Finite Group Databasebeta

← #11775096

Subgroups — #11775096

Order 1152.

448 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 67 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#10593801C211yesmaximal, characteristic
3#10591274C211yesmaximal, characteristic
4#10590072C214yesmaximal
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×C3×C4⋊Dic3—21no—
7C3×#924—21no—
8#63982C2212yes—
9#63957—21no—
10C2×Dic32—21no—
11#63919C411yescharacteristic, complemented
12#63873C411yescharacteristic, complemented
13#63870—21no—
14#63843—21no—
15#63838C412yescomplemented
16C22⋊#622C2212yes—
17#63779—21no—
18C4×#622—21no—
19#63579C2212yes—
20#5622—61no—
21Dic3×C4⋊C4—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3×Dic3—22no—
26C2×C3×Dic6—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—24no—
35C3×C4⋊Dic3—21no—
36C3×Dic3⋊C4—22no—
37#3724—21no—
38#3724—21no—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41Dic32—22no—
42Dic32—42no—
43#1503—91nomaximal, Sylow
44C3×C22⋊Q8—61no—
45C2×C3×C4⋊C4—61no—
46Q8×Dic3—61no—
47#944—61no—
48C2×C4⋊Dic3—21no—
49#924—21no—
50C2×C4×Dic3—61no—
51C2×C4×Dic3—61no—
52C2×C4×Dic3—62no—
53#889—62no—
54#888—61no—
55#887—62no—
56#887—61no—
57#878—62no—
58#877—62no—
59C3⋊#95—62no—
60C23×C32C2×D411yescharacteristic
61C2×C32×C4—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3SD1612yes—
68C2×C3⋊Dic3Q1612yes—
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—
76C3×Dic6—42no—
77#627—42no—
78#622—42no—
79#533—91no—
80#431—91no—
81C4×C4⋊C4—91no—
82#328—94no—
83C2×C3×Q8—61no—
84C22×C3×C4—21no—
85C22×C3×C4—21no—
86C22×C3×C4—62no—
87C22×Dic3—22no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C22×Dic3—61no—
91C22×Dic3—61no—
92C2×Dic6—21no—
93C2×Dic6—62no—
94C3×C4⋊C4—61no—
95C3×C4⋊C4—62no—
96C3×C4⋊C4—64no—
97C3×C22⋊C4—62no—
98#217—22no—
99C4⋊Dic3—21no—
100C4⋊Dic3—24no—
101C4⋊Dic3—62no—
102Dic3⋊C4—22no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—61no—
114C4×Dic3—61no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C4×Dic3—124no—
118C22×C32—21no—
119C22×C32—21no—
120C22×C32C2×C22⋊C411yescharacteristic
121C22×C32C2×SD1611yescharacteristic
122C22×C32C2×Q1611yescharacteristic
123C32×C4—21no—
124C32×C4#10412yes—
125C3⋊Dic3—21no—
126C3⋊Dic3—21no—
127C3⋊Dic3#10312yes—
128C3⋊Dic3#10312yes—
129C3×Dic3—44no—
130C3×Dic3—42no—
131C3×Dic3—42no—
132C4⋊Q8—91no—
133C4⋊Q8—91no—
134#125—181no—
135C22⋊Q8—61no—
136C22⋊Q8—92no—
137C4×Q8—92no—
138C4×Q8—181no—
139#117—181no—
140C2×C4⋊C4—61no—
141C2×C42—91no—
142C2×C42—181no—
143C4⋊C8—181no—
144C22⋊C8—92no—
145C4×C8—181no—
146#95—92no—
147C23×C3—21no—
148C23×C3—21no—
149C3×Q8—122no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—42no—
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—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—62no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—61no—
179C2×Dic3—122no—
180C2×Dic3—121no—
181C2×Dic3—121no—
182Dic6—42no—
183Dic6—124no—
184C2×C32—21no—
185C2×C32—21no—
186C2×C32#41011yescharacteristic
187C2×C32C2×#10311yescharacteristic
188C2×C32C2×#10411yescharacteristic
189C2×Q8—61no—
190C2×Q8—92no—
191C22×C4—62no—
192C22×C4—91no—
193C22×C4—91no—
194C22×C4GO+(4,𝔽2)11yescharacteristic
195C2×C8—182no—
196C4⋊C4—64no—
197C4⋊C4—62no—
198C4⋊C4—61no—
199C4⋊C4—92no—
200C4⋊C4—181no—
201C4⋊C4—181no—
202C4⋊C4—182no—
203C22⋊C4—62no—
204C42—91no—
205C42—91no—
206C42—91no—
207C42—91no—
208C42—182no—
209C42—362no—
210C22×C3—21no—
211C22×C3—21no—
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—41no—
221C22×C3—41no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—41no—
226C3×C4—122no—
227C3×C4—124no—
228C3×C4—122no—
229Dic3—42no—
230Dic3—42no—
231Dic3—44no—
232Dic3—62no—
233Dic3—62no—
234Dic3—62no—
235Dic3—62no—
236Dic3—62no—
237Dic3—121no—
238Dic3—121no—
239Dic3—121no—
240C32#150311yescharacteristic, complemented, Sylow
241C23C2×GO+(4,𝔽2)11yescharacteristic
242Q8—122no—
243Q8—362no—
244C2×C4—22no—
245C2×C4—64no—
246C2×C4—62no—
247C2×C4—62no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—91no—
251C2×C4—91no—
252C2×C4—91no—
253C2×C4—91no—
254C2×C4—122no—
255C2×C4—122no—
256C2×C4—361no—
257C2×C4D32⋊C411yescharacteristic
258C2×C4D32⋊C411yescharacteristic
259C8—362no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—41no—
271C2×C3—41no—
272C22—21no—
273C22—21no—
274C22#6422711yescharacteristic
275C22#6422811yescharacteristic
276C22C2×D32⋊C411yescharacteristic
277C4—21no—
278C4—92no—
279C4—92no—
280C4—124no—
281C4—122no—
282C4—122no—
283C4—181no—
284C4—181no—
285C4#6374112yes—
286C3—21no—
287C3—21no—
288C2—21no—
289C2—21no—
290C2#1059334611yescharacteristic
291C2#1059337511yescharacteristic
292C2C2×#6374111yescharacteristic
subgroupG/H
centerC22C2×D32⋊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 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
11. #63919C4semidirect
12. #63873C4semidirect
15. #63838C4semidirect
240. C32#1503semidirect

Maximal subgroups

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

subgroupindex
#105948102
#105938012
#105912742
#105900722
#15039