Finite Group Databasebeta

← #21461850

Subgroups — #21461850

Order 7808.

324 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 66 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#16840840C211yesmaximal, characteristic, complemented
2#16840760C211yesmaximal, characteristic, complemented
3#16840754C211yesmaximal, characteristic, complemented
4D61⋊#100C211yesmaximal, characteristic, complemented
5#16840644C211yesmaximal, characteristic, complemented
6#16840631C211yesmaximal, characteristic, complemented
7C2×#14519801C211yesmaximal, characteristic
8#14519864—22no—
9#14519864—22no—
10D61⋊M16C2211yescharacteristic
11D61⋊M16C2211yescharacteristic
12D61⋊M16C2211yescharacteristic
13C2×#11758217—22no—
14#14519856C2211yescharacteristic
15#14519841—22no—
16#14519839—22no—
17#14519837—22no—
18C2×#11758224C2211yescharacteristic
19C2×D4×D61C2211yescharacteristic
20#14519801—22no—
21#14519801—22no—
22C2×#11758190C411yescharacteristic, complemented
23C2×#11758200C411yescharacteristic, complemented
24C2×#11758199C411yescharacteristic, complemented
25C2×#11758189C2211yescharacteristic
26C2×D8×C61C411yescharacteristic, complemented
27C23×D61—21no—
28C2×D4×C61C2×C411yescharacteristic
29C2×D4×C61C2×C411yescharacteristic
30C2×C22⋊D61—21no—
31C2×C22⋊D61—21no—
32C22×Dic61—21no—
33#11758224—21no—
34#11758224—21no—
35#11758224D412yes—
36#11758224D412yes—
37D4×D61—21no—
38D4×D61—21no—
39D4×D61—21no—
40D4×D61—21no—
41C2×D244C2×C411yescharacteristic
42C2×C4×D61C2311yescharacteristic
43C2×Dic122C2×C411yescharacteristic
44C22⋊#6923—21no—
45#11758217—24no—
46#11758217—21no—
47#11758217—21no—
48#11758217D412yes—
49C2×#92420—24no—
50C4⋊#6923—21no—
51C4×#6923—21no—
52#11758213—21no—
53#11758213—21no—
54#11758213—21no—
55D61⋊C8—21no—
56D61⋊C8—21no—
57D61⋊C8D412yes—
58D8×C61—22no—
59C2×C8×C61C2×C411yescharacteristic
60#11758200—22no—
61#11758199—22no—
62C2×#92418C2×C411yescharacteristic
63#11758190—22no—
64#11758189—21no—
65#11758189—21no—
66C23×C61—21no—
67C23×C61—21no—
68C22×D61—21no—
69C22×D61—41no—
70C22×D61—41no—
71C22×D61—82no—
72C22×D61#4111yescharacteristic
73C2×#6923—41no—
74D4×C61—21no—
75D4×C61—21no—
76D4×C61—21no—
77D4×C61C22⋊C412yes—
78C2×C4×C61C22×C411yescharacteristic
79C22⋊D61—22no—
80C22⋊D61—22no—
81C22⋊D61—41no—
82C22⋊D61—41no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—22no—
86C2×Dic61C2×D411yescharacteristic
87D244—21no—
88D244—21no—
89C4×D61C2×D411yescharacteristic
90C4×D61C2×D411yescharacteristic
91C4×D61C2×D411yescharacteristic
92C4×D61#4111yescharacteristic
93Dic122—21no—
94Dic122C22⋊C412yes—
95#92420—22no—
96#92420—22no—
97#92420—41no—
98C8×C61—21no—
99#92418—21no—
100C22×C61—22no—
101C22×C61—41no—
102C22×C61—81no—
103C22×C61—81no—
104C22×C61C4×D411yescharacteristic
105C2×D61—41no—
106C2×D61—41no—
107C2×D61—82no—
108C2×D61—82no—
109C2×D61—81no—
110C2×D61#12111yescharacteristic
111C2×D61#12311yescharacteristic
112#6923—81no—
113C4×C61C2×C22⋊C411yescharacteristic
114C4×C61C4×D411yescharacteristic
115Dic61—22no—
116Dic61#12011yescharacteristic
117Dic61#12111yescharacteristic
118#1903—611nomaximal, Sylow
119C2×C61—21no—
120C2×C61—42no—
121C2×C61—81no—
122C2×C61#38611yescharacteristic
123D61—21no—
124D61—21no—
125D61—81no—
126C2×AGL(1,ℤ/8)—611no—
127#568—611no—
128#421—611no—
129#418—611no—
130C2×#100—611no—
131#344—611no—
132#338—611no—
133C61#190311yescharacteristic, complemented, Sylow
134C2×#41—611no—
135C22×D4—611no—
136AGL(1,ℤ/8)—1222no—
137AGL(1,ℤ/8)—1222no—
138C2×SD16—611no—
139C2×SD16—611no—
140C2×D8—611no—
141C2×D8#692311yescharacteristic, complemented
142#131—1222no—
143#131—1222no—
144C2×M16—611no—
145C2×M16—611no—
146C2×M16—611no—
147C2×M16—611no—
148C2×M16—1222no—
149#117—611no—
150#104—1222no—
151#102—1222no—
152#100—1222no—
153C24—1221no—
154#41—612no—
155#41—612no—
156#41—1221no—
157#41—1221no—
158C2×Q8—611no—
159C2×D4—611no—
160C2×D4—1221no—
161C2×D4—1221no—
162C2×D4—1221no—
163C2×D4—1221no—
164C2×D4—1221no—
165C2×D4—1221no—
166C2×D4C2×#692311yescharacteristic
167C2×D4C2×#692311yescharacteristic
168C22×C4—611no—
169C22×C4—1221no—
170SD16—1222no—
171SD16—1222no—
172D8—22no—
173D8—1222no—
174M16—612no—
175M16—1221no—
176M16—1221no—
177M16—1221no—
178M16—1221no—
179M16—1221no—
180M16—1224no—
181M16—1221no—
182M16—1221no—
183C2×C8—612no—
184C2×C8—611no—
185C2×C8—1221no—
186C2×C8—1224no—
187C2×C8—1221no—
188C2×C8C2×#692311yescharacteristic
189C4⋊C4—1221no—
190C22⋊C4—1221no—
191C42—1221no—
192C23—21no—
193C23—21no—
194C23—611no—
195C23—1221no—
196C23—4882no—
197C23—2441no—
198C23—2441no—
199Q8—612no—
200Q8—1221no—
201D4—21no—
202D4—21no—
203D4—21no—
204D4—1222no—
205D4—1222no—
206D4—1221no—
207D4—1221no—
208D4—2441no—
209D4—2441no—
210D4C22⋊#692312yes—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—611no—
214C2×C4—611no—
215C2×C4—611no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1221no—
219C2×C4—2441no—
220C2×C4C22×#692311yescharacteristic
221C8—21no—
222C8—1222no—
223C8—1222no—
224C8—1221no—
225C8—2441no—
226C22—22no—
227C22—41no—
228C22—81no—
229C22—81no—
230C22—611no—
231C22—611no—
232C22—4881no—
233C22—4882no—
234C22—4882no—
235C22—2441no—
236C22—2441no—
237C22D4×#692311yescharacteristic
238C4—611no—
239C4—611no—
240C4—1222no—
241C4—4881no—
242C4C2×C22⋊#692311yescharacteristic
243C4D4×#692311yescharacteristic
244C2—21no—
245C2—42no—
246C2—81no—
247C2—1221no—
248C2—1221no—
249C2—4881no—
250C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×D8×C61C4
socleC2×C61#386
hypercenterC2×D8#6923
hypocenterC61#1903
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #16840840C2semidirect
2. #16840760C2semidirect
3. #16840754C2semidirect
4. D61⋊#100C2semidirect
5. #16840644C2semidirect
6. #16840631C2semidirect
22. C2×#11758190C4semidirect
23. C2×#11758200C4semidirect
24. C2×#11758199C4semidirect
26. C2×D8×C61C4semidirect
133. C61#1903semidirect
141. C2×D8#6923semidirect