Finite Group Databasebeta

← #21445777

Subgroups — #21445777

Order 7808.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C2×#14519825C211yesmaximal, characteristic
2C2×#14519705C212yesmaximal, complemented
3#16839761C212yesmaximal, complemented
4C2×#14519696C211yesmaximal, characteristic, complemented
5C61×#391C211yesmaximal, characteristic, complemented
6#14519825—22no—
7#14519825—24no—
8#14519825C414yescomplemented
9C2×#11758226—22no—
10C2×#11758222—22no—
11C2×#11758222C2212yes—
12C2×Q8×D61—22no—
13C2×#11758194C2212yes—
14#14519705—24no—
15#14519700—22no—
16#14519697—22no—
17#14519696—22no—
18C22×Q8×C61C2211yescharacteristic
19C2×C4⋊C4×C61C2211yescharacteristic
20C2×C42×C61C2211yescharacteristic
21#95×C61—22no—
22C2×Q8×C61—22no—
23C2×Q8×C61—22no—
24C2×Q8×C61C2×C412yes—
25C2×Q8×C61D412yes—
26C22×C4×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61D412yes—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—22no—
31#11758226—28no—
32#11758226—28no—
33Q8×D61—28no—
34Q8×D61—28no—
35#11758222—28no—
36#11758222—28no—
37#11758222—22no—
38#11758222—22no—
39#11758222C2×C414yes—
40#11758222D414yes—
41C2×D244—22no—
42C2×D244D412yes—
43C2×C4×D61—24no—
44C2×C4×D61—22no—
45C2×Dic122—22no—
46C2×Dic122D412yes—
47C4⋊C4×C61—22no—
48C42×C61—22no—
49#11758194—22no—
50#11758194—22no—
51C2×#92418—22no—
52C23×C61C2×D411yescharacteristic
53C22×D61—22no—
54Q8×C61—24no—
55Q8×C61—24no—
56C2×C4×C61—22no—
57C2×C4×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61—42no—
62C2×C4×C61—41no—
63C2×C4×C61C22⋊C414yes—
64C2×C4×C61C22×C411yescharacteristic
65C2×C4×C61C2×D412yes—
66C2×C4×C61C2×D412yes—
67C2×C4×C61C2×D411yescharacteristic
68C22⋊D61—24no—
69C22⋊D61—24no—
70C2×Dic61—22no—
71D244—28no—
72D244—22no—
73D244C22⋊C414yes—
74C4×D61—216no—
75C4×D61—24no—
76C4×D61—24no—
77Dic122—28no—
78Dic122—22no—
79Dic122C22⋊C414yes—
80#92418—42no—
81C22×C61—21no—
82C22×C61—21no—
83C22×C61C2×C22⋊C411yescharacteristic
84C22×C61#12011yescharacteristic
85C22×C61#12011yescharacteristic
86C2×D61—24no—
87C2×D61—42no—
88C2×D61—42no—
89C4×C61—24no—
90C4×C61—42no—
91C4×C61—81no—
92C4×C61C2×C22⋊C412yes—
93C4×C61#12012yes—
94Dic61—24no—
95#1793—611nomaximal, Sylow
96C2×C61—21no—
97C2×C61—21no—
98C2×C61#37911yescharacteristic
99C2×C61#45411yescharacteristic
100C2×C61#45611yescharacteristic
101D61—44no—
102C2×2−1+4—611no—
103C2×#104—612no—
104#417—612no—
105C2×#101—611no—
106#391D6111yescharacteristic, complemented
107C61#179311yescharacteristic, complemented, Sylow
1082−1+4—614no—
1092−1+4—1224no—
1102−1+4—1222no—
111C2×#41—612no—
112C2×#41—1222no—
113C2×#41—1222no—
114C22×Q8—1222no—
115C22×Q8C2×D6111yescharacteristic
116C2×M16—612no—
117C2×C4⋊C4C2×D6111yescharacteristic
118C2×C42C2×D6111yescharacteristic
119#104—1224no—
120#103—1222no—
121#102—1222no—
122#101—1222no—
123#95—22no—
124#41—614no—
125#41—614no—
126#41—1228no—
127#41—1228no—
128#41—1228no—
129#41—1228no—
130#41—1222no—
131#41—1222no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—612no—
135C2×Q8—1222no—
136C2×Q8—1228no—
137C2×Q8—1228no—
138C2×Q8C4×D6112yes—
139C2×Q8D24412yes—
140C2×D4—612no—
141C2×D4—1222no—
142C2×D4—1222no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—1224no—
146C22×C4—1222no—
147C22×C4C22⋊D6112yes—
148C22×C4C22×D6111yescharacteristic
149M16—1222no—
150M16—1222no—
151C2×C8—1222no—
152C4⋊C4—22no—
153C42—22no—
154C23—1222no—
155C23C2×C22⋊D6111yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—614no—
159Q8—1228no—
160Q8—1222no—
161D4—614no—
162D4—1228no—
163D4—1224no—
164D4—1224no—
165D4—1222no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—12216no—
174C2×C4—1222no—
175C2×C4—1224no—
176C2×C4—1224no—
177C2×C4#1175819814yes—
178C2×C4C2×C4×D6111yescharacteristic
179C2×C4C2×D24411yescharacteristic
180C2×C4D4×D6112yes—
181C2×C4D4×D6112yes—
182C8—2442no—
183C22—21no—
184C22—21no—
185C22—1224no—
186C22—2442no—
187C22—2442no—
188C22C2×#1175819811yescharacteristic
189C22#1451974511yescharacteristic
190C22#1451974511yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—1224no—
195C4C22⋊C4×D6112yes—
196C4#1451974712yes—
197C2—21no—
198C2—21no—
199C2—2444no—
200C2#1683961711yescharacteristic
201C2#1683993411yescharacteristic
202C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#391C2
socleC22×C61#120
hypercenter#391D61
hypocenterC61#1793
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#14519705C2semidirect
3. #16839761C2semidirect
4. C2×#14519696C2semidirect
5. C61×#391C2semidirect
8. #14519825C4semidirect
106. #391D61semidirect
107. C61#1793semidirect