Finite Group Databasebeta

← #21453841

Subgroups — #21453841

Order 7808.

644 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519751C211yesmaximal, characteristic, complemented
2#16839688C212yesmaximal, complemented
3#16839687C212yesmaximal, complemented
4#16839671C212yesmaximal, complemented
5#16839670C214yesmaximal, complemented
6#16839670C212yesmaximal, complemented
7#16839625C211yesmaximal, characteristic, complemented
8C2×#121×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C22⋊D61C2212yes—
11C22×C22⋊D61C2214yes—
12#14519751—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C22⋊Dic61C2214yes—
15C2×C22⋊Dic61C2212yes—
16C2×#11758198C2212yes—
17C2×#11758198C2214yes—
18#14519684C2214yes—
19#14519684C2212yes—
20#14519684C2212yes—
21C22×D4×C61C2212yes—
22C22×D4×C61C2211yescharacteristic
23C23×C4×C61C2211yescharacteristic
24#121×C61—24no—
25C2×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C4×C61C2212yes—
27C24×C61C2312yes—
28C24×C61C2311yescharacteristic
29C23×D61C2312yes—
30C2×D4×C61—24no—
31C2×D4×C61—22no—
32C2×D4×C61—42no—
33C2×D4×C61—44no—
34C22×C4×C61—42no—
35C22×C4×C61D414yescomplemented
36C22×C4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2311yescharacteristic
39C2×C22⋊D61—24no—
40C2×C22⋊D61—44no—
41C2×C22⋊D61—44no—
42C2×C22⋊D61—44no—
43C2×C22⋊D61—44no—
44C22×Dic61C2314yes—
45C22×Dic61C2312yes—
46C2×D244—22no—
47C2×D244—42no—
48C4⋊C4×C61—22no—
49C22⋊C4×C61—24no—
50C22⋊Dic61—42no—
51C22⋊Dic61—44no—
52#11758198—24no—
53#11758198—44no—
54C4⋊Dic61—22no—
55C23×C61—22no—
56C23×C61—22no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61—22no—
60C23×C61—22no—
61C23×C61—24no—
62C23×C61—24no—
63C23×C61C2×D412yes—
64C23×C61C2411yescharacteristic
65C22×D61—22no—
66C22×D61—22no—
67C22×D61—24no—
68C22×D61—24no—
69C22×D61—22no—
70D4×C61—44no—
71D4×C61—48no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—24no—
76C2×C4×C61—44no—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C22⋊D61—48no—
80C22⋊D61—416no—
81C2×Dic61—22no—
82C2×Dic61—24no—
83C2×Dic61—24no—
84C2×Dic61—24no—
85C2×Dic61—24no—
86D244—44no—
87C22×C61—22no—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—44no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—44no—
95C22×C61—44no—
96C22×C61C22×D411yescharacteristic
97C22×C61H(5,𝔽2)12yes—
98C22×C61H(5,𝔽2)12yes—
99C22×C61H(5,𝔽2)12yes—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—42no—
103C2×D61—44no—
104C2×D61—44no—
105C4×C61—22no—
106C4×C61—22no—
107C4×C61—42no—
108Dic61—42no—
109Dic61—44no—
110#2815—611nomaximal, Sylow
111C2×C61—42no—
112C2×C61—82no—
113C2×C61#53411yescharacteristic
114C2×C61#53511yescharacteristic
115C2×C61#53511yescharacteristic
116C2×C61#56014yes—
117D61—82no—
118C2×#121—611no—
119C2×#121D6111yescharacteristic, complemented
120#397—612no—
121#397—612no—
122#392—612no—
123#392—614no—
124#392—612no—
125#381—611no—
126C61#281511yescharacteristic, complemented, Sylow
127C22×D4—612no—
128C22×D4—614no—
129C22×D4—611no—
130C22×D4C2×D6112yes—
131C22×D4C2×D6111yescharacteristic
132C23×C4C2×D6111yescharacteristic
133#121—24no—
134#121—1224no—
135C2×C4⋊C4—611no—
136C2×C4⋊C4C2×D6111yescharacteristic
137C2×C22⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C22⋊C4—614no—
140C2×C22⋊C4—614no—
141C2×C22⋊C4C2×D6112yes—
142#95—612no—
143#95—612no—
144#95—614no—
145C24—612no—
146C24C22×D6112yes—
147C24C22×D6111yescharacteristic
148C2×D4—24no—
149C2×D4—22no—
150C2×D4—42no—
151C2×D4—44no—
152C2×D4—1224no—
153C2×D4—1222no—
154C2×D4—2442no—
155C2×D4—2444no—
156C2×D4—2444no—
157C2×D4—2444no—
158C2×D4—2444no—
159C22×C4—42no—
160C22×C4—614no—
161C22×C4—612no—
162C22×C4C22⋊D6114yescomplemented
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—1222no—
168C22⋊C4—24no—
169C22⋊C4—1224no—
170C22⋊C4—2444no—
171C22⋊C4—2442no—
172C22⋊C4—2444no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—24no—
178C23—24no—
179C23—22no—
180C23—22no—
181C23—1222no—
182C23—1222no—
183C23—1222no—
184C23—1224no—
185C23—1224no—
186C23C2×C22⋊D6112yes—
187C23C23×D6111yescharacteristic
188D4—44no—
189D4—48no—
190D4—2444no—
191D4—2448no—
192D4—24416no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—44no—
198C2×C4—1222no—
199C2×C4—1224no—
200C2×C4—1224no—
201C2×C4—1224no—
202C2×C4—1224no—
203C2×C4C2×C22⋊D6112yes—
204C2×C4C2×C22⋊D6112yes—
205C22—22no—
206C22—22no—
207C22—22no—
208C22—44no—
209C22—44no—
210C22—44no—
211C22—42no—
212C22—42no—
213C22—42no—
214C22—2444no—
215C22—2444no—
216C22—2442no—
217C22—2442no—
218C22—2442no—
219C22C22×C22⋊D6111yescharacteristic
220C22#1451982212yes—
221C22#1451982212yes—
222C22#1451982312yes—
223C4—22no—
224C4—22no—
225C4—42no—
226C4—2444no—
227C4—2442no—
228C2—42no—
229C2—82no—
230C2—4882no—
231C2#1684032111yescharacteristic
232C2#1684032611yescharacteristic
233C2#1684032911yescharacteristic
234C2#1684050014yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#121×C61C2
hypercenterC2×#121D61
hypocenterC61#2815
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. #16839688C2semidirect
3. #16839687C2semidirect
4. #16839671C2semidirect
5. #16839670C2semidirect
6. #16839670C2semidirect
7. #16839625C2semidirect
8. C2×#121×C61C2semidirect
35. C22×C4×C61D4semidirect
119. C2×#121D61semidirect
126. C61#2815semidirect
162. C22×C4C22⋊D61semidirect