Finite Group Databasebeta

← #21446221

Subgroups — #21446221

Order 7808.

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

normal subgroups only

This group has 344 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
1C2×#14519765C211yesmaximal, characteristic
2#16840239C211yesmaximal, characteristic, complemented
3#16839768C211yesmaximal, characteristic
4#16839766C211yesmaximal, characteristic
5C2×#14519695C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C61×#339C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519765—22no—
12#14519765C414yescomplemented
13C4×Dic122—22no—
14#14519742—22no—
15#14519736C2211yescharacteristic
16#14519733—22no—
17C2×#11758198—22no—
18#14519699—22no—
19#14519697—22no—
20#14519695—22no—
21C2×M16×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23C2×C42×C61C2211yescharacteristic
24C23×D61—21no—
25C22×C4×C61—21no—
26C22×C4×C61C2311yescharacteristic
27C22×Dic61D412yes—
28C2×D244—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244C2×C412yes—
34C2×Dic122—21no—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122C2×C412yes—
39C2×Dic122D412yes—
40M16×C61—21no—
41M16×C61—21no—
42C2×C8×C61—21no—
43C4⋊C4×C61D412yes—
44C22⋊C4×C61—21no—
45C42×C61—21no—
46C42×C61—21no—
47C42×C61C2×C412yes—
48C22⋊Dic61—21no—
49#11758198—28no—
50C4⋊Dic61D412yes—
51#11758196—24no—
52C4×Dic61—24no—
53C4×Dic61—21no—
54#11758194—21no—
55#11758194—21no—
56C2×#92418—21no—
57C23×C61C2×D411yescharacteristic
58C22×D61—22no—
59C22×D61—44no—
60C22×D61—41no—
61C22×D61—41no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—42no—
65C2×C4×C61C22×C411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61C22⋊C414yes—
75D244—22no—
76D244—22no—
77D244—41no—
78D244—41no—
79Dic122—22no—
80Dic122—22no—
81Dic122—22no—
82Dic122—22no—
83C8×C61—41no—
84#92418—41no—
85C22×C61—22no—
86C22×C61C2×C22⋊C411yescharacteristic
87C22×C61#12011yescharacteristic
88C22×C61#12311yescharacteristic
89C2×D61—44no—
90C2×D61—42no—
91C2×D61—82no—
92C2×D61—82no—
93C4×C61—42no—
94C4×C61—42no—
95C4×C61C4×D411yescharacteristic
96C4×C61C4×D411yescharacteristic
97C4×C61#12111yescharacteristic
98C4×C61#12111yescharacteristic
99Dic61—24no—
100Dic61—42no—
101#1888—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—21no—
104C2×C61#38611yescharacteristic
105C2×C61#45412yes—
106D61—82no—
107C2×#124—611no—
108#519—611no—
109#418—611no—
110#418—611no—
111C2×#101—611no—
112#339—611no—
113#339D6111yescharacteristic, complemented
114C61#188811yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C22×D4—611no—
117C2×M16—611no—
118C2×M16C2×D6111yescharacteristic
119#124—614no—
120#124—1222no—
121C4×Q8—1222no—
122C4×Q8—1222no—
123#117—611no—
124#117—1222no—
125#117C2×D6111yescharacteristic
126C2×C22⋊C4—1222no—
127C2×C42C2×D6111yescharacteristic
128#102—1222no—
129#102—1222no—
130#101—1222no—
131C24—1221no—
132C2×Q8—612no—
133C2×Q8—612no—
134C2×Q8—1221no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×D4—612no—
139C2×D4—1221no—
140C2×D4—1221no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4—1221no—
144C22×C4—21no—
145C22×C4—612no—
146C22×C4C22×D6111yescharacteristic
147M16—21no—
148M16—21no—
149M16—1221no—
150M16—1221no—
151C2×C8—21no—
152C2×C8—1221no—
153C4⋊C4—612no—
154C4⋊C4—1224no—
155C4⋊C4D24412yes—
156C22⋊C4—21no—
157C22⋊C4—1228no—
158C22⋊C4—1221no—
159C42—21no—
160C42—21no—
161C42—1224no—
162C42—1221no—
163C42C4×D6112yes—
164C23—1222no—
165C23—2444no—
166C23—2441no—
167C23—2441no—
168C23D4×D6111yescharacteristic
169Q8—1222no—
170Q8—1222no—
171Q8—1222no—
172Q8—1222no—
173D4—1222no—
174D4—1222no—
175D4—2441no—
176D4—2441no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—614no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4C2×C4×D6111yescharacteristic
185C2×C4C2×D24411yescharacteristic
186C2×C4#1175822211yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4D4×D6111yescharacteristic
189C2×C4#1175822611yescharacteristic
190C8—41no—
191C8—2441no—
192C22—22no—
193C22—4882no—
194C22—4882no—
195C22—2444no—
196C22—2442no—
197C22C22⋊C4×D6111yescharacteristic
198C22#1451974711yescharacteristic
199C22#1451976211yescharacteristic
200C4—42no—
201C4—42no—
202C4—1224no—
203C4—2442no—
204C4#1451973911yescharacteristic
205C4C4×D24411yescharacteristic
206C4#1451975011yescharacteristic
207C4#1451975211yescharacteristic
208C2—21no—
209C2—21no—
210C2—4882no—
211C2#1683964011yescharacteristic
212C2#1683993612yes—
subgroupG/H
centerC22#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#339C2
socleC22×C61#120
hypercenter#339D61
hypocenterC61#1888
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #16840239C2semidirect
5. C2×#14519695C2semidirect
6. #16839522C2semidirect
7. C61×#339C2semidirect
12. #14519765C4semidirect
113. #339D61semidirect
114. C61#1888semidirect