Finite Group Databasebeta

← #11801932

Subgroups — #11801932

Order 1152.

854 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 854 conjugacy classes of subgroups — too many to draw. Only its 170 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⋊D3×#117C211yesmaximal, characteristic
2C4×C22⋊#157C212yesmaximal
3#10593758C214yesmaximal, complemented
4#10593747C214yesmaximal
5C4×C4⋊#157C212yesmaximal, complemented
6#10593733C211yesmaximal, characteristic, complemented
7C42×#157C211yesmaximal, characteristic, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157C2214yes—
10C2×C4⋊#157C2214yes—
11C2×C4×#157C2212yes—
12C2×C4×#157C2212yes—
13C2×C4×#157C2214yes—
14C32×#117C411yescharacteristic, complemented
15#64135C411yescharacteristic, complemented
16#64101C412yescomplemented
17C4⋊C4×C3⋊D3C2212yes—
18C22⋊C4×C3⋊D3C2212yes—
19#64086C412yescomplemented
20#64081C411yescharacteristic, complemented
21#64081C411yescharacteristic, complemented
22C42×C3⋊D3C2211yescharacteristic
23C42×C3⋊D3C2211yescharacteristic
24#63781C2214yes—
25#63781C2214yes—
26#63781C2214yes—
27D3×#117—62no—
28C23×C3⋊D3C2311yescharacteristic
29C22×#157C2314yes—
30C22×#157C2314yes—
31C22×C32×C4C2×C411yescharacteristic
32C22×C3⋊Dic3C2×C411yescharacteristic
33C2×C4×C3⋊D3—24no—
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3C2×C411yescharacteristic
36C2×C4×C3⋊D3C2312yes—
37C2×C4×C3⋊D3C2312yes—
38C2×C4×C3⋊D3C2311yescharacteristic
39C2×C4×C3⋊D3C2311yescharacteristic
40C22⋊#157—28no—
41C4⋊#157—28no—
42C4×#157—28no—
43C4×#157—24no—
44C4×#157—24no—
45C32×C4⋊C4C2×C412yes—
46C32×C22⋊C4C2×C412yes—
47C32×C42C2×C411yescharacteristic
48C32×C42C2×C411yescharacteristic
49#3757C2×C412yes—
50#3752C2×C412yes—
51#3752C2×C412yes—
52C4⋊(C3⋊Dic3)C2×C412yes—
53#3750C2×C412yes—
54#3750C2×C412yes—
55C4×C3⋊Dic3C2×C411yescharacteristic
56C4×C3⋊Dic3C2×C411yescharacteristic
57C4×C3⋊Dic3C2×C412yes—
58C4×C3⋊Dic3C2×C412yes—
59#2298—91nomaximal, Sylow
60C22×C4×D3—62no—
61C3×#117—22no—
62#926—62no—
63#892—64no—
64D3×C4⋊C4—64no—
65D3×C22⋊C4—64no—
66#877—64no—
67#872—62no—
68#872—62no—
69C42×D3—62no—
70C42×D3—62no—
71C23×C32C22×C411yescharacteristic
72C22×C3⋊D3—22no—
73C22×C3⋊D3—24no—
74C22×C3⋊D3C22×C411yescharacteristic
75C22×C3⋊D3C2411yescharacteristic
76C2×#157—24no—
77C2×#157—24no—
78C2×#157—24no—
79C2×#157—24no—
80C2×#157—24no—
81C2×#157#4118yes—
82C2×C32×C4—22no—
83C2×C32×C4C22×C412yes—
84C2×C32×C4C22×C412yes—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C22×C411yescharacteristic
87C2×C3⋊Dic3—22no—
88C2×C3⋊Dic3C22×C412yes—
89C2×C3⋊Dic3C22×C412yes—
90C2×C3⋊Dic3C22×C411yescharacteristic
91C2×C3⋊Dic3C22×C411yescharacteristic
92C4×C3⋊D3—22no—
93C4×C3⋊D3—22no—
94C4×C3⋊D3—22no—
95C4×C3⋊D3—24no—
96C4×C3⋊D3—24no—
97C4×C3⋊D3#4114yes—
98C2×#117—91no—
99#388—94no—
100#387—94no—
101C4×C4⋊C4—92no—
102C4×C22⋊C4—92no—
103#376—91no—
104C43—91no—
105C23×D3—62no—
106C22×C3×C4—22no—
107C22×Dic3—62no—
108C2×C4×D3—62no—
109C2×C4×D3—62no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—64no—
113C2×C4×D3—64no—
114C2×C4×D3—616no—
115C3×C4⋊C4—24no—
116C3×C22⋊C4—24no—
117C3×C42—22no—
118C3×C42—22no—
119#217—64no—
120(C2×D3)⋊C4—64no—
121(C2×D3)⋊C4—64no—
122C4⋊Dic3—64no—
123Dic3⋊C4—64no—
124Dic3⋊C4—64no—
125C4×Dic3—62no—
126C4×Dic3—62no—
127C4×Dic3—64no—
128C4×Dic3—64no—
129C22×C32—21no—
130C22×C32—22no—
131C22×C32C23×C411yescharacteristic
132C2×C3⋊D3—21no—
133C2×C3⋊D3—22no—
134C2×C3⋊D3—44no—
135C2×C3⋊D3C2×#4112yes—
136C2×C3⋊D3C2×#4114yes—
137#157—28no—
138#157—44no—
139C32×C4—21no—
140C32×C4—22no—
141C32×C4—22no—
142C32×C4#11712yes—
143C3⋊Dic3—21no—
144C3⋊Dic3—22no—
145C3⋊Dic3—22no—
146C3⋊Dic3#11712yes—
147C23×C4—91no—
148#117—91no—
149#117—92no—
150#117—92no—
151#117—91no—
152#117—91no—
153#117#15711yescharacteristic, complemented
154C2×C4⋊C4—92no—
155C2×C4⋊C4—94no—
156C2×C22⋊C4—92no—
157C2×C22⋊C4—94no—
158C2×C42—91no—
159C2×C42—91no—
160C2×C42—92no—
161C2×C42—94no—
162C2×C42—92no—
163#95—94no—
164#95—94no—
165#95—94no—
166C23×C3—22no—
167C22×D3—62no—
168C22×D3—62no—
169C22×D3—68no—
170C22×D3—128no—
171C2×C3×C4—28no—
172C2×C3×C4—22no—
173C2×C3×C4—24no—
174C2×C3×C4—24no—
175C2×C3×C4—22no—
176C2×Dic3—62no—
177C2×Dic3—62no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—68no—
181C4×D3—68no—
182C4×D3—68no—
183C4×D3—68no—
184C4×D3—68no—
185C4×D3—128no—
186C4×D3—128no—
187C2×C32—41no—
188C2×C32C2×#11711yescharacteristic
189C2×C32C4×#4112yes—
190C3⋊D3—41no—
191C3⋊D3#52914yes—
192C24—91no—
193C22×C4—91no—
194C22×C4—94no—
195C22×C4—91no—
196C22×C4—91no—
197C22×C4—92no—
198C22×C4—92no—
199C22×C4—91no—
200C22×C4—91no—
201C22×C4—94no—
202C22×C4—184no—
203C22×C4C2×#15711yescharacteristic
204C4⋊C4—92no—
205C4⋊C4—92no—
206C4⋊C4—92no—
207C4⋊C4—188no—
208C4⋊C4C2×#15712yes—
209C22⋊C4—92no—
210C22⋊C4—92no—
211C22⋊C4—92no—
212C22⋊C4—188no—
213C22⋊C4C2×#15712yes—
214C42—92no—
215C42—92no—
216C42—91no—
217C42—91no—
218C42—184no—
219C42—184no—
220C42—188no—
221C42C2×#15711yescharacteristic
222C42C2×#15711yescharacteristic
223C22×C3—24no—
224C22×C3—22no—
225C22×C3—44no—
226C2×D3—64no—
227C2×D3—68no—
228C2×D3—64no—
229C2×D3—124no—
230C2×D3—1216no—
231C3×C4—24no—
232C3×C4—24no—
233C3×C4—44no—
234C3×C4—44no—
235Dic3—64no—
236Dic3—64no—
237Dic3—124no—
238Dic3—124no—
239C32#229811yescharacteristic, complemented, Sylow
240C23—91no—
241C23—91no—
242C23—184no—
243C23—182no—
244C23C22×#15711yescharacteristic
245C2×C4—22no—
246C2×C4—91no—
247C2×C4—94no—
248C2×C4—98no—
249C2×C4—92no—
250C2×C4—92no—
251C2×C4—91no—
252C2×C4—182no—
253C2×C4—184no—
254C2×C4—184no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—184no—
258C2×C4—184no—
259C2×C4—182no—
260C2×C4—184no—
261C2×C4—184no—
262C2×C4—184no—
263C2×C4C22×#15712yes—
264C2×C4C22×#15712yes—
265C2×C4C22×#15711yescharacteristic
266C2×C4C22×#15711yescharacteristic
267C2×C3—22no—
268C2×C3—24no—
269C2×C3—44no—
270D3—68no—
271D3—124no—
272C22—21no—
273C22—22no—
274C22—92no—
275C22—94no—
276C22—181no—
277C22—182no—
278C22—364no—
279C22C23×#15711yescharacteristic
280C4—21no—
281C4—22no—
282C4—22no—
283C4—92no—
284C4—188no—
285C4—181no—
286C4—182no—
287C4—182no—
288C4—364no—
289C4#6428612yes—
290C3—22no—
291C2—41no—
292C2—94no—
293C2—361no—
294C2C2×#6428611yescharacteristic
295C2#41×#15712yes—
subgroupG/H
centerC2×C4C22×#157
commutator, socleC22×C32C23×C4
FrattiniC22C23×#157
FittingC32×#117C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenter#117#157
hypocenterC32#2298
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #10593758C2semidirect
5. C4×C4⋊#157C2semidirect
6. #10593733C2semidirect
7. C42×#157C2semidirect
14. C32×#117C4semidirect
15. #64135C4semidirect
16. #64101C4semidirect
19. #64086C4semidirect
20. #64081C4semidirect
21. #64081C4semidirect
153. #117#157semidirect
239. C32#2298semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
C4×C22⋊#1572
#105937582
#105937472
C4×C4⋊#1572
#105937332
C42×#1572
#22989