Finite Group Databasebeta

← #21461779

Subgroups — #21461779

Order 7808.

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

normal subgroups only

This group has 286 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#16840706C211yesmaximal, 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⋊#6923C2211yescharacteristic
16C2×C4⋊#6923C2211yescharacteristic
17#14519846—21no—
18#14519845—21no—
19#14519840—21no—
20#14519839—21no—
21(C2×#6923)⋊C4—22no—
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⋊#6923D411yescharacteristic
53C4⋊#6923D411yescharacteristic
54C4×#6923—22no—
55C4×#6923—21no—
56#11758213—21no—
57D61⋊C8—21no—
58M16×C61C2×C411yescharacteristic, complemented
59C42×C61C2×C411yescharacteristic, complemented
60C4×Dic61—21no—
61C4×Dic61C2×C411yescharacteristic, complemented
62#11758194C2×C411yescharacteristic, complemented
63#11758189—21no—
64C8×D61—21no—
65C22×D61—21no—
66C22×D61C2×D411yescharacteristic
67C2×#6923—21no—
68C2×#6923—22no—
69C2×#6923—21no—
70C2×#6923—42no—
71C2×#6923—42no—
72C2×#6923—41no—
73C2×#6923—82no—
74Q8×C61C4⋊C411yescharacteristic
75D4×C61—21no—
76D4×C61C4⋊C411yescharacteristic
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61C22×C411yescharacteristic
80C22⋊D61—21no—
81C22⋊D61—21no—
82C22⋊D61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61#4111yescharacteristic
86D244—21no—
87D244C4⋊C411yescharacteristic
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—41no—
92C4×D61—41no—
93C4×D61C2×D411yescharacteristic
94C4×D61C2×D411yescharacteristic
95C4×D61C2×Q811yescharacteristic
96C4×D61#4111yescharacteristic
97Dic122—21no—
98Dic122C4⋊C411yescharacteristic
99#92420—41no—
100C8×C61—21no—
101#92418—21no—
102C22×C61—21no—
103C22×C61C4×D411yescharacteristic
104C2×D61—21no—
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—41no—
108C2×D61—41no—
109C2×D61#12011yescharacteristic
110C2×D61C22⋊Q811yescharacteristic
111#6923—41no—
112#6923—42no—
113#6923—41no—
114#6923—81no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61C2×C4⋊C411yescharacteristic
118C4×C61C4×D411yescharacteristic
119Dic61—21no—
120Dic61—41no—
121Dic61C22⋊Q811yescharacteristic
122Dic61#12311yescharacteristic
123#1860—611nomaximal, Sylow
124C2×C61—21no—
125C2×C61—41no—
126C2×C61#38511yescharacteristic
127D61—21no—
128D61—41no—
129D61#45411yescharacteristic
130D61#45511yescharacteristic
131#520—611no—
132#428—611no—
133C2×#104—611no—
134#417—611no—
135#382—611no—
136#343—611no—
137#339—611no—
138C61#186011yescharacteristic, complemented, Sylow
139C2×#41—611no—
140C2×M16—611no—
141C2×M16—611no—
142C4×Q8—1221no—
143C4×D4—1222no—
144C4×D4—1221no—
145#117—611no—
146#117—1221no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—1221no—
150C2×C42—611no—
151#107—1221no—
152#106—1221no—
153#104—611no—
154#104—611no—
155#104—611no—
156#104#692311yescharacteristic, complemented
157#103—1221no—
158#102—1221no—
159#95—1222no—
160#41—611no—
161#41—611no—
162#41—611no—
163#41—1221no—
164#41—1221no—
165#41C2×#692311yescharacteristic
166C2×Q8—611no—
167C2×D4—611no—
168C2×D4—1221no—
169C22×C4—611no—
170C22×C4—612no—
171C22×C4—1221no—
172C22×C4—1221no—
173C22×C4—1222no—
174C22×C4—1221no—
175M16—611no—
176M16—1221no—
177M16—1221no—
178M16—1221no—
179M16C2×#692311yescharacteristic, complemented
180C2×C8—1221no—
181C2×C8—1221no—
182C4⋊C4—611no—
183C4⋊C4—611no—
184C4⋊C4—1221no—
185C4⋊C4—1221no—
186C4⋊C4—1221no—
187C4⋊C4—1221no—
188C4⋊C4—1222no—
189C22⋊C4—1221no—
190C22⋊C4—1222no—
191C42—611no—
192C42—1221no—
193C42—1221no—
194C42—1222no—
195C42C2×#692311yescharacteristic, complemented
196C23—611no—
197C23—1221no—
198Q8—611no—
199Q8—1221no—
200Q8C4⋊#692311yescharacteristic
201D4—21no—
202D4—611no—
203D4—1221no—
204D4—1221no—
205D4—1221no—
206D4—1221no—
207D4C4⋊#692311yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—611no—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—611no—
214C2×C4—611no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—4882no—
224C2×C4—2441no—
225C2×C4—2441no—
226C2×C4—2441no—
227C2×C4—2442no—
228C2×C4—2442no—
229C2×C4C22×#692311yescharacteristic
230C8—21no—
231C8—1221no—
232C8—2441no—
233C22—21no—
234C22—611no—
235C22—611no—
236C22—1221no—
237C22—1221no—
238C22—1221no—
239C22—2441no—
240C22—2441no—
241C22D4×#692311yescharacteristic
242C4—21no—
243C4—41no—
244C4—611no—
245C4—611no—
246C4—1221no—
247C4—4881no—
248C4—2441no—
249C4—2441no—
250C4—2442no—
251C4—2441no—
252C4C2×C4⋊#692311yescharacteristic
253C4D4×#692311yescharacteristic
254C2—21no—
255C2—41no—
256C2—611no—
257C2—611no—
258C2—1221no—
259C2—2441no—
260C2#1684070911yescharacteristic
subgroupG/H
centerC2#16840709
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#104×C61C4
socleC2×C61#385
hypercenter#104#6923
hypocenterC61#1860
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. #16840706C2semidirect
5. #16840641C2semidirect
6. #16840633C2semidirect
25. #14519705C4semidirect
26. #14519704C4semidirect
27. #14519703C4semidirect
28. #104×C61C4semidirect
58. M16×C61C2×C4semidirect
59. C42×C61C2×C4semidirect
61. C4×Dic61C2×C4semidirect
62. #11758194C2×C4semidirect
138. C61#1860semidirect
156. #104#6923semidirect
179. M16C2×#6923semidirect
195. C42C2×#6923semidirect