yescharacteristic
186C2×C3×C4D3×D411yescharacteristic
187C2×C3×C4C2×#6711yescharacteristic
188C2×C3×C4C2×#6711yescharacteristic
189C2×Dic3—41no—
190C2×Dic3—41no—
191C2×Dic3—122no—
192C2×Dic3—121no—
193C2×Dic3—121no—
194Dic6—42no—
195Dic6—42no—
196Dic6—122no—
197Dic6—122no—
198Dic6—242no—
199C3×C8—62no—
200C3×C8—62no—
201C3⋊C8—22no—
202C3⋊C8—22no—
203C3⋊C8—34no—
204C3⋊C8—34no—
205C3⋊C8—64no—
206C2×C32#49211yescharacteristic
207C2×C32#49711yescharacteristic
208C2×C32#49711yescharacteristic
209C2×Q8—21no—
210C2×Q8—61no—
211C2×Q8—61no—
212C2×Q8—181no—
213Q16—364no—
214C2×C8—32no—
215C2×C8—32no—
216C2×C8—92no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—61no—
220C4⋊C4—61no—
221C4⋊C4—61no—
222C4⋊C4—61no—
223C4⋊C4—181no—
224C4⋊C4—181no—
225C42C2×D3211yescharacteristic
226C22×C3—21no—
227C22×C3#94011yescharacteristic
228C22×C3#94011yescharacteristic
229C3×C4—22no—
230C3×C4—22no—
231C3×C4—22no—
232C3×C4—82no—
233C3×C4—81no—
234C3×C4—81no—
235C3×C4—241no—
236C3×C4—241no—
237C3×C4D3×SD1612yes—
238C3×C4D3×SD1612yes—
239C3×C4#91512yes—
240C3×C4#91812yes—
241C3×C4#94212yes—
242C3×C4#95112yes—
243Dic3—81no—
244Dic3—81no—
245Dic3—242no—
246Dic3—241no—
247Dic3—241no—
248C32#171611yescharacteristic, complemented, Sylow
249Q8—42no—
250Q8—122no—
251Q8—122no—
252Q8—362no—
253C2×C4—41no—
254C2×C4—121no—
255C2×C4—121no—
256C2×C4—361no—
257C2×C4D3×#6711yescharacteristic
258C2×C4D3×#6711yescharacteristic
259C2×C4#381111yescharacteristic
260C8—62no—
261C8—62no—
262C8—94no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3#506011yescharacteristic
267C2×C3#508611yescharacteristic
268C2×C3#516711yescharacteristic
269C2×C3#517511yescharacteristic
270C2×C3#517511yescharacteristic
271C2×C3#519011yescharacteristic
272C22#6397911yescharacteristic
273C4—81no—
274C4—241no—
275C4—241no—
276C4—721no—
277C4#6392912yes—
278C4#6394012yes—
279C4#6394812yes—
280C3—21no—
281C3#7121711yescharacteristic, complemented
282C3#7133711yescharacteristic, complemented
283C2#1059149111yescharacteristic
284C2#1059160811yescharacteristic
285C2#1059162011yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#127
hypercenterC4⋊Q8D32
hypocenterC32#1716
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
248. C32#1716semidirect
281. C3#71217semidirect
282. C3#71337semidirect

Maximal subgroups

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

subgroupindex
#105927792
C3×#50802
C3×#50792
#105903872
#105903032
#105902882
#105890792
#713373
#712173