Finite Group Databasebeta

← #21461706

Subgroups — #21461706

Order 7808.

256 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C2×#14519848C211yesmaximal, characteristic, complemented
2#16840772C211yesmaximal, characteristic, complemented
3#16840759C212yesmaximal
4#16840645C212yesmaximal, complemented
5#131×D61C211yesmaximal, characteristic
6C2×#11758213C2212yes—
7#14519856C2212yes—
8#14519848—21no—
9#14519848—21no—
10#14519846—21no—
11#14519845—21no—
12#14519842—22no—
13#14519841—22no—
14#41×D61C2211yescharacteristic
15#14519785—21no—
16#14519785C411yescharacteristic, complemented
17#14519784C411yescharacteristic, complemented
18#14519783—21no—
19#14519783C411yescharacteristic, complemented
20M16×D61—21no—
21M16×D61C2211yescharacteristic
22C2×C8×D61—21no—
23C2×C8×D61C2211yescharacteristic
24#131×C61C411yescharacteristic, complemented
25#41×C61C2×C411yescharacteristic
26#11758226D411yescharacteristic
27Q8×D61Q811yescharacteristic
28#11758224—21no—
29#11758224D411yescharacteristic
30D4×D61—21no—
31D4×D61Q811yescharacteristic
32#11758222—21no—
33#11758222C2×C411yescharacteristic
34C2×C4×D61—21no—
35C2×C4×D61C2311yescharacteristic
36C22⋊#6923—22no—
37C2×#92420—22no—
38C4⋊#6923—22no—
39C4×#6923—22no—
40#11758213—22no—
41#11758213—22no—
42M16×C61—21no—
43M16×C61C2×C411yescharacteristic
44C2×C8×C61—21no—
45C2×C8×C61C2×C411yescharacteristic
46#11758194—21no—
47#11758194C2×C411yescharacteristic
48C2×#92418—21no—
49C2×#92418C2×C411yescharacteristic
50#11758189—21no—
51#11758189—21no—
52#11758189—21no—
53C8×D61—21no—
54C8×D61—21no—
55C8×D61—21no—
56C8×D61D411yescharacteristic
57C8×D61D411yescharacteristic
58C8×D61D411yescharacteristic
59C8×D61D411yescharacteristic
60C22×D61—21no—
61C22×D61#4111yescharacteristic
62C2×#6923—42no—
63Q8×C61C4⋊C411yescharacteristic
64D4×C61—21no—
65D4×C61C4⋊C411yescharacteristic
66C2×C4×C61—21no—
67C2×C4×C61C22×C411yescharacteristic
68C22⋊D61—21no—
69C22⋊D61—21no—
70C22⋊D61—21no—
71C2×Dic61—21no—
72C2×Dic61#4111yescharacteristic
73D244—21no—
74D244C4⋊C411yescharacteristic
75C4×D61—21no—
76C4×D61—21no—
77C4×D61—21no—
78C4×D61C2×D411yescharacteristic
79C4×D61C2×D411yescharacteristic
80C4×D61C2×D411yescharacteristic
81C4×D61C2×Q811yescharacteristic
82Dic122—21no—
83Dic122C4⋊C411yescharacteristic
84#92420—42no—
85C8×C61—21no—
86C8×C61C22⋊C411yescharacteristic
87C8×C61C22⋊C411yescharacteristic
88#92418—21no—
89#92418C22⋊C411yescharacteristic
90#92418C22⋊C411yescharacteristic
91C22×C61—21no—
92C22×C61#11711yescharacteristic
93C2×D61—21no—
94C2×D61—41no—
95C2×D61—42no—
96C2×D61#12111yescharacteristic
97C2×D61C22⋊Q811yescharacteristic
98#6923—82no—
99C4×C61—21no—
100C4×C61C2×C22⋊C411yescharacteristic
101C4×C61C2×C4⋊C411yescharacteristic
102Dic61—21no—
103Dic61#12111yescharacteristic
104Dic61C22⋊Q811yescharacteristic
105#1814—611nomaximal, Sylow
106C2×C61—21no—
107C2×C61—41no—
108C2×C61#38011yescharacteristic
109D61—21no—
110D61—21no—
111D61—41no—
112C2×#131—611no—
113C2×#108—611no—
114#427—611no—
115#421—612no—
116#344—612no—
117C61#181411yescharacteristic, complemented, Sylow
118C2×#41—611no—
119#131—611no—
120#131—611no—
121#131—611no—
122#131—1221no—
123#131—1221no—
124#131#692311yescharacteristic, complemented
125C2×M16—611no—
126C2×M16—612no—
127C2×M16—1221no—
128C22×C8—611no—
129C22×C8—1221no—
130#117—612no—
131#108—1221no—
132#108—1221no—
133#107—1221no—
134#106—1221no—
135#104—1222no—
136#104—1222no—
137#41—611no—
138#41—611no—
139#41—611no—
140#41—1221no—
141#41—1221no—
142#41C2×#692311yescharacteristic
143C2×Q8—611no—
144C2×D4—611no—
145C2×D4—1221no—
146C22×C4—611no—
147C22×C4—1221no—
148M16—21no—
149M16—611no—
150M16—1221no—
151M16—1221no—
152M16—1221no—
153M16—1221no—
154M16—1222no—
155M16—1222no—
156M16C2×#692311yescharacteristic
157C2×C8—21no—
158C2×C8—611no—
159C2×C8—611no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8—611no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—1221no—
166C2×C8—1221no—
167C2×C8—1222no—
168C2×C8C2×#692311yescharacteristic
169C4⋊C4—1222no—
170C22⋊C4—1222no—
171C42—1222no—
172C23—611no—
173C23—1221no—
174Q8—611no—
175Q8—1221no—
176Q8C4⋊#692311yescharacteristic
177D4—21no—
178D4—611no—
179D4—1221no—
180D4—1221no—
181D4—1221no—
182D4—1221no—
183D4C4⋊#692311yescharacteristic
184C2×C4—21no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—1221no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—2442no—
195C2×C4C22×#692311yescharacteristic
196C8—21no—
197C8—611no—
198C8—611no—
199C8—1221no—
200C8—2442no—
201C8C22⋊#692311yescharacteristic
202C8C22⋊#692311yescharacteristic
203C22—21no—
204C22—611no—
205C22—611no—
206C22—1221no—
207C22—2441no—
208C22—2442no—
209C22#1451985611yescharacteristic
210C4—21no—
211C4—611no—
212C4—611no—
213C4—1221no—
214C4—4882no—
215C4C2×C22⋊#692311yescharacteristic
216C4C2×C4⋊#692311yescharacteristic
217C2—21no—
218C2—41no—
219C2—1221no—
220C2—1221no—
221C2—2441no—
222C2#1684070411yescharacteristic
subgroupG/H
centerC2#16840704
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#131×C61C4
socleC2×C61#380
hypercenter#131#6923
hypocenterC61#1814
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131

Complements

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

NH ≅ G/Ntype
1. C2×#14519848C2semidirect
2. #16840772C2semidirect
4. #16840645C2semidirect
16. #14519785C4semidirect
17. #14519784C4semidirect
19. #14519783C4semidirect
24. #131×C61C4semidirect
117. C61#1814semidirect
124. #131#6923semidirect