Finite Group Databasebeta

← #11771827

Subgroups — #11771827

Order 1152.

336 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 31 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#10591394C211yesmaximal, characteristic
2#10590202C211yesmaximal, characteristic, complemented
3#10589168C211yesmaximal, characteristic, complemented
4C22×#625C411yescharacteristic
5C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
6C2×C3×(C2×D3)⋊C4—21no—
7C2×C3×#208—21no—
8C2×(C2×D3)⋊Dic3—21no—
9C22⋊#622—21no—
10#63579C411yescharacteristic
11#4961—61no—
12#4554—61no—
13C23×C3×D3—21no—
14C22×C32×C4D411yescharacteristic
15C22×C3⋊Dic3C2×C411yescharacteristic
16C22×C3⋊Dic3D411yescharacteristic
17C22×C3×Dic3—21no—
18C2×#625—41no—
19C2×#625—42no—
20C2×#622—41no—
21C4⋊(C3⋊Dic3)—41no—
22C3×(C2×D3)⋊C4—41no—
23C3×(C2×D3)⋊C4—41no—
24C3×#208—22no—
25C3×#208—41no—
26C2×C3×C3⋊C8—41no—
27(C2×D3)⋊Dic3—42no—
28#1345—91nomaximal, Sylow
29C22×#67—61no—
30C2×C3×M16—61no—
31C2×C3×C22⋊C4—61no—
32C2×#217—61no—
33C2×(C2×D3)⋊C4—21no—
34C2×(C2×D3)⋊C4—61no—
35C2×C4⋊Dic3—61no—
36C2×C4⋊Dic3—61no—
37C2×#208—21no—
38C3⋊#95—61no—
39C23×C32C22⋊C411yescharacteristic
40C22×C3×D3—22no—
41C22×C3×D3—41no—
42C22×C3×D3—41no—
43C22×C3×D3—41no—
44C22×C3×D3—41no—
45C22×C3×D3—41no—
46C22×C3×D3—41no—
47C2×C32×C4—21no—
48C2×C32×C4—21no—
49C2×C32×C4D811yescharacteristic
50C2×C32×C4SD1611yescharacteristic
51C2×C3⋊Dic3—21no—
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3—41no—
55C2×C3×Dic3—41no—
56C2×C3×Dic3—41no—
57C2×C3×Dic3—41no—
58#625—42no—
59#625—42no—
60#622—81no—
61C3×C3⋊C8—42no—
62#394—91no—
63#343—91no—
64#324—91no—
65C24×C3—61no—
66C23×D3—21no—
67C22×C3×C4—21no—
68C22×C3×C4—21no—
69C22×C3×C4—61no—
70C2×#67—122no—
71C2×#67—122no—
72C2×#67—122no—
73C22×Dic3—21no—
74C22×Dic3—61no—
75C22×Dic3—61no—
76C22×Dic3—61no—
77C22×Dic3—61no—
78C3×M16—62no—
79C3×M16—121no—
80C2×C3×C8—121no—
81C3×C22⋊C4—121no—
82C3×C22⋊C4—121no—
83#217—122no—
84(C2×D3)⋊C4—41no—
85(C2×D3)⋊C4—41no—
86(C2×D3)⋊C4—122no—
87C4⋊Dic3—122no—
88C4⋊Dic3—121no—
89C4⋊Dic3—121no—
90#208—22no—
91#208—41no—
92C2×C3⋊C8—41no—
93C22×C32—21no—
94C22×C32—21no—
95C22×C32#9911yescharacteristic
96C22×C32#10211yescharacteristic
97C22×C32#10411yescharacteristic
98C2×C3×D3—42no—
99C2×C3×D3—42no—
100C2×C3×D3—42no—
101C2×C3×D3—81no—
102C2×C3×D3—81no—
103C2×C3×D3—81no—
104C2×C3×D3—81no—
105C32×C4—21no—
106C32×C4—21no—
107C3⋊Dic3—41no—
108C3⋊Dic3—41no—
109C3×Dic3—81no—
110C22×D4—91no—
111C2×M16—61no—
112C2×C4⋊C4—91no—
113C2×C22⋊C4—61no—
114C2×C22⋊C4—181no—
115C22⋊C8—181no—
116#95—91no—
117C23×C3—21no—
118C23×C3—21no—
119C23×C3—62no—
120C23×C3—121no—
121C23×C3—121no—
122C23×C3—121no—
123C23×C3—121no—
124C23×C3—121no—
125C23×C3—121no—
126C22×D3—22no—
127C22×D3—41no—
128C22×D3—41no—
129C22×D3—41no—
130C22×D3—41no—
131C22×D3—41no—
132C22×D3—41no—
133C2×C3×C4—21no—
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—21no—
141C2×C3×C4—41no—
142C2×C3×C4—41no—
143C2×C3×C4—121no—
144C2×C3×C4—121no—
145C2×C3×C4—121no—
146#67—124no—
147#67—124no—
148C2×Dic3—41no—
149C2×Dic3—41no—
150C2×Dic3—41no—
151C2×Dic3—62no—
152C2×Dic3—121no—
153C2×Dic3—121no—
154C2×Dic3—121no—
155C2×Dic3—121no—
156C2×Dic3—121no—
157C2×Dic3—121no—
158C2×Dic3—121no—
159C2×Dic3—241no—
160C2×Dic3—241no—
161C3×C8—122no—
162C3⋊C8—42no—
163C2×C32—21no—
164C2×C32—21no—
165C2×C32#32711yescharacteristic
166C2×C32AΣL(1,𝔽16)11yescharacteristic
167C2×C32#35511yescharacteristic
168C3×D3—82no—
169C24—61no—
170C2×D4—361no—
171C2×D4—362no—
172C22×C4—61no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4GO+(4,𝔽2)11yescharacteristic
176M16—62no—
177M16—121no—
178C2×C8—121no—
179C2×C8—361no—
180C4⋊C4—361no—
181C22⋊C4—121no—
182C22⋊C4—121no—
183C22⋊C4—362no—
184C22×C3—21no—
185C22×C3—21no—
186C22×C3—21no—
187C22×C3—21no—
188C22×C3—21no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—21no—
194C22×C3—41no—
195C22×C3—41no—
196C22×C3—122no—
197C22×C3—122no—
198C22×C3—122no—
199C22×C3—241no—
200C22×C3—241no—
201C22×C3—241no—
202C22×C3—241no—
203C2×D3—42no—
204C2×D3—42no—
205C2×D3—42no—
206C2×D3—81no—
207C2×D3—81no—
208C2×D3—81no—
209C2×D3—81no—
210C3×C4—21no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—21no—
214C3×C4—41no—
215C3×C4—41no—
216C3×C4—241no—
217Dic3—81no—
218Dic3—122no—
219Dic3—241no—
220Dic3—241no—
221Dic3—241no—
222C32#134511yescharacteristic, complemented, Sylow
223C23—62no—
224C23—121no—
225C23—121no—
226C23—121no—
227C23—121no—
228C23—121no—
229C23—121no—
230C23D32⋊C411yescharacteristic
231D4—362no—
232D4—362no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—121no—
236C2×C4—121no—
237C2×C4—121no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—361no—
241C2×C4—361no—
242C2×C4#377411yescharacteristic
243C2×C4#377511yescharacteristic
244C8—122no—
245C8—721no—
246C2×C3—21no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—41no—
257C2×C3—41no—
258C2×C3—242no—
259D3—82no—
260C22—21no—
261C22—21no—
262C22—122no—
263C22—122no—
264C22—122no—
265C22—241no—
266C22—241no—
267C22—241no—
268C22—241no—
269C22#6373811yescharacteristic
270C22#6373911yescharacteristic
271C22#6374111yescharacteristic
272C4—21no—
273C4—21no—
274C4—241no—
275C4—361no—
276C4—361no—
277C3—21no—
278C3—21no—
279C2—21no—
280C2—21no—
281C2—242no—
282C2#1059005711yescharacteristic
283C2#1059005911yescharacteristic
284C2#1059007111yescharacteristic
subgroupG/H
centerC22#63738
commutatorC22×C3⋊Dic3C2×C4
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#99
prime radicalC22×#625C4
cosocleC2×C4⋊(C3⋊Dic3)C22
hypocenterC32#1345
LCSG ▷ C22×C3⋊Dic3 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10590202C2semidirect
3. #10589168C2semidirect
222. C32#1345semidirect

Maximal subgroups

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

subgroupindex
#105913942
#105902022
#105891682
#13459