Finite Group Databasebeta

← #21457285

Subgroups — #21457285

Order 7808.

346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840385C212yesmaximal, complemented
2#16840051C212yesmaximal, complemented
3#16840045C212yesmaximal, complemented
4#16840015C211yesmaximal, characteristic
5#16839993C212yesmaximal, complemented
6#16839986C212yesmaximal, complemented
7#16839980C212yesmaximal, complemented
8#16839790C211yesmaximal, characteristic, complemented
9C61×#470C211yesmaximal, characteristic, complemented
10C2×#11758201C2212yes—
11C2×D488C2211yescharacteristic
12C22×#92418C2211yescharacteristic
13#14519776C2212yes—
14#14519772—22no—
15#14519766C2212yes—
16#14519763—22no—
17#14519759—22no—
18#14519757—22no—
19#14519751C2212yes—
20Q8×Dic61C2212yes—
21#14519739C2212yes—
22#14519736C2211yescharacteristic
23#14519709C2211yescharacteristic
24#14519708C2212yes—
25#14519706C2212yes—
26#14519706C2212yes—
27#14519701C2212yes—
28#14519699C2212yes—
29#14519697C2212yes—
30C2×Q16×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic
32C22⋊Q8×C61C2212yes—
33#106×C61C2211yescharacteristic
34#103×C61C2212yes—
35C2×Q8×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—22no—
38C2×D244C2312yes—
39C2×C4×D61—22no—
40C2×Dic122—22no—
41Q16×C61—41no—
42M16×C61—41no—
43C2×C8×C61C2311yescharacteristic
44C2×C8×C61C2311yescharacteristic
45C4⋊C4×C61—22no—
46C4⋊C4×C61C2312yes—
47C22⋊C4×C61—22no—
48C22⋊Dic61D411yescharacteristic
49C22⋊Dic61D411yescharacteristic
50#11758201—42no—
51#11758198—22no—
52#11758198—22no—
53#11758198—22no—
54#11758198—22no—
55C4⋊Dic61—22no—
56C4⋊Dic61D412yes—
57C4⋊Dic61C2312yes—
58#11758196—22no—
59C4×Dic61—22no—
60C4×Dic61C2312yes—
61C2×#92418—41no—
62C2×#92418C2312yes—
63D488—41no—
64C23×C61C2×D411yescharacteristic
65C22×D61—22no—
66Q8×C61—22no—
67Q8×C61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2411yescharacteristic
74C22⋊D61—82no—
75C2×Dic61—22no—
76C2×Dic61C2×D412yes—
77C2×Dic61C2×D412yes—
78D244—22no—
79D244—22no—
80C4×D61—82no—
81Dic122—82no—
82C8×C61—21no—
83C8×C61—21no—
84#92418—22no—
85C22×C61—21no—
86C22×C61—22no—
87C22×C61C22×D411yescharacteristic
88C2×D61—42no—
89C2×D61—42no—
90C2×D61—42no—
91C4×C61—21no—
92C4×C61—42no—
93C4×C61—42no—
94C4×C61H(5,𝔽2)11yescharacteristic
95C4×C612−1+411yescharacteristic
96Dic61—22no—
97Dic61—22no—
98Dic61—42no—
99#3263—611nomaximal, Sylow
100C2×C61—41no—
101C2×C61#53711yescharacteristic
102C2×C61#57712yes—
103D61—82no—
104#542—612no—
105#476—612no—
106#475—612no—
107#470D6111yescharacteristic, complemented
108#469—611no—
109#465—612no—
110#464—612no—
111#463—612no—
112#424—611no—
113C61#326311yescharacteristic, complemented, Sylow
114C2×Q16C2×D6111yescharacteristic
115C2×SD16—612no—
116C2×D8—611no—
117C2×M16C2×D6111yescharacteristic
118C22×C8—611no—
119C4⋊Q8—612no—
120#126—1222no—
121#124—612no—
122#124—1222no—
123#123—1222no—
124C22⋊Q8—1222no—
125C22⋊Q8C2×D6112yes—
126#121—612no—
127C4×Q8—612no—
128C4×D4—612no—
129#117—611no—
130#106—611no—
131#106—612no—
132#106C2×D6111yescharacteristic
133C4⋊C8—612no—
134C4⋊C8—612no—
135#103—612no—
136#103C2×D6112yes—
137#102—612no—
138#102—612no—
139C2×Q8—1222no—
140C2×Q8C22×D6112yes—
141C2×D4—612no—
142C2×D4—1222no—
143C22×C4—1222no—
144C22×C4C22×D6111yescharacteristic
145Q16—41no—
146SD16—2442no—
147D8—2441no—
148M16—41no—
149C2×C8—612no—
150C2×C8—2441no—
151C2×C8C22×D6111yescharacteristic
152C2×C8C22×D6111yescharacteristic
153C4⋊C4—22no—
154C4⋊C4—612no—
155C4⋊C4—612no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4C22×D6112yes—
159C22⋊C4—22no—
160C22⋊C4—611no—
161C22⋊C4—611no—
162C22⋊C4—1222no—
163C22⋊C4—1222no—
164C22⋊C4—1222no—
165C22⋊C4—1222no—
166C42—612no—
167C42—1222no—
168C23—1222no—
169C23D4×D6111yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—4882no—
173D4—1222no—
174D4—1222no—
175D4—4882no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—612no—
181C2×C4—612no—
182C2×C4—1222no—
183C2×C4—4882no—
184C2×C4D4×D6111yescharacteristic
185C2×C4C23×D6111yescharacteristic
186C8—21no—
187C8—21no—
188C8—1222no—
189C22—22no—
190C22—21no—
191C22—2442no—
192C22—2442no—
193C22—2442no—
194C22C2×D4×D6111yescharacteristic
195C4—21no—
196C4—42no—
197C4—42no—
198C4—1222no—
199C4—1222no—
200C4—2442no—
201C4#1451982211yescharacteristic
202C4#1451982411yescharacteristic
203C2—41no—
204C2—4882no—
205C2#1684033911yescharacteristic
206C2#1684057112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#470C2
socleC22×C61C22×D4
hypercenter#470D61
hypocenterC61#3263
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #16840385C2semidirect
2. #16840051C2semidirect
3. #16840045C2semidirect
5. #16839993C2semidirect
6. #16839986C2semidirect
7. #16839980C2semidirect
8. #16839790C2semidirect
9. C61×#470C2semidirect
107. #470D61semidirect
113. C61#3263semidirect