Finite Group Databasebeta

← #21455471

Subgroups — #21455471

Order 7808.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#11758202C211yesmaximal, characteristic, complemented
2C2×#14519784C211yesmaximal, characteristic
3#16840333C211yesmaximal, characteristic
4#16840018C214yesmaximal, complemented
5#16840001C214yesmaximal, complemented
6#16839798C211yesmaximal, characteristic, complemented
7#16839771C211yesmaximal, characteristic, complemented
8#16839770C211yesmaximal, characteristic, complemented
9C61×#536C211yesmaximal, characteristic
10C22×Dic122C2211yescharacteristic
11C2×#11758202—24no—
12C2×#11758202C2212yes—
13C2×#11758202C2212yes—
14#14519784—24no—
15C2×#11758194C2212yes—
16C2×#11758194C2211yescharacteristic
17C22×#92418C2212yes—
18C22×#92418C2211yescharacteristic
19#14519775—21no—
20#14519764—21no—
21#14519758—22no—
22#14519756C2214yes—
23#14519736C2211yescharacteristic
24#14519710C2212yes—
25#14519708C2212yes—
26#14519701C2214yes—
27#14519700C2214yes—
28C2×#41×C61C2211yescharacteristic
29C22×Q8×C61C2211yescharacteristic
30C4⋊Q8×C61—21no—
31#124×C61—21no—
32#123×C61—22no—
33C22⋊Q8×C61C2214yes—
34#117×C61C2211yescharacteristic
35#41×C61—22no—
36#41×C61—22no—
37C2×Q8×C61—21no—
38C2×Q8×C61—22no—
39C2×Q8×C61—22no—
40C2×Q8×C61D411yescharacteristic
41C2×Q8×C61C2312yes—
42C2×D4×C61D412yes—
43C2×D4×C61D411yescharacteristic
44C22×C4×C61—21no—
45C22×C4×C61C2312yes—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61—21no—
48C2×Dic122—22no—
49C2×Dic122—22no—
50C2×Dic122—21no—
51C2×Dic122C2312yes—
52C4⋊C4×C61—24no—
53C4⋊C4×C61C2312yes—
54C22⋊C4×C61—21no—
55C22⋊C4×C61—24no—
56C42×C61—21no—
57C22⋊Dic61—21no—
58C22⋊Dic61—24no—
59#11758202—24no—
60#11758202—24no—
61C4⋊Dic61C2312yes—
62#11758196—24no—
63C4×Dic61—21no—
64#11758194—22no—
65#11758194—24no—
66C2×#92418—24no—
67C2×#92418D414yes—
68C2×#92418C2312yes—
69C2×#92418C2311yescharacteristic
70C2×#92418C2311yescharacteristic
71C23×C61C2×D412yes—
72C23×C61C2×D411yescharacteristic
73Q8×C61—22no—
74Q8×C61—22no—
75Q8×C61—22no—
76Q8×C61—42no—
77D4×C61—24no—
78D4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—42no—
84C2×C4×C61C2×D412yes—
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D412yes—
87C2×C4×C61#4112yes—
88C2×C4×C61C2411yescharacteristic
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—42no—
92Dic122—22no—
93Dic122—22no—
94Dic122—42no—
95#92418—22no—
96#92418C2×D412yes—
97#92418C2×D412yes—
98C22×C61—22no—
99C22×C61—22no—
100C22×C61—24no—
101C22×C61#12112yes—
102C22×C61C22×D411yescharacteristic
103C4×C61—22no—
104C4×C61—42no—
105C4×C61—42no—
106C4×C61#12112yes—
107C4×C61C22×D411yescharacteristic
108C4×C61C2×#4111yescharacteristic
109Dic61—42no—
110Dic61—42no—
111#3059—611nomaximal, Sylow
112C2×C61—22no—
113C2×C61—42no—
114C2×C61C2×#12111yescharacteristic
115C2×C61#57812yes—
116C22×Q16—611no—
117C2×#131—611no—
118#536—611no—
119#536D6111yescharacteristic
120#470—614no—
121#467—614no—
122#427—611no—
123#419—611no—
124#419—611no—
125C61#305911yescharacteristic, complemented, Sylow
126C2×#41C2×D6111yescharacteristic
127C22×Q8—611no—
128C22×Q8C2×D6111yescharacteristic
129C2×Q16—612no—
130C2×Q16—612no—
131C2×Q16—1224no—
132#131—1224no—
133C2×M16—611no—
134C2×M16—612no—
135C22×C8—611no—
136C22×C8—612no—
137C4⋊Q8—21no—
138C4⋊Q8—1221no—
139#124—21no—
140#124—1221no—
141#123—22no—
142#123—1222no—
143C22⋊Q8—614no—
144C22⋊Q8C2×D6114yes—
145#117—611no—
146#117C2×D6111yescharacteristic
147#107—612no—
148#106—612no—
149#103—614no—
150#103—614no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—612no—
157C2×Q8—1221no—
158C2×Q8—1222no—
159C2×Q8—1222no—
160C2×Q8C22⋊D6111yescharacteristic
161C2×Q8C22×D6112yes—
162C2×D4C22⋊D6112yes—
163C2×D4C22⋊D6111yescharacteristic
164C22×C4—21no—
165C22×C4—1221no—
166C22×C4C22×D6112yes—
167C22×C4C22×D6111yescharacteristic
168Q16—1224no—
169Q16—1224no—
170M16—1224no—
171M16—1222no—
172C2×C8—614no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—612no—
176C2×C8—1224no—
177C4⋊C4—24no—
178C4⋊C4—612no—
179C4⋊C4—1224no—
180C4⋊C4C22×D6112yes—
181C22⋊C4—21no—
182C22⋊C4—24no—
183C22⋊C4—1221no—
184C22⋊C4—1224no—
185C42—21no—
186C42—1221no—
187C23C2×C22⋊D6112yes—
188C23C2×C22⋊D6111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—1222no—
194Q8—1222no—
195Q8—2442no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—2442no—
206C2×C4D4×D6112yes—
207C2×C4#1175822412yes—
208C2×C4C2×C22⋊D6112yes—
209C2×C4C2×C22⋊D6111yescharacteristic
210C2×C4C23×D6111yescharacteristic
211C8—612no—
212C8—612no—
213C8—1222no—
214C22—22no—
215C22—22no—
216C22—24no—
217C22#1451974912yes—
218C22C22×C22⋊D6111yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—2442no—
223C4—2442no—
224C4#1451974912yes—
225C4C2×D4×D6111yescharacteristic
226C4C2×#1175822411yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#1451974911yescharacteristic
230C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC22×C61C22×D4
hypercenter#536D61
hypocenterC61#3059
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#11758202C2semidirect
4. #16840018C2semidirect
5. #16840001C2semidirect
6. #16839798C2semidirect
7. #16839771C2semidirect
8. #16839770C2semidirect
125. C61#3059semidirect