Finite Group Databasebeta

← #11783922

Subgroups — #11783922

Order 1152.

546 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 87 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#10593966C211yesmaximal, characteristic
2#10593733C211yesmaximal, characteristic, complemented
3C2×#63731C212yesmaximal
4C4×#3712C211yesmaximal, characteristic, complemented
5#10590047C212yesmaximal, complemented
6C2×#3798C2211yescharacteristic
7C2×C4×#157C2212yes—
8C42×C3⋊D3C2211yescharacteristic
9C3×#872—21no—
10#63902C412yescomplemented
11#63881—22no—
12C4×D3×Dic3—21no—
13#63874C2211yescharacteristic
14#63838C412yescomplemented
15C2×#3712C2212yes—
16#63781—22no—
17#63731C418yescomplemented
18C3×C4×C3⋊C8—21no—
19#63555—21no—
20#5522—61no—
21C4×ΓL(1,𝔽25)—61no—
22C22×#157—22no—
23C2×C4×C3⋊D3D412yes—
24C2×C4×C3⋊D3C2311yescharacteristic
25C2×C3×C4×D3—21no—
26C2×#627C2×C411yescharacteristic
27C2×#626—21no—
28C2×#625C2×C411yescharacteristic
29C2×D3×Dic3—22no—
30#3798—22no—
31#3798C2×C414yes—
32C4×#157—22no—
33C4×#157C2×C414yescomplemented
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C412yes—
36C4×C3⋊Dic3D411yescharacteristic
37C3×(C2×D3)⋊C4—22no—
38C3×Dic3⋊C4—22no—
39C3×C4×Dic3—21no—
40C2×C3×C3⋊C8—22no—
41#3724C2×C412yes—
42#3722—21no—
43Dic32—22no—
44#3712—22no—
45#3712C2×C414yescomplemented
46#1759—91nomaximal, Sylow
47C2×#235—61no—
48C3×#117—61no—
49C2×C4×Dic3—61no—
50C2×ΓL(1,𝔽25)—62no—
51#893—62no—
52#887—62no—
53#67⋊C4—62no—
54#67⋊C4—62no—
55#872—21no—
56#872—61no—
57C42×D3—61no—
58C42×D3—61no—
59C42×D3—61no—
60C3×C4×C8—61no—
61#815—62no—
62C4×C3⋊C8—21no—
63C22×C3⋊D3C2×D411yescharacteristic
64C22×C3×D3—21no—
65C2×#157—24no—
66C2×#157—44no—
67C2×C32×C4C22⋊C412yes—
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3C22⋊C412yes—
70C2×C3⋊Dic3C22×C411yescharacteristic
71C4×C3⋊D3—42no—
72C4×C3⋊D3C22×C412yes—
73C4×C3⋊D3#4112yes—
74C2×C3×Dic3—21no—
75C2×C3×Dic3—22no—
76C3×C4×D3—24no—
77#627—21no—
78#627C4212yes—
79#626—24no—
80#625—21no—
81#625C4212yes—
82D3×Dic3—44no—
83C3×C3⋊C8—24no—
84C4×#41—91no—
85C2×#104—92no—
86C4×M16—91no—
87#376—91no—
88#339—92no—
89C22×C3×C4—61no—
90C2×#67—61no—
91C2×#67—61no—
92C22×Dic3—62no—
93#235—64no—
94#235—64no—
95C2×D12—61no—
96C2×C4×D3—21no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×Dic6—61no—
103C2×C3×C8—62no—
104C3×C4⋊C4—62no—
105C3×C22⋊C4—62no—
106C3×C42—21no—
107C3×C42—21no—
108C3×C42—61no—
109(C2×D3)⋊C4—22no—
110(C2×D3)⋊C4—62no—
111Dic3⋊C4—22no—
112Dic3⋊C4—62no—
113C4×Dic3—21no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C4×Dic3—62no—
120C2×C3⋊C8—22no—
121ΓL(1,𝔽25)—64no—
122ΓL(1,𝔽25)—64no—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3—22no—
125C2×C3⋊D3C4×D412yes—
126C2×C3×D3—22no—
127C2×C3×D3—42no—
128#157—44no—
129C32×C4—22no—
130C32×C4C4×D412yes—
131C3⋊Dic3—22no—
132C3⋊Dic3C2×C4211yescharacteristic
133C3⋊Dic3#11711yescharacteristic
134C3×Dic3—22no—
135C3×Dic3—42no—
136C2×#41—91no—
137C2×M16—92no—
138C4×Q8—92no—
139C4×D4—92no—
140C4×D4—182no—
141#117—61no—
142#117—91no—
143C2×C42—91no—
144C2×C42—92no—
145C2×C42—181no—
146#104—98no—
147#97—181no—
148C4×C8—61no—
149#95—182no—
150C23×C3—61no—
151C22×D3—21no—
152C22×D3—61no—
153C22×D3—61no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—64no—
159C2×C3×C4—61no—
160C2×C3×C4—62no—
161#67—62no—
162#67—64no—
163#67—62no—
164C2×Dic3—21no—
165C2×Dic3—22no—
166C2×Dic3—62no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—62no—
170C2×Dic3—124no—
171D12—64no—
172C4×D3—24no—
173C4×D3—62no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—62no—
177C4×D3—124no—
178C4×D3—124no—
179C4×D3—124no—
180Dic6—62no—
181Dic6—62no—
182C3×C8—64no—
183C3⋊C8—24no—
184C2×C32C4×C22⋊C411yescharacteristic
185C2×C32#42112yes—
186C3⋊D3—22no—
187C3×D3—42no—
188#41—94no—
189#41—182no—
190C2×Q8—91no—
191C2×D4—91no—
192C2×D4—181no—
193C22×C4—61no—
194C22×C4—91no—
195C22×C4—92no—
196C22×C4—182no—
197C22×C4—182no—
198M16—94no—
199M16—182no—
200C2×C8—62no—
201C4⋊C4—62no—
202C4⋊C4—92no—
203C22⋊C4—62no—
204C22⋊C4—181no—
205C42—61no—
206C42—91no—
207C42—92no—
208C42—94no—
209C42—182no—
210C42—182no—
211C42GO+(4,𝔽2)11yescharacteristic
212C22×C3—21no—
213C22×C3—21no—
214C22×C3—62no—
215C22×C3—122no—
216C2×D3—22no—
217C2×D3—42no—
218C2×D3—62no—
219C2×D3—62no—
220C2×D3—122no—
221C2×D3—122no—
222C3×C4—24no—
223C3×C4—22no—
224C3×C4—22no—
225C3×C4—42no—
226C3×C4—62no—
227C3×C4—122no—
228Dic3—22no—
229Dic3—42no—
230Dic3—61no—
231Dic3—61no—
232Dic3—61no—
233Dic3—61no—
234Dic3—64no—
235Dic3—122no—
236C32#175911yescharacteristic, complemented, Sylow
237C23—61no—
238C23—91no—
239Q8—92no—
240Q8—181no—
241D4—92no—
242D4—184no—
243D4—181no—
244C2×C4—61no—
245C2×C4—64no—
246C2×C4—62no—
247C2×C4—91no—
248C2×C4—92no—
249C2×C4—92no—
250C2×C4—92no—
251C2×C4—184no—
252C2×C4—362no—
253C2×C4—364no—
254C2×C4—364no—
255C2×C4D32⋊C412yes—
256C2×C4C2×GO+(4,𝔽2)11yescharacteristic
257C8—64no—
258C2×C3—22no—
259C2×C3—22no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—122no—
263D3—42no—
264D3—122no—
265D3—122no—
266C22—62no—
267C22—92no—
268C22—122no—
269C22—182no—
270C22C2×D32⋊C411yescharacteristic
271C4—22no—
272C4—62no—
273C4—91no—
274C4—91no—
275C4—122no—
276C4—182no—
277C4—364no—
278C4C4×GO+(4,𝔽2)12yes—
279C3—21no—
280C3—21no—
281C2—122no—
282C2—182no—
283C2#1059332412yes—
284C2C4×D32⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC3⋊Dic3C2×C42
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3798C22
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1759
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593733C2semidirect
4. C4×#3712C2semidirect
5. #10590047C2semidirect
10. #63902C4semidirect
14. #63838C4semidirect
17. #63731C4semidirect
33. C4×#157C2×C4semidirect
45. #3712C2×C4semidirect
236. C32#1759semidirect

Maximal subgroups

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

subgroupindex
#105939662
#105937332
C2×#637312
C4×#37122
#105900472
#17599