Finite Group Databasebeta

← #27193506

Subgroups — #27193506

Order 13184.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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×#15692999C211yesmaximal, characteristic
2#20267753C211yesmaximal, characteristic
3C22⋊C8×D103C211yesmaximal, characteristic
4#20267517C211yesmaximal, characteristic, complemented
5#20267516C211yesmaximal, characteristic, complemented
6#20267516C211yesmaximal, characteristic, complemented
7#324×C103C211yesmaximal, characteristic, complemented
8C22×Dic206C411yescharacteristic
9C22×C4×D103C2211yescharacteristic
10C2×#13110088—21no—
11C2×C8×D103—21no—
12#15692999—21no—
13#15692999—21no—
14#15692999—21no—
15#15692999—21no—
16C2×Dic103⋊C4C411yescharacteristic
17C2×Dic103⋊C4C2211yescharacteristic
18C2×(C2×D103)⋊C4C411yescharacteristic
19C2×(C2×D103)⋊C4C411yescharacteristic
20C22⋊(C103⋊C8)C2211yescharacteristic
21C22⋊(C103⋊C8)C2211yescharacteristic
22(C2×D103)⋊C8—21no—
23(C2×D103)⋊C8—21no—
24C2×C4⋊C4×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26C22⋊C8×C103C2211yescharacteristic
27C23×D103C2×C411yescharacteristic
28C2×Dic206—21no—
29C2×Dic206—21no—
30C2×Dic206—42no—
31C22×Dic103C2×C411yescharacteristic
32C22×Dic103C2×C411yescharacteristic
33C22×Dic103C2×C411yescharacteristic
34C2×C4×D103—42no—
35C2×C4×D103D411yescharacteristic
36C2×C4×D103D411yescharacteristic
37C2×C4×D103D411yescharacteristic
38C2×C4×D103D411yescharacteristic
39#13110088—42no—
40C2×C103⋊C8—21no—
41C2×C103⋊C8—21no—
42C8×D103—42no—
43Dic103⋊C4—21no—
44Dic103⋊C4—21no—
45Dic103⋊C4—21no—
46Dic103⋊C4—21no—
47(C2×D103)⋊C4—21no—
48(C2×D103)⋊C4—21no—
49(C2×D103)⋊C4—21no—
50(C2×D103)⋊C4—21no—
51C22×C4×C103C2×C411yescharacteristic
52C22×C4×C103C2×C411yescharacteristic
53C22×C4×C103C2311yescharacteristic
54C2×C8×C103—21no—
55C2×C8×C103—21no—
56C4⋊C4×C103—21no—
57C4⋊C4×C103—21no—
58C23×C103C22×C411yescharacteristic
59C22×D103—21no—
60C22×D103—21no—
61C22×D103—22no—
62C22×D103—41no—
63C22×D103C22⋊C411yescharacteristic
64C22×D103C22⋊C411yescharacteristic
65C2×C4×C103—21no—
66C2×C4×C103—21no—
67C2×C4×C103—21no—
68C2×C4×C103—21no—
69C2×C4×C103—41no—
70C2×C4×C103—41no—
71C2×C4×C103C2×D411yescharacteristic
72C2×C4×C103C2×D411yescharacteristic
73C2×Dic103—22no—
74C2×Dic103—21no—
75C2×Dic103—21no—
76C2×Dic103—21no—
77C2×Dic103—21no—
78C2×Dic103—41no—
79C2×Dic103C22⋊C411yescharacteristic
80C2×Dic103C22⋊C411yescharacteristic
81C4×D103—22no—
82C4×D103—22no—
83C4×D103—41no—
84C4×D103—41no—
85Dic206—42no—
86Dic206—42no—
87C8×C103—41no—
88C8×C103—41no—
89C103⋊C8—41no—
90C103⋊C8—41no—
91C22×C103—21no—
92C22×C103—21no—
93C22×C103C2×C22⋊C411yescharacteristic
94C22×C103#13111yescharacteristic
95C22×C103#13111yescharacteristic
96C2×D103—21no—
97C2×D103—21no—
98C2×D103—21no—
99C2×D103—21no—
100C2×D103—21no—
101C2×D103—42no—
102C2×D103—42no—
103C2×D103#10112yes—
104C4×C103—21no—
105C4×C103—21no—
106C4×C103—41no—
107C4×C103—41no—
108Dic103—21no—
109Dic103—41no—
110Dic103—41no—
111Dic103#9912yes—
112C2×C103—21no—
113C2×C103—21no—
114C2×C103#40811yescharacteristic
115C2×C103C2×#9911yescharacteristic
116C2×C103C2×#10111yescharacteristic
117D103—22no—
118D103—41no—
119#1472—1031nomaximal, Sylow
120C103#147211yescharacteristic, complemented, Sylow
121C2×C22⋊Q8—1031no—
122#407—1031no—
123C2×C22⋊C8—1031no—
124#324—1031no—
125#324—1031no—
126#324—1031no—
127#324D10311yescharacteristic, complemented
128C22×Q8—1031no—
129C23×C4—1031no—
130C2×M16—2061no—
131C22×C8—2061no—
132C22⋊Q8—2061no—
133C22⋊Q8—2061no—
134C22⋊Q8—2061no—
135C22⋊Q8—2061no—
136C2×C4⋊C4—1031no—
137C2×C4⋊C4—1031no—
138C2×C4⋊C4C2×D10311yescharacteristic
139C2×C22⋊C4—1031no—
140C2×C22⋊C4—1031no—
141C22⋊C8—1031no—
142C22⋊C8—1031no—
143C22⋊C8—2061no—
144C22⋊C8—2061no—
145C22⋊C8C2×D10311yescharacteristic
146C22⋊C8C2×D10311yescharacteristic
147C24—1031no—
148C2×Q8—4122no—
149C2×Q8—2061no—
150C2×Q8—2061no—
151C22×C4—1031no—
152C22×C4—1031no—
153C22×C4—1031no—
154C22×C4—1031no—
155C22×C4—1031no—
156C22×C4—1031no—
157C22×C4—1031no—
158C22×C4—4122no—
159C22×C4C4×D10311yescharacteristic
160C22×C4C4×D10311yescharacteristic
161C22×C4C22×D10311yescharacteristic
162M16—4122no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—4122no—
166C2×C8—2061no—
167C2×C8—2061no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—2061no—
171C4⋊C4—2061no—
172C4⋊C4—2061no—
173C4⋊C4—2061no—
174C22⋊C4—2061no—
175C22⋊C4—2061no—
176C22⋊C4—2061no—
177C22⋊C4—2061no—
178C23—1031no—
179C23—1031no—
180C23—4121no—
181C23—2062no—
182C23—2061no—
183C23—2061no—
184C23C2×C4×D10311yescharacteristic
185Q8—4122no—
186Q8—4122no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—1031no—
194C2×C4—1031no—
195C2×C4—4121no—
196C2×C4—4121no—
197C2×C4—4121no—
198C2×C4—2062no—
199C2×C4—2062no—
200C2×C4—2062no—
201C2×C4—2061no—
202C2×C4—2061no—
203C2×C4—2061no—
204C2×C4—2061no—
205C2×C4D4×D10311yescharacteristic
206C2×C4D4×D10311yescharacteristic
207C8—41no—
208C8—41no—
209C8—4121no—
210C8—4121no—
211C22—21no—
212C22—21no—
213C22—1032no—
214C22—4122no—
215C22—4122no—
216C22—2061no—
217C22—2061no—
218C22—2061no—
219C22—2061no—
220C22—2061no—
221C22C22⋊C4×D10311yescharacteristic
222C22#1569302711yescharacteristic
223C22#1569302911yescharacteristic
224C4—21no—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—1032no—
229C4—4121no—
230C4—4121no—
231C4—2061no—
232C2—21no—
233C2—21no—
234C2—4121no—
235C2—2062no—
236C2#2026775611yescharacteristic
237C2#99×D10311yescharacteristic
238C2#101×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC23×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#324×C103C2
socleC22×C103C2×C22⋊C4
prime radicalC23×D103C2×C4
cosocleC22×C4×C103C23
hypercenter#324D103
hypocenterC103#1472
LCSG ▷ C23×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
4. #20267517C2semidirect
5. #20267516C2semidirect
6. #20267516C2semidirect
7. #324×C103C2semidirect
120. C103#1472semidirect
127. #324D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929992
#202677532
C22⋊C8×D1032
#202675172
#202675162
#324×C1032
#1472103