Finite Group Databasebeta

← #21449446

Subgroups — #21449446

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×#11758226C211yesmaximal, characteristic
2C2×#14519775C211yesmaximal, characteristic, complemented
3C2×#14519765C211yesmaximal, characteristic, complemented
4C2×#14519757C211yesmaximal, characteristic, complemented
5#16839680C214yesmaximal, complemented
6#16839663C211yesmaximal, characteristic, complemented
7#16839636C214yesmaximal, complemented
8C4×#11758198C211yesmaximal, characteristic, complemented
9C61×#391C211yesmaximal, characteristic, complemented
10C2×#11758226—24no—
11C2×#11758226—24no—
12C2×#11758226—24no—
13C22×Dic122C2211yescharacteristic
14C22×D244C2212yes—
15C22×D244C2211yescharacteristic
16C22×C4×D61C2212yes—
17C22×C4×D61C2211yescharacteristic
18#14519775—24no—
19#14519765—24no—
20#14519757—24no—
21C2×C4⋊Dic61C2212yes—
22C2×#11758196C2214yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2214yes—
26C2×#11758198C2214yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29C22×Q8×C61C2211yescharacteristic
30C2×C4⋊C4×C61C2211yescharacteristic
31C2×C42×C61C2211yescharacteristic
32#95×C61C2214yes—
33C23×D61C2312yes—
34C23×D61C2311yescharacteristic
35C2×Q8×C61—22no—
36C2×Q8×C61—22no—
37C2×Q8×C61D414yes—
38C22×C4×C61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×Dic61C2312yes—
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2312yes—
45#11758226—232no—
46C2×D244—24no—
47C2×D244—24no—
48C2×D244—24no—
49C2×D244—22no—
50C2×D244—22no—
51C2×D244D414yes—
52C2×C4×D61—24no—
53C2×C4×D61—24no—
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—24no—
57C2×C4×D61D414yes—
58C2×Dic122—22no—
59C2×Dic122—22no—
60C2×Dic122—22no—
61C4⋊C4×C61—22no—
62C42×C61—22no—
63#11758198—24no—
64#11758198—28no—
65#11758198—24no—
66#11758198—28no—
67C4⋊Dic61—24no—
68#11758196—28no—
69C4×Dic61—22no—
70C23×C61C2411yescharacteristic
71C22×D61—22no—
72C22×D61—21no—
73C22×D61—22no—
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—24no—
77C22×D61—22no—
78C22×D61—24no—
79C22×D61C2×D414yes—
80C22×D61C2×D412yes—
81Q8×C61—28no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—24no—
87C2×C4×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61C2×D414yes—
90C2×C4×C61C2×D412yes—
91C2×C4×C61C2×D412yes—
92C2×C4×C61C2×D412yes—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61C2×D412yes—
101C2×Dic61#4114yescomplemented
102D244—216no—
103D244—28no—
104C4×D61—216no—
105C4×D61—28no—
106Dic122—44no—
107C22×C61C22×D411yescharacteristic
108C22×C61C22×D411yescharacteristic
109C22×C61C22×D411yescharacteristic
110C22×C61C2×#4112yes—
111C22×C612−1+412yes—
112C2×D61—24no—
113C2×D61—22no—
114C2×D61—22no—
115C2×D61—22no—
116C2×D61—28no—
117C2×D61—42no—
118C2×D61—42no—
119C2×D61—42no—
120C2×D61—42no—
121C2×D61—44no—
122C4×C61—24no—
123C4×C61—42no—
124C4×C61—42no—
125C4×C61#12014yes—
126Dic61—22no—
127Dic61—24no—
128Dic61—42no—
129#2432—611nomaximal, Sylow
130C2×C61C2×#12011yescharacteristic
131C2×C61#53211yescharacteristic
132C2×C61#53611yescharacteristic
133C2×C61#54712yes—
134C2×C61#54812yes—
135D61—42no—
136D61—44no—
137C22×#41—611no—
138C2×C4⋊Q8—611no—
139C2×#124—611no—
140C2×C22⋊Q8—611no—
141#394—614no—
142#391D6111yescharacteristic, complemented
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—611no—
153C22×D4—612no—
154C23×C4—611no—
155C23×C4—612no—
156C4⋊Q8—1224no—
157#124—1224no—
158C22⋊Q8—1224no—
159C2×C4⋊C4—612no—
160C2×C4⋊C4—614no—
161C2×C4⋊C4C2×D6111yescharacteristic
162C2×C22⋊C4—612no—
163C2×C22⋊C4—614no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4—614no—
166C2×C42—611no—
167C2×C42C2×D6111yescharacteristic
168#95—612no—
169#95C2×D6114yes—
170C24—611no—
171C24—612no—
172#41—12232no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—1222no—
176C2×Q8—1222no—
177C2×Q8—1222no—
178C2×Q8D24414yes—
179C2×D4—614no—
180C2×D4—1224no—
181C2×D4—1224no—
182C2×D4—1224no—
183C2×D4—1222no—
184C2×D4—1222no—
185C22×C4—611no—
186C22×C4—612no—
187C22×C4—614no—
188C22×C4—612no—
189C22×C4—1224no—
190C22×C4—1224no—
191C22×C4—1224no—
192C22×C4—1222no—
193C22×C4—1222no—
194C22×C4C22×D6112yes—
195C22×C4C22×D6112yes—
196C22×C4C22×D6112yes—
197C22×C4C22×D6111yescharacteristic
198C4⋊C4—22no—
199C4⋊C4—1224no—
200C4⋊C4—1228no—
201C22⋊C4—1224no—
202C22⋊C4—1228no—
203C22⋊C4—1224no—
204C22⋊C4—1228no—
205C42—22no—
206C42—1222no—
207C23—612no—
208C23—614no—
209C23—1222no—
210C23—1221no—
211C23—1222no—
212C23—1221no—
213C23—1222no—
214C23—1224no—
215C23—1222no—
216C23—1224no—
217C23C23×D6111yescharacteristic
218Q8—28no—
219Q8—2444no—
220D4—12216no—
221D4—1228no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—612no—
230C2×C4—614no—
231C2×C4—12216no—
232C2×C4—1221no—
233C2×C4—1222no—
234C2×C4—1221no—
235C2×C4—1222no—
236C2×C4—1228no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4C2×D24414yes—
241C2×C4C2×D24412yes—
242C2×C4D4×D6112yes—
243C2×C4D4×D6112yes—
244C22—1224no—
245C22—1222no—
246C22—1222no—
247C22—1222no—
248C22—1228no—
249C22—2442no—
250C22—2442no—
251C22—2442no—
252C22—2442no—
253C22—2444no—
254C22C2×D4×D6111yescharacteristic
255C22C2×D4×D6111yescharacteristic
256C22C22×D24411yescharacteristic
257C22#41×D6112yes—
258C22#1451982512yes—
259C4—24no—
260C4—42no—
261C4—42no—
262C4—1222no—
263C4—1224no—
264C4—2442no—
265C4#1451974714yes—
266C2—2442no—
267C2—2444no—
268C2C2×#1451974711yescharacteristic
269C2#1684031111yescharacteristic
270C2#1684033711yescharacteristic
271C2#1684041412yes—
272C2#1684042412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#391C2
hypercenter#391D61
hypocenterC61#2432
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#14519775C2semidirect
3. C2×#14519765C2semidirect
4. C2×#14519757C2semidirect
5. #16839680C2semidirect
6. #16839663C2semidirect
7. #16839636C2semidirect
8. C4×#11758198C2semidirect
9. C61×#391C2semidirect
101. C2×Dic61#41semidirect
142. #391D61semidirect
146. C61#2432semidirect