Finite Group Databasebeta

← #21447760

Subgroups — #21447760

Order 7808.

220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14519796C211yesmaximal, characteristic
2C2×Dic488C211yesmaximal, characteristic, complemented
3C2×#14519721C211yesmaximal, characteristic, complemented
4#16840004C211yesmaximal, characteristic, complemented
5#16839565C211yesmaximal, characteristic, complemented
6#16839541C211yesmaximal, characteristic, complemented
7C61×#357C211yesmaximal, characteristic, complemented
8C2×#11758224—21no—
9#14519796—22no—
10#14519796—22no—
11C2×Dic244C2211yescharacteristic
12C2×Dic244C2211yescharacteristic
13C2×#11758200—21no—
14C2×C8×D61C2211yescharacteristic
15#14519757—21no—
16Dic488—22no—
17#14519721—22no—
18C2×#11758185C2211yescharacteristic
19#14519700—21no—
20C2×D8×C61C2211yescharacteristic
21C2×C16×C61C2211yescharacteristic
22#107×C61C2211yescharacteristic
23C2×D4×C61—21no—
24C2×C22⋊D61—41no—
25C22×Dic61—41no—
26#11758224—24no—
27#11758224—42no—
28C2×C4×D61D411yescharacteristic
29C2×Dic122—21no—
30C2×Dic122—21no—
31D8×C61—21no—
32D8×C61D412yes—
33C2×C8×C61C2311yescharacteristic
34C4⋊C4×C61—21no—
35#11758200—24no—
36#11758198—41no—
37C4⋊Dic61—41no—
38C2×#92418D411yescharacteristic
39Dic244—21no—
40Dic244—21no—
41Dic244—21no—
42Dic244D412yes—
43C8×D61—21no—
44C8×D61—21no—
45C16×C61—21no—
46#11758185—21no—
47C23×C61—41no—
48C22×D61D811yescharacteristic
49D4×C61—22no—
50D4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61C2×D411yescharacteristic
53C22⋊D61—44no—
54C2×Dic61—44no—
55C2×Dic61—41no—
56C2×Dic61—41no—
57C2×Dic61D811yescharacteristic
58C4×D61—21no—
59C4×D61—21no—
60Dic122—22no—
61Dic122—41no—
62Dic122—41no—
63Dic122—41no—
64C8×C61C2×D411yescharacteristic
65C8×C61C2×D411yescharacteristic
66#92418—21no—
67C22×C61—42no—
68C22×C61—81no—
69C22×C61—81no—
70C22×C61C2×D811yescharacteristic
71C2×D61—21no—
72C2×D61—21no—
73C2×D61—21no—
74C4×C61—81no—
75C4×C61#12011yescharacteristic
76C4×C61AGL(1,ℤ/8)11yescharacteristic
77Dic61—21no—
78Dic61—42no—
79Dic61—81no—
80#2189—611nomaximal, Sylow
81C2×C61—82no—
82C2×C61#44711yescharacteristic
83C2×C61#50811yescharacteristic
84C2×C61#51011yescharacteristic
85D61—41no—
86C2×#135—611no—
87C2×Q32—611no—
88C2×SD32—611no—
89#467—611no—
90#358—611no—
91#357D6111yescharacteristic, complemented
92C22⋊C16—611no—
93C61#218911yescharacteristic, complemented, Sylow
94C2×#41—1221no—
95#135—1222no—
96#135—1222no—
97C2×Q16—611no—
98C2×Q16—611no—
99C2×SD16—1221no—
100C2×D8C2×D6111yescharacteristic
101C22×C8—611no—
102C22⋊Q8—1221no—
103Q32—1222no—
104SD32—1222no—
105C2×C16—611no—
106C2×C16C2×D6111yescharacteristic
107#107C2×D6111yescharacteristic
108#103—1221no—
109#41—1224no—
110#41—2442no—
111C2×Q8—1221no—
112C2×Q8—1221no—
113C2×D4—21no—
114C2×D4—2441no—
115C22×C4—611no—
116C22×C4—2441no—
117Q16—612no—
118Q16—1221no—
119Q16—1221no—
120Q16—1221no—
121SD16—1224no—
122D8—21no—
123D8D24412yes—
124C2×C8—611no—
125C2×C8—1221no—
126C2×C8—1221no—
127C2×C8C22×D6111yescharacteristic
128C4⋊C4—21no—
129C4⋊C4—2441no—
130C22⋊C4—2441no—
131C16—21no—
132C16—1221no—
133C23—41no—
134C23—611no—
135Q8—1222no—
136Q8—2441no—
137Q8—2441no—
138Q8—2441no—
139D4—22no—
140D4—41no—
141D4—2444no—
142C2×C4—41no—
143C2×C4—611no—
144C2×C4—1221no—
145C2×C4—1221no—
146C2×C4—2444no—
147C2×C4—2441no—
148C2×C4—2441no—
149C2×C4D4×D6111yescharacteristic
150C8—1221no—
151C8C2×D24411yescharacteristic
152C8D4×D6111yescharacteristic
153C22—42no—
154C22—81no—
155C22—81no—
156C22—1221no—
157C22—1221no—
158C22—1221no—
159C22D8×D6111yescharacteristic
160C4—81no—
161C4—1221no—
162C4—4881no—
163C4—2442no—
164C4#1451974711yescharacteristic
165C4#1451980411yescharacteristic
166C2—82no—
167C2—2441no—
168C2#1683989711yescharacteristic
169C2#1684019111yescharacteristic
170C2#1684020111yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#357C2
socleC22×C61C2×D8
hypercenter#357D61
hypocenterC61#2189
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×Dic488C2semidirect
3. C2×#14519721C2semidirect
4. #16840004C2semidirect
5. #16839565C2semidirect
6. #16839541C2semidirect
7. C61×#357C2semidirect
91. #357D61semidirect
93. C61#2189semidirect