Finite Group Databasebeta

← #21456730

Subgroups — #21456730

Order 7808.

402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840341C212yesmaximal, complemented
2#16840094C212yesmaximal, complemented
3#16840079C212yesmaximal, complemented
4#16840020C211yesmaximal, characteristic, complemented
5#16839989C212yesmaximal, complemented
6#16839925C212yesmaximal, complemented
7#16839904C212yesmaximal, complemented
8#16839730C211yesmaximal, characteristic, complemented
9C61×#469C211yesmaximal, characteristic, complemented
10C2×#11758222C2211yescharacteristic
11C2×#11758224C2212yes—
12C2×Dic244C2211yescharacteristic
13C2×#11758200C2212yes—
14C22×#92418C2211yescharacteristic
15#14519757C2212yes—
16#14519756C2212yes—
17#14519754—22no—
18#14519750—22no—
19#14519749—22no—
20#14519748—22no—
21#14519748C2212yes—
22C4⋊C4×D61C2212yes—
23#14519709C2211yescharacteristic
24#14519708C2212yes—
25#14519702C2212yes—
26#14519700C2212yes—
27#14519698C2212yes—
28#14519689C2212yes—
29#14519689C2212yes—
30C2×D8×C61C2211yescharacteristic
31C2×M16×C61C2211yescharacteristic
32#121×C61C2212yes—
33#106×C61C2211yescharacteristic
34#102×C61C2212yes—
35C2×D4×C61—22no—
36C2×D4×C61C2312yes—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—22no—
39C2×C22⋊D61—22no—
40C2×C22⋊D61D412yes—
41C22×Dic61—22no—
42#11758224—42no—
43#11758224—42no—
44#11758222—41no—
45#11758222—41no—
46C2×D244D411yescharacteristic
47C2×C4×D61—22no—
48C2×C4×D61C2312yes—
49C2×Dic122D411yescharacteristic
50C2×Dic122C2312yes—
51D8×C61—41no—
52M16×C61—41no—
53C2×C8×C61C2311yescharacteristic
54C2×C8×C61C2311yescharacteristic
55C4⋊C4×C61C2312yes—
56C22⋊C4×C61—22no—
57C22⋊Dic61—22no—
58C22⋊Dic61—22no—
59#11758200—42no—
60#11758198—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61C2312yes—
63#11758196—22no—
64#11758196—22no—
65C2×#92418—41no—
66C2×#92418C2312yes—
67Dic244—41no—
68C23×C61—22no—
69C23×C61C2×D411yescharacteristic
70C22×D61C2×D412yes—
71D4×C61—22no—
72D4×C61—22no—
73D4×C61—82no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2411yescharacteristic
79C22⋊D61—42no—
80C22⋊D61—44no—
81C22⋊D61—82no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—44no—
85C2×Dic61C2×D412yes—
86D244—41no—
87C4×D61—22no—
88C4×D61—22no—
89C4×D61—82no—
90Dic122—22no—
91Dic122—22no—
92Dic122—41no—
93C8×C61—21no—
94C8×C61—21no—
95#92418—22no—
96C22×C61—21no—
97C22×C61—22no—
98C22×C61—42no—
99C22×C61—42no—
100C22×C61—42no—
101C22×C61C22×D411yescharacteristic
102C2×D61—22no—
103C2×D61—22no—
104C2×D61—22no—
105C4×C61—21no—
106C4×C61—42no—
107C4×C61H(5,𝔽2)11yescharacteristic
108C4×C61H(5,𝔽2)11yescharacteristic
109Dic61—22no—
110Dic61—42no—
111Dic61—42no—
112#3204—611nomaximal, Sylow
113C2×C61—41no—
114C2×C61—82no—
115C2×C61#53411yescharacteristic
116C2×C61#57712yes—
117D61—42no—
118#537—612no—
119#483—612no—
120#481—612no—
121#470—611no—
122#469D6111yescharacteristic, complemented
123#465—612no—
124#452—612no—
125#449—612no—
126#408—611no—
127C61#320411yescharacteristic, complemented, Sylow
128C2×#41—611no—
129C2×#41—612no—
130C2×Q16—611no—
131C2×SD16—612no—
132C2×D8C2×D6111yescharacteristic
133C2×M16C2×D6111yescharacteristic
134C22×C8—611no—
135C22⋊Q8—612no—
136C22⋊Q8—612no—
137C22⋊Q8—1222no—
138#121—612no—
139#121—1222no—
140#121—1222no—
141#121—1222no—
142#121C2×D6112yes—
143C2×C4⋊C4—612no—
144#106—611no—
145#106—612no—
146#106C2×D6111yescharacteristic
147#103—612no—
148#103—612no—
149#102—612no—
150#102C2×D6112yes—
151C22⋊C8—612no—
152C22⋊C8—612no—
153#41—2441no—
154#41—2441no—
155#41—2442no—
156#41—2442no—
157C2×Q8—611no—
158C2×Q8—612no—
159C2×D4—22no—
160C2×D4—612no—
161C2×D4—611no—
162C2×D4—1222no—
163C2×D4—1222no—
164C2×D4C22×D6112yes—
165C22×C4—612no—
166C22×C4—1222no—
167C22×C4—1222no—
168C22×C4C22×D6111yescharacteristic
169Q16—2441no—
170SD16—2442no—
171D8—41no—
172M16—41no—
173C2×C8—612no—
174C2×C8—2441no—
175C2×C8C22×D6111yescharacteristic
176C2×C8C22×D6111yescharacteristic
177C4⋊C4—612no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C4⋊C4—1222no—
181C4⋊C4C22×D6112yes—
182C22⋊C4—22no—
183C22⋊C4—1222no—
184C22⋊C4—1222no—
185C22⋊C4—1222no—
186C23—22no—
187C23—612no—
188C23D4×D6111yescharacteristic
189Q8—1222no—
190Q8—1222no—
191Q8—2441no—
192D4—22no—
193D4—22no—
194D4—82no—
195D4—4882no—
196D4—2441no—
197D4—2442no—
198D4—2444no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—612no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—4882no—
208C2×C4—2444no—
209C2×C4D4×D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—21no—
212C8—21no—
213C8—1222no—
214C22—22no—
215C22—21no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—1222no—
220C22—1222no—
221C22—1222no—
222C22C2×D4×D6111yescharacteristic
223C4—21no—
224C4—42no—
225C4—1222no—
226C4—2442no—
227C4—2442no—
228C4#1451982211yescharacteristic
229C4#1451982311yescharacteristic
230C2—41no—
231C2—82no—
232C2—2442no—
233C2#1684032011yescharacteristic
234C2#1684057212yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#469C2
socleC22×C61C22×D4
hypercenter#469D61
hypocenterC61#3204
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #16840341C2semidirect
2. #16840094C2semidirect
3. #16840079C2semidirect
4. #16840020C2semidirect
5. #16839989C2semidirect
6. #16839925C2semidirect
7. #16839904C2semidirect
8. #16839730C2semidirect
9. C61×#469C2semidirect
122. #469D61semidirect
127. C61#3204semidirect