Finite Group Databasebeta

← #21461249

Subgroups — #21461249

Order 7808.

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

normal subgroups only

This group has 264 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#16840781C211yesmaximal, characteristic, complemented
2#16840706C211yesmaximal, characteristic, complemented
3#16840614C212yesmaximal, complemented
4#16840613C212yesmaximal, complemented
5#16840309C211yesmaximal, characteristic
6C2×C4⋊#6923—21no—
7C4⋊#92420—21no—
8#14519834C2212yes—
9C4×#92420—21no—
10(C2×#6923)⋊C4—21no—
11(C2×#6923)⋊C4C2212yes—
12C2×#11758222—21no—
13#14519776C411yescharacteristic, complemented
14#14519773C411yescharacteristic, complemented
15#14519763—21no—
16#14519752C2211yescharacteristic
17#14519750—21no—
18#14519748C2211yescharacteristic
19C4×D244C411yescharacteristic, complemented
20C4×C22⋊D61—21no—
21C42×D61C2211yescharacteristic
22C4×D4×C61C411yescharacteristic, complemented
23C22×#6923—22no—
24C2×D4×C61C2×C411yescharacteristic
25C22×C4×C61—21no—
26C2×C22⋊D61—21no—
27C2×C22⋊D61—21no—
28C2×C22⋊D61—21no—
29#11758222—42no—
30#11758222—42no—
31C2×D244—21no—
32C2×D244C2×C411yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61D411yescharacteristic
35C2×C4×D61D411yescharacteristic
36C2×C4×D61C2311yescharacteristic
37C2×Dic122—21no—
38C2×#92420—22no—
39C4⋊#6923—42no—
40C4⋊C4×C61C2×C411yescharacteristic
41C22⋊C4×C61—21no—
42C42×C61C2×C411yescharacteristic
43C22⋊Dic61—21no—
44#11758198—21no—
45#11758198—21no—
46C4⋊Dic61C2×C411yescharacteristic
47#11758196—21no—
48C4×Dic61C2×C411yescharacteristic
49C4×Dic61D411yescharacteristic
50C4×Dic61D411yescharacteristic
51C23×C61—21no—
52C22×D61—21no—
53C22×D61C2×D411yescharacteristic
54C2×#6923—42no—
55C2×#6923—42no—
56C2×#6923—42no—
57D4×C61—41no—
58C2×C4×C61—21no—
59C2×C4×C61—42no—
60C2×C4×C61C22⋊C411yescharacteristic
61C2×C4×C61C22⋊C411yescharacteristic
62C2×C4×C61C22×C411yescharacteristic
63C22⋊D61—42no—
64C22⋊D61—41no—
65C22⋊D61—41no—
66C22⋊D61—42no—
67C2×Dic61—21no—
68C2×Dic61C22⋊C411yescharacteristic
69C2×Dic61C22⋊C411yescharacteristic
70C2×Dic61C2×D411yescharacteristic
71D244—41no—
72D244—41no—
73D244—41no—
74C4×D61—41no—
75C4×D61—41no—
76C4×D61—42no—
77C4×D61D812yes—
78C4×D61SD1612yes—
79Dic122—42no—
80#92420—42no—
81C22×C61—41no—
82C22×C61—41no—
83C22×C61—41no—
84C22×C61C2×C22⋊C411yescharacteristic
85C2×D61—21no—
86C2×D61—21no—
87C2×D61—41no—
88C2×D61—41no—
89C2×D61—41no—
90C2×D61C2×D811yescharacteristic
91C2×D61C2×SD1611yescharacteristic
92#6923—82no—
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—41no—
96C4×C61#10212yes—
97Dic61—21no—
98Dic61—21no—
99Dic61—41no—
100Dic61#10212yes—
101#1517—611nomaximal, Sylow
102C2×C61—81no—
103C2×C61#41011yescharacteristic
104C2×C61C2×#10211yescharacteristic
105C2×C61#42111yescharacteristic
106D61—21no—
107D61—21no—
108D61—81no—
109#532—611no—
110#431—611no—
111#382—611no—
112#327—612no—
113#327—612no—
114C61#151711yescharacteristic, complemented, Sylow
115C2×#41—1221no—
116C4⋊Q8—611no—
117#127—611no—
118#124—1221no—
119#121—611no—
120#121—611no—
121#121—1221no—
122C4×D4—611no—
123C4×D4—1221no—
124C4×D4#692311yescharacteristic, complemented
125C2×C4⋊C4—1221no—
126C2×C42—611no—
127C4⋊C8—1221no—
128C22⋊C8—612no—
129C4×C8—1221no—
130#95—612no—
131#95—1221no—
132#41—2442no—
133#41—2442no—
134C2×Q8—1221no—
135C2×D4—611no—
136C2×D4—1221no—
137C2×D4—1221no—
138C2×D4—1221no—
139C2×D4—1221no—
140C2×D4C2×#692311yescharacteristic
141C22×C4—21no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4—1221no—
146C22×C4—1222no—
147C2×C8—1222no—
148C4⋊C4—611no—
149C4⋊C4—1221no—
150C4⋊C4—2442no—
151C4⋊C4C2×#692311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—1221no—
154C22⋊C4—1221no—
155C22⋊C4—1221no—
156C42—611no—
157C42—611no—
158C42—611no—
159C42C2×#692311yescharacteristic
160C23—21no—
161C23—611no—
162C23—1221no—
163Q8—2442no—
164D4—41no—
165D4—2441no—
166D4—2441no—
167D4—2441no—
168D4—2442no—
169D4—2442no—
170D4—2441no—
171D4—2441no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—611no—
175C2×C4—612no—
176C2×C4—612no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—1221no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4—2442no—
183C2×C4—2442no—
184C2×C4—2442no—
185C2×C4—2442no—
186C2×C4C22⋊#692311yescharacteristic
187C2×C4C22⋊#692311yescharacteristic
188C2×C4C22×#692311yescharacteristic
189C8—2442no—
190C22—41no—
191C22—41no—
192C22—41no—
193C22—611no—
194C22—611no—
195C22—1221no—
196C22—1221no—
197C22—2441no—
198C22—2441no—
199C22—2441no—
200C22C2×C22⋊#692311yescharacteristic
201C4—21no—
202C4—21no—
203C4—41no—
204C4—612no—
205C4—1221no—
206C4—1221no—
207C4—4882no—
208C4—2441no—
209C4#1451983912yes—
210C2—81no—
211C2—1221no—
212C2—1221no—
213C2—4881no—
214C2#1684074111yescharacteristic
215C2C2×#1451983911yescharacteristic
216C2#1684075911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4×D4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC4×D4#6923
hypocenterC61#1517
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #16840781C2semidirect
2. #16840706C2semidirect
3. #16840614C2semidirect
4. #16840613C2semidirect
13. #14519776C4semidirect
14. #14519773C4semidirect
19. C4×D244C4semidirect
22. C4×D4×C61C4semidirect
114. C61#1517semidirect
124. C4×D4#6923semidirect