Finite Group Databasebeta

← #11779465

Subgroups — #11779465

Order 1152.

473 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C3×#5722C211yesmaximal, characteristic
2#10592791C211yesmaximal, characteristic
3#10590283C212yesmaximal
4C3×#4546C211yesmaximal, characteristic
5#10589083C212yesmaximal
6#71940—31nomaximal
7#68505—31nomaximal
8C32×C4⋊Q8C2211yescharacteristic
9C2×#3756—22no—
10#64078C2211yescharacteristic
11C3×#944—22no—
12C3×#888—22no—
13C3×#887—22no—
14C3×C4×Dic6C2212yes—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2212yes—
17#63575—22no—
18#63566—22no—
19C3×Q82—31no—
20#5722D311yescharacteristic
21#5092—31no—
22#5092—31no—
23#5092—61no—
24#5021—32no—
25#4850—32no—
26C3×#333—31no—
27#4546D311yescharacteristic
28#4535—32no—
29#4484—32no—
30C2×C32×Q8D412yes—
31C2×#634—21no—
32C2×C3×Dic6—22no—
33C2×C3×Dic6D412yes—
34C32×C4⋊C4—22no—
35C32×C42C2311yescharacteristic
36#3756—44no—
37C4⋊(C3⋊Dic3)—22no—
38C2×C3⋊(C3⋊C8)—21no—
39C3×C4⋊Dic3D412yes—
40C3×Dic3⋊C4—24no—
41C3×Dic3⋊C4—22no—
42C3×C4×Dic3—22no—
43C3×C4×Dic3—22no—
44C2×C3×C3⋊C8—22no—
45#1633—91noSylow
46C3×C4⋊Q8—21no—
47C3×C4⋊Q8—62no—
48C3×C4⋊Q8—62no—
49C3×C4⋊Q8C2×D311yescharacteristic
50C3×C4⋊Q8C2×D311yescharacteristic
51C3×C4×Q8—32no—
52C3×C4×Q8—62no—
53#944—22no—
54C2×#216—64no—
55C2×#216—62no—
56C2×#216—62no—
57#888—22no—
58#887—22no—
59#869—31no—
60#869—31no—
61#869—61no—
62C4×Dic6C2×D312yes—
63C3×C4⋊C8—32no—
64#835—62no—
65#818—62no—
66#816—62no—
67#807—62no—
68C4⋊(C3⋊C8)C2×D312yes—
69C4×C3⋊C8—31no—
70C4×C3⋊C8—31no—
71C4×C3⋊C8—61no—
72C32×Q8—42no—
73C2×C32×C4—22no—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D412yes—
76C2×C3⋊Dic3—41no—
77#634—42no—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80C3×Dic6—22no—
81C3×Dic6—82no—
82C3×Dic6Q1614yescomplemented
83C3⋊(C3⋊C8)—22no—
84C3×C3⋊C8—42no—
85Q82—31no—
86#494—91no—
87#477—92no—
88#333—31no—
89Q8⋊C8—92no—
90C2×C3×Q8—22no—
91C2×C3×Q8—32no—
92C2×C3×Q8—62no—
93C2×C3×Q8D1212yes—
94C2×C3×Q8#6712yes—
95C2×Dic6—22no—
96C2×Dic6—62no—
97C2×Dic6—61no—
98C2×Dic6—61no—
99C2×Dic6#6712yes—
100C2×C3×C8—62no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C3×C4⋊C4—32no—
104C3×C4⋊C4—42no—
105C3×C4⋊C4—64no—
106C3×C4⋊C4—62no—
107C3×C42—21no—
108C3×C42—62no—
109C3×C42—62no—
110C3×C42C22×D311yescharacteristic
111C3×C42C22×D311yescharacteristic
112#216—124no—
113#216—124no—
114#216—128no—
115C4⋊Dic3—62no—
116C4⋊Dic3—62no—
117C4⋊Dic3—122no—
118C4⋊Dic3#6712yes—
119Dic3⋊C4—24no—
120Dic3⋊C4—22no—
121C4×Dic3—22no—
122C4×Dic3—22no—
123C2×C3⋊C8—22no—
124C2×C3⋊C8—62no—
125C2×C3⋊C8—61no—
126C2×C3⋊C8—61no—
127C22×C32#12011yescharacteristic
128C32×C4—21no—
129C32×C4—42no—
130C32×C4C2×Q1612yes—
131C32×C4#13712yes—
132C3⋊Dic3—81no—
133C3×Dic3—24no—
134C3×Dic3—42no—
135C2×Q16—182no—
136C4⋊Q8—62no—
137C4⋊Q8—62no—
138C4⋊Q8—91no—
139C4⋊Q8D3211yescharacteristic
140C4×Q8—32no—
141C4×Q8—62no—
142#107—182no—
143C4⋊C8—32no—
144#103—182no—
145C4×C8—91no—
146C3×Q8—34no—
147C3×Q8—42no—
148C3×Q8—42no—
149C3×Q8—44no—
150C3×Q8—62no—
151C3×Q8—242no—
152C2×C3×C4—22no—
153C2×C3×C4—22no—
154C2×C3×C4—21no—
155C2×C3×C4—22no—
156C2×C3×C4—42no—
157C2×C3×C4—62no—
158C2×C3×C4—62no—
159C2×C3×C4C2×D1211yescharacteristic
160C2×C3×C4D3×D412yes—
161C2×C3×C4C2×#6711yescharacteristic
162C2×C3×C4C2×#6712yes—
163C2×Dic3—22no—
164C2×Dic3—22no—
165C2×Dic3—122no—
166C2×Dic3—121no—
167C2×Dic3—121no—
168Dic6—22no—
169Dic6—82no—
170Dic6—124no—
171Dic6—122no—
172Dic6—122no—
173Dic6#21614yescomplemented
174C3×C8—122no—
175C3⋊C8—42no—
176C3⋊C8—64no—
177C3⋊C8—62no—
178C3⋊C8—62no—
179C2×C32#45112yes—
180C2×C32#45311yescharacteristic
181C2×Q8—32no—
182C2×Q8—62no—
183C2×Q8—181no—
184C2×Q8#62612yes—
185Q16—364no—
186C2×C8—62no—
187C2×C8—181no—
188C4⋊C4—22no—
189C4⋊C4—32no—
190C4⋊C4—64no—
191C4⋊C4—62no—
192C4⋊C4—182no—
193C42—62no—
194C42—62no—
195C42C2×D3211yescharacteristic
196C22×C3—21no—
197C22×C3#88211yescharacteristic
198C22×C3#95311yescharacteristic
199C3×C4—22no—
200C3×C4—21no—
201C3×C4—21no—
202C3×C4—22no—
203C3×C4—22no—
204C3×C4—42no—
205C3×C4—42no—
206C3×C4—64no—
207C3×C4—82no—
208C3×C4—122no—
209C3×C4#91512yes—
210C3×C4D3×Q1612yes—
211C3×C4#94212yes—
212C3×C4C2×#21612yes—
213Dic3—24no—
214Dic3—42no—
215Dic3—242no—
216Dic3—241no—
217Dic3—241no—
218C32#163311yescharacteristic, complemented, Sylow
219Q8—34no—
220Q8—42no—
221Q8—62no—
222Q8—242no—
223Q8—362no—
224C2×C4—22no—
225C2×C4—62no—
226C2×C4—62no—
227C2×C4—361no—
228C2×C4C2×#62611yescharacteristic
229C2×C4D3×#6712yes—
230C8—122no—
231C8—182no—
232C2×C3—21no—
233C2×C3—22no—
234C2×C3#474711yescharacteristic
235C2×C3#480912yes—
236C2×C3#522812yes—
237C2×C3#524111yescharacteristic
238C22#6397711yescharacteristic
239C4—21no—
240C4—42no—
241C4—64no—
242C4—122no—
243C4—721no—
244C4D3×#21612yes—
245C4#6394612yes—
246C3—21no—
247C3#6850511yescharacteristic, complemented
248C3#7194011yescharacteristic, complemented
249C2#1059151011yescharacteristic
250C2#1059159512yes—
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socle, prime radicalC22×C32#120
hypercenterC4⋊Q8D32
hypocenterC32#1633
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
82. C3×Dic6Q16semidirect
173. Dic6#216semidirect
218. C32#1633semidirect
247. C3#68505semidirect
248. C3#71940semidirect

Maximal subgroups

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

subgroupindex
C3×#57222
#105927912
#105902832
C3×#45462
#105890832
#719403
#685053