Finite Group Databasebeta

← #11771826

Subgroups — #11771826

Order 1152.

375 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C3×#4991C211yesmaximal, characteristic
2#10589394C211yesmaximal, characteristic, complemented
3C3×#4530C211yesmaximal, characteristic, complemented
4#67647—31nomaximal
5#67493—31nomaximal
6C22×C3×D12C411yescharacteristic
7C2×C32×C4⋊C4C2211yescharacteristic
8C2×C3×(C2×D3)⋊C4—21no—
9C2×C3×(C2×D3)⋊C4—21no—
10C2×C3×#208—21no—
11#63657—21no—
12C3×C3⋊#95C411yescharacteristic
13C3×#394—31no—
14#4991D311yescharacteristic
15C3×#343—31no—
16#4530D311yescharacteristic, complemented
17#4528—31no—
18#4528—31no—
19#4528—61no—
20C23×C3×D3—21no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C32×C4D411yescharacteristic
23C22×C32×C4D411yescharacteristic
24C22×C3×Dic3—21no—
25C2×C3×D12—41no—
26C2×C3×D12—42no—
27C32×C4⋊C4—41no—
28C2×C3⋊(C3⋊C8)—41no—
29C3×(C2×D3)⋊C4—42no—
30C3×(C2×D3)⋊C4—41no—
31C3×(C2×D3)⋊C4—41no—
32C3×#208—22no—
33C3×#208—41no—
34C2×C3×C3⋊C8—41no—
35#1345—91noSylow
36C22×C3×D4—31no—
37C22×D12Dic311yescharacteristic
38C2×C3×M16—61no—
39C2×C3×C4⋊C4—21no—
40C2×C3×C4⋊C4C2×D311yescharacteristic
41C2×C3×C4⋊C4C2×D311yescharacteristic
42C2×C3×C22⋊C4—61no—
43C2×C3×C22⋊C4—61no—
44C2×(C2×D3)⋊C4—21no—
45C2×(C2×D3)⋊C4—21no—
46C2×#208—21no—
47C3×#95—31no—
48C3⋊#95Dic311yescharacteristic
49#830—62no—
50#830—61no—
51#830—61no—
52C23×C32C22⋊C411yescharacteristic
53C22×C3×D3—22no—
54C22×C3×D3—41no—
55C22×C3×D3—41no—
56C22×C3×D3—41no—
57C22×C3×D3—41no—
58C22×C3×D3—41no—
59C22×C3×D3—41no—
60C2×C32×C4—21no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4—21no—
64C2×C32×C4—41no—
65C2×C32×C4—41no—
66C2×C32×C4D811yescharacteristic
67C2×C32×C4SD1611yescharacteristic
68C2×C3×Dic3—41no—
69C2×C3×Dic3—41no—
70C2×C3×Dic3—41no—
71C3×D12—42no—
72C3×D12—42no—
73C3⋊(C3⋊C8)—81no—
74C3×C3⋊C8—42no—
75#394—31no—
76#343—31no—
77#324—91no—
78C24×C3—61no—
79C23×D3—21no—
80C2×C3×D4—121no—
81C2×C3×D4—122no—
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×C3×C4—61no—
86C22×C3×C4C4×D311yescharacteristic
87C22×C3×C4D1211yescharacteristic
88C22×C3×C4C2×Dic311yescharacteristic
89C22×C3×C4#6711yescharacteristic
90C22×C3×C4#6711yescharacteristic
91C22×C3×C4#6711yescharacteristic
92C22×Dic3—21no—
93C2×D12—41no—
94C2×D12—42no—
95C3×M16—62no—
96C3×M16—121no—
97C2×C3×C8—121no—
98C3×C4⋊C4—41no—
99C3×C4⋊C4—41no—
100C3×C4⋊C4—42no—
101C3×C22⋊C4—122no—
102C3×C22⋊C4—121no—
103C3×C22⋊C4—121no—
104(C2×D3)⋊C4—42no—
105(C2×D3)⋊C4—41no—
106(C2×D3)⋊C4—41no—
107#208—22no—
108#208—41no—
109C2×C3⋊C8—41no—
110C2×C3⋊C8—122no—
111C2×C3⋊C8—121no—
112C2×C3⋊C8—121no—
113C22×C32—21no—
114C22×C32—21no—
115C22×C32#9911yescharacteristic
116C22×C32#10211yescharacteristic
117C22×C32#10411yescharacteristic
118C2×C3×D3—42no—
119C2×C3×D3—42no—
120C2×C3×D3—42no—
121C2×C3×D3—81no—
122C2×C3×D3—81no—
123C2×C3×D3—81no—
124C2×C3×D3—81no—
125C32×C4—21no—
126C32×C4—21no—
127C32×C4—41no—
128C32×C4—41no—
129C3×Dic3—81no—
130C22×D4—31no—
131C2×M16—61no—
132C2×C4⋊C4D3211yescharacteristic
133C2×C22⋊C4—61no—
134C2×C22⋊C4—61no—
135C22⋊C8—181no—
136#95—31no—
137C23×C3—21no—
138C23×C3—62no—
139C23×C3—121no—
140C23×C3—121no—
141C23×C3—121no—
142C23×C3—121no—
143C23×C3—121no—
144C23×C3—121no—
145C23×C3(C2×D3)⋊C411yescharacteristic
146C23×C3#21711yescharacteristic
147C22×D3—22no—
148C22×D3—41no—
149C22×D3—41no—
150C22×D3—41no—
151C22×D3—41no—
152C22×D3—41no—
153C22×D3—41no—
154C3×D4—122no—
155C3×D4—122no—
156C2×C3×C4—21no—
157C2×C3×C4—21no—
158C2×C3×C4—21no—
159C2×C3×C4—21no—
160C2×C3×C4—22no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—41no—
168C2×C3×C4—41no—
169C2×C3×C4—41no—
170C2×C3×C4—41no—
171C2×C3×C4—41no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4—81no—
175C2×C3×C4—81no—
176C2×C3×C4—121no—
177C2×C3×C4—121no—
178C2×C3×C4—121no—
179C2×C3×C4#21311yescharacteristic
180C2×C3×C4#21311yescharacteristic
181C2×C3×C4#21411yescharacteristic
182C2×C3×C4#21511yescharacteristic
183C2×Dic3—41no—
184C2×Dic3—41no—
185C2×Dic3—41no—
186D12—42no—
187D12—42no—
188C3×C8—122no—
189C3⋊C8—42no—
190C3⋊C8—242no—
191C3⋊C8—241no—
192C3⋊C8—241no—
193C2×C32—21no—
194C2×C32—21no—
195C2×C32#32711yescharacteristic
196C2×C32AΣL(1,𝔽16)11yescharacteristic
197C2×C32#35511yescharacteristic
198C3×D3—82no—
199C24—61no—
200C2×D4—121no—
201C2×D4—122no—
202C22×C4—61no—
203C22×C4D3×Dic311yescharacteristic
204C22×C4#62511yescharacteristic
205C22×C4#62611yescharacteristic
206M16—62no—
207M16—121no—
208C2×C8—121no—
209C2×C8—361no—
210C4⋊C4—41no—
211C22⋊C4—122no—
212C22⋊C4—121no—
213C22⋊C4—121no—
214C22×C3—21no—
215C22×C3—21no—
216C22×C3—21no—
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—21no—
221C22×C3—41no—
222C22×C3—41no—
223C22×C3—122no—
224C22×C3—122no—
225C22×C3—122no—
226C22×C3—241no—
227C22×C3—241no—
228C22×C3—241no—
229C22×C3—241no—
230C22×C3#80511yescharacteristic
231C22×C3#80611yescharacteristic
232C22×C3#80911yescharacteristic
233C22×C3#83211yescharacteristic
234C22×C3#83411yescharacteristic
235C22×C3#83711yescharacteristic
236C2×D3—42no—
237C2×D3—42no—
238C2×D3—42no—
239C2×D3—81no—
240C2×D3—81no—
241C2×D3—81no—
242C2×D3—81no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—41no—
248C3×C4—41no—
249C3×C4—42no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4—81no—
255C3×C4—241no—
256Dic3—81no—
257C32#134511yescharacteristic, complemented, Sylow
258C23—62no—
259C23—121no—
260C23—121no—
261C23—121no—
262C23—121no—
263C23—121no—
264C23—121no—
265C23(C2×D3)⋊Dic311yescharacteristic
266D4—122no—
267D4—122no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—121no—
275C2×C4—121no—
276C2×C4—121no—
277C2×C4#371311yescharacteristic
278C2×C4#371511yescharacteristic
279C8—122no—
280C8—721no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—21no—
288C2×C3—41no—
289C2×C3—41no—
290C2×C3—242no—
291C2×C3#445111yescharacteristic
292C2×C3#447511yescharacteristic
293C2×C3#447711yescharacteristic
294C2×C3#453611yescharacteristic
295C2×C3#453711yescharacteristic
296C2×C3#454211yescharacteristic
297D3—82no—
298C22—21no—
299C22—21no—
300C22—122no—
301C22—122no—
302C22—122no—
303C22—241no—
304C22—241no—
305C22—241no—
306C22—241no—
307C22#6356211yescharacteristic
308C22#6356911yescharacteristic
309C22#6358011yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—241no—
315C3—21no—
316C3#6749311yescharacteristic, complemented
317C3#6764711yescharacteristic, complemented
318C2—21no—
319C2—21no—
320C2—242no—
321C2#1058914911yescharacteristic
322C2#1058917311yescharacteristic
323C2#1058918211yescharacteristic
subgroupG/H
centerC22#63580
commutatorC22×C32×C4C2×C4
Frattini, hypercenterC2×C4⋊C4D32
Fitting, cosocleC2×C32×C4⋊C4C22
socleC22×C32#99
prime radicalC22×C3×D12C4
hypocenterC32#1345
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
2. #10589394C2semidirect
3. C3×#4530C2semidirect
16. #4530D3semidirect
257. C32#1345semidirect
316. C3#67493semidirect
317. C3#67647semidirect

Maximal subgroups

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

subgroupindex
C3×#49912
#105893942
C3×#45302
#676473
#674933