Finite Group Databasebeta

← #21447080

Subgroups — #21447080

Order 7808.

276 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C22×#11758200C211yesmaximal, characteristic
2#16839790C211yesmaximal, characteristic, complemented
3#16839772C211yesmaximal, characteristic, complemented
4#16839767C211yesmaximal, characteristic
5C2×#14519695C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C2×#100×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758200—22no—
10C2×#11758200—22no—
11C2×#11758200—22no—
12C2×#11758194C2211yescharacteristic
13C22×#92418C2211yescharacteristic
14#14519736C2211yescharacteristic
15#14519706—22no—
16#14519702—22no—
17#14519698—22no—
18#14519695—22no—
19C22×D4×C61C2211yescharacteristic
20C2×M16×C61C2211yescharacteristic
21C2×M16×C61C2211yescharacteristic
22#100×C61—22no—
23C24×C61—21no—
24C2×D4×C61—21no—
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61D412yes—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×Dic122—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122D412yes—
38M16×C61—21no—
39M16×C61—21no—
40M16×C61—21no—
41M16×C61—21no—
42C2×C8×C61—21no—
43C2×C8×C61—21no—
44C22⋊Dic61—21no—
45#11758200—28no—
46C4⋊Dic61D412yes—
47C4×Dic61—21no—
48#11758194—21no—
49#11758194—21no—
50C2×#92418—21no—
51C2×#92418—21no—
52C2×#92418—21no—
53C2×#92418D412yes—
54C23×C61—22no—
55C23×C61—41no—
56C23×C61—41no—
57C23×C61—82no—
58C23×C61#4111yescharacteristic
59D4×C61—22no—
60D4×C61—22no—
61D4×C61—41no—
62D4×C61—41no—
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61#4111yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×Dic61—22no—
70C2×Dic61—22no—
71C2×Dic61—41no—
72C2×Dic61—41no—
73Dic122—22no—
74Dic122—22no—
75Dic122—41no—
76Dic122—41no—
77C8×C61—41no—
78C8×C61—41no—
79#92418—22no—
80#92418—41no—
81C22×C61—22no—
82C22×C61—42no—
83C22×C61—82no—
84C22×C61—82no—
85C22×C61—82no—
86C22×C61#12111yescharacteristic
87C22×C61#12311yescharacteristic
88C22×C61#12311yescharacteristic
89C4×C61#12011yescharacteristic
90C4×C61#12111yescharacteristic
91C4×C61#12111yescharacteristic
92C4×C61#12411yescharacteristic
93Dic61—42no—
94Dic61—42no—
95#2046—611nomaximal, Sylow
96C2×C61—21no—
97C2×C61—21no—
98C2×C61—82no—
99C2×C61#39411yescharacteristic
100C2×C61#47112yes—
101C22×SD16—611no—
102#424—611no—
103#419—611no—
104#418—611no—
105C2×#101—611no—
106C2×#100D6111yescharacteristic
107#341—611no—
108C61#204611yescharacteristic, complemented, Sylow
109C22×Q8—611no—
110C22×D4C2×D6111yescharacteristic
111C2×SD16—1222no—
112C2×SD16—1222no—
113C2×SD16—1222no—
114C2×M16—611no—
115C2×M16C2×D6111yescharacteristic
116C2×M16C2×D6111yescharacteristic
117C22×C8—611no—
118#117—611no—
119C4⋊C8—1222no—
120#103—1222no—
121#102—1222no—
122#101—1222no—
123#100—22no—
124C24—21no—
125C2×Q8—612no—
126C2×Q8—1221no—
127C2×Q8—1221no—
128C2×Q8—1221no—
129C2×Q8—1221no—
130C2×Q8—1221no—
131C2×D4—21no—
132C2×D4—21no—
133C2×D4—21no—
134C2×D4—21no—
135C2×D4—21no—
136C2×D4C22⋊D6112yes—
137C22×C4—1221no—
138C22×C4C22×D6111yescharacteristic
139SD16—1228no—
140M16—21no—
141M16—21no—
142M16—21no—
143M16—21no—
144M16—1221no—
145M16—1221no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—612no—
149C2×C8—1221no—
150C2×C8—1221no—
151C2×C8—1221no—
152C4⋊C4—612no—
153C22⋊C4—1221no—
154C42—1221no—
155C23—22no—
156C23—41no—
157C23—41no—
158C23—82no—
159C23#1175822211yescharacteristic
160Q8—1222no—
161Q8—1222no—
162Q8—2441no—
163Q8—2441no—
164D4—22no—
165D4—22no—
166D4—41no—
167D4—41no—
168C2×C4—1222no—
169C2×C4—1222no—
170C2×C4—2441no—
171C2×C4—2441no—
172C2×C4#1175822211yescharacteristic
173C2×C4D4×D6111yescharacteristic
174C2×C4D4×D6111yescharacteristic
175C2×C4D4×D6111yescharacteristic
176C2×C4#1175822411yescharacteristic
177C2×C4C2×C22⋊D6111yescharacteristic
178C8—41no—
179C8—41no—
180C8—1222no—
181C8—2441no—
182C22—22no—
183C22—42no—
184C22—82no—
185C22—82no—
186C22—82no—
187C22#1451975011yescharacteristic
188C22#1451975911yescharacteristic
189C22#1451976011yescharacteristic
190C4—2442no—
191C4—2442no—
192C4#1451974511yescharacteristic
193C4#1451974911yescharacteristic
194C4#1451975011yescharacteristic
195C4#1451976311yescharacteristic
196C2—21no—
197C2—21no—
198C2—82no—
199C2#1683967711yescharacteristic
200C2#1684002412yes—
subgroupG/H
centerC22#14519750
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#100×C61C2
socleC22×C61#121
hypercenterC2×#100D61
hypocenterC61#2046
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #16839790C2semidirect
3. #16839772C2semidirect
5. C2×#14519695C2semidirect
6. #16839526C2semidirect
108. C61#2046semidirect