Finite Group Databasebeta

← #21456476

Subgroups — #21456476

Order 7808.

338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840370C212yesmaximal
2#16840162C211yesmaximal, characteristic, complemented
3#16840140C211yesmaximal, characteristic, complemented
4#16840129C212yesmaximal, complemented
5#16840021C211yesmaximal, characteristic
6#16840017C211yesmaximal, characteristic
7#16840002C212yesmaximal
8#16839870C211yesmaximal, characteristic, complemented
9C4×#11758202C212yesmaximal, complemented
10#16839719C211yesmaximal, characteristic
11C61×#441C211yesmaximal, characteristic, complemented
12C2×Dic244C2211yescharacteristic
13C2×#11758202C2212yes—
14C2×#11758189C2211yescharacteristic
15C2×C8×D61C2211yescharacteristic
16#14519775C2212yes—
17#14519772—22no—
18#14519771—22no—
19#14519769—22no—
20#14519768C2212yes—
21#14519767—22no—
22#14519757C2212yes—
23#14519753C2212yes—
24C4×Dic122C2212yes—
25#14519734C2211yescharacteristic
26#14519710C2212yes—
27#14519709C2211yescharacteristic
28#14519702C2212yes—
29#14519701C2212yes—
30#14519700C2212yes—
31#14519687C2211yescharacteristic
32C4×#92418C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×Q16×C61C2211yescharacteristic
35C4×Q8×C61C2212yes—
36#106×C61C2211yescharacteristic
37#103×C61C2212yes—
38#97×C61C2211yescharacteristic
39C2×Q8×C61C2312yes—
40C2×C4×D61C2311yescharacteristic
41C2×Dic122C2312yes—
42Q16×C61—22no—
43C2×C8×C61C2311yescharacteristic
44C2×C8×C61C2311yescharacteristic
45C4⋊C4×C61—22no—
46C4⋊C4×C61C2312yes—
47C42×C61—22no—
48C42×C61C2311yescharacteristic
49#11758202—24no—
50#11758198—22no—
51#11758198—22no—
52#11758198D412yes—
53C4⋊Dic61—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61C2312yes—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60#11758196—22no—
61#11758196D412yes—
62C4×Dic61—22no—
63C4×Dic61C2311yescharacteristic
64C2×#92418C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66Dic244—22no—
67#11758189—22no—
68C8×D61—22no—
69C22×D61C2×D411yescharacteristic
70Q8×C61—22no—
71Q8×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61C2×D412yes—
75C2×C4×C61C2411yescharacteristic
76C2×Dic61—22no—
77C2×Dic61—22no—
78C2×Dic61C2×D412yes—
79C2×Dic61C2×D411yescharacteristic
80C4×D61—21no—
81C4×D61—21no—
82Dic122—22no—
83Dic122—22no—
84C8×C61—21no—
85C8×C61#4112yes—
86#92418—21no—
87#92418#4112yes—
88C22×C61C22×D411yescharacteristic
89C2×D61—21no—
90C2×D61—22no—
91C4×C61—22no—
92C4×C61—42no—
93C4×C61—42no—
94C4×C61C2×#4111yescharacteristic
95C4×C61C2×#4111yescharacteristic
96Dic61—21no—
97Dic61—22no—
98Dic61—42no—
99Dic61—42no—
100#3177—611nomaximal, Sylow
101C2×C61#53211yescharacteristic
102C2×C61#57812yes—
103D61—41no—
104#541—612no—
105#499—611no—
106#494—611no—
107#491—612no—
108#470—611no—
109#470—611no—
110#467—612no—
111#441—611no—
112#441D6111yescharacteristic, complemented
113C4×Q16—612no—
114#405—611no—
115C61#317711yescharacteristic, complemented, Sylow
116C2×Q16—612no—
117C2×Q16—611no—
118C2×Q16C2×D6111yescharacteristic
119C2×M16—611no—
120C22×C8—611no—
121C4⋊Q8—612no—
122#126—1222no—
123#126—1222no—
124#125—612no—
125#125—1222no—
126#125—1222no—
127C22⋊Q8—612no—
128C22⋊Q8—612no—
129C4×Q8—612no—
130C4×Q8C2×D6112yes—
131#117—611no—
132#107—612no—
133#106—611no—
134#106C2×D6111yescharacteristic
135#103—612no—
136#103—612no—
137#103—612no—
138#103C2×D6112yes—
139#97—611no—
140#97C2×D6111yescharacteristic
141C4×C8—611no—
142C4×C8—611no—
143C2×Q8—612no—
144C2×Q8C22×D6112yes—
145C22×C4—611no—
146Q16—22no—
147Q16—1224no—
148Q16—1222no—
149M16—1222no—
150C2×C8—611no—
151C2×C8—611no—
152C2×C8—1222no—
153C2×C8C22×D6111yescharacteristic
154C2×C8C22×D6111yescharacteristic
155C4⋊C4—22no—
156C4⋊C4—612no—
157C4⋊C4—612no—
158C4⋊C4—1222no—
159C4⋊C4—1222no—
160C4⋊C4—1222no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4C22×D6112yes—
166C22⋊C4—612no—
167C22⋊C4—1222no—
168C22⋊C4—1222no—
169C42—22no—
170C42—611no—
171C42—1222no—
172C42C22×D6111yescharacteristic
173C23—611no—
174Q8—22no—
175Q8—22no—
176Q8—1222no—
177Q8—1222no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—612no—
181C2×C4—611no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4D4×D6112yes—
187C2×C4C23×D6111yescharacteristic
188C8—21no—
189C8—612no—
190C8—1221no—
191C8#1175822212yes—
192C22—1221no—
193C22—1222no—
194C22C2×D4×D6111yescharacteristic
195C4—22no—
196C4—42no—
197C4—42no—
198C4—1221no—
199C4—1222no—
200C4—2442no—
201C4—2442no—
202C4#41×D6111yescharacteristic
203C4C2×#1175822211yescharacteristic
204C2—2441no—
205C2#1684030911yescharacteristic
206C2#1684057812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3177
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
2. #16840162C2semidirect
3. #16840140C2semidirect
4. #16840129C2semidirect
8. #16839870C2semidirect
9. C4×#11758202C2semidirect
11. C61×#441C2semidirect
112. #441D61semidirect
115. C61#3177semidirect