Finite Group Databasebeta

← #21447375

Subgroups — #21447375

Order 7808.

210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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#16839810C211yesmaximal, characteristic, complemented
2#16839788C211yesmaximal, characteristic, complemented
3#16839780C211yesmaximal, characteristic
4#16839778C211yesmaximal, characteristic
5#16839728C211yesmaximal, characteristic
6#16839518C211yesmaximal, characteristic, complemented
7C61×#424C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519712—22no—
13#14519706—22no—
14#14519705—22no—
15#14519703—22no—
16#14519689—22no—
17C2×M16×C61C2211yescharacteristic
18C22×C8×C61C2211yescharacteristic
19#117×C61C2211yescharacteristic
20C4⋊C8×C61—22no—
21C22×C4×C61C2311yescharacteristic
22C2×C22⋊D61—21no—
23#11758222—21no—
24#11758222—21no—
25#11758222—21no—
26#11758222—21no—
27C2×D244Q811yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122Q811yescharacteristic
30M16×C61—21no—
31M16×C61—21no—
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C22⋊C4×C61—21no—
38C42×C61D412yes—
39C22⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4×Dic61D412yes—
42#11758194—21no—
43#11758194—21no—
44#11758194—21no—
45#11758194—21no—
46C2×#92418—21no—
47C2×#92418D412yes—
48C23×C61#4111yescharacteristic
49C22×D61—21no—
50C2×C4×C61—22no—
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×Q811yescharacteristic
55C2×C4×C61#4111yescharacteristic
56C2×C4×C61#4111yescharacteristic
57C22⋊D61—41no—
58C22⋊D61—41no—
59C2×Dic61—21no—
60C2×Dic61—22no—
61D244—21no—
62D244—21no—
63C4×D61—41no—
64C4×D61—41no—
65Dic122—21no—
66Dic122—21no—
67C8×C61—41no—
68C8×C61—41no—
69#92418—22no—
70#92418—41no—
71C22×C61—41no—
72C22×C61C22⋊Q811yescharacteristic
73C22×C61#12311yescharacteristic
74C22×C61#12311yescharacteristic
75C2×D61—42no—
76C2×D61—41no—
77C4×C61—42no—
78C4×C61C22⋊Q811yescharacteristic
79C4×C61C22⋊Q811yescharacteristic
80C4×C61#12311yescharacteristic
81C4×C61#12711yescharacteristic
82Dic61—42no—
83Dic61—41no—
84#2098—611nomaximal, Sylow
85C2×C61—21no—
86C2×C61—21no—
87C2×C61—21no—
88C2×C61#39911yescharacteristic
89D61—81no—
90#430—611no—
91#424—611no—
92#424D6111yescharacteristic, complemented
93#421—611no—
94#421—611no—
95#408—611no—
96H(3,ℤ/4)—611no—
97C61#209811yescharacteristic, complemented, Sylow
98C2×#41—611no—
99C2×M16—611no—
100C2×M16—611no—
101C2×M16C2×D6111yescharacteristic
102C22×C8C2×D6111yescharacteristic
103#117—611no—
104#117C2×D6111yescharacteristic
105#108—1222no—
106C4⋊C8—22no—
107C4⋊C8—1222no—
108#104—1222no—
109#104—1222no—
110C22⋊C8—1222no—
111#41—1221no—
112#41—1221no—
113#41—1221no—
114#41—1221no—
115C2×Q8—611no—
116C2×D4—611no—
117C2×D4—1221no—
118C22×C4—1221no—
119C22×C4C22×D6111yescharacteristic
120M16—21no—
121M16—21no—
122M16—1221no—
123M16—1221no—
124M16—1221no—
125M16—1221no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—612no—
131C2×C8—1221no—
132C4⋊C4—21no—
133C4⋊C4—1221no—
134C22⋊C4—21no—
135C22⋊C4—1221no—
136C42—612no—
137C42C22⋊D6112yes—
138C23—1221no—
139C23#1175822211yescharacteristic
140Q8—1221no—
141Q8—1221no—
142D4—1221no—
143D4—1221no—
144D4—2441no—
145D4—2441no—
146C2×C4—22no—
147C2×C4—1221no—
148C2×C4—1222no—
149C2×C4—2441no—
150C2×C4—2441no—
151C2×C4#1175822211yescharacteristic
152C2×C4D4×D6111yescharacteristic
153C2×C4D4×D6111yescharacteristic
154C2×C4Q8×D6111yescharacteristic
155C2×C4#1175822611yescharacteristic
156C2×C4C2×C22⋊D6111yescharacteristic
157C8—41no—
158C8—41no—
159C8—1222no—
160C8—2441no—
161C22—41no—
162C22—2442no—
163C22—2441no—
164C22#1451975511yescharacteristic
165C22#1451976011yescharacteristic
166C22#1451976211yescharacteristic
167C4—42no—
168C4—2442no—
169C4—2441no—
170C4#1451975311yescharacteristic
171C4#1451975511yescharacteristic
172C4#1451976211yescharacteristic
173C4#1451977311yescharacteristic
174C2—21no—
175C2—21no—
176C2—21no—
177C2—4881no—
178C2#1683969711yescharacteristic
subgroupG/H
centerC4#14519773
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#424C2
socleC2×C61#399
hypercenter#424D61
hypocenterC61#2098
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #16839810C2semidirect
2. #16839788C2semidirect
6. #16839518C2semidirect
7. C61×#424C2semidirect
92. #424D61semidirect
97. C61#2098semidirect