Finite Group Databasebeta

← #11802781

Subgroups — #11802781

Order 1152.

1681 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 1681 conjugacy classes of subgroups — too many to draw. Only its 276 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
1C22×#3757C211yesmaximal, characteristic
2C3×#5247C212yesmaximal
3#10591720C212yesmaximal, complemented
4#10591705C212yesmaximal, complemented
5#10591703C218yesmaximal, complemented
6#73820—32nomaximal
7C25×C32C2211yescharacteristic
8C23×C3⋊Dic3C2211yescharacteristic
9C23×C3⋊Dic3C2211yescharacteristic
10C2×#3757C418yescomplemented
11C2×#3757C2214yes—
12C2×C3×#217C2214yes—
13C2×C3×#217C2214yes—
14C2×C3×#217C2214yes—
15C2×#3724C2214yescomplemented
16C2×Dic32C2214yescomplemented
17#63579C2214yescomplemented
18#63579C2214yescomplemented
19C22×#217—32no—
20C22×#217—61no—
21C3×#379—32no—
22#5247D312yes—
23#4945—38no—
24#4944—38no—
25#4942—34no—
26Dic3×C22⋊C4—34no—
27C24×C32—24no—
28C24×C32—42no—
29C24×C32—42no—
30C24×C32C2×C414yes—
31C24×C32C2312yes—
32C24×C32C2311yescharacteristic
33C22×C3⋊Dic3—42no—
34C22×C3⋊Dic3—42no—
35C22×C3⋊Dic3C2×C414yes—
36C22×C3⋊Dic3C2×C414yes—
37C22×C3⋊Dic3C2312yes—
38C22×C3⋊Dic3C2312yes—
39C22×C3×Dic3C2318yes—
40#3757C2×C4116yes—
41C3×#217—28no—
42C3×#217—44no—
43C3×#217—44no—
44#3724—44no—
45Dic32—44no—
46#2312—91noSylow
47C25×C3—21no—
48C25×C3C2×D312yes—
49C23×Dic3—32no—
50C23×Dic3—32no—
51C23×Dic3—61no—
52C23×Dic3—61no—
53C2×C3×C22⋊C4—34no—
54C2×C3×C22⋊C4—34no—
55C2×C3×C22⋊C4—34no—
56C2×#217—316no—
57C2×#217—34no—
58C2×#217—34no—
59C2×#217—68no—
60C2×#217—64no—
61C2×#217C2×D314yes—
62C2×#217C2×D314yes—
63C2×#217C2×D314yes—
64C2×Dic3⋊C4—38no—
65C2×C4×Dic3—38no—
66C3⋊#95—38no—
67C3⋊#95—38no—
68C23×C32—22no—
69C23×C32—22no—
70C23×C32—28no—
71C23×C32—24no—
72C23×C32—24no—
73C23×C32—24no—
74C23×C32—44no—
75C23×C32—44no—
76C23×C32—416no—
77C23×C32C22×C414yes—
78C23×C32C22×C412yes—
79C23×C32#4114yes—
80C23×C32C2411yescharacteristic
81C2×C3⋊Dic3—24no—
82C2×C3⋊Dic3—24no—
83C2×C3⋊Dic3—44no—
84C2×C3⋊Dic3—44no—
85C2×C3⋊Dic3C22×C414yes—
86C2×C3⋊Dic3C22×C414yes—
87C2×C3×Dic3—28no—
88C2×C3×Dic3—28no—
89C2×C3×Dic3—28no—
90C22×C22⋊C4—91no—
91#388—98no—
92#380—92no—
93#379—32no—
94C4×C22⋊C4—92no—
95C24×C3—28no—
96C24×C3—28no—
97C24×C3—24no—
98C24×C3—21no—
99C24×C3—22no—
100C24×C3—44no—
101C24×C3—44no—
102C24×C3—44no—
103C24×C3—44no—
104C24×C3C4×D318yes—
105C24×C3C22×D312yes—
106C24×C3C22×D312yes—
107C24×C3C22×D312yes—
108C22×C3×C4—38no—
109C22×Dic3—34no—
110C22×Dic3—34no—
111C22×Dic3—38no—
112C22×Dic3—38no—
113C22×Dic3—64no—
114C22×Dic3—64no—
115C22×Dic3—62no—
116C22×Dic3—62no—
117C22×Dic3—124no—
118C22×Dic3—124no—
119C22×Dic3—124no—
120C22×Dic3—124no—
121C22×Dic3C22×D318yes—
122C3×C22⋊C4—68no—
123C3×C22⋊C4—124no—
124C3×C22⋊C4—124no—
125#217—28no—
126#217—316no—
127#217—316no—
128#217—44no—
129#217—44no—
130#217—616no—
131Dic3⋊C4—128no—
132C4×Dic3—128no—
133C22×C32—22no—
134C22×C32—22no—
135C22×C32—28no—
136C22×C32—24no—
137C22×C32—24no—
138C22×C32—24no—
139C22×C32—416no—
140C22×C32—48no—
141C22×C32#11714yes—
142C22×C32C23×C411yescharacteristic
143C22×C32C2×#4112yes—
144C22×C32H(5,𝔽2)12yes—
145C22×C32H(5,𝔽2)12yes—
146C3⋊Dic3—24no—
147C3⋊Dic3—24no—
148C3×Dic3—48no—
149C25D3211yescharacteristic
150C23×C4—91no—
151C23×C4—91no—
152C2×C4⋊C4—94no—
153C2×C22⋊C4—34no—
154C2×C22⋊C4—34no—
155C2×C22⋊C4—34no—
156C2×C22⋊C4—98no—
157C2×C22⋊C4—94no—
158C2×C42—94no—
159#95—94no—
160#95—94no—
161C23×C3—24no—
162C23×C3—24no—
163C23×C3—24no—
164C23×C3—24no—
165C23×C3—28no—
166C23×C3—216no—
167C23×C3—216no—
168C23×C3—24no—
169C23×C3—24no—
170C23×C3—24no—
171C23×C3—24no—
172C23×C3—24no—
173C23×C3—24no—
174C23×C3—21no—
175C23×C3—24no—
176C23×C3—22no—
177C23×C3—24no—
178C23×C3—44no—
179C23×C3—44no—
180C23×C3—48no—
181C23×C3—48no—
182C23×C3—48no—
183C23×C3—48no—
184C23×C3—432no—
185C23×C3—432no—
186C23×C3C2×C4×D314yes—
187C23×C3C2×C4×D314yes—
188C23×C3C2×C4×D314yes—
189C23×C3#23718yes—
190C23×C3C23×D312yes—
191C2×C3×C4—68no—
192C2×C3×C4—68no—
193C2×C3×C4—68no—
194C2×Dic3—28no—
195C2×Dic3—28no—
196C2×Dic3—28no—
197C2×Dic3—38no—
198C2×Dic3—38no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—68no—
202C2×Dic3—68no—
203C2×Dic3—124no—
204C2×Dic3—124no—
205C2×Dic3—128no—
206C2×Dic3—128no—
207C2×Dic3—128no—
208C2×Dic3—128no—
209C2×C32—24no—
210C2×C32—44no—
211C2×C32C2×#11711yescharacteristic
212C2×C32#51811yescharacteristic
213C2×C32#51811yescharacteristic
214C2×C32#53814yes—
215C24—24no—
216C24—42no—
217C24—42no—
218C24#62414yes—
219C24C2×D3212yes—
220C24C2×D3211yescharacteristic
221C22×C4—38no—
222C22×C4—92no—
223C22×C4—92no—
224C22×C4—94no—
225C22×C4—94no—
226C22×C4—362no—
227C22×C4—362no—
228C4⋊C4—364no—
229C22⋊C4—68no—
230C22⋊C4—916no—
231C22⋊C4—124no—
232C22⋊C4—124no—
233C42—364no—
234C22×C3—24no—
235C22×C3—24no—
236C22×C3—216no—
237C22×C3—24no—
238C22×C3—24no—
239C22×C3—216no—
240C22×C3—28no—
241C22×C3—24no—
242C22×C3—24no—
243C22×C3—24no—
244C22×C3—24no—
245C22×C3—24no—
246C22×C3—24no—
247C22×C3—22no—
248C22×C3—21no—
249C22×C3—22no—
250C22×C3—22no—
251C22×C3—24no—
252C22×C3—44no—
253C22×C3—44no—
254C22×C3—432no—
255C22×C3—432no—
256C22×C3—416no—
257C22×C3—48no—
258C22×C3—48no—
259C22×C3#87718yes—
260C22×C3C22×C4×D312yes—
261C22×C3C2×#23714yes—
262C22×C3#100414yes—
263C22×C3#100414yes—
264C3×C4—128no—
265Dic3—48no—
266Dic3—68no—
267Dic3—68no—
268Dic3—124no—
269Dic3—124no—
270C32#231211yescharacteristic, complemented, Sylow
271C23—22no—
272C23—22no—
273C23—24no—
274C23—24no—
275C23—24no—
276C23—28no—
277C23—44no—
278C23—44no—
279C23—416no—
280C23#380514yes—
281C23C2×#62414yes—
282C23C2×#62412yes—
283C23C22×D3211yescharacteristic
284C2×C4—68no—
285C2×C4—68no—
286C2×C4—68no—
287C2×C4—94no—
288C2×C4—94no—
289C2×C4—184no—
290C2×C4—184no—
291C2×C4—364no—
292C2×C4—364no—
293C2×C3—28no—
294C2×C3—28no—
295C2×C3—21no—
296C2×C3—24no—
297C2×C3—21no—
298C2×C3—21no—
299C2×C3—48no—
300C2×C3—44no—
301C2×C3—44no—
302C2×C3C2×#87712yes—
303C2×C3#548612yes—
304C2×C3#548612yes—
305C2×C3#559318yes—
306C22—28no—
307C22—22no—
308C22—22no—
309C22—24no—
310C22—24no—
311C22—24no—
312C22—416no—
313C22—48no—
314C22#6395714yes—
315C22C2×#380512yes—
316C22C22×#62411yescharacteristic
317C22#6433012yes—
318C22#6433012yes—
319C4—128no—
320C4—184no—
321C4—184no—
322C3—21no—
323C3#7382012yescomplemented
324C2—24no—
325C2—44no—
326C2C2×#6395711yescharacteristic
327C2#1059550814yes—
328C2#1059551011yescharacteristic
329C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
Fitting, prime radicalC25×C32C22
socle, cosocleC23×C32C24
hypercenterC25D32
hypocenterC32#2312
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
3. #10591720C2semidirect
4. #10591705C2semidirect
5. #10591703C2semidirect
10. C2×#3757C4semidirect
15. C2×#3724C22semidirect
16. C2×Dic32C22semidirect
17. #63579C22semidirect
18. #63579C22semidirect
270. C32#2312semidirect
323. C3#73820semidirect

Maximal subgroups

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

subgroupindex
C22×#37572
C3×#52472
#105917202
#105917052
#105917032
#738203