Finite Group Databasebeta

← #21445913

Subgroups — #21445913

Order 7808.

300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#14519735C211yesmaximal, characteristic
2C2×#14519689C211yesmaximal, characteristic
3#16839619C211yesmaximal, characteristic
4#16839525C211yesmaximal, characteristic, complemented
5#16839524C211yesmaximal, characteristic, complemented
6#16839524C211yesmaximal, characteristic, complemented
7C61×#340C211yesmaximal, characteristic, complemented
8C22×C4×D61C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10#14519735—22no—
11#14519735C414yescomplemented
12C2×C4⋊Dic61C2211yescharacteristic
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758198—21no—
15C2×#11758198—21no—
16C2×C4×Dic61—21no—
17#14519689—22no—
18#14519684—21no—
19C22×C8×C61C2211yescharacteristic
20C2×C4⋊C4×C61C2211yescharacteristic
21C2×C4⋊C4×C61C2211yescharacteristic
22C23×D61D411yescharacteristic
23C22×C4×C61—21no—
24C22×C4×C61—21no—
25C22×C4×C61C2311yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61D411yescharacteristic
29C2×C4×D61—21no—
30C2×C4×D61—21no—
31C2×C4×D61—21no—
32C2×C4×D61—21no—
33C2×C4×D61C2×C412yes—
34C2×C4×D61D412yes—
35C2×C8×C61—21no—
36C2×C8×C61—21no—
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61C2×C412yes—
42#11758198—24no—
43#11758198—42no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4⋊Dic61C2×C412yes—
48C4×Dic61—24no—
49C2×#92418—21no—
50C2×#92418—21no—
51C2×#92418—21no—
52C23×C61C2×D411yescharacteristic
53C22×D61—21no—
54C22×D61—21no—
55C22×D61—21no—
56C22×D61—21no—
57C22×D61—21no—
58C22×D61—21no—
59C22×D61C22⋊C412yes—
60C2×C4×C61—22no—
61C2×C4×C61—41no—
62C2×C4×C61—41no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—41no—
66C2×C4×C61C22×C411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C2×C4×C61#4111yescharacteristic
71C2×C4×C61#4111yescharacteristic
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—22no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80C2×Dic61C22⋊C412yes—
81C4×D61—22no—
82C4×D61—22no—
83C4×D61—22no—
84C4×D61—22no—
85C8×C61—41no—
86#92418—41no—
87C22×C61C2×C22⋊C411yescharacteristic
88C22×C61#12311yescharacteristic
89C22×C61#12311yescharacteristic
90C22×C61#13511yescharacteristic
91C22×C61#13511yescharacteristic
92C22×C61AGL(1,ℤ/8)11yescharacteristic
93C22×C61#13711yescharacteristic
94C2×D61—22no—
95C2×D61—22no—
96C2×D61—22no—
97C2×D61—41no—
98C2×D61—41no—
99C2×D61—41no—
100C2×D61—41no—
101C4×C61—42no—
102C4×C61—81no—
103C4×C61#11711yescharacteristic
104C4×C61#11711yescharacteristic
105C4×C61#12311yescharacteristic
106C4×C61#12311yescharacteristic
107Dic61—22no—
108Dic61—42no—
109Dic61—81no—
110#1825—611nomaximal, Sylow
111C2×C61#38111yescharacteristic
112C2×C61#41611yescharacteristic
113C2×C61#41711yescharacteristic
114C2×C61#48211yescharacteristic
115C2×C61#48211yescharacteristic
116C2×C61#48511yescharacteristic
117C2×C61#48511yescharacteristic
118D61—42no—
119C2×#117—611no—
120C2×C22⋊C8—611no—
121#380—611no—
122#340—611no—
123#340—611no—
124#340—611no—
125#340D6111yescharacteristic, complemented
126C61#182511yescharacteristic, complemented, Sylow
127C23×C4—611no—
128C22×C8—611no—
129C22×C8C2×D6111yescharacteristic
130#117—614no—
131#117—1222no—
132C2×C4⋊C4—611no—
133C2×C4⋊C4—611no—
134C2×C4⋊C4C2×D6111yescharacteristic
135C2×C4⋊C4C2×D6111yescharacteristic
136C2×C22⋊C4—1221no—
137C2×C22⋊C4—1221no—
138C2×C42—1221no—
139C22⋊C8—1222no—
140#95—1221no—
141C24—611no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—611no—
145C22×C4—612no—
146C22×C4—612no—
147C22×C4—1221no—
148C22×C4—1221no—
149C22×C4—1221no—
150C22×C4—1221no—
151C22×C4—1221no—
152C22×C4—1221no—
153C22×C4C22×D6111yescharacteristic
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8—1221no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—612no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4C4×D6112yes—
168C22⋊C4—1224no—
169C22⋊C4—2442no—
170C42—1224no—
171C23—612no—
172C23—1221no—
173C23—1221no—
174C23—1221no—
175C23—1221no—
176C23—1221no—
177C23—1221no—
178C23D4×D6111yescharacteristic
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—612no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1222no—
189C2×C4—1222no—
190C2×C4—1222no—
191C2×C4—1222no—
192C2×C4—1222no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4—2441no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4C2×C4×D6111yescharacteristic
199C2×C4#1175822211yescharacteristic
200C2×C4#1175822211yescharacteristic
201C2×C4D4×D6111yescharacteristic
202C2×C4#1175822411yescharacteristic
203C2×C4#1175822611yescharacteristic
204C8—41no—
205C8—2441no—
206C22—1222no—
207C22—1222no—
208C22—1222no—
209C22—2441no—
210C22—2441no—
211C22—2441no—
212C22—2441no—
213C22C22⋊C4×D6111yescharacteristic
214C22#1451975911yescharacteristic
215C22#1451976211yescharacteristic
216C22#1451979811yescharacteristic
217C22#1451980011yescharacteristic
218C22#1451980111yescharacteristic
219C22#1451980611yescharacteristic
220C4—42no—
221C4—81no—
222C4—1222no—
223C4—4881no—
224C4—2442no—
225C4#1451973411yescharacteristic
226C4#1451973511yescharacteristic
227C4#1451975911yescharacteristic
228C4#1451976211yescharacteristic
229C2—2442no—
230C2#1683962411yescharacteristic
231C2#1683975711yescharacteristic
232C2#1683976011yescharacteristic
233C2#1684008511yescharacteristic
234C2#1684008911yescharacteristic
235C2#1684010211yescharacteristic
236C2#1684010611yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#340C2
socleC23×C61C2×D4
hypercenter#340D61
hypocenterC61#1825
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. #16839525C2semidirect
5. #16839524C2semidirect
6. #16839524C2semidirect
7. C61×#340C2semidirect
11. #14519735C4semidirect
125. #340D61semidirect
126. C61#1825semidirect