Finite Group Databasebeta

← #21451986

Subgroups — #21451986

Order 7808.

434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14519772C211yesmaximal, characteristic
2C2×#14519768C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic
4#16839696C212yesmaximal, complemented
5#16839692C211yesmaximal, characteristic, complemented
6#16839689C211yesmaximal, characteristic
7#16839686C212yesmaximal
8#16839659C212yesmaximal, complemented
9#16839654C212yesmaximal
10#16839613C211yesmaximal, characteristic, complemented
11C61×#400C211yesmaximal, characteristic, complemented
12#14519772—24no—
13#14519768—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2212yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×C4×Dic61C2212yes—
28C2×C4×Dic61C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2211yescharacteristic
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2311yescharacteristic
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2312yes—
48C4⋊C4×C61—22no—
49C4⋊C4×C61—22no—
50#11758198—22no—
51#11758198—22no—
52#11758198—22no—
53#11758198—24no—
54#11758198—42no—
55C4⋊Dic61—22no—
56C4⋊Dic61—24no—
57C4⋊Dic61—22no—
58#11758196—24no—
59#11758196—22no—
60#11758196—24no—
61#11758196—24no—
62#11758196—42no—
63C4×Dic61—42no—
64C4×Dic61D414yes—
65C23×C61C2411yescharacteristic
66C22×D61—21no—
67C22×D61—22no—
68C22×D61—21no—
69C22×D61—22no—
70C22×D61—21no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D412yes—
84C2×Dic61—22no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61C2×D412yes—
95C2×Dic61C2×D412yes—
96C2×Dic61#4114yes—
97C22×C61C22×D411yescharacteristic
98C22×C61C2×#4112yes—
99C22×C61H(5,𝔽2)11yescharacteristic
100C22×C612−1+412yes—
101C22×C612−1+411yescharacteristic
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—41no—
105C2×D61—42no—
106C2×D61—42no—
107C4×C61—22no—
108C4×C61—42no—
109C4×C61—41no—
110C4×C61—41no—
111C4×C61—42no—
112Dic61—22no—
113Dic61—22no—
114Dic61—24no—
115Dic61—41no—
116Dic61—42no—
117#2664—611nomaximal, Sylow
118C2×C61#53211yescharacteristic
119C2×C61#53611yescharacteristic
120C2×C61#53711yescharacteristic
121C2×C61#53912yes—
122C2×C61#54112yes—
123D61—81no—
124C2×#126—611no—
125C2×#125—611no—
126#400D6111yescharacteristic, complemented
127#399—611no—
128#398—611no—
129#398—612no—
130#397—611no—
131#396—612no—
132#389—612no—
133#388—612no—
134C4×C4⋊C4—611no—
135C61#266411yescharacteristic, complemented, Sylow
136#126—1224no—
137#125—1224no—
138C2×C4⋊C4—612no—
139C2×C4⋊C4—612no—
140C2×C4⋊C4—611no—
141C2×C4⋊C4—611no—
142C2×C4⋊C4—611no—
143C2×C4⋊C4—612no—
144C2×C4⋊C4—612no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4C2×D6111yescharacteristic
147C2×C4⋊C4C2×D6111yescharacteristic
148C2×C22⋊C4—611no—
149C2×C22⋊C4—611no—
150C2×C22⋊C4—611no—
151C2×C22⋊C4—612no—
152C2×C22⋊C4—612no—
153C2×C42—611no—
154C2×C42—612no—
155#95—611no—
156#95—612no—
157#95—612no—
158#95C2×D6111yescharacteristic
159#95C2×D6112yes—
160#95C2×D6112yes—
161C24—611no—
162C22×C4—612no—
163C22×C4—611no—
164C22×C4—611no—
165C22×C4—611no—
166C22×C4—612no—
167C22×C4C22×D6111yescharacteristic
168C22×C4C22×D6112yes—
169C22×C4C22×D6111yescharacteristic
170C22×C4C22×D6112yes—
171C22×C4C22×D6111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—1224no—
175C4⋊C4—1224no—
176C4⋊C4—1224no—
177C4⋊C4—1222no—
178C4⋊C4—1224no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4—2442no—
182C22⋊C4—1224no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C22⋊C4—2442no—
187C42—614no—
188C42—2442no—
189C23—1221no—
190C23—1222no—
191C23—1221no—
192C23—1222no—
193C23—1221no—
194C23C23×D6111yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—612no—
208C2×C4—612no—
209C2×C4—614no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4D4×D6112yes—
221C22—2441no—
222C22—2441no—
223C22—2441no—
224C22—2442no—
225C22—2442no—
226C22C2×D4×D6111yescharacteristic
227C22#41×D6112yes—
228C22#1451982311yescharacteristic
229C22#1451982412yes—
230C22#1451982511yescharacteristic
231C4—22no—
232C4—42no—
233C4—41no—
234C4—41no—
235C4—42no—
236C4—1222no—
237C4—1222no—
238C4—1224no—
239C4—2441no—
240C4—2442no—
241C2—4881no—
242C2#1684031111yescharacteristic
243C2#1684033411yescharacteristic
244C2#1684034211yescharacteristic
245C2#1684035312yes—
246C2#1684037112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2664
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. C2×#14519768C2semidirect
4. #16839696C2semidirect
5. #16839692C2semidirect
8. #16839659C2semidirect
10. #16839613C2semidirect
11. C61×#400C2semidirect
126. #400D61semidirect
135. C61#2664semidirect