Finite Group Databasebeta

← #21457266

Subgroups — #21457266

Order 7808.

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

normal subgroups only

This group has 346 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#16840374C211yesmaximal, characteristic, complemented
2#16840367C211yesmaximal, characteristic
3#16840070C212yesmaximal, complemented
4#16840063C212yesmaximal, complemented
5#16840008C212yesmaximal, complemented
6#16839991C212yesmaximal, complemented
7#16839968C212yesmaximal, complemented
8#16839963C212yesmaximal, complemented
9C61×#424C211yesmaximal, characteristic, complemented
10C2×#11758190C2212yes—
11C2×#11758190C2212yes—
12#14519777C2211yescharacteristic
13#14519774C2211yescharacteristic
14#14519770—22no—
15#14519769C2211yescharacteristic
16#14519769C2211yescharacteristic
17#14519767—22no—
18#14519762—22no—
19#14519756C2212yes—
20#14519751C2212yes—
21#14519750—22no—
22C4×Dic122C2212yes—
23C4×D244C2212yes—
24#14519711C2212yes—
25#14519709C2212yes—
26#14519702C2212yes—
27#14519702C2212yes—
28#14519699C2212yes—
29#14519699C2212yes—
30C2×M16×C61C2211yescharacteristic
31C22×C8×C61C2211yescharacteristic
32#117×C61C2211yescharacteristic
33C4⋊C8×C61C2212yes—
34C4⋊C8×C61C2212yes—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—22no—
37C2×D244—22no—
38C2×D244C2312yes—
39C2×C4×D61—22no—
40C2×Dic122C2312yes—
41M16×C61—41no—
42C2×C8×C61—41no—
43C2×C8×C61C2312yes—
44C2×C8×C61C2312yes—
45C4⋊C4×C61D412yes—
46C22⋊C4×C61D412yes—
47C42×C61C2311yescharacteristic
48C42×C61C2311yescharacteristic
49C22⋊Dic61—22no—
50#11758198—22no—
51#11758198—22no—
52C4⋊Dic61—22no—
53C4⋊Dic61C2312yes—
54C4⋊Dic61C2312yes—
55#11758196—22no—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59C4×Dic61—22no—
60#11758190—42no—
61#11758190—42no—
62C23×C61C2×D411yescharacteristic
63C22×D61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61C2×D412yes—
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D412yes—
69C2×C4×C61C2411yescharacteristic
70C22⋊D61—82no—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74D244—22no—
75D244—22no—
76D244—82no—
77C4×D61—82no—
78Dic122—22no—
79Dic122—22no—
80C8×C61—22no—
81C8×C61—22no—
82C22×C61—21no—
83C22×C61—22no—
84C22×C61C22×D411yescharacteristic
85C2×D61—42no—
86C2×D61—42no—
87C2×D61—42no—
88C4×C61—21no—
89C4×C61—22no—
90C4×C61—22no—
91C4×C61H(5,𝔽2)11yescharacteristic
92C4×C612−1+411yescharacteristic
93Dic61—42no—
94Dic61—42no—
95Dic61—42no—
96#3260—611nomaximal, Sylow
97C2×C61—41no—
98C2×C61#53711yescharacteristic
99C2×C61#57712yes—
100D61—82no—
101#541—611no—
102#540—611no—
103#479—612no—
104#478—612no—
105#468—612no—
106#465—612no—
107#461—612no—
108#460—612no—
109#424D6111yescharacteristic, complemented
110C61#326011yescharacteristic, complemented, Sylow
111C2×SD16—612no—
112C2×SD16—612no—
113C2×M16C2×D6111yescharacteristic
114C22×C8C2×D6111yescharacteristic
115C4⋊Q8—611no—
116#127—611no—
117#126—1222no—
118#125—611no—
119#125—611no—
120#125—1222no—
121#123—1222no—
122C22⋊Q8—612no—
123#121—612no—
124#121—1222no—
125C4×Q8—612no—
126C4×D4—612no—
127#117C2×D6111yescharacteristic
128#107—612no—
129#106—612no—
130C4⋊C8C2×D6112yes—
131C4⋊C8C2×D6112yes—
132#103—612no—
133#103—612no—
134#102—612no—
135#102—612no—
136C2×Q8—612no—
137C2×D4—612no—
138C2×D4—1222no—
139C2×D4—1222no—
140C22×C4—1222no—
141C22×C4C22×D6111yescharacteristic
142SD16—2442no—
143SD16—2442no—
144M16—41no—
145C2×C8—41no—
146C2×C8C22×D6112yes—
147C2×C8C22×D6112yes—
148C4⋊C4—612no—
149C4⋊C4—612no—
150C4⋊C4—1222no—
151C4⋊C4—1222no—
152C4⋊C4—1222no—
153C4⋊C4—1222no—
154C4⋊C4—1222no—
155C4⋊C4D24412yes—
156C22⋊C4—1222no—
157C22⋊C4—1222no—
158C22⋊C4—1222no—
159C22⋊C4D24412yes—
160C42—1222no—
161C42C22×D6111yescharacteristic
162C42C22×D6111yescharacteristic
163C23—1222no—
164C23C2×D24411yescharacteristic
165Q8—1222no—
166Q8—1222no—
167D4—1222no—
168D4—1222no—
169D4—4882no—
170D4—4882no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—1222no—
176C2×C4—4882no—
177C2×C4C2×D24412yes—
178C2×C4C2×D24412yes—
179C2×C4C2×D24411yescharacteristic
180C2×C4C23×D6111yescharacteristic
181C8—22no—
182C8—22no—
183C22—22no—
184C22—21no—
185C22—2442no—
186C22—2442no—
187C22—2442no—
188C22C22×D24411yescharacteristic
189C4—22no—
190C4—22no—
191C4—21no—
192C4—2442no—
193C4—2442no—
194C4—2442no—
195C4#1451982211yescharacteristic
196C4#1451982511yescharacteristic
197C2—41no—
198C2—4882no—
199C2#1684034311yescharacteristic
200C2#1684057412yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#424C2
socleC22×C61C22×D4
hypercenter#424D61
hypocenterC61#3260
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #16840374C2semidirect
3. #16840070C2semidirect
4. #16840063C2semidirect
5. #16840008C2semidirect
6. #16839991C2semidirect
7. #16839968C2semidirect
8. #16839963C2semidirect
9. C61×#424C2semidirect
109. #424D61semidirect
110. C61#3260semidirect