Finite Group Databasebeta

← #11775095

Subgroups — #11775095

Order 1152.

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

normal subgroups only

This group has 448 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
1#10595050C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic
3C4×#3724C211yesmaximal, characteristic
4#10590072C214yesmaximal
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C3×#926—21no—
7C2×C3×C4×Dic3—21no—
8#63982—21no—
9#63982C2212yes—
10C2×#3724—21no—
11#63919C411yescharacteristic, complemented
12#63919C411yescharacteristic, complemented
13C4×#627—21no—
14C4×#627C412yescomplemented
15#63872—21no—
16C22⋊#622C2212yes—
17C4⋊#622—21no—
18C4×#622—21no—
19#63579C2212yes—
20#5517—61no—
21C4×Dic3⋊C4—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3×Dic3—22no—
26C2×#627—21no—
27C2×#627C2×C412yes—
28C2×#622—22no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C3×#217—22no—
34C3×C4⋊Dic3—21no—
35C3×C4⋊Dic3—21no—
36C3×C4×Dic3—22no—
37C3×C4×Dic3—42no—
38#3724—24no—
39#3724—21no—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42Dic3⋊Dic3—22no—
43#1503—91nomaximal, Sylow
44C3×#117—61no—
45C2×C3×C42—61no—
46#926—21no—
47C2×Dic3⋊C4—62no—
48C2×C4×Dic3—21no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51#890—61no—
52#890—61no—
53#888—61no—
54#888—61no—
55#878—62no—
56#878—62no—
57C4×Dic6—62no—
58C4×Dic6—62no—
59C3⋊#95—62no—
60C23×C32C2×D411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4SD1612yes—
64C2×C32×C4Q1612yes—
65C2×C3⋊Dic3—22no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3×Dic3—24no—
72C2×C3×Dic3—22no—
73C2×C3×Dic3—22no—
74C2×C3×Dic3—42no—
75C2×C3×Dic3—42no—
76#627—42no—
77#627—42no—
78#622—42no—
79#533—91no—
80#431—91no—
81C4×C4⋊C4—91no—
82#328—94no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—62no—
86C22×Dic3—22no—
87C22×Dic3—61no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C2×Dic6—62no—
92C2×Dic6—62no—
93C3×C4⋊C4—61no—
94C3×C4⋊C4—61no—
95C3×C22⋊C4—62no—
96C3×C42—62no—
97C3×C42—122no—
98#217—22no—
99C4⋊Dic3—21no—
100C4⋊Dic3—21no—
101C4⋊Dic3—62no—
102C4⋊Dic3—62no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107Dic3⋊C4—68no—
108C4×Dic3—22no—
109C4×Dic3—42no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32C2×C22⋊C411yescharacteristic
121C22×C32C2×SD1611yescharacteristic
122C22×C32C2×Q1611yescharacteristic
123C32×C4#10312yes—
124C32×C4#10312yes—
125C3⋊Dic3—21no—
126C3⋊Dic3—21no—
127C3⋊Dic3—21no—
128C3⋊Dic3#10412yes—
129C3×Dic3—44no—
130C3×Dic3—42no—
131C3×Dic3—42no—
132C4⋊Q8—91no—
133C4⋊Q8—91no—
134#125—181no—
135C22⋊Q8—92no—
136C22⋊Q8—181no—
137C4×Q8—92no—
138C4×Q8—181no—
139#117—61no—
140C2×C4⋊C4—181no—
141C2×C42—61no—
142C2×C42—91no—
143C4⋊C8—181no—
144C22⋊C8—92no—
145C4×C8—181no—
146#95—92no—
147C23×C3—21no—
148C23×C3—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—62no—
158C2×C3×C4—62no—
159C2×C3×C4—64no—
160C2×C3×C4—122no—
161C2×C3×C4—122no—
162C2×Dic3—22no—
163C2×Dic3—22no—
164C2×Dic3—24no—
165C2×Dic3—42no—
166C2×Dic3—42no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—64no—
176C2×Dic3—122no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179Dic6—124no—
180Dic6—124no—
181C2×C32—21no—
182C2×C32—21no—
183C2×C32#41011yescharacteristic
184C2×C32C2×#10311yescharacteristic
185C2×C32C2×#10411yescharacteristic
186C2×Q8—92no—
187C2×Q8—181no—
188C22×C4—62no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4GO+(4,𝔽2)11yescharacteristic
192C2×C8—182no—
193C4⋊C4—61no—
194C4⋊C4—61no—
195C4⋊C4—92no—
196C4⋊C4—182no—
197C4⋊C4—182no—
198C4⋊C4—181no—
199C4⋊C4—184no—
200C22⋊C4—62no—
201C42—62no—
202C42—91no—
203C42—91no—
204C42—91no—
205C42—91no—
206C42—122no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—21no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—41no—
216C22×C3—41no—
217C3×C4—22no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—122no—
222C3×C4—122no—
223C3×C4—124no—
224Dic3—42no—
225Dic3—42no—
226Dic3—44no—
227Dic3—62no—
228Dic3—62no—
229Dic3—62no—
230Dic3—62no—
231Dic3—121no—
232Dic3—121no—
233Dic3—121no—
234Dic3—121no—
235C32#150311yescharacteristic, complemented, Sylow
236C23C2×GO+(4,𝔽2)11yescharacteristic
237Q8—362no—
238Q8—362no—
239C2×C4—64no—
240C2×C4—62no—
241C2×C4—62no—
242C2×C4—91no—
243C2×C4—91no—
244C2×C4—91no—
245C2×C4—91no—
246C2×C4—122no—
247C2×C4—122no—
248C2×C4—182no—
249C2×C4—361no—
250C2×C4D32⋊C411yescharacteristic
251C2×C4D32⋊C411yescharacteristic
252C2×C4#377512yes—
253C2×C4#377612yes—
254C8—362no—
255C2×C3—22no—
256C2×C3—22no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—41no—
264C2×C3—41no—
265C22—21no—
266C22—21no—
267C22C2×D32⋊C411yescharacteristic
268C22C2×#377511yescharacteristic
269C22C2×#377611yescharacteristic
270C4—92no—
271C4—124no—
272C4—122no—
273C4—122no—
274C4—181no—
275C4—181no—
276C4—181no—
277C4#6374012yes—
278C4#6374012yes—
279C3—21no—
280C3—21no—
281C2—21no—
282C2—21no—
283C2#1059334511yescharacteristic
284C2#1059338011yescharacteristic
285C2C2×#6374011yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1503
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
11. #63919C4semidirect
12. #63919C4semidirect
14. C4×#627C4semidirect
235. C32#1503semidirect

Maximal subgroups

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

subgroupindex
#105950502
#105937952
C4×#37242
#105900722
#15039