Finite Group Databasebeta

← #21461905

Subgroups — #21461905

Order 7808.

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

normal subgroups only

This group has 232 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, complemented
2#16840754C211yesmaximal, characteristic
3C2×#14519839C211yesmaximal, characteristic
4#16840728C211yesmaximal, characteristic, complemented
5#16840641C211yesmaximal, characteristic, complemented
6#16840637C211yesmaximal, characteristic, complemented
7#100×D61C211yesmaximal, characteristic
8D61⋊M16C2211yescharacteristic
9C2×D61⋊C8C2211yescharacteristic
10#14519856C2211yescharacteristic
11C2×C4⋊#6923C2211yescharacteristic
12#14519846—21no—
13#14519845—21no—
14#14519839—21no—
15#14519839—21no—
16#14519839—21no—
17#14519839—21no—
18#14519831—21no—
19C8×#6923—21no—
20C2×D4×D61C2211yescharacteristic
21M16×D61C2211yescharacteristic
22M16×D61C2211yescharacteristic
23#14519694C411yescharacteristic, complemented
24#14519693C411yescharacteristic, complemented
25#14519693C411yescharacteristic, complemented
26#100×C61C411yescharacteristic, complemented
27C23×D61—21no—
28C22×#6923—21no—
29C2×D4×C61C2×C411yescharacteristic
30C2×C22⋊D61—21no—
31D4×D61—21no—
32D4×D61—21no—
33D4×D61—21no—
34D4×D61—21no—
35C2×D244C2×C411yescharacteristic
36C2×C4×D61C2311yescharacteristic
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—
58C23×C61—21no—
59C22×D61—21no—
60C22×D61—41no—
61C22×D61—41no—
62C22×D61—81no—
63C22×D61—81no—
64C22×D61#4111yescharacteristic
65C2×#6923—21no—
66C2×#6923—21no—
67C2×#6923—41no—
68C2×#6923—81no—
69D4×C61—21no—
70D4×C61—21no—
71C2×C4×C61C22×C411yescharacteristic
72C22⋊D61—41no—
73C22⋊D61—41no—
74C2×Dic61#4111yescharacteristic
75D244—21no—
76D244—21no—
77C4×D61C2×D411yescharacteristic
78C4×D61C2×D411yescharacteristic
79C4×D61#4111yescharacteristic
80C4×D61#4111yescharacteristic
81#92420—21no—
82#92420—21no—
83#92420—41no—
84C8×C61—21no—
85C8×C61—21no—
86#92418—21no—
87#92418—21no—
88C22×C61—41no—
89C22×C61—81no—
90C22×C61#11711yescharacteristic
91C2×D61—21no—
92C2×D61—21no—
93C2×D61—41no—
94C2×D61—82no—
95C2×D61—81no—
96C2×D61—81no—
97C2×D61—81no—
98C2×D61#12111yescharacteristic
99C2×D61#12611yescharacteristic
100#6923—41no—
101#6923—41no—
102#6923—81no—
103C4×C61C4×D411yescharacteristic
104C4×C61C4×D411yescharacteristic
105Dic61#12311yescharacteristic
106Dic61#12411yescharacteristic
107#1931—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—81no—
110C2×C61#38811yescharacteristic
111D61—21no—
112D61—81no—
113D61#47111yescharacteristic
114D61#47211yescharacteristic
115#428—611no—
116#418—611no—
117C2×#102—611no—
118C2×#100—611no—
119#405—611no—
120#343—611no—
121#341—611no—
122C61#193111yescharacteristic, complemented, Sylow
123C22×D4—611no—
124C2×M16—611no—
125C2×M16—611no—
126C2×M16—611no—
127C22×C8—611no—
128#117—611no—
129C2×C4⋊C4—611no—
130#107—1221no—
131#106—1221no—
132#102—1221no—
133#102—1221no—
134#102—1221no—
135#102—1221no—
136#100—611no—
137#100—611no—
138#100—611no—
139#100#692311yescharacteristic, complemented
140#97—1221no—
141C4×C8—1221no—
142C24—1221no—
143C2×D4—611no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C2×D4—1221no—
149C2×D4C2×#692311yescharacteristic
150C22×C4—611no—
151C22×C4—1221no—
152M16—611no—
153M16—611no—
154M16—1221no—
155M16—1221no—
156M16—1221no—
157M16—1221no—
158M16C2×#692311yescharacteristic
159M16C2×#692311yescharacteristic
160C2×C8—611no—
161C2×C8—611no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—1221no—
166C2×C8—1221no—
167C4⋊C4—611no—
168C4⋊C4—611no—
169C4⋊C4—1221no—
170C4⋊C4—1221no—
171C22⋊C4—1221no—
172C42—1221no—
173C23—21no—
174C23—611no—
175C23—1221no—
176C23—4881no—
177C23—4881no—
178C23—2441no—
179C23—2441no—
180D4—21no—
181D4—21no—
182D4—1221no—
183D4—1221no—
184D4—2441no—
185D4—2441no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—4881no—
194C2×C4—2441no—
195C2×C4C22×#692311yescharacteristic
196C8—21no—
197C8—21no—
198C8—1221no—
199C8—1221no—
200C8—1221no—
201C8—1221no—
202C8—2441no—
203C22—41no—
204C22—81no—
205C22—611no—
206C22—611no—
207C22—1221no—
208C22—1221no—
209C22—4881no—
210C22—4881no—
211C22—4881no—
212C22—4882no—
213C22—2441no—
214C22#1451985611yescharacteristic
215C4—611no—
216C4—611no—
217C4—4881no—
218C4—2441no—
219C4—2441no—
220C4D4×#692311yescharacteristic
221C4D4×#692311yescharacteristic
222C2—21no—
223C2—81no—
224C2—611no—
225C2—611no—
226C2—1221no—
227C2—4881no—
228C2#1684071211yescharacteristic
subgroupG/H
centerC2#16840712
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#100×C61C4
socleC2×C61#388
hypercenter#100#6923
hypocenterC61#1931
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #16840773C2semidirect
4. #16840728C2semidirect
5. #16840641C2semidirect
6. #16840637C2semidirect
23. #14519694C4semidirect
24. #14519693C4semidirect
25. #14519693C4semidirect
26. #100×C61C4semidirect
122. C61#1931semidirect
139. #100#6923semidirect