Finite Group Databasebeta

← #11791673

Subgroups — #11791673

Order 1152.

442 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 75 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#10593948C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4#10590049C212yesmaximal
5#10590049C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×C4×#157—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×#870—21no—
10#63900C2211yescharacteristic
11#63900C2211yescharacteristic
12#63883—21no—
13#63883—21no—
14#63872—21no—
15#63870C412yescomplemented
16#63870C412yescomplemented
17C2×#3710C2212yes—
18#63781—21no—
19C3×C4⋊(C3⋊C8)—21no—
20#63572—21no—
21D3×#125—61no—
22D3×C4⋊C8—61no—
23C22×#157—22no—
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×#624—21no—
28C2×#624—21no—
29C4⋊#157—22no—
30C4⋊#157Q814yes—
31C4×#157—42no—
32C32×C42D411yescharacteristic
33C4×C3⋊Dic3C2×C411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3D411yescharacteristic
36C3×C4⋊Dic3—21no—
37C3×C4⋊Dic3—21no—
38C3×Dic3⋊C4—22no—
39C3×Dic3⋊C4—22no—
40C2×C3×C3⋊C8—22no—
41#3724C2×C412yes—
42#3724C2×C412yes—
43Dic3⋊Dic3—22no—
44Dic3⋊Dic3—22no—
45#3710—24no—
46#1989—91nomaximal, Sylow
47C3×#125—61no—
48C2×D3×C8—62no—
49D3×C4⋊C4—61no—
50D3×C4⋊C4—61no—
51D3×C4⋊C4—62no—
52D3×C4⋊C4—62no—
53#890—61no—
54#890—61no—
55#889—62no—
56#889—62no—
57C42×D3—61no—
58C42×D3—61no—
59#870—21no—
60C3×C4⋊C8—61no—
61Dic3⋊C8—62no—
62C4⋊(C3⋊C8)—21no—
63C22×C3⋊D3C2×D411yescharacteristic
64C2×#157—24no—
65C2×#157—42no—
66C2×#157—42no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C22⋊C411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C3⋊Dic3C22⋊C411yescharacteristic
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22×C411yescharacteristic
73C4×C3⋊D3—22no—
74C4×C3⋊D3—21no—
75C4×C3⋊D3—21no—
76C4×C3⋊D3C2×Q812yes—
77C4×C3⋊D3#4112yes—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80#624—42no—
81#624—41no—
82#624—41no—
83C3×C3⋊C8—42no—
84C2×#125—91no—
85C2×C4⋊C8—91no—
86C4×C4⋊C4—91no—
87#340—92no—
88#340—92no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C4×D3—61no—
92C2×C4×D3—61no—
93C2×C4×D3—61no—
94C2×C4×D3—61no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C3×C8—62no—
98C3×C4⋊C4—62no—
99C3×C4⋊C4—62no—
100C3×C4⋊C4—61no—
101C3×C4⋊C4—61no—
102C3×C42—21no—
103C3×C42—21no—
104C4⋊Dic3—21no—
105C4⋊Dic3—21no—
106C4⋊Dic3—62no—
107C4⋊Dic3—62no—
108Dic3⋊C4—22no—
109Dic3⋊C4—22no—
110Dic3⋊C4—62no—
111Dic3⋊C4—62no—
112Dic3⋊C4—62no—
113Dic3⋊C4—62no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C2×C3⋊C8—22no—
121D3×C8—124no—
122C22×C32C2×C22⋊C411yescharacteristic
123C2×C3⋊D3C22⋊Q812yes—
124C2×C3⋊D3#13512yes—
125C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
126C2×C3⋊D3#13711yescharacteristic
127#157—44no—
128C32×C4—21no—
129C32×C4—21no—
130C32×C4#12411yescharacteristic
131C32×C4C4⋊Q811yescharacteristic
132C3⋊Dic3—21no—
133C3⋊Dic3—21no—
134C3⋊Dic3C4×Q812yes—
135C3×Dic3—42no—
136C3×Dic3—42no—
137C22×C8—92no—
138#125—61no—
139#125—92no—
140#125—92no—
141#125—181no—
142C2×C4⋊C4—91no—
143C2×C4⋊C4—91no—
144C2×C4⋊C4—92no—
145C2×C4⋊C4—181no—
146C2×C4⋊C4—181no—
147C2×C42—91no—
148C2×C42—181no—
149C4⋊C8—61no—
150C4⋊C8—181no—
151#95—181no—
152C22×D3—61no—
153C22×D3—61no—
154C2×C3×C4—21no—
155C2×C3×C4—21no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—62no—
161C2×C3×C4—62no—
162C2×Dic3—22no—
163C2×Dic3—22no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C4×D3—62no—
171C4×D3—62no—
172C4×D3—62no—
173C4×D3—62no—
174C4×D3—64no—
175C4×D3—121no—
176C4×D3—121no—
177C4×D3—122no—
178C4×D3—121no—
179C4×D3—121no—
180C4×D3—124no—
181C4×D3—122no—
182C4×D3—122no—
183C3×C8—122no—
184C3⋊C8—42no—
185C2×C32#39111yescharacteristic
186C2×C32#41611yescharacteristic
187C2×C32#41711yescharacteristic
188C3⋊D3#47812yes—
189C3⋊D3#47912yes—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—91no—
193C22×C4—181no—
194C22×C4—181no—
195C22×C4—182no—
196C2×C8—62no—
197C2×C8—184no—
198C4⋊C4—61no—
199C4⋊C4—61no—
200C4⋊C4—62no—
201C4⋊C4—62no—
202C4⋊C4—92no—
203C4⋊C4—92no—
204C4⋊C4—94no—
205C4⋊C4—182no—
206C4⋊C4—182no—
207C4⋊C4—182no—
208C42—91no—
209C42—91no—
210C42—91no—
211C42—362no—
212C42GO+(4,𝔽2)11yescharacteristic
213C22×C3—21no—
214C22×C3—21no—
215C2×D3—62no—
216C2×D3—62no—
217C2×D3—62no—
218C2×D3—62no—
219C2×D3—61no—
220C2×D3—61no—
221C2×D3—61no—
222C2×D3—61no—
223C3×C4—22no—
224C3×C4—21no—
225C3×C4—21no—
226C3×C4—21no—
227C3×C4—21no—
228C3×C4—41no—
229C3×C4—41no—
230C3×C4—41no—
231C3×C4—122no—
232C3×C4—122no—
233Dic3—42no—
234Dic3—42no—
235Dic3—62no—
236Dic3—62no—
237Dic3—62no—
238Dic3—121no—
239Dic3—121no—
240Dic3—121no—
241C32#198911yescharacteristic, complemented, Sylow
242C23—91no—
243C2×C4—62no—
244C2×C4—62no—
245C2×C4—91no—
246C2×C4—92no—
247C2×C4—92no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—181no—
251C2×C4—182no—
252C2×C4—181no—
253C2×C4—184no—
254C2×C4—362no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4—362no—
258C2×C4—362no—
259C2×C4D32⋊C411yescharacteristic
260C2×C4D32⋊C411yescharacteristic
261C2×C4C2×GO+(4,𝔽2)11yescharacteristic
262C8—122no—
263C2×C3—21no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269D3—62no—
270D3—62no—
271D3—62no—
272D3—62no—
273C22—92no—
274C22—91no—
275C22—91no—
276C22—92no—
277C22C2×D32⋊C411yescharacteristic
278C4—21no—
279C4—21no—
280C4—92no—
281C4—122no—
282C4—122no—
283C4—181no—
284C4—181no—
285C4—364no—
286C4#6422111yescharacteristic
287C4#6422211yescharacteristic
288C3—21no—
289C3—21no—
290C2—92no—
291C2—92no—
292C2#1059331711yescharacteristic
293C2#1059331911yescharacteristic
294C2#1059334211yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1989
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
15. #63870C4semidirect
16. #63870C4semidirect
241. C32#1989semidirect

Maximal subgroups

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

subgroupindex
#105939482
C4×C4⋊#1572
#105903312
#105900492
#19899