Finite Group Databasebeta

← #11774218

Subgroups — #11774218

Order 1152.

498 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 89 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×#3797C211yesmaximal, characteristic
2C4×#3787C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4#10590032C214yesmaximal, complemented
5C2×#3797C411yescharacteristic
6C2×#3787—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×Dic6—21no—
9C4×#627C2212yes—
10#63900C411yescharacteristic
11#63883—21no—
12C4×#624—21no—
13#63843—21no—
14#63838C412yes—
15C2×#3710—21no—
16C4×#622—21no—
17C4×#622C2212yes—
18C3×C4⋊(C3⋊C8)—21no—
19#63572C2212yes—
20C4×D3×Q8—61no—
21D3×C4⋊C8—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627C2×C412yes—
27C2×#624—21no—
28C2×#624—21no—
29#3797—22no—
30#3797C814yescomplemented
31C2×#622—22no—
32#3787—24no—
33C32×C42D411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C3×C4⋊Dic3—21no—
38C3×Dic3⋊C4—22no—
39C3×C4×Dic3—22no—
40C2×C3×C3⋊C8—22no—
41#3724C2×C412yes—
42Dic3⋊Dic3—22no—
43Dic32—22no—
44#3710—42no—
45C2×Q8⋊C8—91nomaximal, Sylow
46C2×D3×Q8—61no—
47C3×C4×Q8—61no—
48Q8×Dic3—61no—
49C2×D3×C8—62no—
50D3×C4⋊C4—61no—
51D3×C4⋊C4—62no—
52#887—62no—
53#887—61no—
54C42×D3—61no—
55C42×D3—61no—
56C42×D3—62no—
57C4×Dic6—21no—
58C4×Dic6—62no—
59C3×C4⋊C8—61no—
60Dic3⋊C8—62no—
61C4⋊(C3⋊C8)—21no—
62C22×C3⋊D3C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C4×C3⋊D3—22no—
70C4×C3⋊D3C2×C812yes—
71C4×C3⋊D3M1612yes—
72C4×C3⋊D3SD1612yes—
73C4×C3⋊D3Q1612yes—
74C2×C3×Dic3—22no—
75C2×C3×Dic3—22no—
76C3×Dic6—24no—
77#627—22no—
78#627C2×C814yescomplemented
79#624—24no—
80#624—42no—
81#622—24no—
82C3×C3⋊C8—42no—
83C2×C4×Q8—91no—
84C2×C4⋊C8—91no—
85C2×C4×C8—91no—
86Q8⋊C8—94no—
87C2×C3×Q8—61no—
88D3×Q8—64no—
89D3×Q8—64no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—61no—
93C2×C4×D3—61no—
94C2×C4×D3—61no—
95C2×C4×D3—61no—
96C2×C4×D3—62no—
97C2×C4×D3—62no—
98C2×Dic6—21no—
99C2×Dic6—62no—
100C2×C3×C8—62no—
101C3×C4⋊C4—62no—
102C3×C4⋊C4—61no—
103C3×C42—21no—
104C3×C42—21no—
105C3×C42—62no—
106C4⋊Dic3—21no—
107C4⋊Dic3—62no—
108Dic3⋊C4—22no—
109Dic3⋊C4—62no—
110Dic3⋊C4—62no—
111C4×Dic3—22no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C2×C3⋊C8—22no—
121D3×C8—124no—
122C22×C32C2×C22⋊C411yescharacteristic
123C2×C3⋊D3C22⋊C812yes—
124C2×C3⋊D3#10312yes—
125C2×C3⋊D3#10412yes—
126C32×C4—21no—
127C32×C4C22⋊C812yes—
128C32×C4C2×SD1611yescharacteristic
129C32×C4C2×Q1611yescharacteristic
130C3⋊Dic3—21no—
131C3⋊Dic3#10312yes—
132C3⋊Dic3C22×C811yescharacteristic
133C3⋊Dic3C2×M1611yescharacteristic
134C3×Dic3—24no—
135C3×Dic3—42no—
136C22×Q8—91no—
137C22×C8—181no—
138C22×C8—181no—
139C4×Q8—61no—
140C4×Q8—92no—
141C4×Q8—92no—
142C4×Q8—181no—
143C2×C4⋊C4—91no—
144C2×C4⋊C4—181no—
145C2×C42—91no—
146C2×C42—181no—
147C4⋊C8—61no—
148C4⋊C8—92no—
149C4×C8—92no—
150C4×C8—181no—
151C22×D3—61no—
152C22×D3—61no—
153C3×Q8—64no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—62no—
161C2×C3×C4—62no—
162C2×Dic3—22no—
163C2×Dic3—22no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C4×D3—62no—
171C4×D3—62no—
172C4×D3—62no—
173C4×D3—62no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—62no—
178C4×D3—68no—
179C4×D3—122no—
180C4×D3—122no—
181C4×D3—124no—
182Dic6—24no—
183Dic6—64no—
184Dic6—64no—
185C3×C8—122no—
186C3⋊C8—42no—
187C2×C32C2×C22⋊C811yescharacteristic
188C2×C32C2×#10311yescharacteristic
189C2×C32C2×#10411yescharacteristic
190C3⋊D3Q8⋊C814yescomplemented
191C2×Q8—61no—
192C2×Q8—92no—
193C2×Q8—94no—
194C2×Q8—182no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—91no—
198C22×C4—181no—
199C22×C4—181no—
200C2×C8—62no—
201C2×C8—182no—
202C2×C8—184no—
203C2×C8—362no—
204C4⋊C4—61no—
205C4⋊C4—62no—
206C4⋊C4—92no—
207C4⋊C4—182no—
208C42—62no—
209C42—91no—
210C42—91no—
211C42—91no—
212C42—182no—
213C42GO+(4,𝔽2)11yescharacteristic
214C22×C3—21no—
215C22×C3—21no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—62no—
221C2×D3—62no—
222C3×C4—21no—
223C3×C4—21no—
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—22no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—41no—
230C3×C4—64no—
231C3×C4—122no—
232Dic3—24no—
233Dic3—42no—
234Dic3—61no—
235Dic3—61no—
236Dic3—62no—
237Dic3—62no—
238Dic3—61no—
239Dic3—61no—
240Dic3—121no—
241Dic3—121no—
242C32C2×Q8⋊C811yescharacteristic, complemented, Sylow
243C23—91no—
244Q8—64no—
245Q8—94no—
246Q8—182no—
247C2×C4—62no—
248C2×C4—62no—
249C2×C4—91no—
250C2×C4—91no—
251C2×C4—92no—
252C2×C4—92no—
253C2×C4—92no—
254C2×C4—92no—
255C2×C4—91no—
256C2×C4—182no—
257C2×C4—184no—
258C2×C4—362no—
259C2×C4D32⋊C411yescharacteristic
260C2×C4D32⋊C411yescharacteristic
261C2×C4C2×GO+(4,𝔽2)11yescharacteristic
262C8—122no—
263C8—184no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270D3—64no—
271D3—64no—
272C22—92no—
273C22—92no—
274C22—92no—
275C22C2×D32⋊C411yescharacteristic
276C4—21no—
277C4—64no—
278C4—91no—
279C4—91no—
280C4—92no—
281C4—122no—
282C4—181no—
283C4D32⋊C812yes—
284C4#6422711yescharacteristic
285C4#6422811yescharacteristic
286C3—21no—
287C3—21no—
288C2—94no—
289C2C2×D32⋊C811yescharacteristic
290C2#1059332511yescharacteristic
291C2#1059337511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C22×C8
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32C2×Q8⋊C8
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590032C2semidirect
30. #3797C8semidirect
78. #627C2×C8semidirect
190. C3⋊D3Q8⋊C8semidirect
242. C32C2×Q8⋊C8semidirect

Maximal subgroups

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

subgroupindex
C4×#37972
C4×#37872
#105903312
#105900322
C2×Q8⋊C89