Finite Group Databasebeta

← #11770848

Subgroups — #11770848

Order 1152.

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

normal subgroups only

This group has 430 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
1C4×C22⋊#157C211yesmaximal, characteristic
2#10591152C211yesmaximal, characteristic
3C2×#63557C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C412yes—
6C2×C4×#157—21no—
7C22×C3×C3⋊C8—21no—
8C2×#3710C412yescomplemented
9#63781—21no—
10C3×#830—21no—
11#63557—21no—
12#63557—21no—
13#63557C412yescomplemented
14C2×(C2×D3)⋊C8—61no—
15D3×C22⋊C8—61no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×#157—22no—
18C22×C32×C4D411yescharacteristic
19C22×C3⋊Dic3Q811yescharacteristic
20C2×C4×C3⋊D3—42no—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C22⋊#157—22no—
26C22⋊#157C814yescomplemented
27C4×#157—42no—
28C2×C3×C3⋊C8—22no—
29C2×C3×C3⋊C8—22no—
30C2×C3×C3⋊C8—42no—
31#3710—42no—
32#1282—91nomaximal, Sylow
33C22×C4×D3—61no—
34C22×C4×D3—61no—
35C22×C3×C8—61no—
36C22×C3⋊C8—21no—
37C2×D3×C8—62no—
38C3×C22⋊C8—61no—
39#830—21no—
40(C2×D3)⋊C8—62no—
41(C2×D3)⋊C8—62no—
42(C2×D3)⋊C8—62no—
43C23×C32C4⋊C411yescharacteristic
44C22×C3⋊D3—41no—
45C22×C3⋊D3—41no—
46C22×C3⋊D3C4211yescharacteristic
47C22×C3⋊D3C22⋊C411yescharacteristic
48C22×C3⋊D3C2×C812yes—
49C22×C3⋊D3M1612yes—
50C2×#157—24no—
51C2×#157—42no—
52C2×#157—42no—
53C2×C32×C4—22no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3C4⋊C411yescharacteristic
58C2×C3⋊Dic3C4⋊C411yescharacteristic
59C4×C3⋊D3—22no—
60C4×C3⋊D3—22no—
61C4×C3⋊D3—41no—
62C4×C3⋊D3—41no—
63C3×C3⋊C8—42no—
64C3×C3⋊C8—42no—
65C2×C22⋊C8—91no—
66C2×C22⋊C8—91no—
67C4×C22⋊C4—91no—
68C23×D3—61no—
69C23×D3—61no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×Dic3—61no—
73C22×Dic3—61no—
74C2×C4×D3—61no—
75C2×C4×D3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—124no—
83C2×C4×D3—122no—
84C2×C4×D3—122no—
85C2×C3×C8—62no—
86C2×C3×C8—62no—
87C2×C3×C8—122no—
88C2×C3⋊C8—22no—
89C2×C3⋊C8—22no—
90C2×C3⋊C8—42no—
91D3×C8—124no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32#9511yescharacteristic
95C22×C32C4⋊C812yes—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3—42no—
101C2×C3⋊D3—42no—
102C2×C3⋊D3C4×C811yescharacteristic
103C2×C3⋊D3#9711yescharacteristic
104C2×C3⋊D3C22⋊C812yes—
105#157—44no—
106C32×C4—21no—
107C32×C4#9912yes—
108C3⋊Dic3—21no—
109C3⋊Dic3—21no—
110C23×C4—91no—
111C22×C8—61no—
112C22×C8—92no—
113C2×C22⋊C4—92no—
114C2×C42—181no—
115C22⋊C8—61no—
116C22⋊C8—92no—
117C22⋊C8—181no—
118C22⋊C8—181no—
119#95—181no—
120C23×C3—21no—
121C23×C3—21no—
122C22×D3—61no—
123C22×D3—61no—
124C22×D3—61no—
125C22×D3—61no—
126C22×D3—62no—
127C22×D3—62no—
128C22×D3—62no—
129C22×D3—62no—
130C22×D3—122no—
131C22×D3—122no—
132C22×D3—122no—
133C22×D3—122no—
134C2×C3×C4—22no—
135C2×C3×C4—22no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—42no—
141C2×Dic3—61no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—122no—
146C2×Dic3—122no—
147C4×D3—64no—
148C4×D3—122no—
149C4×D3—122no—
150C4×D3—122no—
151C4×D3—122no—
152C4×D3—121no—
153C4×D3—121no—
154C4×D3—121no—
155C4×D3—121no—
156C4×D3—122no—
157C3×C8—122no—
158C3×C8—122no—
159C3⋊C8—42no—
160C3⋊C8—42no—
161C2×C32—22no—
162C2×C32#33611yescharacteristic
163C2×C32#34211yescharacteristic
164C2×C32#34411yescharacteristic
165C3⋊D3—21no—
166C3⋊D3—21no—
167C3⋊D3—22no—
168C24—91no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—182no—
175C22×C4—362no—
176C22×C4GO+(4,𝔽2)11yescharacteristic
177C2×C8—62no—
178C2×C8—62no—
179C2×C8—122no—
180C2×C8—362no—
181C22⋊C4—94no—
182C22⋊C4—182no—
183C42—362no—
184C22×C3—22no—
185C22×C3—22no—
186C22×C3—22no—
187C22×C3—22no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—41no—
191C22×C3—41no—
192C2×D3—61no—
193C2×D3—61no—
194C2×D3—61no—
195C2×D3—61no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—62no—
199C2×D3—62no—
200C2×D3—121no—
201C2×D3—121no—
202C2×D3—121no—
203C2×D3—121no—
204C2×D3—121no—
205C2×D3—121no—
206C2×D3—124no—
207C2×D3—124no—
208C2×D3—124no—
209C2×D3—124no—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—22no—
213C3×C4—22no—
214C3×C4—41no—
215Dic3—62no—
216Dic3—121no—
217Dic3—121no—
218Dic3—121no—
219C32#128211yescharacteristic, complemented, Sylow
220C23—91no—
221C23—91no—
222C23—92no—
223C23—92no—
224C23—361no—
225C23—361no—
226C23#377311yescharacteristic
227C2×C4—22no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—182no—
231C2×C4—182no—
232C2×C4—184no—
233C2×C4—361no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4—362no—
237C2×C4—362no—
238C2×C4D32⋊C411yescharacteristic
239C2×C4D32⋊C411yescharacteristic
240C8—122no—
241C8—122no—
242C2×C3—24no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—42no—
250D3—62no—
251D3—62no—
252D3—122no—
253D3—122no—
254D3—121no—
255D3—121no—
256C22—21no—
257C22—21no—
258C22—92no—
259C22—91no—
260C22—91no—
261C22—181no—
262C22—181no—
263C22—181no—
264C22—181no—
265C22—362no—
266C22—362no—
267C22#6373212yes—
268C22#6373711yescharacteristic
269C4—21no—
270C4—181no—
271C4—181no—
272C4—364no—
273C4#6373812yes—
274C3—21no—
275C3—21no—
276C2—22no—
277C2—182no—
278C2—181no—
279C2—181no—
280C2#1059004411yescharacteristic
281C2#1059005511yescharacteristic
282C2#1059007611yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊D3C4×C8
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1282
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×#3710C4semidirect
13. #63557C4semidirect
26. C22⋊#157C8semidirect
219. C32#1282semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#1572
#105911522
C2×#635572
#12829