Finite Group Databasebeta

← #11774537

Subgroups — #11774537

Order 1152.

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

normal subgroups only

This group has 388 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#10595050C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4#10590032C214yesmaximal, complemented
5C2×#3792—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#926—21no—
8#63982—21no—
9#63982C412yes—
10#63919C411yescharacteristic
11#63919C411yescharacteristic
12C4×#627—21no—
13C4×#627C2212yes—
14#63872—21no—
15#63777—21no—
16C4×#622C2212yes—
17C3×#830—21no—
18#63572C2212yes—
19#63553—21no—
20#5517—61no—
21#4718—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×#627—21no—
26C2×#627C2×C412yes—
27#3792—24no—
28C2×#622—22no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×#217—22no—
34C3×C4⋊Dic3—21no—
35C3×C4⋊Dic3—21no—
36C3×C4×Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#3724—21no—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41Dic3⋊Dic3—22no—
42#1485—91nomaximal, Sylow
43C3×#117—61no—
44#926—21no—
45C2×C4×Dic3—61no—
46C2×C4×Dic3—61no—
47#890—61no—
48#890—61no—
49#888—61no—
50#888—61no—
51#878—62no—
52#878—62no—
53C4×Dic6—62no—
54C4×Dic6—62no—
55C3×C22⋊C8—61no—
56#830—21no—
57Dic3⋊C8—62no—
58C8×Dic3—62no—
59C23×C32C22⋊C411yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—22no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3×Dic3—22no—
70C2×C3×Dic3—22no—
71#627—24no—
72#627—42no—
73#622—24no—
74C3×C3⋊C8—42no—
75#533—91no—
76#431—91no—
77C4×M16—91no—
78Q8⋊C8—94no—
79C22×C3×C4—21no—
80C22×C3×C4—21no—
81C22×Dic3—61no—
82C22×Dic3—61no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C2×Dic6—62no—
86C2×Dic6—62no—
87C2×C3×C8—62no—
88C3×C4⋊C4—61no—
89C3×C4⋊C4—61no—
90C3×C22⋊C4—62no—
91C3×C42—62no—
92#217—22no—
93C4⋊Dic3—21no—
94C4⋊Dic3—21no—
95C4⋊Dic3—62no—
96C4⋊Dic3—62no—
97Dic3⋊C4—62no—
98Dic3⋊C4—62no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101C4×Dic3—22no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C2×C3⋊C8—22no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32C2×C22⋊C411yescharacteristic
115C32×C4—21no—
116C32×C4#13712yes—
117C3⋊Dic3—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3#10412yes—
120C3⋊Dic3#13112yes—
121C3×Dic3—42no—
122C3×Dic3—42no—
123C2×M16—181no—
124C4⋊Q8—91no—
125C4⋊Q8—91no—
126#125—181no—
127C22⋊Q8—92no—
128C22⋊Q8—181no—
129C4×Q8—92no—
130C4×Q8—181no—
131#117—61no—
132C2×C42—91no—
133C4⋊C8—92no—
134C22⋊C8—61no—
135#97—181no—
136C4×C8—92no—
137C4×C8—181no—
138C23×C3—21no—
139C23×C3—21no—
140C2×C3×C4—24no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—42no—
146C2×C3×C4—62no—
147C2×C3×C4—62no—
148C2×Dic3—22no—
149C2×Dic3—22no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—64no—
159C2×Dic3—122no—
160C2×Dic3—122no—
161C2×Dic3—122no—
162Dic6—124no—
163Dic6—124no—
164C3×C8—122no—
165C3⋊C8—42no—
166C2×C32—41no—
167C2×C32#40811yescharacteristic
168C2×C32#41911yescharacteristic
169C2×C32C2×#10411yescharacteristic
170C2×Q8—92no—
171C2×Q8—181no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4GO+(4,𝔽2)11yescharacteristic
175M16—184no—
176C2×C8—62no—
177C2×C8—182no—
178C4⋊C4—61no—
179C4⋊C4—61no—
180C4⋊C4—92no—
181C4⋊C4—182no—
182C4⋊C4—182no—
183C4⋊C4—181no—
184C22⋊C4—62no—
185C42—62no—
186C42—91no—
187C42—91no—
188C42—91no—
189C42—91no—
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—41no—
195C22×C3—41no—
196C22×C3—41no—
197C22×C3—41no—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—22no—
201C3×C4—41no—
202C3×C4—122no—
203C3×C4—122no—
204Dic3—42no—
205Dic3—42no—
206Dic3—62no—
207Dic3—62no—
208Dic3—62no—
209Dic3—62no—
210Dic3—62no—
211Dic3—121no—
212Dic3—121no—
213Dic3—121no—
214C32#148511yescharacteristic, complemented, Sylow
215C23D32⋊C411yescharacteristic
216Q8—184no—
217Q8—362no—
218C2×C4—22no—
219C2×C4—62no—
220C2×C4—62no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—182no—
226C2×C4—182no—
227C2×C4D32⋊C411yescharacteristic
228C2×C4C2×GO+(4,𝔽2)11yescharacteristic
229C8—122no—
230C8—184no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3—21no—
235C2×C3—21no—
236C2×C3—21no—
237C2×C3—42no—
238C2×C3—42no—
239C22—21no—
240C22—21no—
241C22—21no—
242C22C2×D32⋊C411yescharacteristic
243C4—21no—
244C4—92no—
245C4—92no—
246C4—122no—
247C4—122no—
248C4—181no—
249C4—181no—
250C4#6423912yes—
251C3—21no—
252C3—21no—
253C2—41no—
254C2#1059330811yescharacteristic
255C2#1059332511yescharacteristic
256C2#1059350311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1485
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590032C2semidirect
214. C32#1485semidirect

Maximal subgroups

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

subgroupindex
#105950502
C4×#37922
#105910612
#105900322
#14859