Finite Group Databasebeta

← #21456444

Subgroups — #21456444

Order 7808.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840373C211yesmaximal, characteristic, complemented
2#16840366C211yesmaximal, characteristic
3#16840164C211yesmaximal, characteristic, complemented
4#16840130C211yesmaximal, characteristic, complemented
5#16840126C211yesmaximal, characteristic, complemented
6#16840005C212yesmaximal, complemented
7#16839988C212yesmaximal, complemented
8#16839863C212yesmaximal, complemented
9SD16×Dic61C212yesmaximal, complemented
10#16839716C211yesmaximal, characteristic, complemented
11C61×#492C211yesmaximal, characteristic, complemented
12C2×#11758189C2211yescharacteristic
13C2×C8×D61C2211yescharacteristic
14#14519772—22no—
15#14519769C2211yescharacteristic
16#14519769C2211yescharacteristic
17#14519767—22no—
18#14519758—22no—
19#14519753C2212yes—
20#14519749—22no—
21#14519748C2212yes—
22Q8×Dic61C2212yes—
23D4×Dic61C2212yes—
24#14519734C2211yescharacteristic
25#14519711C2212yes—
26#14519709C2212yes—
27#14519701C2212yes—
28#14519701C2212yes—
29#14519698C2212yes—
30#14519698C2212yes—
31#14519688C2211yescharacteristic
32#14519687C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×SD16×C61C2212yes—
35C2×SD16×C61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#127×C61C2211yescharacteristic
38C4×C8×C61C2211yescharacteristic
39C2×Q8×C61C2312yes—
40C2×D4×C61—22no—
41C2×D4×C61C2312yes—
42C2×C22⋊D61—22no—
43C22×Dic61—22no—
44C2×C4×D61C2311yescharacteristic
45SD16×C61—24no—
46SD16×C61—24no—
47C2×C8×C61C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C4⋊C4×C61—22no—
50C42×C61C2311yescharacteristic
51C22⋊Dic61—22no—
52C22⋊Dic61—22no—
53#11758198—22no—
54#11758198D412yes—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57C4⋊Dic61C2312yes—
58#11758196—22no—
59#11758196—22no—
60#11758196—22no—
61#11758196D412yes—
62C4×Dic61—22no—
63C4×Dic61C2311yescharacteristic
64C2×#92418C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66#11758189—22no—
67C8×D61—22no—
68C23×C61—22no—
69C22×D61C2×D411yescharacteristic
70Q8×C61—22no—
71Q8×C61—22no—
72D4×C61—22no—
73D4×C61—22no—
74D4×C61—82no—
75C2×C4×C61—22no—
76C2×C4×C61C2×D412yes—
77C2×C4×C61C2411yescharacteristic
78C22⋊D61—82no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—82no—
82C2×Dic61C2×D412yes—
83C2×Dic61C2×D411yescharacteristic
84C4×D61—21no—
85C4×D61—21no—
86C8×C61#4112yes—
87C8×C61#4112yes—
88#92418—21no—
89#92418—21no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61C22×D411yescharacteristic
94C2×D61—21no—
95C2×D61—22no—
96C4×C61—22no—
97C4×C61—42no—
98C4×C61C2×#4111yescharacteristic
99C4×C61C2×#4111yescharacteristic
100Dic61—21no—
101Dic61—22no—
102Dic61—42no—
103Dic61—42no—
104#3174—611nomaximal, Sylow
105C2×C61—82no—
106C2×C61#53211yescharacteristic
107C2×C61#57712yes—
108D61—41no—
109#541—611no—
110#540—611no—
111#499—611no—
112#492D6111yescharacteristic, complemented
113#491—611no—
114#490—611no—
115#468—612no—
116#465—612no—
117#440—612no—
118C4×SD16—612no—
119#405—611no—
120C61#317411yescharacteristic, complemented, Sylow
121C2×SD16C2×D6112yes—
122C2×SD16C2×D6112yes—
123C2×M16—611no—
124C22×C8—611no—
125C4⋊Q8C2×D6111yescharacteristic
126#127C2×D6111yescharacteristic
127#126—1222no—
128#125—611no—
129#125—611no—
130#125—1222no—
131#123—1222no—
132C22⋊Q8—612no—
133#121—612no—
134#121—1222no—
135C4×Q8—612no—
136C4×D4—612no—
137#117—611no—
138#107—612no—
139#106—612no—
140#103—612no—
141#103—612no—
142#102—612no—
143#102—612no—
144#97—611no—
145#97—611no—
146C4×C8—611no—
147C4×C8C2×D6111yescharacteristic
148C2×Q8C22×D6112yes—
149C2×D4—22no—
150C2×D4—1222no—
151C2×D4C22×D6112yes—
152C22×C4—611no—
153C22×C4—1222no—
154SD16—24no—
155SD16—24no—
156M16—1222no—
157C2×C8—611no—
158C2×C8—611no—
159C2×C8—1222no—
160C2×C8C22×D6111yescharacteristic
161C2×C8C22×D6111yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—612no—
164C4⋊C4—612no—
165C4⋊C4—612no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4—1222no—
170C22⋊C4—612no—
171C22⋊C4—1222no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C42—611no—
175C42—1222no—
176C42C22×D6111yescharacteristic
177C23—22no—
178C23—611no—
179Q8—22no—
180Q8—22no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—4882no—
185C2×C4—22no—
186C2×C4—612no—
187C2×C4—611no—
188C2×C4—1221no—
189C2×C4—1221no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—4882no—
193C2×C4D4×D6112yes—
194C2×C4C23×D6111yescharacteristic
195C8—1221no—
196C8—1221no—
197C8#1175822412yes—
198C8#1175822412yes—
199C22—42no—
200C22—42no—
201C22—42no—
202C22—1221no—
203C22—1222no—
204C22C2×D4×D6111yescharacteristic
205C4—22no—
206C4—42no—
207C4—1221no—
208C4—1222no—
209C4—2442no—
210C4—2442no—
211C4C2×#1175822411yescharacteristic
212C4C2×#1175822411yescharacteristic
213C2—82no—
214C2—2441no—
215C2#1684031011yescharacteristic
216C2#1684056812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#492C2
socleC22×C61C22×D4
hypercenter#492D61
hypocenterC61#3174
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #16840373C2semidirect
3. #16840164C2semidirect
4. #16840130C2semidirect
5. #16840126C2semidirect
6. #16840005C2semidirect
7. #16839988C2semidirect
8. #16839863C2semidirect
9. SD16×Dic61C2semidirect
10. #16839716C2semidirect
11. C61×#492C2semidirect
112. #492D61semidirect
120. C61#3174semidirect