Finite Group Databasebeta

← #21461707

Subgroups — #21461707

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×#14519845C211yesmaximal, characteristic, complemented
3#16840753C212yesmaximal
4#16840641C212yesmaximal, complemented
5#131×D61C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7C2×C4⋊#6923C2212yes—
8#14519848—21no—
9#14519847—21no—
10#14519845—21no—
11#14519845—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—22no—
95C2×D61—21no—
96C2×D61—42no—
97C2×D61#12111yescharacteristic
98C2×D61C22⋊Q811yescharacteristic
99#6923—82no—
100C4×C61—21no—
101C4×C61C2×C22⋊C411yescharacteristic
102C4×C61C2×C4⋊C411yescharacteristic
103Dic61—21no—
104Dic61#12111yescharacteristic
105Dic61C22⋊Q811yescharacteristic
106#1815—611nomaximal, Sylow
107C2×C61—21no—
108C2×C61—41no—
109C2×C61#38011yescharacteristic
110D61—21no—
111D61—41no—
112D61#47112yes—
113C2×#131—611no—
114C2×#108—611no—
115C2×#106—611no—
116#417—612no—
117#343—612no—
118C61#181511yescharacteristic, complemented, Sylow
119C2×#41—611no—
120#131—611no—
121#131—611no—
122#131—611no—
123#131—1221no—
124#131—1221no—
125#131#692311yescharacteristic, complemented
126C2×M16—611no—
127C2×M16—612no—
128C2×M16—1221no—
129C22×C8—611no—
130C22×C8—1221no—
131C2×C4⋊C4—612no—
132#108—1221no—
133#108—1221no—
134#106—1221no—
135#106—1221no—
136#103—1222no—
137#102—1222no—
138#41—611no—
139#41—611no—
140#41—611no—
141#41—1221no—
142#41—1221no—
143#41C2×#692311yescharacteristic
144C2×Q8—611no—
145C2×D4—611no—
146C2×D4—1221no—
147C22×C4—611no—
148C22×C4—1221no—
149C22×C4—1222no—
150M16—21no—
151M16—611no—
152M16—1221no—
153M16—1221no—
154M16—1221no—
155M16—1221no—
156M16—1222no—
157M16—1222no—
158M16C2×#692311yescharacteristic
159C2×C8—21no—
160C2×C8—611no—
161C2×C8—611no—
162C2×C8—611no—
163C2×C8—611no—
164C2×C8—611no—
165C2×C8—1221no—
166C2×C8—1221no—
167C2×C8—1221no—
168C2×C8—1221no—
169C2×C8—1222no—
170C2×C8C2×#692311yescharacteristic
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C23—611no—
174C23—1221no—
175Q8—611no—
176Q8—1221no—
177Q8C4⋊#692311yescharacteristic
178D4—21no—
179D4—611no—
180D4—1221no—
181D4—1221no—
182D4—1221no—
183D4—1221no—
184D4C4⋊#692311yescharacteristic
185C2×C4—21no—
186C2×C4—611no—
187C2×C4—611no—
188C2×C4—611no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—4882no—
196C2×C4—2442no—
197C2×C4C22×#692311yescharacteristic
198C8—21no—
199C8—611no—
200C8—611no—
201C8—1221no—
202C8—2442no—
203C8C22⋊#692311yescharacteristic
204C8C22⋊#692311yescharacteristic
205C22—21no—
206C22—611no—
207C22—611no—
208C22—1222no—
209C22—1221no—
210C22—2442no—
211C22#1451985611yescharacteristic
212C4—21no—
213C4—611no—
214C4—611no—
215C4—1221no—
216C4—4882no—
217C4C2×C22⋊#692311yescharacteristic
218C4C2×C4⋊#692311yescharacteristic
219C2—21no—
220C2—41no—
221C2—612no—
222C2—1221no—
223C2—2441no—
224C2#1684070411yescharacteristic
subgroupG/H
centerC2#16840704
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#131×C61C4
socleC2×C61#380
hypercenter#131#6923
hypocenterC61#1815
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×#14519845C2semidirect
4. #16840641C2semidirect
16. #14519785C4semidirect
17. #14519784C4semidirect
19. #14519783C4semidirect
24. #131×C61C4semidirect
118. C61#1815semidirect
125. #131#6923semidirect