Finite Group Databasebeta

← #21461708

Subgroups — #21461708

Order 7808.

264 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 74 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
1D61⋊#108C211yesmaximal, characteristic, complemented
2C2×#14519846C211yesmaximal, characteristic, complemented
3#16840753C212yesmaximal
4#16840641C212yesmaximal, complemented
5#131×D61C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7C2×C4⋊#6923C2212yes—
8#14519848—21no—
9#14519847—21no—
10#14519846—21no—
11#14519846—21no—
12#14519840—22no—
13#14519839—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
25C22×#6923—22no—
26#41×C61C2×C411yescharacteristic
27#11758226Q811yescharacteristic
28Q8×D61D411yescharacteristic
29#11758224—21no—
30#11758224Q811yescharacteristic
31D4×D61—21no—
32D4×D61D411yescharacteristic
33#11758222—21no—
34#11758222C2×C411yescharacteristic
35C2×C4×D61—21no—
36C2×C4×D61C2311yescharacteristic
37#11758217—22no—
38C4⋊#6923—22no—
39C4⋊#6923—22no—
40#11758213—22no—
41D61⋊C8—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—
63C2×#6923—82no—
64Q8×C61C4⋊C411yescharacteristic
65D4×C61—21no—
66D4×C61C4⋊C411yescharacteristic
67C2×C4×C61—21no—
68C2×C4×C61C22×C411yescharacteristic
69C22⋊D61—21no—
70C22⋊D61—21no—
71C22⋊D61—21no—
72C2×Dic61—21no—
73C2×Dic61#4111yescharacteristic
74D244—21no—
75D244C4⋊C411yescharacteristic
76C4×D61—21no—
77C4×D61—21no—
78C4×D61—21no—
79C4×D61C2×D411yescharacteristic
80C4×D61C2×D411yescharacteristic
81C4×D61C2×D411yescharacteristic
82C4×D61C2×Q811yescharacteristic
83Dic122—21no—
84Dic122C4⋊C411yescharacteristic
85#92420—42no—
86C8×C61—21no—
87C8×C61C22⋊C411yescharacteristic
88C8×C61C22⋊C411yescharacteristic
89#92418—21no—
90#92418C22⋊C411yescharacteristic
91#92418C22⋊C411yescharacteristic
92C22×C61—21no—
93C22×C61#11711yescharacteristic
94C2×D61—21no—
95C2×D61—21no—
96C2×D61—21no—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61#12111yescharacteristic
100C2×D61C22⋊Q811yescharacteristic
101#6923—82no—
102C4×C61—21no—
103C4×C61C2×C22⋊C411yescharacteristic
104C4×C61C2×C4⋊C411yescharacteristic
105Dic61—21no—
106Dic61#12111yescharacteristic
107Dic61C22⋊Q811yescharacteristic
108#1816—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—41no—
111C2×C61#38011yescharacteristic
112D61—21no—
113D61—41no—
114D61#47211yescharacteristic
115D61#47311yescharacteristic
116C2×#131—611no—
117C2×#108—611no—
118C2×#107—611no—
119#417—612no—
120#343—612no—
121C61#181611yescharacteristic, complemented, Sylow
122C2×#41—611no—
123#131—611no—
124#131—611no—
125#131—611no—
126#131—1221no—
127#131—1221no—
128#131#692311yescharacteristic, complemented
129C2×M16—611no—
130C2×M16—612no—
131C2×M16—1221no—
132C22×C8—611no—
133C22×C8—1221no—
134C2×C4⋊C4—612no—
135#108—1221no—
136#108—1221no—
137#107—1221no—
138#107—1221no—
139#103—1222no—
140#102—1222no—
141#41—611no—
142#41—611no—
143#41—611no—
144#41—1221no—
145#41—1221no—
146#41C2×#692311yescharacteristic
147C2×Q8—611no—
148C2×D4—611no—
149C2×D4—1221no—
150C22×C4—611no—
151C22×C4—1221no—
152C22×C4—1222no—
153M16—21no—
154M16—611no—
155M16—1221no—
156M16—1221no—
157M16—1221no—
158M16—1221no—
159M16—1222no—
160M16—1222no—
161M16C2×#692311yescharacteristic
162C2×C8—21no—
163C2×C8—611no—
164C2×C8—611no—
165C2×C8—611no—
166C2×C8—611no—
167C2×C8—611no—
168C2×C8—1221no—
169C2×C8—1221no—
170C2×C8—1221no—
171C2×C8—1221no—
172C2×C8—1222no—
173C2×C8C2×#692311yescharacteristic
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C23—611no—
177C23—1221no—
178Q8—611no—
179Q8—1221no—
180Q8C4⋊#692311yescharacteristic
181D4—21no—
182D4—611no—
183D4—1221no—
184D4—1221no—
185D4—1221no—
186D4—1221no—
187D4C4⋊#692311yescharacteristic
188C2×C4—21no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—611no—
192C2×C4—611no—
193C2×C4—611no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—4882no—
199C2×C4—2442no—
200C2×C4C22×#692311yescharacteristic
201C8—21no—
202C8—611no—
203C8—611no—
204C8—1221no—
205C8—2442no—
206C8C22⋊#692311yescharacteristic
207C8C22⋊#692311yescharacteristic
208C22—21no—
209C22—611no—
210C22—611no—
211C22—1221no—
212C22—1221no—
213C22—1221no—
214C22—2441no—
215C22—2441no—
216C22#1451985611yescharacteristic
217C4—21no—
218C4—611no—
219C4—611no—
220C4—1221no—
221C4—4882no—
222C4C2×C22⋊#692311yescharacteristic
223C4C2×C4⋊#692311yescharacteristic
224C2—21no—
225C2—41no—
226C2—611no—
227C2—611no—
228C2—1221no—
229C2—2441no—
230C2#1684070411yescharacteristic
subgroupG/H
centerC2#16840704
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#131×C61C4
socleC2×C61#380
hypercenter#131#6923
hypocenterC61#1816
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. D61⋊#108C2semidirect
2. C2×#14519846C2semidirect
4. #16840641C2semidirect
16. #14519785C4semidirect
17. #14519784C4semidirect
19. #14519783C4semidirect
24. #131×C61C4semidirect
121. C61#1816semidirect
128. #131#6923semidirect