Finite Group Databasebeta

← #11775915

Subgroups — #11775915

Order 1152.

396 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 59 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
1#10594810C211yesmaximal, characteristic
2#10593806C211yesmaximal, characteristic
3C2×#63555C211yesmaximal, characteristic
4#10590036C214yesmaximal, complemented
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C3×#924—21no—
7C22×C3×C3⋊C8—21no—
8#63982—21no—
9#63957C412yes—
10#63919C411yescharacteristic
11#63873C411yescharacteristic
12#63870C2212yes—
13#63843—21no—
14#63838—21no—
15C22⋊#622—21no—
16#63777C2212yes—
17C4⋊#622—21no—
18#63555—21no—
19#63555C2212yes—
20#5622—61no—
21C2×#815—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627—21no—
27C2×#622—22no—
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32C3×#217—22no—
33C3×C4⋊Dic3—21no—
34C3×Dic3⋊C4—22no—
35C2×C3×C3⋊C8—24no—
36C2×C3×C3⋊C8—22no—
37#3724—21no—
38#3724C2×C412yes—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41Dic32—22no—
42#1531—91nomaximal, Sylow
43C22×C3×C8—61no—
44C3×C22⋊Q8—61no—
45Q8×Dic3—61no—
46#944—61no—
47#924—21no—
48C2×C4×Dic3—61no—
49C2×C4×Dic3—61no—
50C22×C3⋊C8—21no—
51#889—62no—
52#888—61no—
53#887—62no—
54#887—61no—
55#878—62no—
56#877—62no—
57#815—62no—
58#815—62no—
59C23×C32C22⋊C411yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3×Dic3—22no—
70C2×C3×Dic3—22no—
71C3×Dic6—42no—
72#627—42no—
73#622—42no—
74C3×C3⋊C8—24no—
75#533—91no—
76#432—91no—
77C2×#97—91no—
78#330—94no—
79C2×C3×Q8—61no—
80C22×C3×C4—21no—
81C22×C3×C4—21no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C2×Dic6—21no—
87C2×Dic6—62no—
88C2×C3×C8—62no—
89C2×C3×C8—64no—
90C3×C4⋊C4—61no—
91C3×C4⋊C4—62no—
92C3×C22⋊C4—62no—
93#217—22no—
94C4⋊Dic3—21no—
95C4⋊Dic3—62no—
96Dic3⋊C4—22no—
97Dic3⋊C4—62no—
98Dic3⋊C4—62no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C2×C3⋊C8—22no—
112C2×C3⋊C8—24no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32#10112yes—
116C22×C32C2×C22⋊C411yescharacteristic
117C32×C4—21no—
118C32×C4#10412yes—
119C3⋊Dic3—21no—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3×Dic3—42no—
124C3×Dic3—42no—
125C22×C8—61no—
126C4⋊Q8—91no—
127C4⋊Q8—91no—
128#125—92no—
129C22⋊Q8—61no—
130C22⋊Q8—181no—
131C4×Q8—181no—
132C4×Q8—181no—
133#117—92no—
134C2×C42—91no—
135C4⋊C8—181no—
136C22⋊C8—181no—
137#97—92no—
138#97—92no—
139#97—181no—
140C23×C3—21no—
141C23×C3—21no—
142C3×Q8—122no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—42no—
150C2×C3×C4—62no—
151C2×C3×C4—62no—
152C2×Dic3—22no—
153C2×Dic3—22no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—64no—
163C2×Dic3—122no—
164C2×Dic3—122no—
165C2×Dic3—122no—
166Dic6—42no—
167Dic6—124no—
168C3×C8—64no—
169C3⋊C8—24no—
170C2×C32—22no—
171C2×C32C2×#10111yescharacteristic
172C2×C32C2×#10411yescharacteristic
173C2×C32#42111yescharacteristic
174C2×Q8—61no—
175C2×Q8—181no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4GO+(4,𝔽2)11yescharacteristic
179C2×C8—64no—
180C2×C8—62no—
181C2×C8—182no—
182C4⋊C4—62no—
183C4⋊C4—61no—
184C4⋊C4—92no—
185C4⋊C4—92no—
186C4⋊C4—182no—
187C4⋊C4—181no—
188C22⋊C4—62no—
189C42—91no—
190C42—91no—
191C42—91no—
192C42—91no—
193C42—182no—
194C22×C3—22no—
195C22×C3—22no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—41no—
201C22×C3—41no—
202C3×C4—21no—
203C3×C4—21no—
204C3×C4—22no—
205C3×C4—22no—
206C3×C4—41no—
207C3×C4—122no—
208C3×C4—122no—
209Dic3—42no—
210Dic3—42no—
211Dic3—62no—
212Dic3—62no—
213Dic3—62no—
214Dic3—121no—
215Dic3—121no—
216Dic3—121no—
217Dic3—121no—
218Dic3—121no—
219C32#153111yescharacteristic, complemented, Sylow
220C23D32⋊C411yescharacteristic
221Q8—122no—
222Q8—362no—
223C2×C4—22no—
224C2×C4—62no—
225C2×C4—62no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—182no—
231C2×C4—361no—
232C2×C4D32⋊C411yescharacteristic
233C2×C4C2×GO+(4,𝔽2)11yescharacteristic
234C8—64no—
235C8—362no—
236C2×C3—24no—
237C2×C3—21no—
238C2×C3—21no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—42no—
244C22—21no—
245C22—21no—
246C22#6372812yes—
247C22C2×D32⋊C411yescharacteristic
248C4—21no—
249C4—122no—
250C4—122no—
251C4—181no—
252C4—181no—
253C4—181no—
254C4—181no—
255C4#6374112yes—
256C3—21no—
257C3—21no—
258C2—22no—
259C2C2×#6372811yescharacteristic
260C2#1059332411yescharacteristic
261C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1531
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590036C2semidirect
219. C32#1531semidirect

Maximal subgroups

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

subgroupindex
#105948102
#105938062
C2×#635552
#105900362
#15319