Finite Group Databasebeta

← #11771239

Subgroups — #11771239

Order 1152.

412 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 45 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#10591355C211yesmaximal, characteristic
3#10591159C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3788C412yescomplemented
6C2×#3724—21no—
7C2×#3722C412yes—
8C2×#3712—21no—
9C22⋊#622—21no—
10#63778—21no—
11C3×C3⋊#95—21no—
12C3×#830—21no—
13#63557C412yescomplemented
14#4726—61no—
15#4667—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—
27C2×C3×C3⋊C8—22no—
28#3724—42no—
29#3722—42no—
30#3712—42no—
31#1305—91nomaximal, Sylow
32C22×C4×D3—61no—
33C22×C4×D3—61no—
34C2×(C2×D3)⋊C4—62no—
35C2×Dic3⋊C4—62no—
36C2×ΓL(1,𝔽25)—62no—
37C3×C22⋊C8—61no—
38C3×#95—61no—
39C3⋊#95—21no—
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—41no—
50C2×C32×C4C22⋊C411yescharacteristic
51C2×C32×C4C4⋊C411yescharacteristic
52C2×C3⋊Dic3—22no—
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—124no—
85C2×C3×C8—62no—
86(C2×D3)⋊C4—124no—
87Dic3⋊C4—124no—
88C2×C3⋊C8—22no—
89ΓL(1,𝔽25)—124no—
90C22×C32—21no—
91C22×C32—21no—
92C22×C32#9511yescharacteristic
93C22×C32#10011yescharacteristic
94C22×C32#10111yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3—21no—
101C2×C3⋊D3—42no—
102C2×C3⋊D3—42no—
103C32×C4—21no—
104C32×C4—21no—
105C3⋊Dic3—21no—
106C3⋊Dic3#9912yes—
107C3×Dic3—82no—
108C23×C4—91no—
109C2×M16—92no—
110C2×M16—181no—
111C2×C4⋊C4—181no—
112C2×C22⋊C4—92no—
113C22⋊C8—61no—
114C22⋊C8—92no—
115C22⋊C8—181no—
116C22⋊C8—181no—
117#95—61no—
118C23×C3—21no—
119C23×C3—21no—
120C22×D3—61no—
121C22×D3—61no—
122C22×D3—61no—
123C22×D3—61no—
124C22×D3—62no—
125C22×D3—62no—
126C22×D3—121no—
127C22×D3—121no—
128C22×D3—122no—
129C22×D3—122no—
130C22×D3—122no—
131C22×D3—122no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—42no—
137C2×C3×C4—42no—
138C2×C3×C4—122no—
139C2×C3×C4—122no—
140C2×C3×C4—122no—
141C2×Dic3—42no—
142C2×Dic3—42no—
143C2×Dic3—42no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—61no—
147C2×Dic3—61no—
148C2×Dic3—64no—
149C2×Dic3—122no—
150C4×D3—64no—
151C4×D3—122no—
152C4×D3—122no—
153C4×D3—122no—
154C4×D3—122no—
155C4×D3—122no—
156C4×D3—122no—
157C4×D3—122no—
158C3×C8—122no—
159C3⋊C8—42no—
160C2×C32—21no—
161C2×C32—21no—
162C2×C32#34211yescharacteristic
163C2×C32#34311yescharacteristic
164C2×C32#34411yescharacteristic
165C3⋊D3—41no—
166C3⋊D3—41no—
167C24—91no—
168C22×C4—62no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—362no—
175C22×C4GO+(4,𝔽2)11yescharacteristic
176M16—362no—
177M16—362no—
178C2×C8—62no—
179C2×C8—182no—
180C4⋊C4—362no—
181C22⋊C4—362no—
182C22×C3—22no—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—41no—
191C22×C3—41no—
192C2×D3—62no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—62no—
196C2×D3—121no—
197C2×D3—121no—
198C2×D3—121no—
199C2×D3—121no—
200C2×D3—121no—
201C2×D3—121no—
202C2×D3—121no—
203C2×D3—121no—
204C2×D3—124no—
205C2×D3—124no—
206C2×D3—124no—
207C2×D3—124no—
208C3×C4—22no—
209C3×C4—41no—
210C3×C4—41no—
211C3×C4—41no—
212C3×C4—242no—
213Dic3—62no—
214Dic3—62no—
215Dic3—62no—
216Dic3—82no—
217Dic3—121no—
218C32#130511yescharacteristic, complemented, Sylow
219C23—91no—
220C23—91no—
221C23—181no—
222C23—181no—
223C23—361no—
224C23—361no—
225C23D32⋊C411yescharacteristic
226C2×C4—41no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—122no—
230C2×C4—122no—
231C2×C4—122no—
232C2×C4—182no—
233C2×C4—182no—
234C2×C4—182no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4D32⋊C411yescharacteristic
238C2×C4#377311yescharacteristic
239C8—122no—
240C8—362no—
241C2×C3—22no—
242C2×C3—22no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—41no—
250C2×C3—41no—
251D3—122no—
252D3—122no—
253D3—122no—
254D3—122no—
255C22—21no—
256C22—21no—
257C22—181no—
258C22—181no—
259C22—181no—
260C22—181no—
261C22—181no—
262C22—181no—
263C22—362no—
264C22—362no—
265C22#6372711yescharacteristic
266C22#6372811yescharacteristic
267C22#6373711yescharacteristic
268C4—21no—
269C4—21no—
270C4—92no—
271C4—181no—
272C4—242no—
273C3—21no—
274C3—21no—
275C2—21no—
276C2—21no—
277C2—361no—
278C2—361no—
279C2#1059005211yescharacteristic
280C2#1059005411yescharacteristic
281C2#1059007711yescharacteristic
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
5. C2×#3788C4semidirect
13. #63557C4semidirect
218. C32#1305semidirect

Maximal subgroups

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

subgroupindex
#105938032
#105913552
#105911592
#13059