Finite Group Databasebeta

← #21445760

Subgroups — #21445760

Order 7808.

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

normal subgroups only

This group has 612 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
1C22×#11758222C211yesmaximal, characteristic
2C2×#14519702C212yesmaximal, complemented
3C2×#14519699C212yesmaximal, complemented
4#16839622C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×C61C211yesmaximal, characteristic, complemented
6C2×#11758222—22no—
7C2×#11758222—24no—
8C2×#11758222—24no—
9C2×#11758222C414yescomplemented
10C22×Dic122C2211yescharacteristic
11C22×D244C2211yescharacteristic
12C22×C22⋊D61—21no—
13C22×C4×D61—21no—
14C2×C4⋊Dic61C2212yes—
15C2×C22⋊Dic61—21no—
16#14519702—24no—
17#14519699—24no—
18#14519684—21no—
19C23×C4×C61C2211yescharacteristic
20C22×C8×C61C2212yes—
21C22⋊C8×C61—22no—
22C24×C61D411yescharacteristic
23C23×D61—21no—
24C22×C4×C61—22no—
25C22×C4×C61—22no—
26C22×C4×C61C2×C412yes—
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D412yes—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—28no—
31C2×C22⋊D61—24no—
32C22×Dic61—21no—
33C22×Dic61—22no—
34#11758222—216no—
35#11758222—28no—
36#11758222—28no—
37C2×D244—22no—
38C2×D244—21no—
39C2×D244C2×C412yes—
40C2×D244D414yes—
41C2×C4×D61—28no—
42C2×C4×D61—24no—
43C2×Dic122—22no—
44C2×Dic122—21no—
45C2×Dic122C2×C412yes—
46C2×Dic122D414yes—
47C2×C8×C61—22no—
48C2×C8×C61—22no—
49C2×C8×C61—22no—
50C22⋊Dic61—42no—
51C4⋊Dic61—22no—
52C4⋊Dic61—22no—
53C23×C61—22no—
54C23×C61—22no—
55C23×C61—21no—
56C23×C61—21no—
57C23×C61C22⋊C412yes—
58C23×C61C2×D411yescharacteristic
59C22×D61—22no—
60C22×D61—24no—
61C22×D61—42no—
62C22×D61—41no—
63C22×D61—41no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—22no—
67C2×C4×C61—24no—
68C2×C4×C61C22⋊C412yes—
69C2×C4×C61C22×C411yescharacteristic
70C2×C4×C61C2×D412yes—
71C2×C4×C61C2×D412yes—
72C2×C4×C61C2×D411yescharacteristic
73C22⋊D61—216no—
74C2×Dic61—22no—
75C2×Dic61—24no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—42no—
79D244—22no—
80D244—24no—
81D244C22⋊C414yescomplemented
82C4×D61—216no—
83Dic122—22no—
84Dic122—24no—
85Dic122C22⋊C414yescomplemented
86C8×C61—42no—
87C22×C61—22no—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61C2×C22⋊C411yescharacteristic
93C22×C61#12012yes—
94C22×C61#13512yes—
95C22×C61AGL(1,ℤ/8)11yescharacteristic
96C22×C61#13711yescharacteristic
97C2×D61—24no—
98C2×D61—42no—
99C2×D61—42no—
100C2×D61—44no—
101C2×D61—44no—
102C4×C61—22no—
103C4×C61C2×C22⋊C411yescharacteristic
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61#12012yes—
106Dic61—24no—
107Dic61—82no—
108#1788—611nomaximal, Sylow
109C2×C61—42no—
110C2×C61#37911yescharacteristic
111C2×C61#41611yescharacteristic
112C2×C61#41711yescharacteristic
113C2×C61#44912yes—
114C2×C61#45212yes—
115D61—44no—
116C22×#41—611no—
117C2×#103—612no—
118C2×#102—612no—
119C2×C22⋊C8D6111yescharacteristic, complemented
120#380—611no—
121C61#178811yescharacteristic, complemented, Sylow
122C2×#41—614no—
123C2×#41—1224no—
124C2×#41—1224no—
125C2×#41—1222no—
126C22×Q8—611no—
127C22×D4—611no—
128C22×D4—1221no—
129C23×C4—1221no—
130C23×C4C2×D6111yescharacteristic
131C22×C8C2×D6112yes—
132C2×C4⋊C4—612no—
133C2×C22⋊C4—1221no—
134#103—1224no—
135#102—1224no—
136C22⋊C8—22no—
137#95—1221no—
138C24—1221no—
139C24D24411yescharacteristic
140#41—1228no—
141#41—1228no—
142#41—12216no—
143C2×Q8—612no—
144C2×Q8—614no—
145C2×Q8—1222no—
146C2×Q8—1221no—
147C2×D4—612no—
148C2×D4—614no—
149C2×D4—1228no—
150C2×D4—1224no—
151C2×D4—1222no—
152C2×D4—1221no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—1228no—
156C22×C4—1221no—
157C22×C4—1224no—
158C22×C4—1222no—
159C22×C4C4×D6112yes—
160C22×C4D24411yescharacteristic
161C22×C4C22⋊D6112yes—
162C22×C4C22×D6111yescharacteristic
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—22no—
166C4⋊C4—1222no—
167C4⋊C4—1222no—
168C22⋊C4—2442no—
169C23—21no—
170C23—22no—
171C23—22no—
172C23—21no—
173C23—1222no—
174C23—1224no—
175C23—2441no—
176C23—2442no—
177C23—2441no—
178C23#1175819812yes—
179C23C2×D24411yescharacteristic
180Q8—614no—
181Q8—1222no—
182Q8—1224no—
183D4—614no—
184D4—12216no—
185D4—1222no—
186D4—1224no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—24no—
191C2×C4—12216no—
192C2×C4—1222no—
193C2×C4—1224no—
194C2×C4—2442no—
195C2×C4—2442no—
196C2×C4—2442no—
197C2×C4#1175819812yes—
198C2×C4C2×C4×D6111yescharacteristic
199C2×C4D4×D6112yes—
200C2×C4D4×D6112yes—
201C2×C4C2×C22⋊D6111yescharacteristic
202C8—42no—
203C22—22no—
204C22—22no—
205C22—22no—
206C22—42no—
207C22—42no—
208C22—1224no—
209C22—2442no—
210C22—2442no—
211C22—2444no—
212C22—2444no—
213C22C2×#1175819811yescharacteristic
214C22#1451974712yes—
215C22#1451979912yes—
216C22#1451980511yescharacteristic
217C22#1451981011yescharacteristic
218C4—22no—
219C4—1224no—
220C4—4882no—
221C4C22⋊C4×D6111yescharacteristic
222C4C22⋊C4×D6111yescharacteristic
223C4#1451974512yes—
224C2—42no—
225C2—2444no—
226C2#1683961711yescharacteristic
227C2#1683975911yescharacteristic
228C2#1683976411yescharacteristic
229C2#1683990912yes—
230C2#1683992612yes—
subgroupG/H
centerC23C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×C22⋊C8×C61C2
socleC23×C61C2×D4
hypercenterC2×C22⋊C8D61
hypocenterC61#1788
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14519702C2semidirect
3. C2×#14519699C2semidirect
4. #16839622C2semidirect
5. C2×C22⋊C8×C61C2semidirect
9. C2×#11758222C4semidirect
81. D244C22⋊C4semidirect
85. Dic122C22⋊C4semidirect
119. C2×C22⋊C8D61semidirect
121. C61#1788semidirect