Finite Group Databasebeta

← #21457681

Subgroups — #21457681

Order 7808.

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

normal subgroups only

This group has 420 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
1Q8×D244C211yesmaximal, characteristic, complemented
2#16840415C211yesmaximal, characteristic
3#16840114C211yesmaximal, characteristic, complemented
4#16840094C212yesmaximal, complemented
5#16839992C212yesmaximal, complemented
6#16839968C211yesmaximal, characteristic, complemented
7#16839902C212yesmaximal, complemented
8C4×#11758201C211yesmaximal, characteristic, complemented
9#16839827C211yesmaximal, characteristic, complemented
10#103×D61C212yesmaximal, complemented
11C61×#475C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×Q8×D61C2212yes—
14C2×#11758190C2212yes—
15C2×#11758201C2211yescharacteristic
16C2×C8×D61C2212yes—
17#14519777—21no—
18#14519777C2211yescharacteristic
19#14519762—22no—
20#14519757—22no—
21#14519757C2212yes—
22#14519753—21no—
23#14519752C2212yes—
24C4×D244—21no—
25C4×D244C2211yescharacteristic
26C4×D244C2211yescharacteristic
27C4⋊C4×D61C2212yes—
28#14519708C2211yescharacteristic
29#14519702C2212yes—
30#14519701C2211yescharacteristic
31#14519700C2212yes—
32#14519700C2212yes—
33#14519697C2211yescharacteristic
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×Q8×C61C2211yescharacteristic
38#106×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#103×C61C2212yes—
41C2×Q8×C61—21no—
42C2×Q8×C61C2311yescharacteristic
43#11758226—44no—
44Q8×D61—24no—
45Q8×D61—42no—
46C2×D244—22no—
47C2×D244D411yescharacteristic
48C2×D244C2311yescharacteristic
49C2×C4×D61—22no—
50C2×C4×D61—22no—
51C2×C4×D61—21no—
52C2×C4×D61C2312yes—
53C2×Dic122—22no—
54C2×Dic122C2312yes—
55C2×C8×C61C2312yes—
56C4⋊C4×C61—21no—
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2312yes—
59C4⋊C4×C61C2311yescharacteristic
60C42×C61—21no—
61C42×C61C2311yescharacteristic
62#11758201—22no—
63#11758198—22no—
64#11758198—21no—
65#11758198—22no—
66#11758198D412yes—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61—22no—
70C4⋊Dic61D411yescharacteristic
71C4⋊Dic61C2311yescharacteristic
72#11758196—22no—
73C2×#92418C2311yescharacteristic
74C2×#92418C2311yescharacteristic
75#11758190—42no—
76C8×D61—42no—
77C22×D61—21no—
78C22×D61C2×D412yes—
79Q8×C61—21no—
80Q8×C61—42no—
81Q8×C61#4112yescomplemented
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2411yescharacteristic
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61C2×D412yes—
91D244—21no—
92D244—21no—
93D244—44no—
94D244SD1614yescomplemented
95C4×D61—22no—
96C4×D61—22no—
97C4×D61—44no—
98C4×D61—44no—
99C4×D61—42no—
100Dic122—22no—
101Dic122—22no—
102Dic122—44no—
103C8×C61—22no—
104#92418—21no—
105#92418—21no—
106C22×C61C22×D411yescharacteristic
107C2×D61—22no—
108C2×D61—22no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C2×D61C2×SD1614yes—
113C4×C61—22no—
114C4×C61—21no—
115C4×C61—42no—
116C4×C61—41no—
117C4×C61C2×SD1612yes—
118C4×C61C2×#4111yescharacteristic
119C4×C61H(5,𝔽2)11yescharacteristic
120Dic61—22no—
121Dic61—42no—
122Dic61—41no—
123#3298—611nomaximal, Sylow
124C2×C61#54611yescharacteristic
125C2×C61C22×SD1611yescharacteristic
126C2×C61#57811yescharacteristic
127D61—24no—
128D61—81no—
129D4×Q8—611no—
130#547—611no—
131#487—611no—
132#483—612no—
133#475D6111yescharacteristic, complemented
134#465—612no—
135#461—611no—
136#448—612no—
137C4×SD16—611no—
138C8×D4—611no—
139C2×#103—612no—
140C61#329811yescharacteristic, complemented, Sylow
141C2×#41—1221no—
142C22×Q8—612no—
143C2×SD16—611no—
144C2×SD16—612no—
145C22×C8—612no—
146C4⋊Q8—611no—
147C4⋊Q8—1221no—
148C4⋊Q8C2×D6111yescharacteristic
149#123—1222no—
150C22⋊Q8—612no—
151C22⋊Q8—1222no—
152C22⋊Q8—1221no—
153#121—612no—
154C4×Q8C2×D6111yescharacteristic
155C4×D4—611no—
156C4×D4—611no—
157C4×D4—1221no—
158C2×C4⋊C4—612no—
159#106—611no—
160#106C2×D6112yes—
161C4⋊C8C2×D6111yescharacteristic
162#103—611no—
163#103—612no—
164#103—612no—
165#103—612no—
166#103C2×D6112yes—
167#102—611no—
168C22⋊C8—612no—
169C4×C8—611no—
170#41—2444no—
171C2×Q8—21no—
172C2×Q8—612no—
173C2×Q8—1222no—
174C2×Q8—1224no—
175C2×Q8—2442no—
176C2×Q8C22×D6111yescharacteristic
177C2×D4—611no—
178C2×D4—611no—
179C2×D4—1222no—
180C22×C4—612no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4—1221no—
184SD16—1222no—
185SD16—2442no—
186C2×C8—611no—
187C2×C8—611no—
188C2×C8—2442no—
189C2×C8C22×D6112yes—
190C4⋊C4—21no—
191C4⋊C4—21no—
192C4⋊C4—611no—
193C4⋊C4—611no—
194C4⋊C4—1222no—
195C4⋊C4—1222no—
196C4⋊C4—1221no—
197C4⋊C4—1221no—
198C4⋊C4C22×D6111yescharacteristic
199C4⋊C4C22×D6112yes—
200C22⋊C4—612no—
201C22⋊C4—1222no—
202C22⋊C4—1222no—
203C22⋊C4—1221no—
204C42—21no—
205C42C22×D6111yescharacteristic
206C23—612no—
207C23—1221no—
208Q8—21no—
209Q8—42no—
210Q8—1222no—
211Q8—1222no—
212Q8—2444no—
213Q8#1175822612yescomplemented
214D4—614no—
215D4—1221no—
216D4—1221no—
217D4—2444no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—612no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—1222no—
226C2×C4—2444no—
227C2×C4—2444no—
228C2×C4—2442no—
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4C23×D6111yescharacteristic
232C8—22no—
233C8—1221no—
234C8—1221no—
235C22—614no—
236C22—1222no—
237C22—1222no—
238C22—2441no—
239C22—2441no—
240C22—2441no—
241C22C2×D4×D6111yescharacteristic
242C4—21no—
243C4—22no—
244C4—42no—
245C4—41no—
246C4—1222no—
247C4—2441no—
248C4—2442no—
249C4SD16×D6112yes—
250C4C2×#1175822611yescharacteristic
251C4#1451982311yescharacteristic
252C2—1224no—
253C2—4881no—
254C2#1684040311yescharacteristic
255C2C2×SD16×D6111yescharacteristic
256C2#1684057811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3298
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. Q8×D244C2semidirect
3. #16840114C2semidirect
4. #16840094C2semidirect
5. #16839992C2semidirect
6. #16839968C2semidirect
7. #16839902C2semidirect
8. C4×#11758201C2semidirect
9. #16839827C2semidirect
10. #103×D61C2semidirect
11. C61×#475C2semidirect
81. Q8×C61#41semidirect
94. D244SD16semidirect
133. #475D61semidirect
140. C61#3298semidirect
213. Q8#11758226semidirect