Finite Group Databasebeta

← #21461778

Subgroups — #21461778

Order 7808.

302 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 68 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#16840831C211yesmaximal, characteristic
2#16840773C211yesmaximal, characteristic, complemented
3#16840753C211yesmaximal, characteristic
4#16840708C211yesmaximal, characteristic, complemented
5#16840641C211yesmaximal, characteristic, complemented
6#16840633C211yesmaximal, characteristic, complemented
7#104×D61C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9Q8×#6923—21no—
10D4×#6923—22no—
11D4×#6923—21no—
12#14519856—21no—
13#14519856C2211yescharacteristic
14C2×C4⋊#6923—21no—
15C2×C4⋊#6923—22no—
16C2×C4⋊#6923C2211yescharacteristic
17C2×C4⋊#6923C2211yescharacteristic
18#14519846—21no—
19#14519845—21no—
20#14519840—21no—
21#14519839—21no—
22#41×D61C2211yescharacteristic
23M16×D61C2211yescharacteristic
24C42×D61C2211yescharacteristic
25#14519705C411yescharacteristic, complemented
26#14519704C411yescharacteristic, complemented
27#14519703C411yescharacteristic, complemented
28#104×C61C411yescharacteristic, complemented
29C22×#6923—22no—
30C22×#6923—21no—
31C22×#6923D412yes—
32#41×C61C2×C411yescharacteristic
33#11758226Q811yescharacteristic
34Q8×D61D411yescharacteristic
35#11758224—21no—
36#11758224Q811yescharacteristic
37D4×D61—21no—
38D4×D61D411yescharacteristic
39#11758222—21no—
40#11758222C2×C411yescharacteristic
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61C2311yescharacteristic
44C22⋊#6923—22no—
45C22⋊#6923—21no—
46#11758217—21no—
47C4⋊#6923—22no—
48C4⋊#6923—21no—
49C4⋊#6923—21no—
50C4⋊#6923—21no—
51C4⋊#6923—21no—
52C4⋊#6923—44no—
53C4⋊#6923D411yescharacteristic
54C4⋊#6923D411yescharacteristic
55C4×#6923—22no—
56C4×#6923—21no—
57#11758213—21no—
58D61⋊C8—21no—
59M16×C61C2×C411yescharacteristic, complemented
60C42×C61C2×C411yescharacteristic, complemented
61C4×Dic61—21no—
62C4×Dic61C2×C411yescharacteristic, complemented
63#11758194C2×C411yescharacteristic, complemented
64#11758189—21no—
65C8×D61—21no—
66C22×D61—21no—
67C22×D61C2×D411yescharacteristic
68C2×#6923—21no—
69C2×#6923—22no—
70C2×#6923—21no—
71C2×#6923—42no—
72C2×#6923—42no—
73C2×#6923—41no—
74C2×#6923—82no—
75Q8×C61C4⋊C411yescharacteristic, complemented
76D4×C61—21no—
77D4×C61C4⋊C411yescharacteristic, complemented
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61C22×C411yescharacteristic
81C22⋊D61—21no—
82C22⋊D61—21no—
83C22⋊D61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61#4111yescharacteristic
87D244—21no—
88D244C4⋊C411yescharacteristic, complemented
89C4×D61—22no—
90C4×D61—22no—
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—21no—
94C4×D61C2×D411yescharacteristic
95C4×D61C2×D411yescharacteristic
96C4×D61C2×Q811yescharacteristic
97C4×D61#4111yescharacteristic
98Dic122—21no—
99Dic122C4⋊C411yescharacteristic, complemented
100#92420—41no—
101C8×C61—21no—
102#92418—21no—
103C22×C61—21no—
104C22×C61C4×D411yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—41no—
109C2×D61—41no—
110C2×D61#12011yescharacteristic
111C2×D61C22⋊Q811yescharacteristic
112#6923—42no—
113#6923—41no—
114#6923—41no—
115#6923—81no—
116C4×C61—22no—
117C4×C61—21no—
118C4×C61C2×C4⋊C411yescharacteristic
119C4×C61C4×D411yescharacteristic
120Dic61—22no—
121Dic61—21no—
122Dic61C22⋊Q811yescharacteristic
123Dic61#12311yescharacteristic
124#1859—611nomaximal, Sylow
125C2×C61—21no—
126C2×C61—41no—
127C2×C61#38511yescharacteristic
128D61—21no—
129D61—41no—
130D61#45311yescharacteristic
131D61#45611yescharacteristic
132#520—611no—
133#428—611no—
134C2×#104—611no—
135#417—611no—
136#384—611no—
137#343—611no—
138#339—611no—
139C61#185911yescharacteristic, complemented, Sylow
140C2×#41—611no—
141C2×M16—611no—
142C2×M16—611no—
143C4×Q8—1221no—
144C4×D4—1222no—
145C4×D4—1221no—
146#117—611no—
147#117—1221no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—1221no—
151C2×C4⋊C4—1222no—
152C2×C42—611no—
153#107—1221no—
154#106—1221no—
155#104—611no—
156#104—611no—
157#104—611no—
158#104#692311yescharacteristic, complemented
159#103—1221no—
160#102—1221no—
161#41—611no—
162#41—611no—
163#41—611no—
164#41—1221no—
165#41—1221no—
166#41C2×#692311yescharacteristic
167C2×Q8—611no—
168C2×D4—611no—
169C2×D4—1221no—
170C22×C4—611no—
171C22×C4—612no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—1222no—
175C22×C4—1221no—
176M16—611no—
177M16—1221no—
178M16—1221no—
179M16—1221no—
180M16C2×#692311yescharacteristic, complemented
181C2×C8—1221no—
182C2×C8—1221no—
183C4⋊C4—611no—
184C4⋊C4—611no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1221no—
189C4⋊C4—1222no—
190C4⋊C4—2444no—
191C22⋊C4—1221no—
192C22⋊C4—1222no—
193C42—611no—
194C42—1221no—
195C42—1221no—
196C42—1222no—
197C42C2×#692311yescharacteristic, complemented
198C23—611no—
199C23—1221no—
200Q8—611no—
201Q8—1221no—
202Q8C4⋊#692311yescharacteristic, complemented
203D4—21no—
204D4—611no—
205D4—1221no—
206D4—1221no—
207D4—1221no—
208D4—1221no—
209D4C4⋊#692311yescharacteristic, complemented
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—611no—
213C2×C4—611no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—611no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1221no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1222no—
227C2×C4—4882no—
228C2×C4—2441no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4C22×#692311yescharacteristic
232C8—21no—
233C8—1221no—
234C8—2441no—
235C22—21no—
236C22—611no—
237C22—611no—
238C22—1221no—
239C22—1221no—
240C22—1221no—
241C22—2441no—
242C22—2441no—
243C22D4×#692311yescharacteristic
244C4—22no—
245C4—21no—
246C4—611no—
247C4—611no—
248C4—1222no—
249C4—1221no—
250C4—4881no—
251C4—2441no—
252C4—2442no—
253C4—2441no—
254C4C2×C4⋊#692311yescharacteristic
255C4D4×#692311yescharacteristic
256C2—21no—
257C2—41no—
258C2—611no—
259C2—611no—
260C2—1221no—
261C2—2441no—
262C2#1684070911yescharacteristic
subgroupG/H
centerC2#16840709
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#104×C61C4
socleC2×C61#385
hypercenter#104#6923
hypocenterC61#1859
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #16840773C2semidirect
4. #16840708C2semidirect
5. #16840641C2semidirect
6. #16840633C2semidirect
25. #14519705C4semidirect
26. #14519704C4semidirect
27. #14519703C4semidirect
28. #104×C61C4semidirect
59. M16×C61C2×C4semidirect
60. C42×C61C2×C4semidirect
62. C4×Dic61C2×C4semidirect
63. #11758194C2×C4semidirect
75. Q8×C61C4⋊C4semidirect
77. D4×C61C4⋊C4semidirect
88. D244C4⋊C4semidirect
99. Dic122C4⋊C4semidirect
139. C61#1859semidirect
158. #104#6923semidirect
180. M16C2×#6923semidirect
197. C42C2×#6923semidirect
202. Q8C4⋊#6923semidirect
209. D4C4⋊#6923semidirect