Finite Group Databasebeta

← #21449443

Subgroups — #21449443

Order 7808.

836 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 185 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×#14519775C211yesmaximal, characteristic, complemented
2C2×#14519764C211yesmaximal, characteristic, complemented
3C2×#14519756C211yesmaximal, characteristic, complemented
4#16839676C214yesmaximal, complemented
5#16839669C211yesmaximal, characteristic, complemented
6#16839665C211yesmaximal, characteristic, complemented
7#16839635C214yesmaximal, complemented
8C4×C22⋊Dic61C211yesmaximal, characteristic, complemented
9C22×#41×C61C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11#14519775—24no—
12#14519764—24no—
13#14519756—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×#11758196C2212yes—
16C2×#11758196C2214yes—
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2214yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2214yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2212yes—
24#14519684C2214yes—
25C2×#41×C61—24no—
26C2×#41×C61—24no—
27C2×#41×C61—24no—
28C22×Q8×C61C2211yescharacteristic
29C22×D4×C61C2212yes—
30C22×D4×C61C2211yescharacteristic
31C23×C4×C61C2212yes—
32C23×C4×C61C2211yescharacteristic
33C24×C61C2312yes—
34C24×C61C2311yescharacteristic
35#41×C61—232no—
36C2×Q8×C61—22no—
37C2×Q8×C61—22no—
38C2×Q8×C61D414yes—
39C2×D4×C61—24no—
40C2×D4×C61—24no—
41C2×D4×C61—24no—
42C2×D4×C61—22no—
43C2×D4×C61—22no—
44C2×D4×C61D414yes—
45C22×C4×C61—24no—
46C22×C4×C61—24no—
47C22×C4×C61—24no—
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61D414yes—
51C22×C4×C61C2311yescharacteristic
52C22×C4×C61C2312yes—
53C22×C4×C61C2311yescharacteristic
54C22×Dic61C2312yes—
55C22×Dic61C2312yes—
56C22×Dic61C2312yes—
57C22×Dic61C2312yes—
58C2×Dic122—22no—
59C2×Dic122—22no—
60C2×Dic122—22no—
61C22⋊Dic61—24no—
62C22⋊Dic61—28no—
63C22⋊Dic61—24no—
64C22⋊Dic61—28no—
65C4⋊Dic61—22no—
66#11758196—24no—
67#11758196—28no—
68C4×Dic61—22no—
69C4×Dic61—22no—
70C23×C61—22no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—21no—
74C23×C61—22no—
75C23×C61—24no—
76C23×C61—22no—
77C23×C61—24no—
78C23×C61C2×D414yes—
79C23×C61C2×D412yes—
80C23×C61C2411yescharacteristic
81Q8×C61—28no—
82D4×C61—216no—
83D4×C61—28no—
84C2×C4×C61—216no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—28no—
90C2×C4×C61C2×D412yes—
91C2×C4×C61C2×D414yes—
92C2×C4×C61C2×D412yes—
93C2×C4×C61C2×D412yes—
94C2×C4×C61C2×D412yes—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—24no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61#4114yescomplemented
106Dic122—44no—
107C22×C61—24no—
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—22no—
111C22×C61—28no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—44no—
117C22×C61C22×D411yescharacteristic
118C22×C61C22×D411yescharacteristic
119C22×C61C22×D411yescharacteristic
120C22×C61C2×#4112yes—
121C22×C612−1+412yes—
122C4×C61—22no—
123C4×C61—24no—
124C4×C61#12014yes—
125Dic61—24no—
126Dic61—42no—
127Dic61—42no—
128Dic61—42no—
129#2432—611nomaximal, Sylow
130C2×C61—42no—
131C2×C61—44no—
132C2×C61C2×#12011yescharacteristic
133C2×C61#53211yescharacteristic
134C2×C61#53611yescharacteristic
135C2×C61#54712yes—
136C2×C61#54812yes—
137C22×#41D6111yescharacteristic
138C2×C4⋊Q8—611no—
139C2×#124—611no—
140C2×C22⋊Q8—611no—
141#394—614no—
142#391—611no—
143#390—611no—
144#385—614no—
145C4×C22⋊C4—611no—
146C61#243211yescharacteristic, complemented, Sylow
147C2×#41—24no—
148C2×#41—24no—
149C2×#41—24no—
150C22×Q8—611no—
151C22×Q8C2×D6111yescharacteristic
152C22×D4C2×D6112yes—
153C22×D4C2×D6111yescharacteristic
154C23×C4C2×D6112yes—
155C23×C4C2×D6111yescharacteristic
156C4⋊Q8—1224no—
157#124—1224no—
158C22⋊Q8—1224no—
159C2×C4⋊C4—612no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—614no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—614no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—614no—
166C2×C42—611no—
167C2×C42—611no—
168#95—612no—
169#95—614no—
170C24C22×D6112yes—
171C24C22×D6111yescharacteristic
172#41—232no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—1222no—
176C2×Q8—1222no—
177C2×Q8—1222no—
178C2×Q8C22⋊D6114yes—
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4C22⋊D6114yes—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—24no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—612no—
191C22×C4—612no—
192C22×C4—612no—
193C22×C4—612no—
194C22×C4C22⋊D6114yes—
195C22×C4C22×D6111yescharacteristic
196C22×C4C22×D6112yes—
197C22×C4C22×D6111yescharacteristic
198C4⋊C4—1224no—
199C4⋊C4—1228no—
200C4⋊C4—1222no—
201C22⋊C4—1224no—
202C22⋊C4—1228no—
203C22⋊C4—1224no—
204C22⋊C4—1228no—
205C42—1222no—
206C42—1222no—
207C23—22no—
208C23—21no—
209C23—22no—
210C23—21no—
211C23—22no—
212C23—24no—
213C23—22no—
214C23—24no—
215C23C2×C22⋊D6114yes—
216C23C2×C22⋊D6112yes—
217C23C23×D6111yescharacteristic
218Q8—28no—
219Q8—2444no—
220D4—216no—
221D4—28no—
222C2×C4—216no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—28no—
228C2×C4—614no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1224no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4C2×C22⋊D6112yes—
240C2×C4C2×C22⋊D6114yes—
241C2×C4C2×C22⋊D6112yes—
242C2×C4C2×C22⋊D6112yes—
243C2×C4C2×C22⋊D6112yes—
244C22—24no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—28no—
249C22—42no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—44no—
254C22C22×C22⋊D6111yescharacteristic
255C22C22×C22⋊D6111yescharacteristic
256C22C22×C22⋊D6111yescharacteristic
257C22#41×D6112yes—
258C22#1451982412yes—
259C4—22no—
260C4—24no—
261C4—1224no—
262C4—2442no—
263C4—2442no—
264C4—2442no—
265C4#1451974614yes—
266C2—42no—
267C2—44no—
268C2C2×#1451974611yescharacteristic
269C2#1684030811yescharacteristic
270C2#1684033311yescharacteristic
271C2#1684041112yes—
272C2#1684041912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×#41×C61C2
hypercenterC22×#41D61
hypocenterC61#2432
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#14519775C2semidirect
2. C2×#14519764C2semidirect
3. C2×#14519756C2semidirect
4. #16839676C2semidirect
5. #16839669C2semidirect
6. #16839665C2semidirect
7. #16839635C2semidirect
8. C4×C22⋊Dic61C2semidirect
105. C2×Dic61#41semidirect
146. C61#2432semidirect