Finite Group Databasebeta

← #11771842

Subgroups — #11771842

Order 1152.

323 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 323 conjugacy classes of subgroups — too many to draw. Only its 64 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#10592680C211yesmaximal, characteristic
2C3×#4530C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4#67495—31nomaximal
5#67458—31nomaximal
6C2×C32×C4⋊C4C2211yescharacteristic
7C2×C4⋊(C3⋊Dic3)C411yescharacteristic
8C2×#3750—21no—
9C2×C3×#208—21no—
10#63658—21no—
11#63658C411yescharacteristic
12C3×#830—21no—
13#4981—31no—
14#4981—31no—
15#4981—61no—
16C3×#343—31no—
17C3×#324—31no—
18#4530D311yescharacteristic
19#4528D311yescharacteristic
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3—21no—
25C32×C4⋊C4—41no—
26C4⋊(C3⋊Dic3)—41no—
27#3750—41no—
28#3750—41no—
29C3×#208—22no—
30C3×#208—41no—
31C2×C3×C3⋊C8—41no—
32C2×C3×C3⋊C8—41no—
33#1346—91noSylow
34C2×C3×M16—61no—
35C2×C3×C4⋊C4—21no—
36C2×C3×C4⋊C4C2×D311yescharacteristic
37C2×C3×C4⋊C4C2×D311yescharacteristic
38C2×C4⋊Dic3—31no—
39C2×C4⋊Dic3—31no—
40C2×C4⋊Dic3—61no—
41C2×Dic3⋊C4—62no—
42C2×Dic3⋊C4—61no—
43C2×Dic3⋊C4—61no—
44C2×#208—21no—
45C3×C22⋊C8—61no—
46C3⋊#95—31no—
47C3⋊#95—31no—
48C3⋊#95—61no—
49C3⋊#95—62no—
50C3⋊#95—61no—
51C3⋊#95—61no—
52#830—21no—
53C23×C32C22⋊C411yescharacteristic
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4—21no—
57C2×C32×C4—21no—
58C2×C32×C4—41no—
59C2×C32×C4—41no—
60C2×C32×C4D811yescharacteristic
61C2×C32×C4SD1611yescharacteristic
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3—41no—
68C3×C3⋊C8—42no—
69C3×C3⋊C8—81no—
70#398—91no—
71#343—31no—
72#324—31no—
73C22×C3×C4—21no—
74C22×C3×C4—21no—
75C22×C3×C4—21no—
76C22×C3×C4C4×D311yescharacteristic
77C22×C3×C4C4×D311yescharacteristic
78C22×C3×C4D1211yescharacteristic
79C22×C3×C4D1211yescharacteristic
80C22×C3×C4#6711yescharacteristic
81C22×C3×C4#6711yescharacteristic
82C22×Dic3—62no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—62no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C3×M16—62no—
89C3×M16—121no—
90C2×C3×C8—121no—
91C2×C3×C8—121no—
92C3×C4⋊C4—41no—
93C3×C4⋊C4—41no—
94C3×C4⋊C4—42no—
95C4⋊Dic3—122no—
96C4⋊Dic3—121no—
97C4⋊Dic3—121no—
98Dic3⋊C4—122no—
99Dic3⋊C4—122no—
100Dic3⋊C4—121no—
101Dic3⋊C4—121no—
102Dic3⋊C4—121no—
103Dic3⋊C4—121no—
104#208—22no—
105#208—41no—
106C2×C3⋊C8—41no—
107C2×C3⋊C8—41no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32#9911yescharacteristic
111C22×C32#10211yescharacteristic
112C22×C32#10411yescharacteristic
113C32×C4—21no—
114C32×C4—21no—
115C32×C4—41no—
116C32×C4—41no—
117C3⋊Dic3—42no—
118C3⋊Dic3—81no—
119C2×M16—61no—
120C2×C4⋊C4—91no—
121C2×C4⋊C4—181no—
122C2×C4⋊C4D3211yescharacteristic
123C22⋊C8—61no—
124#95—91no—
125#95—181no—
126C23×C3—21no—
127C23×C3(C2×D3)⋊C411yescharacteristic
128C23×C3(C2×D3)⋊C411yescharacteristic
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—22no—
134C2×C3×C4—21no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—41no—
141C2×C3×C4—41no—
142C2×C3×C4—41no—
143C2×C3×C4—42no—
144C2×C3×C4—41no—
145C2×C3×C4—41no—
146C2×C3×C4—41no—
147C2×C3×C4—41no—
148C2×C3×C4—42no—
149C2×C3×C4#20411yescharacteristic
150C2×C3×C4D2411yescharacteristic
151C2×C3×C4#21311yescharacteristic
152C2×C3×C4#21511yescharacteristic
153C2×Dic3—64no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—122no—
157C2×Dic3—122no—
158C2×Dic3—121no—
159C2×Dic3—121no—
160C2×Dic3—121no—
161C2×Dic3—121no—
162C2×Dic3—122no—
163C2×Dic3—122no—
164C2×Dic3—122no—
165C2×Dic3—121no—
166C2×Dic3—121no—
167C2×Dic3—121no—
168C2×Dic3—121no—
169C2×Dic3—121no—
170C2×Dic3—121no—
171C3×C8—122no—
172C3×C8—241no—
173C3⋊C8—42no—
174C3⋊C8—81no—
175C2×C32—21no—
176C2×C32—21no—
177C2×C32#32711yescharacteristic
178C2×C32#35211yescharacteristic
179C2×C32#35611yescharacteristic
180C22×C4—181no—
181C22×C4—181no—
182C22×C4#62411yescharacteristic
183C22×C4#62611yescharacteristic
184C22×C4#62611yescharacteristic
185M16—62no—
186M16—121no—
187C2×C8—121no—
188C2×C8—121no—
189C4⋊C4—41no—
190C4⋊C4—361no—
191C4⋊C4—361no—
192C4⋊C4—361no—
193C22×C3—22no—
194C22×C3—22no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—21no—
202C22×C3#80511yescharacteristic
203C22×C3#80611yescharacteristic
204C22×C3#80611yescharacteristic
205C22×C3#80911yescharacteristic
206C22×C3#82111yescharacteristic
207C22×C3#82511yescharacteristic
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—41no—
213C3×C4—41no—
214C3×C4—42no—
215C3×C4—41no—
216C3×C4—41no—
217C3×C4—41no—
218C3×C4—41no—
219C3×C4—81no—
220Dic3—124no—
221Dic3—122no—
222Dic3—122no—
223Dic3—242no—
224Dic3—241no—
225Dic3—241no—
226C32#134611yescharacteristic, complemented, Sylow
227C23#372211yescharacteristic
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—182no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4—361no—
238C2×C4—361no—
239C2×C4—361no—
240C2×C4#371411yescharacteristic
241C2×C4#371711yescharacteristic
242C8—122no—
243C8—241no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3#445111yescharacteristic
254C2×C3#447011yescharacteristic
255C2×C3#447211yescharacteristic
256C2×C3#447611yescharacteristic
257C2×C3#447811yescharacteristic
258C2×C3#447811yescharacteristic
259C22—21no—
260C22—21no—
261C22#6356411yescharacteristic
262C22#6357011yescharacteristic
263C22#6358111yescharacteristic
264C4—21no—
265C4—21no—
266C4—41no—
267C4—41no—
268C4—362no—
269C4—721no—
270C3—21no—
271C3#6745811yescharacteristic, complemented
272C3#6749511yescharacteristic, complemented
273C2—21no—
274C2—21no—
275C2#1058915111yescharacteristic
276C2#1058917711yescharacteristic
277C2#1058918511yescharacteristic
subgroupG/H
centerC22#63581
commutatorC22×C32×C4C2×C4
Frattini, hypercenterC2×C4⋊C4D32
Fitting, cosocleC2×C32×C4⋊C4C22
socleC22×C32#99
prime radicalC23×C32C22⋊C4
hypocenterC32#1346
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
226. C32#1346semidirect
271. C3#67458semidirect
272. C3#67495semidirect

Maximal subgroups

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

subgroupindex
#105926802
C3×#45302
C3×#45282
#674953
#674583