Finite Group Databasebeta

← #21444821

Subgroups — #21444821

Order 7808.

254 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840343C211yesmaximal, characteristic
2#16840075C212yesmaximal, complemented
3#16839495C212yesmaximal, complemented
4#16839488C211yesmaximal, characteristic, complemented
5C61×#398C211yesmaximal, characteristic, complemented
6C2×#11758222—21no—
7#14519757—22no—
8#14519752—22no—
9#14519751—21no—
10#14519751C2212yes—
11#14519710—22no—
12#14519697—22no—
13C22⋊#92418C2212yes—
14C2×C4⋊C4×C61—21no—
15C2×C4⋊C4×C61C2211yescharacteristic
16C2×C4⋊C4×C61C2211yescharacteristic
17#95×C61—21no—
18#95×C61C2211yescharacteristic
19C22×C4×C61—21no—
20C22×C4×C61—21no—
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61C2311yescharacteristic
24C2×C22⋊D61—22no—
25#11758222—42no—
26#11758222—42no—
27C2×D244—21no—
28C2×D244—21no—
29C2×D244D412yes—
30C2×C4×D61—22no—
31C2×Dic122—21no—
32C4⋊C4×C61—22no—
33C4⋊C4×C61—22no—
34C4⋊C4×C61—42no—
35#11758198—22no—
36#11758198—22no—
37C4⋊Dic61—21no—
38C4⋊Dic61D412yes—
39C2×#92418—22no—
40C23×C61C2×D411yescharacteristic
41C22×D61—22no—
42C2×C4×C61—21no—
43C2×C4×C61—21no—
44C2×C4×C61—22no—
45C2×C4×C61—21no—
46C2×C4×C61—41no—
47C2×C4×C61—41no—
48C2×C4×C61—41no—
49C2×C4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61D812yes—
54C2×C4×C61C2×D412yes—
55C22⋊D61—42no—
56C22⋊D61—42no—
57C2×Dic61—22no—
58D244—42no—
59D244—42no—
60D244—81no—
61C4×D61—44no—
62Dic122—42no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#12011yescharacteristic
67C22×C61C2×D811yescharacteristic
68C22×C61AGL(1,ℤ/8)11yescharacteristic
69C2×D61—42no—
70C2×D61—42no—
71C2×D61—42no—
72C4×C61—22no—
73C4×C61—22no—
74C4×C61—42no—
75C4×C61—41no—
76C4×C61—81no—
77Dic61—42no—
78#1610—611nomaximal, Sylow
79C2×C61—21no—
80C2×C61—21no—
81C2×C61#44711yescharacteristic
82C2×C61#45611yescharacteristic
83C2×C61#45811yescharacteristic
84D61—82no—
85#537—611no—
86#480—612no—
87#398D6111yescharacteristic, complemented
88#327—612no—
89#324—611no—
90C61#161011yescharacteristic, complemented, Sylow
91C2×#41—1221no—
92C22⋊Q8—1222no—
93#121—612no—
94#121—1222no—
95#121—1221no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4C2×D6111yescharacteristic
98C2×C4⋊C4C2×D6111yescharacteristic
99#107—1222no—
100#102—1222no—
101C22⋊C8—612no—
102#95—21no—
103#95C2×D6111yescharacteristic
104#41—2442no—
105#41—2442no—
106C2×Q8—1221no—
107C2×D4—612no—
108C2×D4—1221no—
109C2×D4—1221no—
110C2×D4—1222no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—1222no—
114C22×C4C22⋊D6111yescharacteristic
115C22×C4C22⋊D6111yescharacteristic
116C22×C4C22×D6111yescharacteristic
117C2×C8—1222no—
118C4⋊C4—22no—
119C4⋊C4—22no—
120C4⋊C4—42no—
121C4⋊C4—612no—
122C4⋊C4—1221no—
123C22⋊C4—1222no—
124C22⋊C4—1222no—
125C23—1222no—
126C23C2×C22⋊D6111yescharacteristic
127Q8—2442no—
128D4—4881no—
129D4—2442no—
130D4—2442no—
131D4—2442no—
132D4—2442no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—1222no—
145C2×C4—2444no—
146C2×C4#1175819912yes—
147C2×C4D4×D6112yes—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—2442no—
152C22—2442no—
153C22—2442no—
154C22#1451974511yescharacteristic
155C22C2×#1175819911yescharacteristic
156C22#1451980211yescharacteristic
157C4—22no—
158C4—22no—
159C4—42no—
160C4—41no—
161C4—81no—
162C4—2442no—
163C2—21no—
164C2—21no—
165C2—4882no—
166C2#1683989511yescharacteristic
167C2#1683994411yescharacteristic
168C2#1683995111yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#398C2
socleC22×C61#120
hypercenter#398D61
hypocenterC61#1610
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
2. #16840075C2semidirect
3. #16839495C2semidirect
4. #16839488C2semidirect
5. C61×#398C2semidirect
87. #398D61semidirect
90. C61#1610semidirect