Finite Group Databasebeta

← #21456964

Subgroups — #21456964

Order 7808.

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

normal subgroups only

This group has 360 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#16840158C211yesmaximal, characteristic, complemented
4#16840114C211yesmaximal, characteristic, complemented
5#16840113C211yesmaximal, characteristic, complemented
6#16840094C214yesmaximal
7#16840046C214yesmaximal, complemented
8#16839813C211yesmaximal, characteristic
9C61×#498C211yesmaximal, characteristic, complemented
10C2×Q8×D61—21no—
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519776—21no—
14#14519776C2212yes—
15#14519775—21no—
16#14519768—21no—
17#14519757C2212yes—
18#14519753—21no—
19Q8×Dic61—21no—
20#14519742C2212yes—
21#14519735—21no—
22C4⋊C4×D61—21no—
23C4⋊C4×D61C2212yes—
24C42×D61C2211yescharacteristic
25#14519708C2214yes—
26#14519706C2212yes—
27#14519702C2214yes—
28#14519700C2214yes—
29#14519689C2212yes—
30C4×#92418C2211yescharacteristic
31C4⋊Q8×C61C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33#106×C61C2214yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37Q8×D61—44no—
38C2×C4×D61—22no—
39C2×C4×D61D411yescharacteristic
40C2×C4×D61D411yescharacteristic
41C2×C4×D61C2311yescharacteristic
42C2×Dic122—21no—
43C2×Dic122—22no—
44C2×Dic122C2312yes—
45C2×C8×C61C2312yes—
46C4⋊C4×C61—21no—
47C4⋊C4×C61—21no—
48C4⋊C4×C61C2312yes—
49C4⋊C4×C61C2312yes—
50C42×C61C2311yescharacteristic
51#11758198—22no—
52C4⋊Dic61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4⋊Dic61—22no—
56C4⋊Dic61C2312yes—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61D411yescharacteristic
62C4×Dic61D411yescharacteristic
63C4×Dic61C2311yescharacteristic
64C2×#92418C2312yes—
65C22×D61C2×D411yescharacteristic
66Q8×C61—42no—
67Q8×C61—42no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2411yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61C2×D411yescharacteristic
76C2×Dic61C2×D411yescharacteristic
77C2×Dic61C2×D411yescharacteristic
78C4×D61—22no—
79C4×D61—22no—
80C4×D61—44no—
81C4×D61SD1614yes—
82Dic122—24no—
83Dic122—42no—
84Dic122—44no—
85C8×C61—22no—
86#92418—22no—
87C22×C61C22×D411yescharacteristic
88C2×D61—21no—
89C2×D61—21no—
90C2×D61C2×SD1612yes—
91C4×C61—42no—
92C4×C61—42no—
93C4×C61C2×SD1612yes—
94C4×C61#13712yes—
95C4×C612−1+412yes—
96Dic61—21no—
97Dic61—21no—
98Dic61—42no—
99Dic61—42no—
100Dic61C2×SD1612yes—
101#3229—611nomaximal, Sylow
102C2×C61#53611yescharacteristic
103C2×C61C22×SD1611yescharacteristic
104C2×C61C2×#13711yescharacteristic
105D61—22no—
106#533—611no—
107C2×C4⋊Q8—611no—
108#498—611no—
109#498D6111yescharacteristic, complemented
110#487—611no—
111#487—611no—
112#483—614no—
113#475—614no—
114#431—611no—
115C61#322911yescharacteristic, complemented, Sylow
116C22×Q8—1221no—
117C4⋊Q8—612no—
118C4⋊Q8—611no—
119C4⋊Q8—611no—
120C4⋊Q8—1221no—
121C4⋊Q8—1221no—
122C4⋊Q8C2×D6111yescharacteristic
123C4⋊Q8C2×D6111yescharacteristic
124#125—1221no—
125C22⋊Q8—612no—
126C22⋊Q8—1221no—
127C4×Q8—612no—
128C4×Q8—1221no—
129#117—1221no—
130C2×C4⋊C4—612no—
131C2×C4⋊C4—1221no—
132C2×C42—611no—
133#106—614no—
134#106C2×D6114yes—
135C4⋊C8—612no—
136#103—614no—
137#103—614no—
138C22⋊C8—612no—
139C4×C8—611no—
140C4×C8C2×D6111yescharacteristic
141C2×Q8—21no—
142C2×Q8—21no—
143C2×Q8—612no—
144C2×Q8—1222no—
145C2×Q8—1221no—
146C2×Q8—2444no—
147C22×C4—611no—
148C22×C4—611no—
149C22×C4—611no—
150C22×C4—1222no—
151C2×C8—612no—
152C2×C8C22×D6112yes—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—612no—
156C4⋊C4—1222no—
157C4⋊C4—1222no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4—1221no—
163C4⋊C4C22×D6112yes—
164C4⋊C4C22×D6112yes—
165C22⋊C4—1222no—
166C42—611no—
167C42—611no—
168C42—611no—
169C42—1222no—
170C42C22×D6111yescharacteristic
171C23—611no—
172Q8—42no—
173Q8—42no—
174Q8—1224no—
175Q8—2444no—
176Q8—2442no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—611no—
180C2×C4—614no—
181C2×C4—611no—
182C2×C4—611no—
183C2×C4—1222no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—2444no—
188C2×C4D4×D6111yescharacteristic
189C2×C4D4×D6111yescharacteristic
190C2×C4C23×D6111yescharacteristic
191C8—22no—
192C8—1222no—
193C22—612no—
194C22—1221no—
195C22—1221no—
196C22C2×D4×D6111yescharacteristic
197C4—42no—
198C4—42no—
199C4—612no—
200C4—1221no—
201C4—1221no—
202C4—2442no—
203C4—2442no—
204C4SD16×D6112yes—
205C4#1451980612yes—
206C4#1451982512yes—
207C2—1222no—
208C2#1684033711yescharacteristic
209C2C2×SD16×D6111yescharacteristic
210C2C2×#1451980611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#498C2
socleC22×C61C22×D4
hypercenter#498D61
hypocenterC61#3229
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
3. #16840158C2semidirect
4. #16840114C2semidirect
5. #16840113C2semidirect
7. #16840046C2semidirect
9. C61×#498C2semidirect
109. #498D61semidirect
115. C61#3229semidirect