Finite Group Databasebeta

← #11785945

Subgroups — #11785945

Order 1152.

545 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 545 conjugacy classes of subgroups — too many to draw. Only its 148 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×#5812C211yesmaximal, characteristic
2C2×#63663C211yesmaximal, characteristic
3C2×C3×#836C211yesmaximal, characteristic
4#10589170C212yesmaximal
5#10589169C212yesmaximal
6#71659—31nomaximal
7#70101—31nomaximal
8C22×C32×Q8C2211yescharacteristic
9C2×#3748C2212yes—
10C3×Q8×Dic3—22no—
11C3×Q8×Dic3—22no—
12C3×#926C414yes—
13C3×#926C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2212yes—
16#63663—22no—
17C3×#836—22no—
18C3×#519—31no—
19#5812D311yescharacteristic
20C2×C3×#101—31no—
21C2×#836—31no—
22C2×#836—31no—
23C2×#836—61no—
24C2×#836D311yescharacteristic
25#4559—32no—
26#4556—32no—
27#4533—32no—
28#4533—32no—
29C2×C32×Q8—22no—
30C2×C32×Q8—22no—
31C2×C32×Q8D412yes—
32C2×C32×Q8D412yes—
33C22×C32×C4C2×C412yes—
34C22×C32×C4C2311yescharacteristic
35#3748—22no—
36#3748—22no—
37C2×C3⋊(C3⋊C8)—22no—
38C3×#217C2×C412yes—
39C3×#217C2×C412yes—
40C3×C4⋊Dic3—24no—
41C3×C4⋊Dic3—21no—
42C3×C4⋊Dic3—21no—
43C3×C4×Dic3—24no—
44C3×C4×Dic3—21no—
45C3×C4×Dic3—21no—
46C3×#208—22no—
47C3×#208—22no—
48C2×C3×C3⋊C8—22no—
49#1830—91noSylow
50C22×C3×Q8—21no—
51C22×C3×Q8C2×D311yescharacteristic
52C22×C3×Q8C2×D311yescharacteristic
53C2×C3×M16—32no—
54C3×C4×Q8—62no—
55C3×C4×Q8—62no—
56C3×#117—34no—
57C3×#117—31no—
58C3×#117—31no—
59Q8×Dic3—22no—
60Q8×Dic3—22no—
61#926Dic314yes—
62#926C2×D311yescharacteristic
63#926C2×D311yescharacteristic
64C2×#208—32no—
65C2×#208—32no—
66C2×#208—62no—
67C2×#208C2×D312yes—
68C3×#101—62no—
69#836—22no—
70#836—64no—
71#836—62no—
72#836—62no—
73C23×C32C22×C411yescharacteristic
74C32×Q8—24no—
75C32×Q8—24no—
76C2×C32×C4—22no—
77C2×C32×C4—22no—
78C2×C32×C4C22⋊C414yes—
79C2×C32×C4C2×D411yescharacteristic
80C2×C32×C4C2×D411yescharacteristic
81C2×C32×C4#4112yes—
82C2×C32×C4#4112yes—
83C2×C3×Dic3—22no—
84C2×C3×Dic3—22no—
85C3⋊(C3⋊C8)—42no—
86C3×C3⋊C8—42no—
87#519—31no—
88C2×#101—31no—
89C2×#101—91no—
90#344—92no—
91#344—92no—
92C2×C3×Q8—22no—
93C2×C3×Q8—22no—
94C2×C3×Q8—22no—
95C2×C3×Q8—22no—
96C2×C3×Q8—22no—
97C2×C3×Q8—22no—
98C2×C3×Q8—42no—
99C2×C3×Q8—42no—
100C2×C3×Q8D1212yes—
101C2×C3×Q8#6712yes—
102C2×C3×Q8#6712yes—
103C2×C3×Q8#6712yes—
104C22×C3×C4—22no—
105C22×C3×C4—21no—
106C22×C3×C4C4×D312yes—
107C22×C3×C4C2×Dic312yes—
108C22×C3×C4C22×D311yescharacteristic
109C22×C3×C4C22×D311yescharacteristic
110C3×M16—62no—
111C3×M16—62no—
112C2×C3×C8—62no—
113C3×C4⋊C4—64no—
114C3×C4⋊C4—61no—
115C3×C4⋊C4—61no—
116C3×C22⋊C4—32no—
117C3×C22⋊C4—32no—
118C3×C42—64no—
119C3×C42—61no—
120C3×C42—61no—
121#217C2×Dic312yes—
122#217C2×Dic312yes—
123C4⋊Dic3—24no—
124C4⋊Dic3—21no—
125C4⋊Dic3—21no—
126C4×Dic3—24no—
127C4×Dic3—21no—
128C4×Dic3—21no—
129#208—22no—
130#208—22no—
131#208—64no—
132#208—62no—
133#208—62no—
134#208—62no—
135#208—62no—
136#208—122no—
137C2×C3⋊C8—22no—
138C2×C3⋊C8—62no—
139C2×C3⋊C8—62no—
140C2×C3⋊C8—122no—
141C22×C32—41no—
142C22×C32C2×C22⋊C411yescharacteristic
143C22×C32#11711yescharacteristic
144C22×C32#11711yescharacteristic
145C32×C4—24no—
146C32×C4#12312yes—
147C32×C4#12312yes—
148C3×Dic3—42no—
149C3×Dic3—42no—
150C22×Q8D3211yescharacteristic
151C2×M16—32no—
152C2×M16—92no—
153C4×Q8—62no—
154C4×Q8—62no—
155#117—34no—
156#117—31no—
157#117—31no—
158#101—62no—
159#101—182no—
160C23×C3—21no—
161C23×C3C2×C4×D311yescharacteristic
162C23×C3C22×Dic311yescharacteristic
163C3×Q8—24no—
164C3×Q8—24no—
165C3×Q8—24no—
166C3×Q8—24no—
167C3×Q8—44no—
168C3×Q8—44no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—24no—
174C2×C3×C4—22no—
175C2×C3×C4—22no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—42no—
179C2×C3×C4—42no—
180C2×C3×C4—62no—
181C2×C3×C4—62no—
182C2×C3×C4(C2×D3)⋊C414yes—
183C2×C3×C4#21714yes—
184C2×C3×C4C2×D1211yescharacteristic
185C2×C3×C4#23512yes—
186C2×C3×C4#23512yes—
187C2×C3×C4#23712yes—
188C2×C3×C4#23712yes—
189C2×C3×C4C2×#6711yescharacteristic
190C2×C3×C4C2×#6711yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×Dic3—22no—
193C2×Dic3—22no—
194C3×C8—122no—
195C3⋊C8—42no—
196C3⋊C8—124no—
197C3⋊C8—122no—
198C3⋊C8—122no—
199C2×C32—21no—
200C2×C32—21no—
201C2×C32—21no—
202C2×C32#38111yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8#62512yes—
206C2×Q8#62612yes—
207C22×C4D3×Dic312yes—
208C22×C4C2×D3211yescharacteristic
209M16—62no—
210M16—62no—
211M16—182no—
212M16—182no—
213C2×C8—62no—
214C2×C8—182no—
215C4⋊C4—64no—
216C4⋊C4—61no—
217C4⋊C4—61no—
218C22⋊C4—32no—
219C22⋊C4—32no—
220C42—64no—
221C42—61no—
222C42—61no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—21no—
226C22×C3—41no—
227C22×C3—41no—
228C22×C3—42no—
229C22×C3#87711yescharacteristic
230C22×C3#87711yescharacteristic
231C22×C3#92611yescharacteristic
232C22×C3#92611yescharacteristic
233C22×C3C2×(C2×D3)⋊C411yescharacteristic
234C22×C3C2×#21711yescharacteristic
235C3×C4—24no—
236C3×C4—24no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—44no—
240C3×C4—122no—
241C3×C4—122no—
242C3×C4#88612yes—
243C3×C4#92912yes—
244C3×C4#92912yes—
245C3×C4#93512yes—
246Dic3—42no—
247Dic3—42no—
248C32#183011yescharacteristic, complemented, Sylow
249C23C2×D3×Dic311yescharacteristic
250Q8—24no—
251Q8—24no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—62no—
255C2×C4—62no—
256C2×C4(C2×D3)⋊Dic314yes—
257C2×C4#380412yes—
258C2×C4#380412yes—
259C2×C4C2×#62511yescharacteristic
260C2×C4C2×#62611yescharacteristic
261C8—122no—
262C8—362no—
263C2×C3—22no—
264C2×C3—21no—
265C2×C3—21no—
266C2×C3—21no—
267C2×C3—21no—
268C2×C3—21no—
269C2×C3—21no—
270C2×C3—21no—
271C2×C3—41no—
272C2×C3—41no—
273C2×C3#494311yescharacteristic
274C2×C3#521111yescharacteristic
275C22—41no—
276C22#6395511yescharacteristic
277C22#6395511yescharacteristic
278C22C2×(C2×D3)⋊Dic311yescharacteristic
279C4—24no—
280C4—122no—
281C4—122no—
282C4#6396112yes—
283C4#6396612yes—
284C3—21no—
285C3#7010111yescharacteristic, complemented
286C3#7165911yescharacteristic, complemented
287C2—21no—
288C2—21no—
289C2—21no—
290C2#1059169611yescharacteristic
subgroupG/H
centerC2#10591696
commutator, prime radicalC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC2×C32#381
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1830
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
248. C32#1830semidirect
285. C3#70101semidirect
286. C3#71659semidirect

Maximal subgroups

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

subgroupindex
C3×#58122
C2×#636632
C2×C3×#8362
#105891702
#105891692
#716593
#701013