Finite Group Databasebeta

← #11771978

Subgroups — #11771978

Order 1152.

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

normal subgroups only

This group has 371 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#10592678C211yesmaximal, characteristic
2C3×#4530C211yesmaximal, characteristic
3C3×#4528C211yesmaximal, characteristic
4#67494—31nomaximal
5#67457—31nomaximal
6C22×#634C411yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×#3750—21no—
9C2×C3×#208—21no—
10#63658—21no—
11#63658C411yescharacteristic
12C3×#830—21no—
13#4979—31no—
14#4979—31no—
15#4979—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—
25C2×#634—41no—
26C2×#634—42no—
27C32×C4⋊C4—41no—
28#3750—42no—
29C3×#208—22no—
30C3×#208—41no—
31C2×C3×C3⋊C8—41no—
32C2×C3×C3⋊C8—41no—
33#1354—91noSylow
34C22×Dic6—31no—
35C22×Dic6—31no—
36C22×Dic6—61no—
37C2×C3×M16—61no—
38C2×C3×C4⋊C4—21no—
39C2×C3×C4⋊C4C2×D311yescharacteristic
40C2×C3×C4⋊C4C2×D311yescharacteristic
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×C4SD1611yescharacteristic
61C2×C32×C4Q1611yescharacteristic
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—41no—
66C2×C3⋊Dic3—41no—
67C2×C3⋊Dic3—41no—
68#634—42no—
69#634—42no—
70C3×C3⋊C8—42no—
71C3×C3⋊C8—81no—
72#395—91no—
73#343—31no—
74#324—31no—
75C22×C3×C4—21no—
76C22×C3×C4—21no—
77C22×C3×C4—21no—
78C22×C3×C4C4×D311yescharacteristic
79C22×C3×C4C4×D311yescharacteristic
80C22×C3×C4D1211yescharacteristic
81C22×C3×C4D1211yescharacteristic
82C22×C3×C4#6711yescharacteristic
83C22×C3×C4#6711yescharacteristic
84C22×Dic3—62no—
85C22×Dic3—62no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C2×Dic6—124no—
91C2×Dic6—122no—
92C2×Dic6—121no—
93C2×Dic6—121no—
94C2×Dic6—122no—
95C2×Dic6—122no—
96C3×M16—62no—
97C3×M16—121no—
98C2×C3×C8—121no—
99C2×C3×C8—121no—
100C3×C4⋊C4—41no—
101C3×C4⋊C4—41no—
102C3×C4⋊C4—42no—
103Dic3⋊C4—122no—
104Dic3⋊C4—122no—
105Dic3⋊C4—124no—
106#208—22no—
107#208—41no—
108C2×C3⋊C8—41no—
109C2×C3⋊C8—41no—
110C22×C32—21no—
111C22×C32—21no—
112C22×C32#9911yescharacteristic
113C22×C32#10311yescharacteristic
114C22×C32#10411yescharacteristic
115C32×C4—21no—
116C32×C4—21no—
117C32×C4—41no—
118C32×C4—41no—
119C3⋊Dic3—42no—
120C3⋊Dic3—42no—
121C22×Q8—91no—
122C2×M16—61no—
123C2×C4⋊C4—181no—
124C2×C4⋊C4D3211yescharacteristic
125C22⋊C8—61no—
126#95—91no—
127#95—181no—
128C23×C3—21no—
129C23×C3(C2×D3)⋊C411yescharacteristic
130C23×C3(C2×D3)⋊C411yescharacteristic
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—22no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—41no—
143C2×C3×C4—41no—
144C2×C3×C4—41no—
145C2×C3×C4—42no—
146C2×C3×C4—41no—
147C2×C3×C4—41no—
148C2×C3×C4—41no—
149C2×C3×C4—41no—
150C2×C3×C4—42no—
151C2×C3×C4#20411yescharacteristic
152C2×C3×C4Dic1211yescharacteristic
153C2×C3×C4#21411yescharacteristic
154C2×C3×C4#21611yescharacteristic
155C2×Dic3—64no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—64no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—122no—
162C2×Dic3—121no—
163C2×Dic3—121no—
164C2×Dic3—122no—
165C2×Dic3—121no—
166C2×Dic3—121no—
167C2×Dic3—122no—
168C2×Dic3—122no—
169C2×Dic3—121no—
170C2×Dic3—121no—
171C2×Dic3—121no—
172C2×Dic3—121no—
173Dic6—124no—
174Dic6—124no—
175Dic6—122no—
176Dic6—122no—
177Dic6—122no—
178Dic6—122no—
179C3×C8—122no—
180C3×C8—241no—
181C3⋊C8—42no—
182C3⋊C8—81no—
183C2×C32—21no—
184C2×C32—21no—
185C2×C32#32811yescharacteristic
186C2×C32AΣL(1,𝔽16)11yescharacteristic
187C2×C32#35611yescharacteristic
188C2×Q8—361no—
189C2×Q8—362no—
190C22×C4—181no—
191C22×C4—181no—
192C22×C4#62411yescharacteristic
193C22×C4#62611yescharacteristic
194C22×C4#62611yescharacteristic
195M16—62no—
196M16—121no—
197C2×C8—121no—
198C2×C8—121no—
199C4⋊C4—41no—
200C4⋊C4—362no—
201C22×C3—22no—
202C22×C3—22no—
203C22×C3—21no—
204C22×C3—21no—
205C22×C3—21no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3—21no—
210C22×C3#80511yescharacteristic
211C22×C3#80611yescharacteristic
212C22×C3#80611yescharacteristic
213C22×C3#81011yescharacteristic
214C22×C3#81611yescharacteristic
215C22×C3#82511yescharacteristic
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—41no—
221C3×C4—41no—
222C3×C4—42no—
223C3×C4—41no—
224C3×C4—41no—
225C3×C4—41no—
226C3×C4—41no—
227C3×C4—81no—
228Dic3—124no—
229Dic3—124no—
230Dic3—122no—
231Dic3—122no—
232Dic3—122no—
233Dic3—122no—
234C32#135411yescharacteristic, complemented, Sylow
235C23#372211yescharacteristic
236Q8—362no—
237Q8—362no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—182no—
245C2×C4—182no—
246C2×C4—361no—
247C2×C4—361no—
248C2×C4—361no—
249C2×C4—361no—
250C2×C4#371611yescharacteristic
251C2×C4#371911yescharacteristic
252C8—122no—
253C8—241no—
254C2×C3—22no—
255C2×C3—22no—
256C2×C3—21no—
257C2×C3—21no—
258C2×C3—21no—
259C2×C3—21no—
260C2×C3—21no—
261C2×C3—21no—
262C2×C3—21no—
263C2×C3#445211yescharacteristic
264C2×C3#446711yescharacteristic
265C2×C3#447111yescharacteristic
266C2×C3#447511yescharacteristic
267C2×C3#447811yescharacteristic
268C2×C3#447811yescharacteristic
269C22—21no—
270C22—21no—
271C22#6356711yescharacteristic
272C22#6357011yescharacteristic
273C22#6358111yescharacteristic
274C4—21no—
275C4—21no—
276C4—41no—
277C4—41no—
278C4—362no—
279C4—362no—
280C3—21no—
281C3#6745711yescharacteristic, complemented
282C3#6749411yescharacteristic, complemented
283C2—21no—
284C2—21no—
285C2#1058915411yescharacteristic
286C2#1058917411yescharacteristic
287C2#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#1354
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
234. C32#1354semidirect
281. C3#67457semidirect
282. C3#67494semidirect

Maximal subgroups

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

subgroupindex
#105926782
C3×#45302
C3×#45282
#674943
#674573