Finite Group Databasebeta

← #21456763

Subgroups — #21456763

Order 7808.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840317C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic
3#16840141C211yesmaximal, characteristic, complemented
4#16840113C211yesmaximal, characteristic, complemented
5#16840112C211yesmaximal, characteristic, complemented
6#16839970C214yesmaximal, complemented
7#16839916C214yesmaximal
8#16839813C211yesmaximal, characteristic
9C61×#494C211yesmaximal, characteristic, complemented
10C2×Q8×D61C2212yes—
11C2×#11758202C2214yes—
12#14519777C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519776—21no—
15#14519776—21no—
16#14519775C2212yes—
17#14519768—21no—
18#14519757—21no—
19#14519753C2212yes—
20Q8×Dic61C2212yes—
21#14519742—21no—
22#14519735—21no—
23C4⋊C4×D61—21no—
24C4⋊C4×D61—21no—
25C42×D61C2211yescharacteristic
26#14519706C2212yes—
27#14519702C2214yes—
28#14519701C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C2×Q16×C61C2214yes—
32C4⋊Q8×C61C2211yescharacteristic
33C4⋊Q8×C61C2211yescharacteristic
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61C2312yes—
36C2×Q8×C61C2312yes—
37Q8×D61—44no—
38C2×C4×D61—22no—
39C2×C4×D61D411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61C2311yescharacteristic
42C2×Dic122—21no—
43C2×Dic122—22no—
44C2×Dic122C2312yes—
45Q16×C61—44no—
46C2×C8×C61C2312yes—
47C4⋊C4×C61—21no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61—21no—
51C42×C61C2311yescharacteristic
52#11758202—44no—
53#11758198—22no—
54C4⋊Dic61—21no—
55C4⋊Dic61—21no—
56C4⋊Dic61—21no—
57C4⋊Dic61—22no—
58C4⋊Dic61C2312yes—
59#11758196—22no—
60#11758196—22no—
61#11758196—22no—
62C4×Dic61—22no—
63C4×Dic61D411yescharacteristic
64C4×Dic61D411yescharacteristic
65C4×Dic61C2311yescharacteristic
66C2×#92418C2312yes—
67C22×D61C2×D411yescharacteristic
68Q8×C61—24no—
69Q8×C61—24no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2411yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61C2×D411yescharacteristic
78C2×Dic61C2×D411yescharacteristic
79C2×Dic61C2×D411yescharacteristic
80C4×D61—22no—
81C4×D61—22no—
82C4×D61—44no—
83C4×D61Q1614yescomplemented
84Dic122—24no—
85Dic122—44no—
86Dic122—42no—
87C8×C61—22no—
88#92418—22no—
89C22×C61C22×D411yescharacteristic
90C2×D61—21no—
91C2×D61—21no—
92C2×D61C2×Q1612yes—
93C4×C61—42no—
94C4×C61—42no—
95C4×C61C2×Q1612yes—
96C4×C61#13712yes—
97C4×C61H(5,𝔽2)12yes—
98Dic61—21no—
99Dic61—21no—
100Dic61—42no—
101Dic61—42no—
102Dic61C2×Q1612yes—
103#3209—611nomaximal, Sylow
104C2×C61#53511yescharacteristic
105C2×C61C22×Q1611yescharacteristic
106C2×C61C2×#13711yescharacteristic
107D61—22no—
108#533—611no—
109C2×C4⋊Q8—611no—
110#494—611no—
111#494D6111yescharacteristic, complemented
112#487—611no—
113#487—611no—
114#462—614no—
115#451—614no—
116#431—611no—
117C61#320911yescharacteristic, complemented, Sylow
118C22×Q8—612no—
119C2×Q16—614no—
120C2×Q16C2×D6114yes—
121C4⋊Q8—612no—
122C4⋊Q8—611no—
123C4⋊Q8—611no—
124C4⋊Q8—1221no—
125C4⋊Q8—1221no—
126C4⋊Q8C2×D6111yescharacteristic
127C4⋊Q8C2×D6111yescharacteristic
128#125—1221no—
129C22⋊Q8—612no—
130C22⋊Q8—1221no—
131C4×Q8—612no—
132C4×Q8—1221no—
133#117—1221no—
134C2×C4⋊C4—1221no—
135C2×C4⋊C4—1221no—
136C2×C42—611no—
137C4⋊C8—612no—
138#103—614no—
139#103—614no—
140C22⋊C8—612no—
141C4×C8—611no—
142C4×C8C2×D6111yescharacteristic
143C2×Q8—612no—
144C2×Q8—1222no—
145C2×Q8—1221no—
146C2×Q8—2444no—
147C2×Q8C22×D6112yes—
148C2×Q8C22×D6112yes—
149C22×C4—611no—
150C22×C4—611no—
151C22×C4—611no—
152C22×C4—1222no—
153Q16—44no—
154Q16—2444no—
155C2×C8—612no—
156C2×C8C22×D6112yes—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—612no—
162C4⋊C4—1222no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C22⋊C4—1222no—
170C42—611no—
171C42—611no—
172C42—611no—
173C42—1222no—
174C42C22×D6111yescharacteristic
175C23—611no—
176Q8—24no—
177Q8—24no—
178Q8—1224no—
179Q8—2444no—
180Q8—2442no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—611no—
184C2×C4—614no—
185C2×C4—611no—
186C2×C4—611no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—2444no—
192C2×C4D4×D6111yescharacteristic
193C2×C4D4×D6111yescharacteristic
194C2×C4C23×D6111yescharacteristic
195C8—22no—
196C8—1222no—
197C22—612no—
198C22—1221no—
199C22—1221no—
200C22C2×D4×D6111yescharacteristic
201C4—42no—
202C4—42no—
203C4—612no—
204C4—1221no—
205C4—1221no—
206C4—2442no—
207C4—2442no—
208C4Q16×D6112yes—
209C4#1451980912yes—
210C4#1451982212yes—
211C2—1222no—
212C2#1684032511yescharacteristic
213C2C2×Q16×D6111yescharacteristic
214C2C2×#1451980911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#494C2
socleC22×C61C22×D4
hypercenter#494D61
hypocenterC61#3209
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #16840141C2semidirect
4. #16840113C2semidirect
5. #16840112C2semidirect
6. #16839970C2semidirect
9. C61×#494C2semidirect
83. C4×D61Q16semidirect
111. #494D61semidirect
117. C61#3209semidirect