Finite Group Databasebeta

← #11807971

Subgroups — #11807971

Order 1152.

993 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 993 conjugacy classes of subgroups — too many to draw. Only its 244 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
1C2×#64153C211yesmaximal, characteristic
2C3×#5229C212yesmaximal
3#10591273C212yesmaximal
4#10591263C214yesmaximal
5#10591229C212yesmaximal
6#10591197C214yesmaximal
7#76497—32nomaximal
8C22×C32×Q8C2211yescharacteristic
9C22×#634C2211yescharacteristic
10#64153C418yescomplemented
11C2×#3750C2214yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4×Dic3C2212yes—
15C2×#3724C2212yes—
16C2×Dic32C2212yes—
17C3×C3⋊#95C2214yes—
18C3×C3⋊#95C2214yes—
19#63579C2212yes—
20#63579C2214yes—
21#63579C2214yes—
22#63579C2212yes—
23C2×#944—32no—
24C2×#944—61no—
25C3×#391—32no—
26#5229D312yes—
27#4978—34no—
28#4933—34no—
29#4655—34no—
30#4652—34no—
31#4651—34no—
32#4646—34no—
33C2×C32×Q8—41no—
34C2×C32×Q8—41no—
35C2×C32×Q8C2×C414yes—
36C22×C32×C4C2312yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3C2312yes—
39C22×C3⋊Dic3C2312yes—
40C2×#634—41no—
41C2×#634—41no—
42C2×#634C2×C414yes—
43C22×C3×Dic3C2314yes—
44C22×C3×Dic3C2314yes—
45#3750C2×C4116yes—
46C4×C3⋊Dic3C2×C414yes—
47C3×C4⋊Dic3—42no—
48C3×C4×Dic3—42no—
49#3724—42no—
50Dic32—42no—
51#2381—91noSylow
52C22×C3×Q8—21no—
53C22×C3×Q8C2×D312yes—
54C22×Dic6—32no—
55C22×Dic6—61no—
56C2×C3×C4⋊C4—32no—
57C2×C3×C42—32no—
58#944—316no—
59#944—68no—
60C2×C4⋊Dic3C2×D312yes—
61C2×Dic3⋊C4—34no—
62C2×Dic3⋊C4—34no—
63C2×Dic3⋊C4—34no—
64C2×Dic3⋊C4—64no—
65C2×C4×Dic3—32no—
66C2×C4×Dic3—34no—
67C2×C4×Dic3—61no—
68C2×C4×Dic3C2×D312yes—
69C3×#95—34no—
70C3×#95—34no—
71C3⋊#95—34no—
72C3⋊#95—34no—
73C3⋊#95—34no—
74C3⋊#95—34no—
75C3⋊#95—34no—
76C3⋊#95—34no—
77C3⋊#95C2×D314yes—
78C3⋊#95C2×D314yes—
79C23×C32C2411yescharacteristic
80C32×Q8—44no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4C22×C412yes—
86C2×C32×C4C22×C414yes—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3—22no—
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C22×C414yes—
91C2×C3⋊Dic3C22×C414yes—
92#634—44no—
93C2×C3×Dic3—24no—
94C2×C3×Dic3—24no—
95C2×C3×Dic3—24no—
96C2×C3×Dic3—24no—
97C2×C3×Dic3—28no—
98C2×C4⋊Q8—91no—
99#391—32no—
100#391—92no—
101#387—94no—
102#387—94no—
103#383—92no—
104C2×C3×Q8—24no—
105C2×C3×Q8—42no—
106C2×C3×Q8—42no—
107C2×C3×Q8—42no—
108C2×C3×Q8—42no—
109C2×C3×Q8C4×D318yes—
110C22×C3×C4—21no—
111C22×C3×C4—22no—
112C22×C3×C4—34no—
113C22×C3×C4—34no—
114C22×C3×C4C22×D312yes—
115C22×C3×C4C22×D312yes—
116C22×C3×C4C22×D312yes—
117C22×Dic3—34no—
118C22×Dic3—34no—
119C22×Dic3—62no—
120C22×Dic3—62no—
121C22×Dic3C22×D314yes—
122C22×Dic3C22×D314yes—
123C2×Dic6—38no—
124C2×Dic6—64no—
125C2×Dic6—122no—
126C2×Dic6—122no—
127C2×Dic6—122no—
128C2×Dic6—122no—
129C3×C4⋊C4—122no—
130C3×C42—122no—
131C4⋊Dic3—42no—
132Dic3⋊C4—316no—
133Dic3⋊C4—316no—
134Dic3⋊C4—616no—
135Dic3⋊C4—124no—
136C4×Dic3—38no—
137C4×Dic3—42no—
138C4×Dic3—64no—
139C4×Dic3—124no—
140C22×C32C23×C411yescharacteristic
141C22×C32H(5,𝔽2)11yescharacteristic
142C22×C32H(5,𝔽2)11yescharacteristic
143C22×C322−1+414yes—
144C32×C4—22no—
145C32×C4—24no—
146C3⋊Dic3—24no—
147C3⋊Dic3—24no—
148C3×Dic3—44no—
149C3×Dic3—44no—
150C22×Q8—91no—
151C22×Q8D3211yescharacteristic
152C4⋊Q8—98no—
153C2×C4⋊C4—32no—
154C2×C4⋊C4—94no—
155C2×C4⋊C4—92no—
156C2×C42—32no—
157C2×C42—91no—
158C2×C42—92no—
159#95—34no—
160#95—34no—
161#95—92no—
162#95—94no—
163#95—92no—
164#95—94no—
165C23×C3—21no—
166C23×C3C23×D312yes—
167C3×Q8—48no—
168C3×Q8—48no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—22no—
177C2×C3×C4—22no—
178C2×C3×C4—24no—
179C2×C3×C4—42no—
180C2×C3×C4—42no—
181C2×C3×C4—64no—
182C2×C3×C4—64no—
183C2×C3×C4—64no—
184C2×C3×C4—68no—
185C2×C3×C4—64no—
186C2×C3×C4C2×C4×D314yes—
187C2×C3×C4C2×C4×D314yes—
188C2×C3×C4C2×C4×D314yes—
189C2×Dic3—24no—
190C2×Dic3—24no—
191C2×Dic3—24no—
192C2×Dic3—24no—
193C2×Dic3—28no—
194C2×Dic3—38no—
195C2×Dic3—38no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—68no—
199C2×Dic3—64no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—64no—
203C2×Dic3—122no—
204C2×Dic3—122no—
205Dic6—128no—
206Dic6—128no—
207C2×C32#51811yescharacteristic
208C2×C32#51912yes—
209C2×C32#56312yes—
210C2×C32#56312yes—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—94no—
214C2×Q8—361no—
215C2×Q8—361no—
216C2×Q8#62414yes—
217C22×C4—34no—
218C22×C4—34no—
219C22×C4—92no—
220C22×C4—92no—
221C22×C4C2×D3211yescharacteristic
222C22×C4C2×D3212yes—
223C4⋊C4—916no—
224C4⋊C4—122no—
225C4⋊C4—362no—
226C42—94no—
227C42—122no—
228C42—362no—
229C22×C3—24no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3C22×C4×D312yes—
234C22×C3#100412yes—
235C22×C3#100412yes—
236C22×C3#100714yes—
237C22×C3#101014yes—
238C3×C4—24no—
239C3×C4—24no—
240C3×C4—24no—
241C3×C4—24no—
242C3×C4—44no—
243C3×C4—124no—
244C3×C4—124no—
245Dic3—44no—
246Dic3—44no—
247Dic3—68no—
248Dic3—68no—
249Dic3—68no—
250Dic3—124no—
251C32#238111yescharacteristic, complemented, Sylow
252C23C22×D3211yescharacteristic
253Q8—44no—
254Q8—364no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—68no—
260C2×C4—64no—
261C2×C4—64no—
262C2×C4—64no—
263C2×C4—64no—
264C2×C4—94no—
265C2×C4—94no—
266C2×C4—184no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4C2×#62412yes—
270C2×C4C2×#62414yes—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3—22no—
274C2×C3—21no—
275C2×C3#548612yes—
276C2×C3#557214yes—
277C2×C3#564614yes—
278C2×C3#567212yes—
279C2×C3#573512yes—
280C22#6431514yes—
281C22C22×#62411yescharacteristic
282C22#6433011yescharacteristic
283C22#6433011yescharacteristic
284C4—22no—
285C4—24no—
286C4—124no—
287C4—124no—
288C4—184no—
289C4—184no—
290C3—21no—
291C3#7649712yescomplemented
292C2#1059533912yes—
293C2#1059539312yes—
294C2#1059541612yes—
295C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×Q8C22
socle, prime radical, cosocleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32#2381
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
10. #64153C4semidirect
251. C32#2381semidirect
291. C3#76497semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
C3×#52292
#105912732
#105912632
#105912292
#105911972
#764973