Finite Group Databasebeta

← #21449450

Subgroups — #21449450

Order 7808.

836 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×#11758224C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic, complemented
3C2×#14519753C211yesmaximal, characteristic, complemented
4#16839677C214yesmaximal, complemented
5#16839668C211yesmaximal, characteristic, complemented
6#16839665C211yesmaximal, characteristic, complemented
7#16839634C214yesmaximal, complemented
8C4×#11758198C211yesmaximal, characteristic, complemented
9C2×#124×C61C211yesmaximal, characteristic, complemented
10C2×#11758224—24no—
11C2×#11758224—24no—
12C2×#11758224—24no—
13C22×Dic122C2211yescharacteristic
14C22×C22⋊D61C2212yes—
15C23×Dic61C2212yes—
16C22×C4×D61C2211yescharacteristic
17#14519775—24no—
18#14519753—24no—
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758196C2212yes—
21C2×#11758196C2214yes—
22C2×C22⋊Dic61C2214yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2214yes—
28C22×Q8×C61C2211yescharacteristic
29C22×D4×C61C2211yescharacteristic
30#124×C61—24no—
31C2×C22⋊C4×C61C2214yes—
32C2×C42×C61C2211yescharacteristic
33C24×C61C2312yes—
34C23×D61C2311yescharacteristic
35C2×Q8×C61—22no—
36C2×Q8×C61—22no—
37C2×Q8×C61—22no—
38C2×D4×C61—22no—
39C2×D4×C61—22no—
40C2×D4×C61D414yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—24no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—24no—
47C22×Dic61—24no—
48C22×Dic61—24no—
49C22×Dic61—24no—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2312yes—
53C22×Dic61C2312yes—
54#11758224—232no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61D414yes—
58C2×Dic122—22no—
59C2×Dic122—22no—
60C2×Dic122D414yes—
61C22⋊C4×C61—28no—
62C42×C61—22no—
63C22⋊Dic61—28no—
64#11758198—24no—
65#11758198—24no—
66C4⋊Dic61—22no—
67#11758196—24no—
68#11758196—28no—
69C4×Dic61—22no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61—24no—
73C23×C61—24no—
74C23×C61C2×D414yes—
75C23×C61C2411yescharacteristic
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61C2×D412yes—
81Q8×C61—44no—
82D4×C61—28no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61C2×D412yes—
90C2×C4×C61C2×D412yes—
91C2×C4×C61C2×D412yes—
92C22⋊D61—216no—
93C2×Dic61—216no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—24no—
102C2×Dic61C2×D414yes—
103C2×Dic61C2×D412yes—
104C2×Dic61#4114yescomplemented
105C4×D61—28no—
106Dic122—28no—
107C22×C61—24no—
108C22×C61—28no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61—44no—
112C22×C61C22×D411yescharacteristic
113C22×C61C22×D411yescharacteristic
114C22×C61C22×D411yescharacteristic
115C22×C61C2×#4112yes—
116C22×C612−1+412yes—
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—22no—
120C2×D61—42no—
121C2×D61—42no—
122C4×C61—42no—
123C4×C61—42no—
124C4×C61#12014yes—
125Dic61—24no—
126Dic61—22no—
127Dic61—24no—
128Dic61—42no—
129#2432—611nomaximal, Sylow
130C2×C61—44no—
131C2×C61C2×#12011yescharacteristic
132C2×C61#53211yescharacteristic
133C2×C61#53611yescharacteristic
134C2×C61#54712yes—
135C2×C61#54812yes—
136D61—42no—
137C22×#41—611no—
138C2×C4⋊Q8—611no—
139C2×#124D6111yescharacteristic, complemented
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—1224no—
148C2×#41—1224no—
149C2×#41—1224no—
150C22×Q8—611no—
151C22×Q8C2×D6111yescharacteristic
152C22×D4—612no—
153C22×D4C2×D6111yescharacteristic
154C23×C4—611no—
155C23×C4—612no—
156C4⋊Q8—1224no—
157#124—24no—
158C22⋊Q8—1224no—
159C2×C4⋊C4—612no—
160C2×C4⋊C4—611no—
161C2×C4⋊C4—614no—
162C2×C22⋊C4—614no—
163C2×C22⋊C4—612no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4C2×D6114yes—
166C2×C42—611no—
167C2×C42C2×D6111yescharacteristic
168#95—612no—
169#95—614no—
170C24—611no—
171C24C22×D6112yes—
172#41—12232no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—614no—
177C2×Q8—1222no—
178C2×Q8—1222no—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4—1224no—
182C2×D4—1224no—
183C2×D4—1224no—
184C2×D4C22⋊D6114yes—
185C22×C4—611no—
186C22×C4—612no—
187C22×C4—612no—
188C22×C4—614no—
189C22×C4—612no—
190C22×C4—1224no—
191C22×C4—1224no—
192C22×C4—1224no—
193C22×C4—1222no—
194C22×C4—1222no—
195C22×C4C22×D6112yes—
196C22×C4C22×D6112yes—
197C22×C4C22×D6111yescharacteristic
198C4⋊C4—1224no—
199C4⋊C4—1228no—
200C4⋊C4—1222no—
201C22⋊C4—28no—
202C22⋊C4—1224no—
203C22⋊C4—1224no—
204C22⋊C4—1228no—
205C42—22no—
206C42—1222no—
207C23—22no—
208C23—22no—
209C23—24no—
210C23—24no—
211C23—612no—
212C23—1221no—
213C23—1221no—
214C23—1222no—
215C23—1222no—
216C23C2×C22⋊D6114yes—
217C23C23×D6111yescharacteristic
218Q8—44no—
219Q8—1228no—
220D4—28no—
221D4—12216no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—612no—
229C2×C4—614no—
230C2×C4—614no—
231C2×C4—12216no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1228no—
239C2×C4—1222no—
240C2×C4—1224no—
241C2×C4D4×D6112yes—
242C2×C4D4×D6112yes—
243C2×C4C2×C22⋊D6112yes—
244C22—24no—
245C22—28no—
246C22—42no—
247C22—42no—
248C22—44no—
249C22—1222no—
250C22—1222no—
251C22—1222no—
252C22—2442no—
253C22—2442no—
254C22C2×D4×D6111yescharacteristic
255C22C2×D4×D6111yescharacteristic
256C22C22×C22⋊D6111yescharacteristic
257C22#41×D6112yes—
258C22#1451982412yes—
259C4—42no—
260C4—42no—
261C4—1222no—
262C4—1224no—
263C4—1224no—
264C4—2442no—
265C4#1451974514yes—
266C2—44no—
267C2—2442no—
268C2C2×#1451974511yescharacteristic
269C2#1684031111yescharacteristic
270C2#1684033211yescharacteristic
271C2#1684041112yes—
272C2#1684042012yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#124×C61C2
hypercenterC2×#124D61
hypocenterC61#2432
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#14519775C2semidirect
3. C2×#14519753C2semidirect
4. #16839677C2semidirect
5. #16839668C2semidirect
6. #16839665C2semidirect
7. #16839634C2semidirect
8. C4×#11758198C2semidirect
9. C2×#124×C61C2semidirect
104. C2×Dic61#41semidirect
139. C2×#124D61semidirect
146. C61#2432semidirect