Finite Group Databasebeta

← #21458173

Subgroups — #21458173

Order 7808.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#16840473C211yesmaximal, characteristic, complemented
2#16840417C211yesmaximal, characteristic
3#16840158C211yesmaximal, characteristic, complemented
4#16840094C212yesmaximal, complemented
5#16840079C212yesmaximal, complemented
6#16840048C211yesmaximal, characteristic, complemented
7#16839990C212yesmaximal, complemented
8C4×#11758200C211yesmaximal, characteristic, complemented
9#16839827C211yesmaximal, characteristic, complemented
10#106×D61C212yesmaximal, complemented
11C61×#476C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13C2×#11758200C2211yescharacteristic
14C2×C8×D61C2212yes—
15#14519777C2211yescharacteristic
16#14519768—21no—
17#14519759—22no—
18#14519757C2212yes—
19#14519756—21no—
20#14519753—22no—
21#14519748C2212yes—
22C4×Dic122C2211yescharacteristic
23C4×D244C2211yescharacteristic
24#14519739—21no—
25C4⋊C4×D61C2212yes—
26C4⋊C4×D61C2212yes—
27#14519709C2212yes—
28#14519708C2212yes—
29#14519708C2211yescharacteristic
30#14519708C2212yes—
31#14519702C2212yes—
32#14519700C2211yescharacteristic
33#14519698C2211yescharacteristic
34#14519689C2212yes—
35C4×#92418C2211yescharacteristic
36C4⋊Q8×C61C2211yescharacteristic
37C4×D4×C61C2211yescharacteristic
38#106×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×Q8×C61—21no—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C2×C22⋊D61—22no—
45#11758222—44no—
46C2×D244D411yescharacteristic
47C2×C4×D61—22no—
48C2×C4×D61—22no—
49C2×C4×D61C2312yes—
50C2×Dic122—21no—
51C2×Dic122C2311yescharacteristic
52C2×C8×C61C2312yes—
53C4⋊C4×C61—21no—
54C4⋊C4×C61C2312yes—
55C4⋊C4×C61C2311yescharacteristic
56C22⋊C4×C61—21no—
57C42×C61C2311yescharacteristic
58C22⋊Dic61—22no—
59#11758200—22no—
60#11758198—22no—
61#11758198D412yes—
62C4⋊Dic61—21no—
63C4⋊Dic61—22no—
64C4⋊Dic61D411yescharacteristic
65C4⋊Dic61C2311yescharacteristic
66C4⋊Dic61C2312yes—
67#11758196—21no—
68#11758196—22no—
69#11758196—22no—
70C4×Dic61—21no—
71C2×#92418C2311yescharacteristic
72C2×#92418C2311yescharacteristic
73C8×D61—24no—
74C23×C61—21no—
75C22×D61C2×D412yes—
76Q8×C61—81no—
77D4×C61—21no—
78D4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—42no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2411yescharacteristic
85C22⋊D61—44no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—22no—
89C2×Dic61C2×D412yes—
90D244SD1614yescomplemented
91C4×D61—22no—
92C4×D61—22no—
93C4×D61—44no—
94C4×D61—82no—
95Dic122—21no—
96Dic122—21no—
97Dic122—42no—
98C8×C61—22no—
99#92418—21no—
100#92418#4112yescomplemented
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61C22×D411yescharacteristic
105C2×D61—22no—
106C2×D61—22no—
107C2×D61C2×SD1614yes—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61—42no—
111C4×C61C2×SD1612yes—
112C4×C61C2×#4111yescharacteristic
113C4×C612−1+411yescharacteristic
114Dic61—22no—
115Dic61—41no—
116Dic61—42no—
117Dic61—41no—
118#3335—611nomaximal, Sylow
119C2×C61—81no—
120C2×C61#54711yescharacteristic
121C2×C61C22×SD1611yescharacteristic
122C2×C61#57711yescharacteristic
123D61—24no—
124#554—611no—
125#547—611no—
126#498—611no—
127#483—612no—
128#481—612no—
129#476D6111yescharacteristic, complemented
130#475—611no—
131#465—612no—
132C4×SD16—611no—
133C8×D4—611no—
134C2×#106—612no—
135C61#333511yescharacteristic, complemented, Sylow
136C2×#41—1221no—
137C2×SD16—611no—
138C22×C8—612no—
139C4⋊Q8—611no—
140C4⋊Q8C2×D6111yescharacteristic
141#125—1221no—
142#123—1222no—
143C22⋊Q8—612no—
144C22⋊Q8—1222no—
145C22⋊Q8—1221no—
146#121—612no—
147C4×Q8—611no—
148C4×D4—611no—
149C4×D4—1221no—
150C4×D4C2×D6111yescharacteristic
151C2×C4⋊C4—612no—
152C2×C4⋊C4—612no—
153#106—612no—
154#106—611no—
155#106—612no—
156#106—612no—
157#106C2×D6112yes—
158C4⋊C8C2×D6111yescharacteristic
159#103—612no—
160#103—611no—
161#102—611no—
162#102C2×D6112yes—
163C22⋊C8—612no—
164C4×C8—611no—
165#41—2444no—
166C2×Q8—21no—
167C2×Q8—611no—
168C2×Q8—1221no—
169C2×D4—611no—
170C2×D4—1222no—
171C2×D4C22×D6111yescharacteristic
172C22×C4—21no—
173C22×C4—612no—
174C22×C4—1222no—
175C22×C4—1222no—
176SD16—1222no—
177C2×C8—611no—
178C2×C8—611no—
179C2×C8—1224no—
180C2×C8C22×D6112yes—
181C4⋊C4—21no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—612no—
185C4⋊C4—1222no—
186C4⋊C4—1222no—
187C4⋊C4—1222no—
188C4⋊C4—1221no—
189C4⋊C4—1221no—
190C4⋊C4C22×D6112yes—
191C4⋊C4C22×D6111yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—612no—
194C22⋊C4—1222no—
195C22⋊C4—1222no—
196C42—1221no—
197C42C22×D6111yescharacteristic
198C23—21no—
199C23—612no—
200Q8—81no—
201Q8—1221no—
202Q8—1221no—
203Q8—2442no—
204D4—21no—
205D4—21no—
206D4—614no—
207D4—2444no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—612no—
212C2×C4—1222no—
213C2×C4—1222no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1222no—
217C2×C4—4882no—
218C2×C4—2444no—
219C2×C4D4×D6111yescharacteristic
220C2×C4D4×D6111yescharacteristic
221C2×C4C23×D6111yescharacteristic
222C8—22no—
223C8—612no—
224C8—1221no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—614no—
229C22—1222no—
230C22—1222no—
231C22C2×D4×D6111yescharacteristic
232C4—21no—
233C4—41no—
234C4—42no—
235C4—1222no—
236C4—2442no—
237C4—2441no—
238C4—2441no—
239C4SD16×D6112yes—
240C4#41×D6111yescharacteristic
241C4#1451982511yescharacteristic
242C2—81no—
243C2—1224no—
244C2#1684041411yescharacteristic
245C2C2×SD16×D6111yescharacteristic
246C2#1684057211yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3335
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840473C2semidirect
3. #16840158C2semidirect
4. #16840094C2semidirect
5. #16840079C2semidirect
6. #16840048C2semidirect
7. #16839990C2semidirect
8. C4×#11758200C2semidirect
9. #16839827C2semidirect
10. #106×D61C2semidirect
11. C61×#476C2semidirect
90. D244SD16semidirect
100. #92418#41semidirect
129. #476D61semidirect
135. C61#3335semidirect