Finite Group Databasebeta

← #21456434

Subgroups — #21456434

Order 7808.

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

normal subgroups only

This group has 362 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#16840377C212yesmaximal, complemented
2#16840159C211yesmaximal, characteristic, complemented
3#16840145C211yesmaximal, characteristic, complemented
4#16840120C212yesmaximal, complemented
5#16840021C211yesmaximal, characteristic, complemented
6#16840012C211yesmaximal, characteristic
7#16839990C212yesmaximal, complemented
8#16839870C211yesmaximal, characteristic, complemented
9C4×#11758200C212yesmaximal, complemented
10#16839719C211yesmaximal, characteristic, complemented
11C61×#442C211yesmaximal, characteristic, complemented
12C2×Dic244C2211yescharacteristic
13C2×#11758200C2212yes—
14C2×#11758189C2211yescharacteristic
15C2×C8×D61C2211yescharacteristic
16#14519776C2212yes—
17#14519770—22no—
18#14519764C2212yes—
19#14519763—22no—
20#14519760—22no—
21#14519757C2212yes—
22#14519756—22no—
23#14519748C2212yes—
24C4×Dic122C2212yes—
25#14519734C2211yescharacteristic
26#14519709C2211yescharacteristic
27#14519708C2212yes—
28#14519702C2212yes—
29#14519700C2212yes—
30#14519698C2212yes—
31#14519687C2211yescharacteristic
32C4×#92418C2211yescharacteristic
33C8×Dic61C2211yescharacteristic
34C2×D8×C61C2211yescharacteristic
35C4×D4×C61C2212yes—
36#106×C61C2211yescharacteristic
37#102×C61C2212yes—
38#97×C61C2211yescharacteristic
39C2×D4×C61C2312yes—
40C22×C4×C61—22no—
41C2×C22⋊D61—22no—
42C2×C4×D61C2311yescharacteristic
43C2×Dic122—22no—
44C2×Dic122C2312yes—
45D8×C61—22no—
46C2×C8×C61C2311yescharacteristic
47C2×C8×C61C2311yescharacteristic
48C4⋊C4×C61C2312yes—
49C22⋊C4×C61—22no—
50C42×C61C2311yescharacteristic
51C22⋊Dic61—22no—
52C22⋊Dic61—22no—
53C22⋊Dic61—22no—
54#11758200—24no—
55#11758198—22no—
56#11758198D412yes—
57C4⋊Dic61—22no—
58C4⋊Dic61C2312yes—
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—
69C23×C61—22no—
70C22×D61C2×D411yescharacteristic
71D4×C61—22no—
72D4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—82no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61C2411yescharacteristic
77C22⋊D61—82no—
78C2×Dic61—22no—
79C2×Dic61—22no—
80C2×Dic61C2×D412yes—
81C2×Dic61C2×D411yescharacteristic
82C4×D61—21no—
83C4×D61—21no—
84Dic122—22no—
85Dic122—22no—
86Dic122—82no—
87C8×C61—21no—
88C8×C61#4112yes—
89#92418—21no—
90#92418#4112yes—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61C22×D411yescharacteristic
95C2×D61—21no—
96C2×D61—22no—
97C4×C61—22no—
98C4×C61—42no—
99C4×C61C2×#4111yescharacteristic
100C4×C61C2×#4111yescharacteristic
101Dic61—21no—
102Dic61—22no—
103Dic61—42no—
104Dic61—42no—
105#3173—611nomaximal, Sylow
106C2×C61—82no—
107C2×C61#53211yescharacteristic
108C2×C61#57712yes—
109D61—41no—
110#542—612no—
111#498—611no—
112#495—611no—
113#489—612no—
114#470—611no—
115#469—611no—
116#465—612no—
117#442D6111yescharacteristic, complemented
118#441—611no—
119C4×SD16—612no—
120#405—611no—
121C61#317311yescharacteristic, complemented, Sylow
122C2×Q16—611no—
123C2×SD16—612no—
124C2×D8C2×D6111yescharacteristic
125C2×M16—611no—
126C22×C8—611no—
127C4⋊Q8—612no—
128#126—1222no—
129#124—612no—
130#124—1222no—
131#123—1222no—
132C22⋊Q8—612no—
133C22⋊Q8—1222no—
134#121—612no—
135C4×Q8—612no—
136C4×D4C2×D6112yes—
137#117—611no—
138#106—611no—
139#106—612no—
140#106C2×D6111yescharacteristic
141#103—612no—
142#103—612no—
143#102—612no—
144#102C2×D6112yes—
145#97—611no—
146#97C2×D6111yescharacteristic
147C4×C8—611no—
148C4×C8—611no—
149C2×Q8—612no—
150C2×Q8—1222no—
151C2×D4—1222no—
152C2×D4C22×D6112yes—
153C22×C4—22no—
154C22×C4—611no—
155Q16—1222no—
156SD16—1224no—
157D8—22no—
158M16—1222no—
159C2×C8—611no—
160C2×C8—611no—
161C2×C8—1222no—
162C2×C8C22×D6111yescharacteristic
163C2×C8C22×D6111yescharacteristic
164C4⋊C4—612no—
165C4⋊C4—612no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C4⋊C4—1222no—
169C4⋊C4C22×D6112yes—
170C22⋊C4—22no—
171C22⋊C4—612no—
172C22⋊C4—1222no—
173C22⋊C4—1222no—
174C22⋊C4—1222no—
175C22⋊C4—1222no—
176C42—611no—
177C42—1222no—
178C42C22×D6111yescharacteristic
179C23—22no—
180C23—611no—
181Q8—1222no—
182Q8—1222no—
183Q8—4882no—
184D4—22no—
185D4—22no—
186D4—4882no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—612no—
190C2×C4—611no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1222no—
194C2×C4—1222no—
195C2×C4D4×D6112yes—
196C2×C4C23×D6111yescharacteristic
197C8—21no—
198C8—612no—
199C8—1221no—
200C8#1175822212yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—1221no—
205C22—1222no—
206C22C2×D4×D6111yescharacteristic
207C4—22no—
208C4—42no—
209C4—1221no—
210C4—1222no—
211C4—2442no—
212C4—2442no—
213C4#41×D6111yescharacteristic
214C4C2×#1175822211yescharacteristic
215C2—82no—
216C2—2441no—
217C2#1684030911yescharacteristic
218C2#1684057212yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3173
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16840377C2semidirect
2. #16840159C2semidirect
3. #16840145C2semidirect
4. #16840120C2semidirect
5. #16840021C2semidirect
7. #16839990C2semidirect
8. #16839870C2semidirect
9. C4×#11758200C2semidirect
10. #16839719C2semidirect
11. C61×#442C2semidirect
117. #442D61semidirect
121. C61#3173semidirect