Finite Group Databasebeta

← #21446731

Subgroups — #21446731

Order 7808.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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×#11758202C211yesmaximal, characteristic
2C2×#14519712C211yesmaximal, characteristic
3#16839772C211yesmaximal, characteristic
4#16839771C211yesmaximal, characteristic
5C2×#14519695C211yesmaximal, characteristic
6#16839720C211yesmaximal, characteristic
7C2×#101×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C2×#11758202—21no—
10C2×#11758202—21no—
11C2×#11758202—22no—
12C2×#11758202C414yescomplemented
13C2×#11758194C2211yescharacteristic
14C22×#92418C2211yescharacteristic
15#14519736C2211yescharacteristic
16#14519712—22no—
17#14519702—22no—
18#14519701—22no—
19#14519695—22no—
20#14519687—21no—
21C8×Dic61—21no—
22C22×Q8×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25#101×C61—22no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61C2×C412yes—
32C22×C4×C61—21no—
33C22×C4×C61C2311yescharacteristic
34C22×Dic61—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122C2×C412yes—
41M16×C61—21no—
42M16×C61—21no—
43M16×C61—21no—
44M16×C61D412yes—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C22⋊Dic61—21no—
48#11758202—24no—
49#11758202—24no—
50C4⋊Dic61D412yes—
51C4×Dic61—21no—
52#11758194—21no—
53#11758194—21no—
54C2×#92418—21no—
55C2×#92418C2×C412yes—
56C2×#92418D411yescharacteristic
57C2×#92418D411yescharacteristic
58C2×#92418D412yes—
59C23×C61#4111yescharacteristic
60Q8×C61—22no—
61Q8×C61—22no—
62Q8×C61—41no—
63Q8×C61—41no—
64C2×C4×C61—22no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61C22×C411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77Dic122—22no—
78Dic122—22no—
79Dic122—41no—
80Dic122—41no—
81C8×C61—22no—
82C8×C61—41no—
83#92418—41no—
84#92418C22⋊C412yes—
85#92418C22⋊C412yes—
86C22×C61—22no—
87C22×C61C4×D411yescharacteristic
88C22×C61#12111yescharacteristic
89C22×C61#12411yescharacteristic
90C4×C61—42no—
91C4×C61C2×C22⋊C411yescharacteristic
92C4×C61C4×D411yescharacteristic
93C4×C61#12111yescharacteristic
94C4×C61#12711yescharacteristic
95Dic61—42no—
96Dic61—42no—
97#1979—611nomaximal, Sylow
98C2×C61—21no—
99C2×C61—21no—
100C2×C61#39011yescharacteristic
101C2×C61#47312yes—
102C22×Q16—611no—
103C2×#108—611no—
104#419—611no—
105#419—611no—
106C2×#101—611no—
107C2×#101D6111yescharacteristic
108#405—611no—
109C61#197911yescharacteristic, complemented, Sylow
110C22×Q8—611no—
111C22×Q8C2×D6111yescharacteristic
112C2×Q16—614no—
113C2×Q16—1221no—
114C2×Q16—1221no—
115C2×Q16—1222no—
116C2×M16—611no—
117C2×M16C2×D6111yescharacteristic
118C2×M16C2×D6111yescharacteristic
119C22×C8—611no—
120#117—611no—
121#108—1222no—
122#103—1222no—
123#103—1222no—
124#101—22no—
125#101—1222no—
126#97—1221no—
127C4×C8—1221no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—612no—
134C2×Q8—1221no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8C4×D6112yes—
140C22×C4—21no—
141C22×C4—1221no—
142C22×C4C22×D6111yescharacteristic
143Q16—1224no—
144Q16—1224no—
145M16—21no—
146M16—21no—
147M16—21no—
148M16—1221no—
149M16—1221no—
150M16C22⋊D6112yes—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—612no—
154C2×C8—611no—
155C2×C8—611no—
156C2×C8—612no—
157C2×C8—1221no—
158C4⋊C4—612no—
159C22⋊C4—1221no—
160C42—1221no—
161C23#1175822211yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—1222no—
167Q8—1222no—
168Q8—2441no—
169Q8—2441no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—1222no—
174C2×C4—1222no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4C2×C4×D6111yescharacteristic
178C2×C4D4×D6111yescharacteristic
179C2×C4D4×D6111yescharacteristic
180C2×C4D4×D6111yescharacteristic
181C2×C4#1175822411yescharacteristic
182C2×C4C2×C22⋊D6111yescharacteristic
183C8—22no—
184C8—41no—
185C8—612no—
186C8—612no—
187C8—2441no—
188C22—22no—
189C22C4×C22⋊D6111yescharacteristic
190C22#1451975011yescharacteristic
191C22#1451976311yescharacteristic
192C4—42no—
193C4—2442no—
194C4—2442no—
195C4C22⋊C4×D6111yescharacteristic
196C4#1451973711yescharacteristic
197C4#1451974911yescharacteristic
198C4#1451977311yescharacteristic
199C2—21no—
200C2—21no—
201C2#1683966211yescharacteristic
202C2#1684003612yes—
subgroupG/H
centerC22#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#101×C61C2
socleC22×C61#121
hypercenterC2×#101D61
hypocenterC61#1979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
12. C2×#11758202C4semidirect
109. C61#1979semidirect