Finite Group Databasebeta

← #21461904

Subgroups — #21461904

Order 7808.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840773C211yesmaximal, characteristic
2#16840755C211yesmaximal, characteristic
3C2×#14519840C211yesmaximal, characteristic
4#16840728C211yesmaximal, characteristic
5#16840641C211yesmaximal, characteristic
6#16840637C211yesmaximal, characteristic
7#101×D61C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9C2×D61⋊C8C2211yescharacteristic
10#14519856C2211yescharacteristic
11C2×C4⋊#6923C2211yescharacteristic
12#14519846—21no—
13#14519845—21no—
14#14519840—21no—
15#14519840—21no—
16#14519840—21no—
17#14519840—21no—
18#14519831—21no—
19C8×#6923—21no—
20C2×Q8×D61C2211yescharacteristic
21M16×D61C2211yescharacteristic
22M16×D61C2211yescharacteristic
23#14519696C411yescharacteristic, complemented
24#14519695C411yescharacteristic, complemented
25#14519695C411yescharacteristic, complemented
26#101×C61C411yescharacteristic, complemented
27C22×#6923—21no—
28C2×Q8×C61C2×C411yescharacteristic
29Q8×D61—21no—
30Q8×D61—21no—
31Q8×D61—21no—
32Q8×D61—21no—
33C2×C4×D61—21no—
34C2×C4×D61C2311yescharacteristic
35C2×Dic122—21no—
36C2×Dic122C2×C411yescharacteristic
37C22⋊#6923—21no—
38#11758217—21no—
39C2×#92420—21no—
40C4⋊#6923—21no—
41C4⋊#6923—21no—
42C4⋊#6923D411yescharacteristic
43C4⋊#6923D411yescharacteristic
44C4×#6923—21no—
45#11758213—21no—
46D61⋊C8—21no—
47D61⋊C8—21no—
48D61⋊C8D411yescharacteristic
49D61⋊C8D411yescharacteristic
50M16×C61C2×C411yescharacteristic
51M16×C61C2×C411yescharacteristic
52#11758194C2×C411yescharacteristic
53#11758194C2×C411yescharacteristic
54#11758189—21no—
55#11758189—21no—
56C8×D61—21no—
57C8×D61—21no—
58C22×D61#4111yescharacteristic
59C2×#6923—21no—
60C2×#6923—21no—
61C2×#6923—41no—
62C2×#6923—81no—
63Q8×C61—21no—
64Q8×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61C22×C411yescharacteristic
67C2×Dic61—21no—
68C2×Dic61#4111yescharacteristic
69C4×D61—41no—
70C4×D61—41no—
71C4×D61C2×D411yescharacteristic
72C4×D61C2×D411yescharacteristic
73C4×D61#4111yescharacteristic
74C4×D61#4111yescharacteristic
75Dic122—21no—
76Dic122—21no—
77Dic122—41no—
78Dic122—41no—
79#92420—21no—
80#92420—21no—
81#92420—41no—
82C8×C61—21no—
83C8×C61—21no—
84#92418—21no—
85#92418—21no—
86C22×C61#11711yescharacteristic
87C2×D61—21no—
88C2×D61—21no—
89C2×D61#12111yescharacteristic
90C2×D61#12611yescharacteristic
91#6923—41no—
92#6923—41no—
93#6923—81no—
94C4×C61—41no—
95C4×C61C4×D411yescharacteristic
96C4×C61C4×D411yescharacteristic
97Dic61—41no—
98Dic61#12311yescharacteristic
99Dic61#12411yescharacteristic
100#1930—611nomaximal, Sylow
101C2×C61—21no—
102C2×C61#38811yescharacteristic
103D61—21no—
104D61#47111yescharacteristic
105D61#47311yescharacteristic
106#428—611no—
107#419—611no—
108C2×#103—611no—
109C2×#101—611no—
110#405—611no—
111#343—611no—
112#341—611no—
113C61#193011yescharacteristic, complemented, Sylow
114C22×Q8—611no—
115C2×M16—611no—
116C2×M16—611no—
117C2×M16—611no—
118C22×C8—611no—
119#117—611no—
120C2×C4⋊C4—611no—
121#107—1221no—
122#106—1221no—
123#103—1221no—
124#103—1221no—
125#103—1221no—
126#103—1221no—
127#101—611no—
128#101—611no—
129#101—611no—
130#101#692311yescharacteristic, complemented
131#97—1221no—
132C4×C8—1221no—
133C2×Q8—611no—
134C2×Q8—1221no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8C2×#692311yescharacteristic
140C22×C4—611no—
141C22×C4—1221no—
142C22×C4—1221no—
143M16—611no—
144M16—611no—
145M16—1221no—
146M16—1221no—
147M16—1221no—
148M16—1221no—
149M16C2×#692311yescharacteristic
150M16C2×#692311yescharacteristic
151C2×C8—611no—
152C2×C8—611no—
153C2×C8—1221no—
154C2×C8—1221no—
155C2×C8—1221no—
156C2×C8—1221no—
157C2×C8—1221no—
158C4⋊C4—611no—
159C4⋊C4—611no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C22⋊C4—1221no—
163C42—1221no—
164C23—611no—
165Q8—21no—
166Q8—21no—
167Q8—1221no—
168Q8—1221no—
169Q8—2441no—
170Q8—2441no—
171C2×C4—21no—
172C2×C4—611no—
173C2×C4—611no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—1221no—
178C2×C4—1221no—
179C2×C4—1221no—
180C2×C4—4881no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4C22×#692311yescharacteristic
185C8—21no—
186C8—21no—
187C8—1221no—
188C8—1221no—
189C8—1221no—
190C8—1221no—
191C8—2441no—
192C22—611no—
193C22—611no—
194C22—1221no—
195C22—1221no—
196C22#1451985611yescharacteristic
197C4—41no—
198C4—611no—
199C4—611no—
200C4—4881no—
201C4—2441no—
202C4—2441no—
203C4—2441no—
204C4D4×#692311yescharacteristic
205C4D4×#692311yescharacteristic
206C2—21no—
207C2—611no—
208C2—611no—
209C2—1221no—
210C2#1684071211yescharacteristic
subgroupG/H
centerC2#16840712
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#101×C61C4
socleC2×C61#388
hypercenter#101#6923
hypocenterC61#1930
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
23. #14519696C4semidirect
24. #14519695C4semidirect
25. #14519695C4semidirect
26. #101×C61C4semidirect
113. C61#1930semidirect
130. #101#6923semidirect