Finite Group Databasebeta

← #11774339

Subgroups — #11774339

Order 1152.

546 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3#10593725C211yesmaximal, characteristic
4Q8⋊#622C212yesmaximal, complemented
5#10590161C212yesmaximal, complemented
6C2×Q8×C3⋊D3C411yescharacteristic
7C32×C4×Q8C411yescharacteristic
8Q8×C3⋊Dic3C2211yescharacteristic
9C4⋊C4×C3⋊D3—21no—
10C4⋊C4×C3⋊D3C411yescharacteristic
11#64096—21no—
12#64096C2211yescharacteristic
13C42×C3⋊D3—21no—
14C42×C3⋊D3C2211yescharacteristic
15C4×#634—21no—
16C4×#634C411yescharacteristic
17#63779—21no—
18#63778—21no—
19#63778—21no—
20C4⋊#622C2212yes—
21C4×#622—21no—
22C4×#622C2212yes—
23C4×D3×Q8—62no—
24C2×C32×Q8C2×C411yescharacteristic
25Q8×C3⋊D3—22no—
26Q8×C3⋊D3C814yescomplemented
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×#634—21no—
33C2×#634C2×C411yescharacteristic
34C2×#622—22no—
35C2×#622—22no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C411yescharacteristic
38C32×C42—21no—
39C32×C42C2×C411yescharacteristic
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)C2×C411yescharacteristic
42#3750—21no—
43#3750—21no—
44#3750—21no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51#1479—91nomaximal, Sylow
52C2×D3×Q8—62no—
53C3×C4×Q8—22no—
54Q8×Dic3—62no—
55D3×C4⋊C4—62no—
56D3×C4⋊C4—64no—
57#887—62no—
58#887—64no—
59C42×D3—62no—
60C42×D3—64no—
61C4×Dic6—62no—
62C4×Dic6—64no—
63C22×C3⋊D3C22⋊C411yescharacteristic
64C32×Q8—21no—
65C32×Q8C2×C812yes—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22×C411yescharacteristic
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4×C3⋊D3—24no—
77C4×C3⋊D3—22no—
78C4×C3⋊D3—41no—
79C4×C3⋊D3—42no—
80C4×C3⋊D3C2×C812yes—
81C4×C3⋊D3M1612yes—
82#634—21no—
83#634—24no—
84#634C2×C812yes—
85#622—42no—
86#622—42no—
87C2×C4×Q8—91no—
88#431—91no—
89#431—91no—
90Q8⋊C8—92no—
91Q8⋊C8—92no—
92C2×C3×Q8—22no—
93D3×Q8—68no—
94D3×Q8—68no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—62no—
98C2×C4×D3—64no—
99C2×C4×D3—64no—
100C2×Dic6—62no—
101C2×Dic6—64no—
102C3×C4⋊C4—24no—
103C3×C4⋊C4—22no—
104C3×C42—24no—
105C3×C42—22no—
106C4⋊Dic3—62no—
107C4⋊Dic3—64no—
108Dic3⋊C4—64no—
109Dic3⋊C4—64no—
110Dic3⋊C4—64no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C4×Dic3—62no—
114C4×Dic3—64no—
115C4×Dic3—64no—
116C4×Dic3—64no—
117C22×C32C2×C22⋊C411yescharacteristic
118C2×C3⋊D3—21no—
119C2×C3⋊D3—21no—
120C2×C3⋊D3C22⋊C812yes—
121C32×C4—22no—
122C32×C4—21no—
123C32×C4—21no—
124C32×C4—41no—
125C32×C4C22×C811yescharacteristic
126C32×C4C2×M1611yescharacteristic
127C3⋊Dic3—22no—
128C3⋊Dic3—21no—
129C3⋊Dic3—41no—
130C3⋊Dic3C22⋊C812yes—
131C3⋊Dic3#13712yes—
132C22×Q8—91no—
133C4×Q8—91no—
134C4×Q8—91no—
135C4×Q8—91no—
136C4×Q8—181no—
137C4×Q8—181no—
138C4×Q8#15711yescharacteristic
139C2×C4⋊C4—91no—
140C2×C4⋊C4—181no—
141C2×C42—91no—
142C2×C42—181no—
143C4⋊C8—92no—
144C4⋊C8—181no—
145C22⋊C8—181no—
146C22⋊C8—181no—
147C4×C8—92no—
148C4×C8—181no—
149C22×D3—62no—
150C3×Q8—24no—
151C3×Q8—24no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—64no—
161C2×Dic3—64no—
162C4×D3—64no—
163C4×D3—64no—
164C4×D3—68no—
165C4×D3—616no—
166C4×D3—124no—
167C4×D3—128no—
168Dic6—64no—
169Dic6—616no—
170Dic6—64no—
171C2×C32C2×C22⋊C811yescharacteristic
172C2×C32#41911yescharacteristic
173C2×C32#42111yescharacteristic
174C3⋊D3—22no—
175C2×Q8—94no—
176C2×Q8—91no—
177C2×Q8—181no—
178C2×Q8—182no—
179C2×Q8C2×#15711yescharacteristic
180C22×C4—91no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—181no—
184C22×C4—181no—
185C2×C8—182no—
186C2×C8—182no—
187C4⋊C4—21no—
188C4⋊C4—91no—
189C4⋊C4—181no—
190C4⋊C4—181no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4C2×#15711yescharacteristic
194C42—21no—
195C42—91no—
196C42—91no—
197C42—91no—
198C42—181no—
199C42—181no—
200C42—181no—
201C42C2×#15711yescharacteristic
202C22×C3—22no—
203C2×D3—64no—
204C2×D3—64no—
205C2×D3—64no—
206C3×C4—28no—
207C3×C4—24no—
208C3×C4—22no—
209C3×C4—22no—
210C3×C4—42no—
211C3×C4—44no—
212Dic3—64no—
213Dic3—64no—
214Dic3—68no—
215Dic3—122no—
216Dic3—124no—
217C32#147911yescharacteristic, complemented, Sylow
218C23—91no—
219Q8—21no—
220Q8—92no—
221Q8—184no—
222Q8—181no—
223Q8#378712yes—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—92no—
229C2×C4—92no—
230C2×C4—91no—
231C2×C4—182no—
232C2×C4—184no—
233C2×C4—181no—
234C2×C4—181no—
235C2×C4—361no—
236C2×C4—362no—
237C2×C4C22⋊#15711yescharacteristic
238C2×C4C22⋊#15711yescharacteristic
239C2×C4C22×#15711yescharacteristic
240C8—362no—
241C8—362no—
242C2×C3—22no—
243C2×C3—22no—
244C2×C3—22no—
245D3—68no—
246C22—92no—
247C22—181no—
248C22—181no—
249C22C2×C22⋊#15711yescharacteristic
250C4—22no—
251C4—21no—
252C4—21no—
253C4—41no—
254C4—92no—
255C4—92no—
256C4—182no—
257C4—181no—
258C4—361no—
259C4C2×#378711yescharacteristic
260C4#6428311yescharacteristic
261C3—22no—
262C2—182no—
263C2#1059380011yescharacteristic
264C2#1059382911yescharacteristic
265C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×Q8#157
hypocenterC32#1479
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
4. Q8⋊#622C2semidirect
5. #10590161C2semidirect
26. Q8×C3⋊D3C8semidirect
217. C32#1479semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105937272
#105937252
Q8⋊#6222
#105901612
#14799