Finite Group Databasebeta

← #21453875

Subgroups — #21453875

Order 7808.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14519768C211yesmaximal, characteristic, complemented
2C2×#14519763C211yesmaximal, characteristic
3#16839699C211yesmaximal, characteristic, complemented
4#16839698C211yesmaximal, characteristic, complemented
5#16839688C211yesmaximal, characteristic, complemented
6#16839686C212yesmaximal, complemented
7#16839685C212yesmaximal, complemented
8#16839683C212yesmaximal, complemented
9#16839678C212yesmaximal
10#16839626C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14#14519768—24no—
15#14519763—24no—
16C2×C4⋊Dic61C2212yes—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×C4×Dic61C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2211yescharacteristic
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C2×C22⋊D61—22no—
44C2×C22⋊D61—42no—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2312yes—
47C22×Dic61C2312yes—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C2×Dic122—22no—
51C2×Dic122—42no—
52C4⋊C4×C61—22no—
53C22⋊C4×C61—22no—
54C22⋊C4×C61—42no—
55C22⋊Dic61—22no—
56C22⋊Dic61—42no—
57#11758198—22no—
58#11758198—22no—
59#11758198—42no—
60#11758198—42no—
61C4⋊Dic61—22no—
62C4⋊Dic61—24no—
63C4⋊Dic61—42no—
64#11758196—24no—
65#11758196—42no—
66#11758196—42no—
67C4×Dic61D414yes—
68C23×C61—21no—
69C23×C61—22no—
70C23×C61—21no—
71C23×C61—22no—
72C23×C61—21no—
73C23×C61C2411yescharacteristic
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—22no—
77C22×D61—22no—
78C22×D61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61C2×D412yes—
89C22⋊D61—44no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61C2×D412yes—
102C2×Dic61C2×D412yes—
103Dic122—44no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61C22×D411yescharacteristic
110C22×C61H(5,𝔽2)11yescharacteristic
111C22×C61H(5,𝔽2)12yes—
112C22×C612−1+412yes—
113C22×C612−1+411yescharacteristic
114C2×D61—41no—
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—42no—
118C2×D61—42no—
119C4×C61—22no—
120C4×C61—41no—
121C4×C61—42no—
122C4×C61—42no—
123Dic61—22no—
124Dic61—22no—
125Dic61—41no—
126Dic61—42no—
127Dic61—42no—
128#2820—611nomaximal, Sylow
129C2×C61—81no—
130C2×C61#53511yescharacteristic
131C2×C61#53611yescharacteristic
132C2×C61#53711yescharacteristic
133C2×C61#56212yes—
134C2×C61#56312yes—
135D61—81no—
136C2×#125—611no—
137C2×#124—611no—
138#399—611no—
139#399—611no—
140#397—611no—
141#397D6111yescharacteristic, complemented
142#396—612no—
143#396—612no—
144#395—612no—
145#394—612no—
146#382—611no—
147C61#282011yescharacteristic, complemented, Sylow
148C22×Q8—611no—
149C22×D4—611no—
150#125—1224no—
151#124—1224no—
152C2×C4⋊C4—612no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4C2×D6111yescharacteristic
159C2×C22⋊C4—611no—
160C2×C22⋊C4—611no—
161C2×C22⋊C4—611no—
162C2×C22⋊C4—612no—
163C2×C22⋊C4—612no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4C2×D6111yescharacteristic
166C2×C22⋊C4C2×D6112yes—
167C2×C42—611no—
168#95—612no—
169#95—611no—
170#95—612no—
171#95C2×D6111yescharacteristic
172#95C2×D6112yes—
173C24—611no—
174C24C22×D6111yescharacteristic
175C2×Q8—1222no—
176C2×Q8—2442no—
177C2×D4—1222no—
178C2×D4—2442no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4—612no—
182C22×C4—611no—
183C22×C4—612no—
184C22×C4C22×D6112yes—
185C22×C4C22×D6112yes—
186C22×C4C22×D6111yescharacteristic
187C22×C4C22×D6111yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—1224no—
190C4⋊C4—1224no—
191C4⋊C4—1222no—
192C4⋊C4—2442no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—1222no—
198C22⋊C4—1222no—
199C22⋊C4—1222no—
200C22⋊C4—2442no—
201C22⋊C4—2442no—
202C22⋊C4—2442no—
203C42—614no—
204C23—21no—
205C23—21no—
206C23—22no—
207C23—22no—
208C23—21no—
209C23—1221no—
210C23—1221no—
211C23—1222no—
212C23—1222no—
213C23—1221no—
214C23C23×D6111yescharacteristic
215Q8—2444no—
216D4—2444no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—612no—
227C2×C4—612no—
228C2×C4—1221no—
229C2×C4—1222no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—1222no—
239C2×C4D4×D6112yes—
240C22—42no—
241C22—42no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—2442no—
246C22—2442no—
247C22—2441no—
248C22—2441no—
249C22—2441no—
250C22C2×D4×D6111yescharacteristic
251C22#1451982211yescharacteristic
252C22#1451982312yes—
253C22#1451982412yes—
254C22#1451982411yescharacteristic
255C4—22no—
256C4—42no—
257C4—41no—
258C4—42no—
259C4—1222no—
260C4—1222no—
261C4—2442no—
262C4—2442no—
263C4—2441no—
264C2—81no—
265C2—4881no—
266C2#1684033011yescharacteristic
267C2#1684033411yescharacteristic
268C2#1684034111yescharacteristic
269C2#1684050912yes—
270C2#1684051412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2820
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519768C2semidirect
3. #16839699C2semidirect
4. #16839698C2semidirect
5. #16839688C2semidirect
6. #16839686C2semidirect
7. #16839685C2semidirect
8. #16839683C2semidirect
10. #16839626C2semidirect
11. C61×#397C2semidirect
141. #397D61semidirect
147. C61#2820semidirect