Finite Group Databasebeta

← #11771238

Subgroups — #11771238

Order 1152.

412 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 47 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#10593803C211yesmaximal, characteristic
2#10591325C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3788—21no—
6C2×C3×C4⋊Dic3—21no—
7C2×#3722C412yes—
8C2×#3712C412yescomplemented
9C22⋊#622—21no—
10#63778C412yescomplemented
11C3×#830—21no—
12#63579—21no—
13#63557—21no—
14#4987—61no—
15#4726—61no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C2×C4×C3⋊D3—42no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3Q811yescharacteristic
24C22×C3×Dic3—22no—
25C2×#622—22no—
26#3788—42no—
27C3×C4⋊Dic3—42no—
28C2×C3×C3⋊C8—22no—
29#3722—42no—
30#3712—42no—
31#1305—91nomaximal, Sylow
32C22×C4×D3—61no—
33C22×C4×D3—61no—
34C2×C3×C4⋊C4—61no—
35C2×(C2×D3)⋊C4—62no—
36C2×C4⋊Dic3—21no—
37C2×ΓL(1,𝔽25)—62no—
38C3×C22⋊C8—61no—
39C3⋊#95—62no—
40#830—21no—
41(C2×D3)⋊C8—62no—
42C23×C32C22⋊C411yescharacteristic
43C22×C3⋊D3—21no—
44C22×C3⋊D3—21no—
45C22×C3⋊D3—41no—
46C22×C3⋊D3—41no—
47C22×C3⋊D3C4211yescharacteristic
48C22×C3⋊D3C4⋊C411yescharacteristic
49C2×C32×C4—22no—
50C2×C32×C4C22⋊C411yescharacteristic
51C2×C32×C4C4⋊C411yescharacteristic
52C2×C3⋊Dic3—41no—
53C2×C3⋊Dic3C22⋊C411yescharacteristic
54C2×C3⋊Dic3C4⋊C411yescharacteristic
55C4×C3⋊D3—22no—
56C4×C3⋊D3—22no—
57C4×C3⋊D3—41no—
58C4×C3⋊D3—41no—
59C2×C3×Dic3—42no—
60C2×C3×Dic3—42no—
61C2×C3×Dic3—42no—
62#622—42no—
63C3×C3⋊C8—42no—
64#407—91no—
65#407—91no—
66#380—91no—
67C23×D3—61no—
68C23×D3—61no—
69C22×C3×C4—21no—
70C22×C3×C4—21no—
71C22×C3×C4—62no—
72C22×Dic3—22no—
73C22×Dic3—61no—
74C22×Dic3—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—61no—
83C2×C4×D3—124no—
84C2×C4×D3—122no—
85C2×C4×D3—122no—
86C2×C3×C8—62no—
87C3×C4⋊C4—122no—
88(C2×D3)⋊C4—124no—
89C4⋊Dic3—42no—
90C2×C3⋊C8—22no—
91ΓL(1,𝔽25)—124no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32#9511yescharacteristic
95C22×C32#10011yescharacteristic
96C22×C32#10111yescharacteristic
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3—21no—
101C2×C3⋊D3—21no—
102C2×C3⋊D3—21no—
103C2×C3⋊D3—42no—
104C2×C3⋊D3—42no—
105C32×C4—21no—
106C32×C4#9912yes—
107C3⋊Dic3—21no—
108C3⋊Dic3—21no—
109C3×Dic3—82no—
110C23×C4—91no—
111C2×M16—92no—
112C2×M16—181no—
113C2×C4⋊C4—61no—
114C2×C22⋊C4—92no—
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—121no—
129C22×D3—121no—
130C22×D3—122no—
131C22×D3—122no—
132C22×D3—121no—
133C22×D3—121no—
134C22×D3—121no—
135C22×D3—121no—
136C2×C3×C4—22no—
137C2×C3×C4—22no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—42no—
143C2×C3×C4—122no—
144C2×C3×C4—122no—
145C2×C3×C4—122no—
146C2×Dic3—42no—
147C2×Dic3—42no—
148C2×Dic3—42no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—61no—
152C2×Dic3—61no—
153C2×Dic3—122no—
154C2×Dic3—121no—
155C2×Dic3—121no—
156C4×D3—64no—
157C4×D3—122no—
158C4×D3—122no—
159C4×D3—122no—
160C4×D3—122no—
161C4×D3—122no—
162C4×D3—122no—
163C4×D3—122no—
164C3×C8—122no—
165C3⋊C8—42no—
166C2×C32—21no—
167C2×C32—21no—
168C2×C32#34211yescharacteristic
169C2×C32#34311yescharacteristic
170C2×C32#34411yescharacteristic
171C3⋊D3—41no—
172C3⋊D3—41no—
173C24—91no—
174C22×C4—62no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—362no—
181C22×C4GO+(4,𝔽2)11yescharacteristic
182M16—362no—
183M16—362no—
184C2×C8—62no—
185C2×C8—182no—
186C4⋊C4—122no—
187C22⋊C4—362no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—21no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—41no—
199C22×C3—41no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—62no—
203C2×D3—62no—
204C2×D3—121no—
205C2×D3—121no—
206C2×D3—121no—
207C2×D3—121no—
208C2×D3—121no—
209C2×D3—121no—
210C2×D3—121no—
211C2×D3—121no—
212C2×D3—122no—
213C2×D3—122no—
214C2×D3—122no—
215C2×D3—122no—
216C2×D3—124no—
217C2×D3—124no—
218C3×C4—22no—
219C3×C4—22no—
220C3×C4—22no—
221C3×C4—41no—
222C3×C4—242no—
223Dic3—62no—
224Dic3—82no—
225Dic3—121no—
226Dic3—121no—
227Dic3—121no—
228C32#130511yescharacteristic, complemented, Sylow
229C23—91no—
230C23—91no—
231C23—181no—
232C23—181no—
233C23—361no—
234C23—361no—
235C23D32⋊C411yescharacteristic
236C2×C4—22no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—122no—
240C2×C4—122no—
241C2×C4—122no—
242C2×C4—182no—
243C2×C4—182no—
244C2×C4—361no—
245C2×C4—361no—
246C2×C4—361no—
247C2×C4D32⋊C411yescharacteristic
248C2×C4#377311yescharacteristic
249C8—122no—
250C8—362no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—41no—
262C2×C3—41no—
263D3—122no—
264D3—122no—
265D3—122no—
266D3—122no—
267C22—21no—
268C22—21no—
269C22—181no—
270C22—181no—
271C22—181no—
272C22—181no—
273C22—181no—
274C22—181no—
275C22—362no—
276C22—362no—
277C22#6372711yescharacteristic
278C22#6372811yescharacteristic
279C22#6373711yescharacteristic
280C4—21no—
281C4—181no—
282C4—181no—
283C4—242no—
284C4#6373812yes—
285C3—21no—
286C3—21no—
287C2—21no—
288C2—21no—
289C2—361no—
290C2—361no—
291C2#1059005211yescharacteristic
292C2#1059005611yescharacteristic
293C2#1059007611yescharacteristic
subgroupG/H
centerC22#63737
commutatorC22×C3⋊D3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1305
LCSG ▷ C22×C3⋊D3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×#3712C4semidirect
10. #63778C4semidirect
228. C32#1305semidirect

Maximal subgroups

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

subgroupindex
#105938032
#105913252
#105911592
#13059