Finite Group Databasebeta

← #11774353

Subgroups — #11774353

Order 1152.

456 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#63838C211yesmaximal, characteristic
2#10593801C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4#10590031C214yesmaximal, complemented
5C22×#627C411yescharacteristic
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C2×C3×Dic3⋊C4—21no—
8C2×#3724C411yescharacteristic
9C2×Dic32—21no—
10#63838—21no—
11#63838—21no—
12#63838C412yes—
13#63838C2212yes—
14C22⋊#622—21no—
15#63779C2212yes—
16C4×#622—21no—
17C3×#830—21no—
18#63572—21no—
19#63553C2212yes—
20C2×#887—61no—
21#4718—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3×Dic3—21no—
26C22×C3×Dic3—21no—
27C2×#627—21no—
28C2×#627—22no—
29C2×#627C814yescomplemented
30C2×#627C2×C412yes—
31C2×#622—22no—
32C4×C3⋊Dic3C2×C411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3D411yescharacteristic
35C4×C3⋊Dic3C2311yescharacteristic
36C3×Dic3⋊C4—22no—
37C3×Dic3⋊C4—22no—
38C2×C3×C3⋊C8—22no—
39#3724—21no—
40#3724C2×C412yes—
41Dic32—22no—
42Dic32—22no—
43#1479—91nomaximal, Sylow
44C22×Dic6—61no—
45C2×C3×C4⋊C4—61no—
46C2×Dic3⋊C4—21no—
47C2×Dic3⋊C4—61no—
48C2×C4×Dic3—61no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52#887—62no—
53#887—62no—
54#887—62no—
55#887—62no—
56C3×C22⋊C8—61no—
57#830—21no—
58Dic3⋊C8—62no—
59C8×Dic3—62no—
60C23×C32C22⋊C411yescharacteristic
61C2×C32×C4—41no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C2×C812yes—
68C2×C3⋊Dic3M1612yes—
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3×Dic3—24no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—42no—
75#627—24no—
76#627—22no—
77#627C2×C814yes—
78#622—42no—
79C3×C3⋊C8—42no—
80C2×C4×Q8—91no—
81#431—91no—
82#431—91no—
83Q8⋊C8—94no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4—61no—
87C22×C3×C4—61no—
88C22×Dic3—21no—
89C22×Dic3—21no—
90C22×Dic3—61no—
91C22×Dic3—61no—
92C22×Dic3—61no—
93C22×Dic3—61no—
94C2×Dic6—62no—
95C2×Dic6—64no—
96C2×Dic6—62no—
97C2×Dic6—64no—
98C2×C3×C8—62no—
99C3×C4⋊C4—62no—
100C3×C4⋊C4—62no—
101Dic3⋊C4—22no—
102Dic3⋊C4—22no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C2×C3⋊C8—22no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32C22⋊C812yes—
121C22×C32C2×C22⋊C411yescharacteristic
122C32×C4—21no—
123C32×C4—21no—
124C3⋊Dic3—21no—
125C3⋊Dic3C22⋊C812yes—
126C3⋊Dic3C22×C811yescharacteristic
127C3⋊Dic3C2×M1611yescharacteristic
128C3⋊Dic3#13712yes—
129C3×Dic3—24no—
130C3×Dic3—42no—
131C22×Q8—91no—
132C4×Q8—92no—
133C4×Q8—92no—
134C4×Q8—181no—
135C4×Q8—181no—
136C2×C4⋊C4—61no—
137C2×C4⋊C4—91no—
138C2×C42—91no—
139C2×C42—181no—
140C4⋊C8—92no—
141C4⋊C8—181no—
142C22⋊C8—61no—
143C22⋊C8—181no—
144C4×C8—92no—
145C4×C8—181no—
146C23×C3—21no—
147C23×C3—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—42no—
153C2×C3×C4—42no—
154C2×C3×C4—62no—
155C2×C3×C4—64no—
156C2×C3×C4—62no—
157C2×C3×C4—122no—
158C2×Dic3—22no—
159C2×Dic3—24no—
160C2×Dic3—22no—
161C2×Dic3—42no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—62no—
166C2×Dic3—62no—
167C2×Dic3—62no—
168C2×Dic3—62no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—64no—
175C2×Dic3—122no—
176Dic6—64no—
177Dic6—68no—
178Dic6—64no—
179C3×C8—122no—
180C3⋊C8—42no—
181C2×C32—22no—
182C2×C32C2×C22⋊C811yescharacteristic
183C2×C32#41911yescharacteristic
184C2×C32#42111yescharacteristic
185C2×Q8—92no—
186C2×Q8—94no—
187C2×Q8—181no—
188C2×Q8—182no—
189C22×C4—61no—
190C22×C4—61no—
191C22×C4—91no—
192C22×C4—91no—
193C22×C4GO+(4,𝔽2)11yescharacteristic
194C2×C8—62no—
195C2×C8—182no—
196C4⋊C4—62no—
197C4⋊C4—62no—
198C4⋊C4—92no—
199C4⋊C4—181no—
200C42—91no—
201C42—91no—
202C42—91no—
203C42—91no—
204C42—182no—
205C42—182no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—41no—
213C22×C3—41no—
214C3×C4—22no—
215C3×C4—41no—
216C3×C4—41no—
217C3×C4—41no—
218C3×C4—64no—
219C3×C4—122no—
220Dic3—24no—
221Dic3—42no—
222Dic3—62no—
223Dic3—61no—
224Dic3—61no—
225Dic3—62no—
226Dic3—61no—
227Dic3—61no—
228Dic3—62no—
229Dic3—62no—
230Dic3—62no—
231Dic3—121no—
232C32#147911yescharacteristic, complemented, Sylow
233C23D32⋊C411yescharacteristic
234Q8—94no—
235Q8—182no—
236Q8—184no—
237C2×C4—41no—
238C2×C4—62no—
239C2×C4—64no—
240C2×C4—62no—
241C2×C4—91no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—91no—
247C2×C4—122no—
248C2×C4—182no—
249C2×C4D32⋊C411yescharacteristic
250C2×C4C2×GO+(4,𝔽2)11yescharacteristic
251C8—122no—
252C8—362no—
253C2×C3—24no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—42no—
261C22—21no—
262C22—21no—
263C22D32⋊C812yes—
264C22C2×D32⋊C411yescharacteristic
265C4—21no—
266C4—21no—
267C4—64no—
268C4—91no—
269C4—91no—
270C4—92no—
271C4—92no—
272C4—122no—
273C4—181no—
274C3—21no—
275C3—21no—
276C2—22no—
277C2C2×D32⋊C811yescharacteristic
278C2#1059332111yescharacteristic
279C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C22×C8
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1479
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590031C2semidirect
29. C2×#627C8semidirect
232. C32#1479semidirect

Maximal subgroups

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

subgroupindex
C2×#638382
#105938012
#105910612
#105900312
#14799