Finite Group Databasebeta

← #21461883

Subgroups — #21461883

Order 7808.

230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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#16840713C211yesmaximal, characteristic
2C4⋊C4×#6923C211yesmaximal, characteristic
3#16840636C211yesmaximal, characteristic
4#16840635C211yesmaximal, characteristic
5#16840635C211yesmaximal, characteristic
6(C2×#6923)⋊C8C211yesmaximal, characteristic
7#107×D61C211yesmaximal, characteristic
8C2×D61⋊C8C2211yescharacteristic
9C2×C4⋊#6923—21no—
10C2×C4⋊#6923C2211yescharacteristic
11C2×C4⋊#6923C2211yescharacteristic
12C2×C4×#6923—21no—
13C2×C4×#6923C2211yescharacteristic
14(C2×#6923)⋊C4—21no—
15(C2×#6923)⋊C4—21no—
16C2×C8×D61C2211yescharacteristic
17C4⋊C4×D61C2211yescharacteristic
18C4⋊C4×D61C2211yescharacteristic
19#14519711C411yescharacteristic, complemented
20#14519710C411yescharacteristic, complemented
21#14519710C411yescharacteristic, complemented
22#107×C61C411yescharacteristic, complemented
23C22×#6923—21no—
24C22×#6923—21no—
25C22×#6923D411yescharacteristic
26C22×#6923D411yescharacteristic
27C2×C4×D61—21no—
28C2×C4×D61—21no—
29C2×C4×D61C2311yescharacteristic
30C2×#92420—21no—
31C4⋊#6923—21no—
32C4⋊#6923—21no—
33C4⋊#6923—21no—
34C4⋊#6923—42no—
35C4⋊#6923Q812yes—
36C4×#6923—21no—
37C4×#6923—21no—
38C4×#6923—42no—
39D61⋊C8—21no—
40D61⋊C8—21no—
41C2×C8×C61C2×C411yescharacteristic
42C4⋊C4×C61C2×C411yescharacteristic
43C4⋊C4×C61C2×C411yescharacteristic
44C4⋊Dic61C2×C411yescharacteristic
45C4⋊Dic61C2×C411yescharacteristic
46#11758196—21no—
47#11758196—21no—
48C2×#92418C2×C411yescharacteristic
49C8×D61—21no—
50C8×D61—21no—
51C22×D61C2×D411yescharacteristic
52C2×#6923—21no—
53C2×#6923—21no—
54C2×#6923—22no—
55C2×#6923—21no—
56C2×#6923—21no—
57C2×#6923—21no—
58C2×#6923—41no—
59C2×#6923—41no—
60C2×#6923—41no—
61C2×#6923—41no—
62C2×#6923—41no—
63C2×#6923Q1612yes—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61C22×C411yescharacteristic
67C2×Dic61—21no—
68C2×Dic61—21no—
69C2×Dic61#4111yescharacteristic
70C4×D61—41no—
71C4×D61—41no—
72C4×D61—41no—
73C4×D61—41no—
74C4×D61C2×Q811yescharacteristic
75C4×D61#4111yescharacteristic
76C4×D61#4111yescharacteristic
77C4×D61#4111yescharacteristic
78#92420—41no—
79C8×C61—21no—
80#92418—21no—
81C22×C61C4×D411yescharacteristic
82C2×D61C22⋊Q811yescharacteristic
83C2×D61#12311yescharacteristic
84C2×D61C2×Q1611yescharacteristic
85C2×D61#13511yescharacteristic
86C2×D61AGL(1,ℤ/8)11yescharacteristic
87C2×D61AGL(1,ℤ/8)11yescharacteristic
88#6923—22no—
89#6923—42no—
90#6923—41no—
91#6923—81no—
92C4×C61—41no—
93C4×C61—41no—
94C4×C61#11711yescharacteristic
95C4×C61C4×Q811yescharacteristic
96Dic61—41no—
97Dic61—41no—
98Dic61#12511yescharacteristic
99Dic61#12611yescharacteristic
100#1921—611nomaximal, Sylow
101C2×C61#38711yescharacteristic
102C2×C61C4×Q1611yescharacteristic
103C2×C61#44211yescharacteristic
104D61#47711yescharacteristic
105D61#47811yescharacteristic
106D61#48211yescharacteristic
107D61#48411yescharacteristic
108C2×#107—611no—
109#389—611no—
110C4×C4⋊C4—611no—
111#340—611no—
112#340—611no—
113#340—611no—
114#336—611no—
115C61#192111yescharacteristic, complemented, Sylow
116C22×C8—611no—
117C22×C8—611no—
118C2×C4⋊C4—611no—
119C2×C4⋊C4—611no—
120C2×C4⋊C4—611no—
121C2×C4⋊C4—611no—
122C2×C4⋊C4—1221no—
123C2×C42—611no—
124C2×C42—1221no—
125#107—611no—
126#107—611no—
127#107—611no—
128#107#692311yescharacteristic, complemented
129#95—1221no—
130#95—1221no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—611no—
134C22×C4—1221no—
135C22×C4—1221no—
136C22×C4—1221no—
137C22×C4—1221no—
138C2×C8—611no—
139C2×C8—1221no—
140C2×C8—1221no—
141C2×C8—1221no—
142C2×C8—1221no—
143C2×C8—1221no—
144C2×C8C2×#692311yescharacteristic
145C4⋊C4—612no—
146C4⋊C4—611no—
147C4⋊C4—611no—
148C4⋊C4—1221no—
149C4⋊C4—1221no—
150C4⋊C4—1221no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—2442no—
154C4⋊C4C2×#692311yescharacteristic
155C4⋊C4C2×#692311yescharacteristic
156C42—1221no—
157C42—1221no—
158C42—2442no—
159C23—611no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—611no—
163C2×C4—611no—
164C2×C4—611no—
165C2×C4—611no—
166C2×C4—611no—
167C2×C4—612no—
168C2×C4—1221no—
169C2×C4—1221no—
170C2×C4—1221no—
171C2×C4—1222no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—1221no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4C22×#692311yescharacteristic
186C8—21no—
187C8—1221no—
188C8—2441no—
189C22—611no—
190C22—611no—
191C22—611no—
192C22—611no—
193C22—611no—
194C22—611no—
195C22D4×#692311yescharacteristic
196C4—41no—
197C4—41no—
198C4—611no—
199C4—611no—
200C4—1222no—
201C4—4881no—
202C4—2441no—
203C4—2442no—
204C4—2441no—
205C4—2441no—
206C4#1451985611yescharacteristic
207C4Q8×#692311yescharacteristic
208C2—611no—
209C2—611no—
210C2—611no—
211C2—611no—
212C2#1684071111yescharacteristic
213C2Q16×#692311yescharacteristic
214C2#1684080311yescharacteristic
subgroupG/H
centerC22D4×#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#107×C61C4
socleC22×C61C4×D4
hypercenter#107#6923
hypocenterC61#1921
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
19. #14519711C4semidirect
20. #14519710C4semidirect
21. #14519710C4semidirect
22. #107×C61C4semidirect
115. C61#1921semidirect
128. #107#6923semidirect