Finite Group Databasebeta

← #21456561

Subgroups — #21456561

Order 7808.

358 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 119 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#16840316C212yesmaximal
2#16840159C211yesmaximal, characteristic, complemented
3#16840140C211yesmaximal, characteristic, complemented
4#16840111C212yesmaximal, complemented
5#16840021C211yesmaximal, characteristic
6#16840019C212yesmaximal
7#16840017C211yesmaximal, characteristic
8#16839870C211yesmaximal, characteristic, complemented
9#16839867C212yesmaximal, complemented
10#16839714C211yesmaximal, characteristic
11C61×#441C211yesmaximal, characteristic, complemented
12C2×Dic244C2211yescharacteristic
13C2×#11758202C2212yes—
14C2×#11758189C2211yescharacteristic
15C2×#11758189C2211yescharacteristic
16#14519776C2212yes—
17#14519775C2212yes—
18#14519767—22no—
19#14519757C2212yes—
20#14519755—22no—
21#14519753C2212yes—
22C4×Dic122—22no—
23C4×Dic122C2212yes—
24#14519734—22no—
25C42×D61C2211yescharacteristic
26#14519709C2211yescharacteristic
27#14519708C2212yes—
28#14519702C2212yes—
29#14519701C2212yes—
30#14519700C2212yes—
31#14519688C2211yescharacteristic
32C8×Dic61C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×Q16×C61C2211yescharacteristic
35C4×Q8×C61C2212yes—
36#106×C61C2211yescharacteristic
37#103×C61C2212yes—
38#97×C61C2211yescharacteristic
39C2×Q8×C61C2312yes—
40C2×C4×D61D412yes—
41C2×C4×D61C2311yescharacteristic
42C2×Dic122—22no—
43C2×Dic122C2312yes—
44Q16×C61—22no—
45C2×C8×C61C2311yescharacteristic
46C2×C8×C61C2311yescharacteristic
47C4⋊C4×C61—22no—
48C4⋊C4×C61C2312yes—
49C42×C61—22no—
50C42×C61C2311yescharacteristic
51#11758202—24no—
52#11758198—22no—
53#11758198—22no—
54C4⋊Dic61—22no—
55C4⋊Dic61C2312yes—
56#11758196—22no—
57#11758196—22no—
58#11758196—22no—
59#11758196—22no—
60#11758196—22no—
61C4×Dic61—22no—
62C4×Dic61D412yes—
63C4×Dic61C2311yescharacteristic
64C2×#92418C2311yescharacteristic
65C2×#92418C2311yescharacteristic
66Dic244—22no—
67#11758189—22no—
68#11758189—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×D411yescharacteristic
79C2×Dic61C2×D412yes—
80C4×D61—21no—
81C4×D61—21no—
82C4×D61—24no—
83Dic122—22no—
84Dic122—22no—
85Dic122—44no—
86C8×C61—21no—
87C8×C61#4112yes—
88#92418—21no—
89#92418#4112yes—
90C22×C61C22×D411yescharacteristic
91C2×D61—21no—
92C2×D61—22no—
93C4×C61—22no—
94C4×C61—42no—
95C4×C61—42no—
96C4×C61C2×#4111yescharacteristic
97C4×C61C2×#4111yescharacteristic
98Dic61—21no—
99Dic61—42no—
100Dic61—42no—
101Dic61#13714yes—
102#3185—611nomaximal, Sylow
103C2×C61#53211yescharacteristic
104C2×C61C2×#13712yes—
105D61—41no—
106#533—612no—
107#498—611no—
108#494—611no—
109#487—612no—
110#470—611no—
111#470—611no—
112#470—612no—
113#441—612no—
114#441—611no—
115#441D6111yescharacteristic, complemented
116C4×M16—611no—
117C61#318511yescharacteristic, complemented, Sylow
118C2×Q16—612no—
119C2×Q16—611no—
120C2×Q16C2×D6111yescharacteristic
121C2×M16—611no—
122C2×M16—611no—
123C4⋊Q8—612no—
124C4⋊Q8—612no—
125#125—1222no—
126C22⋊Q8—612no—
127C22⋊Q8—612no—
128C22⋊Q8—1222no—
129C4×Q8—612no—
130C4×Q8—1222no—
131C4×Q8C2×D6112yes—
132#117—1222no—
133C2×C42—611no—
134#106—611no—
135#106—612no—
136#106C2×D6111yescharacteristic
137#103—612no—
138#103—612no—
139#103—612no—
140#103C2×D6112yes—
141#97—611no—
142#97C2×D6111yescharacteristic
143C4×C8—611no—
144C4×C8—611no—
145C2×Q8—612no—
146C2×Q8—1222no—
147C2×Q8C22×D6112yes—
148C22×C4—612no—
149C22×C4—611no—
150Q16—22no—
151Q16—1224no—
152Q16—1222no—
153M16—1222no—
154M16—1222no—
155C2×C8—611no—
156C2×C8—611no—
157C2×C8C22×D6111yescharacteristic
158C2×C8C22×D6111yescharacteristic
159C4⋊C4—22no—
160C4⋊C4—612no—
161C4⋊C4—1222no—
162C4⋊C4—1222no—
163C4⋊C4—1222no—
164C4⋊C4—1222no—
165C4⋊C4—1222no—
166C4⋊C4—1222no—
167C4⋊C4C22×D6112yes—
168C22⋊C4—1222no—
169C22⋊C4—1222no—
170C42—22no—
171C42—612no—
172C42—611no—
173C42—1222no—
174C42C22×D6111yescharacteristic
175C23—611no—
176Q8—22no—
177Q8—22no—
178Q8—1222no—
179Q8—1222no—
180Q8—2444no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—612no—
184C2×C4—611no—
185C2×C4—1224no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4D4×D6112yes—
191C2×C4C23×D6111yescharacteristic
192C8—21no—
193C8—612no—
194C8—1221no—
195C8#1175822212yes—
196C22—1222no—
197C22—1221no—
198C22C2×D4×D6111yescharacteristic
199C4—22no—
200C4—42no—
201C4—42no—
202C4—614no—
203C4—1221no—
204C4—2442no—
205C4—2442no—
206C4#41×D6111yescharacteristic
207C4C2×#1175822211yescharacteristic
208C2—2441no—
209C2#1684030911yescharacteristic
210C2#137×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#441C2
socleC22×C61C22×D4
hypercenter#441D61
hypocenterC61#3185
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. #16840159C2semidirect
3. #16840140C2semidirect
4. #16840111C2semidirect
8. #16839870C2semidirect
9. #16839867C2semidirect
11. C61×#441C2semidirect
115. #441D61semidirect
117. C61#3185semidirect