Finite Group Databasebeta

← #21446720

Subgroups — #21446720

Order 7808.

296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11758190C211yesmaximal, characteristic
2#16839772C211yesmaximal, characteristic, complemented
3#16839768C211yesmaximal, characteristic
4C2×#14519695C211yesmaximal, characteristic, complemented
5C2×#14519693C211yesmaximal, characteristic
6#16839717C211yesmaximal, characteristic, complemented
7C2×#108×C61C211yesmaximal, characteristic, complemented
8C22×Dic122C2211yescharacteristic
9C22×D244C2211yescharacteristic
10C2×#11758190—21no—
11C2×#11758190—21no—
12C2×#11758190—22no—
13C2×#11758190C414yescomplemented
14C2×#11758194C2211yescharacteristic
15#14519736C2211yescharacteristic
16#14519702—22no—
17#14519699—22no—
18#14519695—22no—
19#14519693—22no—
20#14519687—21no—
21C8×Dic61—21no—
22C2×M16×C61C2211yescharacteristic
23C2×M16×C61C2211yescharacteristic
24C22×C8×C61C2211yescharacteristic
25#108×C61—22no—
26C23×D61—21no—
27C22×C4×C61C2311yescharacteristic
28C22×Dic61—21no—
29C2×D244—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244C2×C412yes—
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×C61—21no—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61C2×C412yes—
48C2×C8×C61D411yescharacteristic
49C2×C8×C61D411yescharacteristic
50C2×C8×C61D412yes—
51C22⋊Dic61—21no—
52C4⋊Dic61D412yes—
53C4×Dic61—21no—
54#11758194—21no—
55#11758194D412yes—
56C2×#92418—21no—
57#11758190—24no—
58#11758190—24no—
59C23×C61#4111yescharacteristic
60C22×D61—22no—
61C22×D61—41no—
62C22×D61—41no—
63C22×D61—82no—
64C2×C4×C61C22×C411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×D411yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×Dic61—22no—
71C2×Dic61—22no—
72C2×Dic61—41no—
73C2×Dic61—41no—
74D244—22no—
75D244—22no—
76D244—41no—
77D244—41no—
78Dic122—22no—
79Dic122—22no—
80Dic122—41no—
81Dic122—41no—
82C8×C61—41no—
83C8×C61—41no—
84C8×C61C22⋊C412yes—
85C8×C61C22⋊C412yes—
86#92418—22no—
87C22×C61—22no—
88C22×C61C4×D411yescharacteristic
89C22×C61#12111yescharacteristic
90C22×C61#12411yescharacteristic
91C2×D61—42no—
92C2×D61—82no—
93C2×D61—82no—
94C2×D61—82no—
95C4×C61C2×C22⋊C411yescharacteristic
96C4×C61C4×D411yescharacteristic
97C4×C61#12111yescharacteristic
98C4×C61#12711yescharacteristic
99Dic61—42no—
100Dic61—42no—
101#1977—611nomaximal, Sylow
102C2×C61—21no—
103C2×C61—21no—
104C2×C61#39011yescharacteristic
105C2×C61#47112yes—
106D61—82no—
107C22×SD16—611no—
108C2×#108D6111yescharacteristic, complemented
109#419—611no—
110#418—611no—
111C2×#101—611no—
112C2×#100—611no—
113#405—611no—
114C61#197711yescharacteristic, complemented, Sylow
115C22×Q8—611no—
116C22×D4—611no—
117C2×SD16—614no—
118C2×SD16—1221no—
119C2×SD16—1221no—
120C2×SD16—1222no—
121C2×M16—611no—
122C2×M16C2×D6111yescharacteristic
123C2×M16C2×D6111yescharacteristic
124C22×C8C2×D6111yescharacteristic
125#117—611no—
126#108—22no—
127#103—1222no—
128#102—1222no—
129#101—1222no—
130#100—1222no—
131#97—1221no—
132C4×C8—1221no—
133C24—1221no—
134C2×Q8—612no—
135C2×Q8—1221no—
136C2×Q8—1221no—
137C2×Q8—1221no—
138C2×Q8—1221no—
139C2×Q8—1221no—
140C2×D4—612no—
141C2×D4—1221no—
142C2×D4—1221no—
143C2×D4—1221no—
144C2×D4—1221no—
145C2×D4—1221no—
146C22×C4—1221no—
147C22×C4C22×D6111yescharacteristic
148SD16—1224no—
149SD16—1224no—
150M16—21no—
151M16—21no—
152M16—21no—
153M16—21no—
154M16—612no—
155M16—1221no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—1221no—
159C2×C8C4×D6112yes—
160C2×C8D24411yescharacteristic
161C2×C8D24411yescharacteristic
162C2×C8C22⋊D6112yes—
163C4⋊C4—612no—
164C22⋊C4—1221no—
165C42—1221no—
166C23—1222no—
167C23—4882no—
168C23—2441no—
169C23—2441no—
170C23#1175822611yescharacteristic
171Q8—1222no—
172Q8—1222no—
173Q8—2441no—
174Q8—2441no—
175D4—1222no—
176D4—1222no—
177D4—2441no—
178D4—2441no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—2441no—
182C2×C4—2441no—
183C2×C4C2×C4×D6111yescharacteristic
184C2×C4C2×D24411yescharacteristic
185C2×C4D4×D6111yescharacteristic
186C2×C4D4×D6111yescharacteristic
187C2×C4#1175822611yescharacteristic
188C2×C4C2×C22⋊D6111yescharacteristic
189C8—41no—
190C8—41no—
191C8—1222no—
192C8#1175819812yes—
193C8#1175819812yes—
194C22—22no—
195C22—4882no—
196C22—4882no—
197C22—4882no—
198C22—2442no—
199C22#1451973911yescharacteristic
200C22#1451975211yescharacteristic
201C22#1451976611yescharacteristic
202C4—2442no—
203C4—2442no—
204C4C2×#1175819811yescharacteristic
205C4#1451973911yescharacteristic
206C4#1451975211yescharacteristic
207C4#1451977311yescharacteristic
208C2—21no—
209C2—21no—
210C2—4882no—
211C2#1683966311yescharacteristic
212C2#1684002612yes—
subgroupG/H
centerC22#14519752
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#108×C61C2
socleC22×C61#121
hypercenterC2×#108D61
hypocenterC61#1977
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#108

Complements

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

NH ≅ G/Ntype
2. #16839772C2semidirect
4. C2×#14519695C2semidirect
6. #16839717C2semidirect
7. C2×#108×C61C2semidirect
13. C2×#11758190C4semidirect
108. C2×#108D61semidirect
114. C61#1977semidirect