Finite Group Databasebeta

← #21461854

Subgroups — #21461854

Order 7808.

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

normal subgroups only

This group has 310 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#16840830C211yesmaximal, characteristic, complemented
2#16840761C211yesmaximal, characteristic
3#16840755C211yesmaximal, characteristic, complemented
4#16840743C211yesmaximal, characteristic
5#16840644C211yesmaximal, characteristic, complemented
6#16840630C211yesmaximal, characteristic, complemented
7C2×#14519809C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9Q8×#6923—22no—
10Q8×#6923—22no—
11#14519856—22no—
12#14519856C2211yescharacteristic
13#14519856C2211yescharacteristic
14#14519856C2211yescharacteristic
15#14519842—22no—
16#14519840—22no—
17#14519836—22no—
18C2×#11758226C2211yescharacteristic
19C2×Q8×D61C2211yescharacteristic
20#14519809—22no—
21#14519809—22no—
22C2×#11758202C411yescharacteristic, complemented
23C2×#11758190C411yescharacteristic, complemented
24C2×#11758201C411yescharacteristic, complemented
25C2×#11758189C2211yescharacteristic
26C2×Q16×C61C411yescharacteristic, complemented
27C2×Q8×C61C2×C411yescharacteristic
28C2×Q8×C61C2×C411yescharacteristic
29#11758226—21no—
30#11758226—21no—
31#11758226—21no—
32#11758226—21no—
33Q8×D61—21no—
34Q8×D61—21no—
35Q8×D61D412yes—
36Q8×D61D412yes—
37C2×D244—21no—
38C2×D244C2×C411yescharacteristic
39C2×C4×D61—21no—
40C2×C4×D61—21no—
41C2×C4×D61C2311yescharacteristic
42C2×Dic122—21no—
43C2×Dic122C2×C411yescharacteristic
44C22⋊#6923—21no—
45C22⋊#6923—21no—
46C22⋊#6923D412yes—
47#11758217—21no—
48C4⋊#6923—24no—
49C4⋊#6923—21no—
50C4⋊#6923—21no—
51C4⋊#6923—21no—
52C4×#6923—24no—
53C4×#6923—21no—
54C4×#6923—21no—
55C4×#6923D412yes—
56#11758213—21no—
57D61⋊C8—21no—
58Q16×C61—22no—
59C2×C8×C61C2×C411yescharacteristic
60#11758202—22no—
61#11758201—22no—
62C2×#92418C2×C411yescharacteristic
63#11758190—22no—
64#11758189—21no—
65#11758189—21no—
66C22×D61—21no—
67C22×D61C2×D411yescharacteristic
68C2×#6923—22no—
69C2×#6923—22no—
70C2×#6923—41no—
71Q8×C61—21no—
72Q8×C61—21no—
73Q8×C61—21no—
74Q8×C61C22⋊C412yes—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61C22×C411yescharacteristic
78C2×Dic61—21no—
79C2×Dic61#4111yescharacteristic
80D244—21no—
81D244—21no—
82D244—41no—
83D244—41no—
84C4×D61—22no—
85C4×D61—22no—
86C4×D61—41no—
87C4×D61—41no—
88C4×D61C2×D411yescharacteristic
89C4×D61C2×D411yescharacteristic
90C4×D61C2×D411yescharacteristic
91C4×D61#4111yescharacteristic
92Dic122—21no—
93Dic122—22no—
94Dic122—22no—
95Dic122C22⋊C412yes—
96#92420—41no—
97C8×C61—21no—
98#92418—21no—
99C22×C61C4×D411yescharacteristic
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—81no—
103C2×D61#12011yescharacteristic
104C2×D61#12111yescharacteristic
105#6923—42no—
106#6923—42no—
107#6923—81no—
108C4×C61—22no—
109C4×C61—41no—
110C4×C61C2×C22⋊C411yescharacteristic
111C4×C61C4×D411yescharacteristic
112Dic61—22no—
113Dic61#12111yescharacteristic
114Dic61#12311yescharacteristic
115#1905—611nomaximal, Sylow
116C2×C61—21no—
117C2×C61#38611yescharacteristic
118D61—21no—
119D61—21no—
120D61—81no—
121C2×#137—611no—
122#519—611no—
123#421—611no—
124#419—611no—
125#410—611no—
126#344—611no—
127H(3,ℤ/4)—611no—
128C61#190511yescharacteristic, complemented, Sylow
129C2×#41—611no—
130C22×Q8—611no—
131#137—1222no—
132#137—1222no—
133C2×Q16—611no—
134C2×Q16#692311yescharacteristic, complemented
135C2×SD16—611no—
136C2×SD16—611no—
137C2×M16—611no—
138C2×M16—611no—
139C4×Q8—1222no—
140C4×Q8—1222no—
141#117—611no—
142#117—611no—
143#117—611no—
144#117—1222no—
145#104—1222no—
146#103—1222no—
147#99—1222no—
148#41—1221no—
149#41—1221no—
150#41—1221no—
151#41—1221no—
152C2×Q8—612no—
153C2×Q8—612no—
154C2×Q8—611no—
155C2×Q8—1221no—
156C2×Q8—1221no—
157C2×Q8—1221no—
158C2×Q8C2×#692311yescharacteristic
159C2×Q8C2×#692311yescharacteristic
160C2×D4—611no—
161C2×D4—1221no—
162C22×C4—611no—
163C22×C4—1221no—
164C22×C4—1221no—
165Q16—22no—
166Q16—1222no—
167SD16—1222no—
168SD16—1222no—
169M16—1221no—
170M16—1221no—
171M16—1221no—
172M16—1221no—
173C2×C8—611no—
174C2×C8—1221no—
175C2×C8C2×#692311yescharacteristic
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C4⋊C4—1221no—
179C4⋊C4—1224no—
180C22⋊C4—612no—
181C22⋊C4—1221no—
182C22⋊C4—1221no—
183C42—612no—
184C42—1221no—
185C42—1221no—
186C42—1224no—
187C23—611no—
188C23—1221no—
189Q8—21no—
190Q8—21no—
191Q8—21no—
192Q8—612no—
193Q8—1222no—
194Q8—1222no—
195Q8—1221no—
196Q8C22⋊#692312yes—
197D4—1221no—
198D4—1221no—
199D4—2441no—
200D4—2441no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—611no—
204C2×C4—611no—
205C2×C4—611no—
206C2×C4—611no—
207C2×C4—611no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1221no—
211C2×C4—1222no—
212C2×C4—1222no—
213C2×C4—2441no—
214C2×C4—2441no—
215C2×C4—2441no—
216C2×C4C22×#692311yescharacteristic
217C8—21no—
218C8—1221no—
219C8—2441no—
220C22—611no—
221C22—611no—
222C22—4881no—
223C22—2441no—
224C22—2441no—
225C22D4×#692311yescharacteristic
226C4—22no—
227C4—41no—
228C4—611no—
229C4—611no—
230C4—1222no—
231C4—4881no—
232C4—2442no—
233C4—2442no—
234C4C2×C22⋊#692311yescharacteristic
235C4D4×#692311yescharacteristic
236C2—21no—
237C2—1221no—
238C2—1221no—
239C2—4881no—
240C2#1684071011yescharacteristic
subgroupG/H
centerC2#16840710
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×Q16×C61C4
socleC2×C61#386
hypercenterC2×Q16#6923
hypocenterC61#1905
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. #16840830C2semidirect
3. #16840755C2semidirect
5. #16840644C2semidirect
6. #16840630C2semidirect
22. C2×#11758202C4semidirect
23. C2×#11758190C4semidirect
24. C2×#11758201C4semidirect
26. C2×Q16×C61C4semidirect
128. C61#1905semidirect
134. C2×Q16#6923semidirect