Finite Group Databasebeta

← #11779471

Subgroups — #11779471

Order 1152.

473 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 473 conjugacy classes of subgroups — too many to draw. Only its 94 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
1Dic62C211yesmaximal, characteristic
2#10592398C211yesmaximal, characteristic
3#10590283C212yesmaximal
4C3×#4456C212yesmaximal
5#10589096C211yesmaximal, characteristic
6#68267—32nomaximal
7C2×#3746—22no—
8#64078C2211yescharacteristic
9#64078C2211yescharacteristic
10C3×C4×Dic6C2212yes—
11#63918—22no—
12Dic3×Dic6—22no—
13#63840—22no—
14C32×C4×C8C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2212yes—
16#63575—22no—
17#63566—22no—
18Q8×Dic6—32no—
19#5021—32no—
20#4850—32no—
21#4699—32no—
22#4699—61no—
23C3×Q8⋊C8—32no—
24#4481—32no—
25#4456D312yes—
26C2×#634—21no—
27C2×#634D412yes—
28C2×C3×Dic6D412yes—
29C2×#627—22no—
30C2×C32×C8—21no—
31C32×C42C2311yescharacteristic
32C4⋊(C3⋊Dic3)—22no—
33C4⋊(C3⋊Dic3)—22no—
34#3746—44no—
35C3×C4⋊Dic3D412yes—
36C3×Dic3⋊C4—22no—
37C3×C4×Dic3—22no—
38C2×C3×C3⋊C8—22no—
39Dic3⋊Dic3—24no—
40Dic32—22no—
41#1633—91noSylow
42C3×C4×Q8—32no—
43Q8×Dic3—62no—
44C2×Dic12—64no—
45C2×Dic12—64no—
46#888—62no—
47#888—64no—
48#869—32no—
49#869—32no—
50#869—61no—
51#869—61no—
52#869—62no—
53C4×Dic6—62no—
54C4×Dic6C2×D312yes—
55C3×C4⋊C8—32no—
56C3×C4×C8—21no—
57C3×C4×C8C2×D312yes—
58#835—62no—
59#818—62no—
60#816—62no—
61#807—62no—
62C4⋊(C3⋊C8)C2×D312yes—
63C2×C32×C4C2×D412yes—
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—41no—
67#634—42no—
68#634—42no—
69C2×C3×Dic3—22no—
70C2×C3×Dic3—22no—
71C3×Dic6—22no—
72C3×Dic6Q1614yescomplemented
73#627—82no—
74C32×C8—22no—
75C3×C3⋊C8—42no—
76Q82—91no—
77#494—91no—
78#477—92no—
79#333—91no—
80Q8⋊C8—32no—
81C2×C3×Q8—32no—
82C2×Dic6—34no—
83C2×Dic6—62no—
84C2×Dic6—62no—
85C2×Dic6—62no—
86C2×Dic6—64no—
87C2×Dic6D1212yes—
88C2×C3×C8—22no—
89C2×C3×C8—22no—
90C2×C3×C8—62no—
91C3×C4⋊C4—32no—
92C3×C4⋊C4—62no—
93C3×C42—21no—
94C3×C42—62no—
95C3×C42C22×D312yes—
96C4⋊Dic3—64no—
97C4⋊Dic3—62no—
98C4⋊Dic3—62no—
99C4⋊Dic3—62no—
100C4⋊Dic3—62no—
101C4⋊Dic3—122no—
102C4⋊Dic3—122no—
103C4⋊Dic3D1212yes—
104Dic3⋊C4—22no—
105Dic3⋊C4—64no—
106C4×Dic3—22no—
107C4×Dic3—64no—
108C2×C3⋊C8—22no—
109Dic12—128no—
110Dic12—128no—
111C22×C32#12011yescharacteristic
112C32×C4—21no—
113C32×C4C2×Q1612yes—
114C32×C4#13712yes—
115C3⋊Dic3—42no—
116C3⋊Dic3—81no—
117C3×Dic3—24no—
118C3×Dic3—42no—
119C2×Q16—182no—
120C4⋊Q8—91no—
121C4⋊Q8—91no—
122C4⋊Q8—182no—
123C4⋊Q8—182no—
124C4×Q8—32no—
125C4×Q8—182no—
126#107—182no—
127C4⋊C8—32no—
128#103—182no—
129C4×C8D3211yescharacteristic
130C3×Q8—34no—
131C3×Q8—62no—
132C2×C3×C4—22no—
133C2×C3×C4—21no—
134C2×C3×C4—62no—
135C2×C3×C4—62no—
136C2×C3×C4C2×D1212yes—
137C2×C3×C4D3×D412yes—
138C2×C3×C4D3×D412yes—
139C2×Dic3—22no—
140C2×Dic3—22no—
141C2×Dic3—64no—
142C2×Dic3—122no—
143C2×Dic3—122no—
144C2×Dic3—122no—
145Dic6—22no—
146Dic6—124no—
147Dic6—124no—
148Dic6—124no—
149Dic6—124no—
150Dic6—244no—
151Dic6Dic1214yescomplemented
152C3×C8—24no—
153C3×C8—24no—
154C3×C8—122no—
155C3⋊C8—42no—
156C2×C32#45112yes—
157C2×C32#45311yescharacteristic
158C2×Q8—32no—
159C2×Q8—92no—
160C2×Q8—182no—
161C2×Q8—181no—
162Q16—364no—
163C2×C8—21no—
164C2×C8—62no—
165C4⋊C4—32no—
166C4⋊C4—62no—
167C4⋊C4—184no—
168C4⋊C4—182no—
169C4⋊C4—182no—
170C42—62no—
171C42—182no—
172C42C2×D3211yescharacteristic
173C22×C3—21no—
174C22×C3#88212yes—
175C3×C4—22no—
176C3×C4—22no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—64no—
180C3×C4—122no—
181C3×C4C2×Dic1212yes—
182C3×C4#90912yes—
183C3×C4#91512yes—
184C3×C4D3×Q1612yes—
185Dic3—24no—
186Dic3—42no—
187Dic3—124no—
188Dic3—242no—
189Dic3—242no—
190Dic3—242no—
191C32#163311yescharacteristic, complemented, Sylow
192Q8—34no—
193Q8—62no—
194Q8—362no—
195Q8—362no—
196Q8—722no—
197C2×C4—62no—
198C2×C4—62no—
199C2×C4—182no—
200C2×C4—361no—
201C2×C4D3×D1212yes—
202C2×C4#381111yescharacteristic
203C8—22no—
204C8—122no—
205C2×C3—21no—
206C2×C3—22no—
207C2×C3#473912yes—
208C2×C3#480912yes—
209C2×C3#482212yes—
210C22#6392311yescharacteristic
211C4—21no—
212C4—64no—
213C4—122no—
214C4—362no—
215C4—721no—
216C4D3×Dic1212yes—
217C4#6380012yes—
218C3—21no—
219C3#6826712yescomplemented
220C2#1059039711yescharacteristic
221C2#1059095212yes—
subgroupG/H
centerC22#63923
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socle, prime radicalC22×C32#120
hypercenterC4×C8D32
hypocenterC32#1633
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
72. C3×Dic6Q16semidirect
151. Dic6Dic12semidirect
191. C32#1633semidirect
219. C3#68267semidirect

Maximal subgroups

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

subgroupindex
Dic622
#105923982
#105902832
C3×#44562
#105890962
#682673