Finite Group Databasebeta

← #21454155

Subgroups — #21454155

Order 7808.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519754C211yesmaximal, characteristic
2C22×C4×Dic61C211yesmaximal, characteristic
3#16839666C212yesmaximal, complemented
4#16839657C212yesmaximal, complemented
5#16839648C212yesmaximal, complemented
6#16839644C212yesmaximal, complemented
7#16839635C211yesmaximal, characteristic
8#16839623C211yesmaximal, characteristic
9#16839623C211yesmaximal, characteristic
10#16839620C211yesmaximal, characteristic
11C61×#385C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15#14519754—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C4×Dic61—24no—
24C2×C4×Dic61C2212yes—
25C2×C4×Dic61C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C22×C4×C61—22no—
39C22×C4×C61—24no—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2312yes—
44C22×Dic61—22no—
45C22×Dic61—22no—
46C22×Dic61—24no—
47C22×Dic61D414yes—
48C22×Dic61Q814yescomplemented
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2312yes—
54C22×Dic61C2311yescharacteristic
55C2×Dic122—22no—
56C2×Dic122—24no—
57C4⋊C4×C61—24no—
58C22⋊C4×C61—22no—
59C22⋊C4×C61—22no—
60C22⋊Dic61—22no—
61C22⋊Dic61—22no—
62C4⋊Dic61—22no—
63#11758196—24no—
64#11758196—22no—
65#11758196—22no—
66#11758196—24no—
67C4×Dic61—24no—
68C4×Dic61—24no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61C2×D412yes—
72C23×C61C2×Q812yes—
73C23×C61#4112yes—
74C23×C61C2411yescharacteristic
75C2×C4×C61—28no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61#4114yes—
86C2×Dic61—28no—
87C2×Dic61—22no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—28no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61C2×D412yes—
99C2×Dic61C2×D412yes—
100C2×Dic61C2×Q814yes—
101C2×Dic61#4114yes—
102Dic122—44no—
103C22×C61—22no—
104C22×C61—22no—
105C22×C61—24no—
106C22×C61—24no—
107C22×C61C22⋊Q814yes—
108C22×C61C22×D411yescharacteristic
109C22×C61C22×Q811yescharacteristic
110C22×C61C2×#4112yes—
111C22×C61C2×#4112yes—
112C22×C61C2×#4111yescharacteristic
113C4×C61—24no—
114C4×C61—41no—
115C4×C61—41no—
116C4×C61—42no—
117Dic61—24no—
118Dic61—22no—
119Dic61—41no—
120Dic61—41no—
121Dic61—42no—
122Dic61#12314yes—
123#2855—611nomaximal, Sylow
124C2×C61—24no—
125C2×C61C2×C22⋊Q811yescharacteristic
126C2×C61C2×#12311yescharacteristic
127C2×C61#52511yescharacteristic
128C2×C61#52912yes—
129C2×C61#53312yes—
130C2×C22⋊Q8—611no—
131C22×C42—611no—
132#391—612no—
133#389—612no—
134#387—612no—
135#387—612no—
136#385—611no—
137#385D6111yescharacteristic
138#381—611no—
139#381—611no—
140#380—611no—
141C61#285511yescharacteristic, complemented, Sylow
142C22×Q8—611no—
143C23×C4—611no—
144C23×C4—611no—
145C23×C4C2×D6111yescharacteristic
146C22⋊Q8—1224no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4—612no—
152C2×C4⋊C4C2×D6112yes—
153C2×C22⋊C4—611no—
154C2×C22⋊C4—611no—
155C2×C22⋊C4C2×D6111yescharacteristic
156C2×C22⋊C4C2×D6111yescharacteristic
157C2×C42—612no—
158C2×C42—612no—
159C2×C42—1224no—
160#95—612no—
161#95—612no—
162#95—612no—
163#95—612no—
164#95—612no—
165#95—612no—
166#95C2×D6112yes—
167C24C22×D6111yescharacteristic
168C2×Q8—1222no—
169C2×Q8—1224no—
170C22×C4—22no—
171C22×C4—24no—
172C22×C4—611no—
173C22×C4—614no—
174C22×C4—614no—
175C22×C4—612no—
176C22×C4—611no—
177C22×C4—612no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—1224no—
181C22×C4—1222no—
182C22×C4—1222no—
183C22×C4C22×D6112yes—
184C22×C4C22×D6111yescharacteristic
185C22×C4C22×D6111yescharacteristic
186C22×C4C22×D6112yes—
187C4⋊C4—24no—
188C4⋊C4—1224no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1224no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—1222no—
196C22⋊C4—1222no—
197C42—1224no—
198C42—1224no—
199C23—22no—
200C23—22no—
201C23#1175822212yes—
202C23D4×D6112yes—
203C23Q8×D6112yes—
204C23C23×D6111yescharacteristic
205Q8—2444no—
206C2×C4—28no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—612no—
217C2×C4—614no—
218C2×C4—612no—
219C2×C4—614no—
220C2×C4—1228no—
221C2×C4—1222no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1228no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4—1222no—
231C2×C4—1222no—
232C2×C4#1175822414yes—
233C22—22no—
234C22—22no—
235C22—24no—
236C22—24no—
237C22#1451975514yes—
238C22C2×D4×D6111yescharacteristic
239C22C2×Q8×D6111yescharacteristic
240C22#41×D6112yes—
241C22C2×#1175822412yes—
242C22C2×#1175822211yescharacteristic
243C4—24no—
244C4—41no—
245C4—41no—
246C4—42no—
247C4—614no—
248C4—1224no—
249C4—1222no—
250C4—2441no—
251C4—2441no—
252C4—2442no—
253C2—24no—
254C2C2×#1451975511yescharacteristic
255C2#123×D6111yescharacteristic
256C2#1684026811yescharacteristic
257C2#1684029212yes—
258C2#1684031412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2855
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #16839666C2semidirect
4. #16839657C2semidirect
5. #16839648C2semidirect
6. #16839644C2semidirect
48. C22×Dic61Q8semidirect
141. C61#2855semidirect