Finite Group Databasebeta

← #21456896

Subgroups — #21456896

Order 7808.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840338C211yesmaximal, characteristic
2#16840154C211yesmaximal, characteristic, complemented
3#16840141C211yesmaximal, characteristic, complemented
4#16840132C211yesmaximal, characteristic, complemented
5#16840119C211yesmaximal, characteristic, complemented
6#16839984C212yesmaximal, complemented
7#16839972C212yesmaximal, complemented
8#16839922C212yesmaximal
9#16839917C212yesmaximal, complemented
10#16839823C211yesmaximal, characteristic, complemented
11C61×#541C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14C2×#11758202C2212yes—
15C2×#11758202C2212yes—
16C2×#11758202C2212yes—
17C2×#11758201C2212yes—
18#14519777C2211yescharacteristic
19#14519777C2211yescharacteristic
20#14519765C2211yescharacteristic
21#14519765C2211yescharacteristic
22#14519761—22no—
23#14519757—22no—
24C4⋊#92418C2212yes—
25#14519700C2212yes—
26#14519700C2212yes—
27#14519700C2212yes—
28#14519697C2212yes—
29C22⋊#92418C2212yes—
30#14519688C2211yescharacteristic
31C4×#92418C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33#126×C61—22no—
34#125×C61—22no—
35#125×C61C2211yescharacteristic
36C22⋊Q8×C61C2212yes—
37C4×Q8×C61C2212yes—
38#117×C61C2211yescharacteristic
39C2×Q8×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—21no—
42C22×Dic61—21no—
43#11758222—42no—
44C2×D244C2311yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122—21no—
47C2×Dic122—42no—
48C2×Dic122C2311yescharacteristic
49C2×Dic122C2311yescharacteristic
50C2×Dic122C2311yescharacteristic
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61—22no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61D412yes—
56C4⋊C4×C61C2312yes—
57C22⋊C4×C61—22no—
58C22⋊C4×C61D412yes—
59C42×C61—22no—
60C42×C61C2311yescharacteristic
61C42×C61C2311yescharacteristic
62#11758202—42no—
63#11758202—42no—
64#11758202—42no—
65#11758201—42no—
66#11758198—22no—
67#11758198—22no—
68C4⋊Dic61—22no—
69C4⋊Dic61—22no—
70C2×#92418C2312yes—
71C2×#92418C2312yes—
72C23×C61C2×D411yescharacteristic
73C22×D61—21no—
74Q8×C61—22no—
75Q8×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61C2×D412yes—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—42no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—42no—
88D244—22no—
89C4×D61—42no—
90Dic122—22no—
91Dic122—22no—
92Dic122—22no—
93Dic122—42no—
94#92418—22no—
95#92418—22no—
96C22×C61—21no—
97C22×C61—22no—
98C22×C61C22×D411yescharacteristic
99C2×D61—41no—
100C2×D61—42no—
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—22no—
104C4×C61—42no—
105C4×C61—42no—
106C4×C61H(5,𝔽2)12yes—
107Dic61—41no—
108Dic61—41no—
109Dic61—41no—
110#3223—611nomaximal, Sylow
111C2×C61—41no—
112C2×C61#53511yescharacteristic
113C2×C61#57812yes—
114D61—81no—
115#541D6111yescharacteristic, complemented
116#536—611no—
117#497—611no—
118#494—611no—
119#491—611no—
120#488—611no—
121#464—612no—
122#462—612no—
123#452—612no—
124#451—612no—
125#433—611no—
126C61#322311yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8—611no—
129C2×Q16—612no—
130C2×Q16—612no—
131C2×Q16—612no—
132C2×SD16—612no—
133C4⋊Q8—611no—
134C4⋊Q8—611no—
135C4⋊Q8C2×D6111yescharacteristic
136#126—22no—
137#125—22no—
138#125C2×D6111yescharacteristic
139#124—611no—
140#124—611no—
141#123—1222no—
142C22⋊Q8—1222no—
143C22⋊Q8C2×D6112yes—
144C4×Q8C2×D6112yes—
145#117C2×D6111yescharacteristic
146C4⋊C8—612no—
147#103—612no—
148#103—612no—
149#103—612no—
150#102—612no—
151C22⋊C8—612no—
152#97—611no—
153C4×C8—611no—
154#41—2442no—
155C2×Q8—611no—
156C2×Q8—611no—
157C2×Q8—611no—
158C2×Q8—1221no—
159C2×Q8—2442no—
160C2×Q8C22×D6112yes—
161C2×D4—611no—
162C2×D4—1221no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4C22×D6111yescharacteristic
166Q16—2442no—
167Q16—2442no—
168Q16—2442no—
169SD16—2442no—
170C2×C8—612no—
171C2×C8—612no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4C22⋊D6112yes—
179C4⋊C4C22×D6112yes—
180C22⋊C4—22no—
181C22⋊C4—1222no—
182C22⋊C4—1222no—
183C22⋊C4C22⋊D6112yes—
184C42—22no—
185C42C22×D6111yescharacteristic
186C42C22×D6111yescharacteristic
187C23—1221no—
188C23C2×C22⋊D6111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—1222no—
192Q8—1222no—
193Q8—1222no—
194Q8—2442no—
195D4—1222no—
196D4—2442no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4C2×C22⋊D6112yes—
206C2×C4C2×C22⋊D6112yes—
207C2×C4C2×C22⋊D6111yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—1222no—
210C8—1222no—
211C22—22no—
212C22—21no—
213C22—2442no—
214C22—2441no—
215C22C22×C22⋊D6111yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—42no—
220C4—42no—
221C4—2441no—
222C4—2441no—
223C4—2441no—
224C4#1451982312yes—
225C2—41no—
226C2—4881no—
227C2#1684032611yescharacteristic
228C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#541C2
socleC22×C61C22×D4
hypercenter#541D61
hypocenterC61#3223
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #16840154C2semidirect
3. #16840141C2semidirect
4. #16840132C2semidirect
5. #16840119C2semidirect
6. #16839984C2semidirect
7. #16839972C2semidirect
9. #16839917C2semidirect
10. #16839823C2semidirect
11. C61×#541C2semidirect
115. #541D61semidirect
126. C61#3223semidirect