Finite Group Databasebeta

← #11858312

Subgroups — #11858312

Order 1152.

814 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 202 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×#64283C211yesmaximal, characteristic
2C22×#3788C211yesmaximal, characteristic
3C3⋊D3×#117C211yesmaximal, characteristic
4#10593755C214yesmaximal, complemented
5#10593743C214yesmaximal, complemented
6#10593729C212yesmaximal, complemented
7#10593728C212yesmaximal, complemented
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×#3792C2212yes—
10C22×#622C2212yes—
11#64283—24no—
12C2×#3788—24no—
13C2×#3788C2212yes—
14C2×#3788C2212yes—
15C2×#3788C2211yescharacteristic
16C2×#3788C2211yescharacteristic
17C2×#3787C2212yes—
18C32×#117C411yescharacteristic
19#64135C411yescharacteristic
20#64101C2212yes—
21C4⋊C4×C3⋊D3C412yes—
22C22⋊C4×C3⋊D3C412yes—
23#64086C2212yes—
24#64081C412yes—
25C42×C3⋊D3C2212yes—
26#63779C2218yescomplemented
27C4⋊#622C2218yescomplemented
28D3×#117—62no—
29C23×C3⋊D3C2×C411yescharacteristic
30C22×C32×C4C2×C411yescharacteristic
31C22×C3⋊Dic3C2311yescharacteristic
32C2×C4×C3⋊D3C2×C414yes—
33C2×C4×C3⋊D3C2×C411yescharacteristic
34C2×C4×C3⋊D3C2×C411yescharacteristic
35C2×C4×C3⋊D3D414yes—
36C2×C4×C3⋊D3Q814yes—
37C2×C4×C3⋊D3C2311yescharacteristic
38C2×C4×C3⋊D3C2311yescharacteristic
39#3792—24no—
40C2×#622—24no—
41C2×#622C2312yes—
42C2×#622C2312yes—
43C2×#622C2314yes—
44#3788—24no—
45#3788—24no—
46#3788—22no—
47#3788—22no—
48#3787—24no—
49C32×C4⋊C4C2×C412yes—
50C32×C22⋊C4C2×C412yes—
51C32×C42C2×C412yes—
52#3757C2×C412yes—
53#3752C2×C414yes—
54C4⋊(C3⋊Dic3)C2×C412yes—
55#3750C2×C414yes—
56C4×C3⋊Dic3C2×C412yes—
57C4×C3⋊Dic3C2314yes—
58#2905—91nomaximal, Sylow
59C22×C4×D3—62no—
60C3×#117—22no—
61#926—62no—
62#892—64no—
63D3×C4⋊C4—64no—
64D3×C22⋊C4—64no—
65#877—64no—
66#872—64no—
67C42×D3—64no—
68C23×C32C22×C411yescharacteristic
69C22×C3⋊D3—42no—
70C22×C3⋊D3C4⋊C414yes—
71C22×C3⋊D3C22×C411yescharacteristic
72C22×C3⋊D3C22×C411yescharacteristic
73C2×C32×C4C4⋊C414yes—
74C2×C32×C4C22×C414yes—
75C2×C32×C4C22×C411yescharacteristic
76C2×C32×C4C22×C411yescharacteristic
77C2×C3⋊Dic3C22×C414yes—
78C2×C3⋊Dic3C22×C411yescharacteristic
79C2×C3⋊Dic3C2×D412yes—
80C2×C3⋊Dic3C2×Q812yes—
81C2×C3⋊Dic3C2411yescharacteristic
82C4×C3⋊D3—44no—
83C4×C3⋊D3C4⋊C414yes—
84C4×C3⋊D3C4⋊C414yes—
85C4×C3⋊D3C2×D412yes—
86C4×C3⋊D3C2×D412yes—
87C4×C3⋊D3C2×Q812yes—
88C4×C3⋊D3C2×Q812yes—
89#622—22no—
90#622—22no—
91#622—24no—
92C22×M16—91no—
93C22×M16—91no—
94C2×#117—91no—
95#424—94no—
96#424—94no—
97#423—92no—
98#423—92no—
99C23×D3—62no—
100C22×C3×C4—22no—
101C22×Dic3—62no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—62no—
105C2×C4×D3—62no—
106C2×C4×D3—68no—
107C2×C4×D3—68no—
108C2×C4×D3—68no—
109C3×C4⋊C4—24no—
110C3×C22⋊C4—24no—
111C3×C42—24no—
112#217—64no—
113(C2×D3)⋊C4—68no—
114C4⋊Dic3—64no—
115Dic3⋊C4—68no—
116C4×Dic3—64no—
117C4×Dic3—68no—
118C22×C32—22no—
119C22×C32C2×C4⋊C412yes—
120C22×C32C23×C411yescharacteristic
121C2×C3⋊D3—22no—
122C2×C3⋊D3—22no—
123C2×C3⋊D3—44no—
124C2×C3⋊D3C2×C4⋊C412yes—
125C2×C3⋊D3C2×C4⋊C412yes—
126C32×C4—24no—
127C32×C4C2×C4⋊C412yes—
128C32×C4C2×C4⋊C412yes—
129C3⋊Dic3—24no—
130C3⋊Dic3C2×C4⋊C412yes—
131C3⋊Dic3C22×D411yescharacteristic
132C3⋊Dic3C22×Q811yescharacteristic
133C23×C4—91no—
134C2×M16—92no—
135C2×M16—91no—
136C2×M16—91no—
137C2×M16—92no—
138C2×M16—92no—
139C2×M16—184no—
140C2×M16—184no—
141C22×C8—92no—
142C22×C8—92no—
143#117—91no—
144#117—92no—
145#117—92no—
146#117—92no—
147#117#15711yescharacteristic
148C2×C4⋊C4—92no—
149C2×C22⋊C4—92no—
150C2×C42—92no—
151C4⋊C8—98no—
152C4⋊C8—98no—
153C23×C3—22no—
154C22×D3—62no—
155C22×D3—68no—
156C22×D3—62no—
157C22×D3—128no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—28no—
161C2×C3×C4—28no—
162C2×Dic3—62no—
163C2×Dic3—64no—
164C2×Dic3—64no—
165C2×Dic3—62no—
166C2×Dic3—68no—
167C4×D3—68no—
168C4×D3—68no—
169C4×D3—64no—
170C4×D3—64no—
171C4×D3—64no—
172C4×D3—64no—
173C4×D3—1216no—
174C2×C32—22no—
175C2×C32C22×C4⋊C411yescharacteristic
176C2×C32#56812yes—
177C3⋊D3—22no—
178C3⋊D3—22no—
179C24—91no—
180C22×C4—91no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4—91no—
185C22×C4—94no—
186C22×C4—94no—
187C22×C4—94no—
188C22×C4C2×#15711yescharacteristic
189M16—184no—
190M16—184no—
191M16—182no—
192M16—182no—
193M16—184no—
194C2×C8—92no—
195C2×C8—94no—
196C2×C8—92no—
197C2×C8—184no—
198C2×C8—184no—
199C4⋊C4—94no—
200C4⋊C4—92no—
201C4⋊C4C2×#15712yes—
202C22⋊C4—92no—
203C22⋊C4—94no—
204C22⋊C4C2×#15712yes—
205C42—94no—
206C42—92no—
207C42C2×#15712yes—
208C22×C3—24no—
209C22×C3—22no—
210C22×C3—44no—
211C2×D3—64no—
212C2×D3—64no—
213C2×D3—68no—
214C2×D3—124no—
215C2×D3—1216no—
216C3×C4—24no—
217C3×C4—24no—
218C3×C4—48no—
219Dic3—64no—
220Dic3—62no—
221Dic3—62no—
222Dic3—128no—
223C32#290511yescharacteristic, complemented, Sylow
224C23—91no—
225C23—91no—
226C23—94no—
227C23—362no—
228C23C22×#15711yescharacteristic
229C2×C4—92no—
230C2×C4—92no—
231C2×C4—91no—
232C2×C4—91no—
233C2×C4—92no—
234C2×C4—92no—
235C2×C4—92no—
236C2×C4—94no—
237C2×C4—92no—
238C2×C4—94no—
239C2×C4—94no—
240C2×C4—364no—
241C2×C4C4⋊#15714yes—
242C2×C4C22×#15714yes—
243C2×C4C22×#15711yescharacteristic
244C2×C4C22×#15711yescharacteristic
245C8—182no—
246C8—182no—
247C8—184no—
248C2×C3—22no—
249C2×C3—24no—
250C2×C3—44no—
251D3—68no—
252D3—124no—
253C22—22no—
254C22—92no—
255C22—92no—
256C22—182no—
257C22—182no—
258C22—364no—
259C22C2×C4⋊#15712yes—
260C22C23×#15711yescharacteristic
261C4—24no—
262C4—91no—
263C4—92no—
264C4—91no—
265C4—184no—
266C4C2×C4⋊#15712yes—
267C4C2×C4⋊#15712yes—
268C3—22no—
269C2—22no—
270C2—182no—
271C2—182no—
272C2C22×C4⋊#15711yescharacteristic
273C2#1059664812yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#117C4
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C3⋊Dic3C24
hypercenter#117#157
hypocenterC32#2905
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10593755C2semidirect
5. #10593743C2semidirect
6. #10593729C2semidirect
7. #10593728C2semidirect
26. #63779C22semidirect
27. C4⋊#622C22semidirect
223. C32#2905semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
C22×#37882
C3⋊D3×#1172
#105937552
#105937432
#105937292
#105937282
#29059