Finite Group Databasebeta

← #21454150

Subgroups — #21454150

Order 7808.

688 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 189 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×#14519760C212yesmaximal, complemented
2C2×#14519751C211yesmaximal, characteristic
3#16839664C212yesmaximal, complemented
4#16839660C212yesmaximal, complemented
5#16839653C214yesmaximal, complemented
6#16839641C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic, complemented
8C22×C42×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C22⋊D61C2212yes—
11#14519760—28no—
12#14519751—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2212yes—
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2214yes—
19C2×#11758198C2214yes—
20#14519684C2212yes—
21#14519684C2214yes—
22C23×C4×C61C2211yescharacteristic
23C23×C4×C61C2211yescharacteristic
24C23×C4×C61C2211yescharacteristic
25C2×C42×C61—24no—
26C2×C42×C61C2212yes—
27C2×C42×C61C2212yes—
28C24×C61C2311yescharacteristic
29C23×D61C2312yes—
30C22×C4×C61—22no—
31C22×C4×C61—22no—
32C22×C4×C61—22no—
33C22×C4×C61—24no—
34C22×C4×C61—24no—
35C22×C4×C61D414yes—
36C22×C4×C61D414yescomplemented
37C22×C4×C61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—24no—
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C22×Dic61C2312yes—
45C22×Dic61C2314yes—
46C2×D244—22no—
47C2×D244—24no—
48C42×C61—24no—
49C42×C61—24no—
50C22⋊Dic61—24no—
51#11758198—24no—
52#11758198—28no—
53#11758198—28no—
54C4⋊Dic61—22no—
55C4⋊Dic61—24no—
56#11758196—28no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61C2×D412yes—
60C23×C61C2×D412yes—
61C23×C61#4112yes—
62C23×C61C2411yescharacteristic
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—24no—
67C22×D61—22no—
68C2×C4×C61—28no—
69C2×C4×C61—28no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—28no—
76C2×C4×C61C2×D414yes—
77C2×C4×C61C2×D412yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61#4114yes—
80C2×C4×C61#4114yes—
81C22⋊D61—48no—
82C2×Dic61—22no—
83C2×Dic61—24no—
84C2×Dic61—22no—
85C2×Dic61—24no—
86C2×Dic61—24no—
87C2×Dic61—22no—
88D244—44no—
89C22×C61—22no—
90C22×C61—22no—
91C22×C61—24no—
92C22×C61—24no—
93C22×C61#12114yes—
94C22×C61C22×D411yescharacteristic
95C22×C61C22×D411yescharacteristic
96C22×C61C2×#4111yescharacteristic
97C22×C61C2×#4112yes—
98C22×C61C2×#4112yes—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—42no—
102C2×D61—44no—
103C2×D61—44no—
104C4×C61—24no—
105C4×C61—22no—
106C4×C61—24no—
107C4×C61#12314yescomplemented
108Dic61—42no—
109Dic61—44no—
110#2854—611nomaximal, Sylow
111C2×C61—24no—
112C2×C61C2×#12111yescharacteristic
113C2×C61C2×#12311yescharacteristic
114C2×C61#52511yescharacteristic
115C2×C61#52912yes—
116C2×C61#53212yes—
117D61—82no—
118C2×#123—612no—
119C2×#121—611no—
120C22×C42D6111yescharacteristic, complemented
121#390—612no—
122#389—612no—
123#388—614no—
124#386—612no—
125#380—611no—
126C61#285411yescharacteristic, complemented, Sylow
127C22×D4—612no—
128C22×D4—611no—
129C23×C4C2×D6111yescharacteristic
130C23×C4C2×D6111yescharacteristic
131C23×C4C2×D6111yescharacteristic
132#123—1228no—
133#121—1224no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—614no—
136C2×C4⋊C4—612no—
137C2×C22⋊C4—612no—
138C2×C22⋊C4—612no—
139C2×C22⋊C4—614no—
140C2×C22⋊C4—614no—
141C2×C42—24no—
142C2×C42C2×D6112yes—
143C2×C42C2×D6112yes—
144#95—612no—
145#95—614no—
146C24—612no—
147C24C22×D6111yescharacteristic
148C2×D4—1224no—
149C2×D4—1224no—
150C2×D4—1224no—
151C2×D4—1224no—
152C2×D4—1222no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4—24no—
158C22×C4—614no—
159C22×C4—612no—
160C22×C4D24414yescomplemented
161C22×C4C22⋊D6114yes—
162C22×C4C22×D6112yes—
163C22×C4C22×D6112yes—
164C22×C4C22×D6111yescharacteristic
165C22×C4C22×D6111yescharacteristic
166C4⋊C4—1228no—
167C4⋊C4—1224no—
168C4⋊C4—1222no—
169C22⋊C4—1224no—
170C22⋊C4—1228no—
171C22⋊C4—1228no—
172C22⋊C4—1224no—
173C42—24no—
174C42—24no—
175C23—22no—
176C23—22no—
177C23—1222no—
178C23—1222no—
179C23—1224no—
180C23—1222no—
181C23—1224no—
182C23C2×D24412yes—
183C23#1175822212yes—
184C23C2×C22⋊D6112yes—
185C23C23×D6111yescharacteristic
186D4—2448no—
187D4—2444no—
188C2×C4—28no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—28no—
195C2×C4—28no—
196C2×C4—1222no—
197C2×C4—1224no—
198C2×C4—1222no—
199C2×C4—1224no—
200C2×C4—1224no—
201C2×C4—1222no—
202C2×C4C2×D24414yes—
203C2×C4#1175822214yes—
204C2×C4#1175822214yes—
205C2×C4C2×C22⋊D6112yes—
206C2×C4C2×C22⋊D6112yes—
207C22—22no—
208C22—22no—
209C22—24no—
210C22—24no—
211C22—2442no—
212C22—2442no—
213C22—2442no—
214C22—2444no—
215C22—2444no—
216C22#1451975114yes—
217C22C22×C22⋊D6111yescharacteristic
218C22C22×D24411yescharacteristic
219C22C2×#1175822211yescharacteristic
220C22C2×#1175822212yes—
221C22C2×#1175822212yes—
222C4—24no—
223C4—22no—
224C4—24no—
225C4—2442no—
226C4—2444no—
227C4#1451976014yescomplemented
228C2—24no—
229C2—4882no—
230C2C2×#1451975111yescharacteristic
231C2C2×#1451976011yescharacteristic
232C2#1684027311yescharacteristic
233C2#1684029612yes—
234C2#1684031212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C42×C61C2
hypercenterC22×C42D61
hypocenterC61#2854
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
1. C2×#14519760C2semidirect
3. #16839664C2semidirect
4. #16839660C2semidirect
5. #16839653C2semidirect
6. #16839641C2semidirect
7. #16839622C2semidirect
8. C22×C42×C61C2semidirect
36. C22×C4×C61D4semidirect
107. C4×C61#123semidirect
120. C22×C42D61semidirect
126. C61#2854semidirect
160. C22×C4D244semidirect
227. C4#14519760semidirect