Finite Group Databasebeta

← #21452546

Subgroups — #21452546

Order 7808.

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

normal subgroups only

This group has 612 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
1C2×#14519758C211yesmaximal, characteristic, complemented
2#16839676C212yesmaximal, complemented
3#16839676C212yesmaximal, complemented
4#16839676C212yesmaximal, complemented
5#16839646C212yesmaximal, complemented
6#16839642C212yesmaximal, complemented
7#16839642C212yesmaximal, complemented
8#16839642C211yesmaximal, characteristic, complemented
9C2×#127×C61C211yesmaximal, characteristic
10C23×Dic61C2211yescharacteristic
11C23×Dic61C2211yescharacteristic
12#14519758—24no—
13C2×#11758196C2212yes—
14C2×#11758196C2212yes—
15C2×C22⋊Dic61C2212yes—
16C2×C22⋊Dic61C2211yescharacteristic
17C2×C22⋊Dic61C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2211yescharacteristic
22C2×C22⋊Dic61C2212yes—
23#14519684C2212yes—
24#14519684C2212yes—
25#14519684C2212yes—
26#14519684C2212yes—
27C22×D4×C61C2212yes—
28C22×D4×C61C2212yes—
29C22×D4×C61C2211yescharacteristic
30C22×D4×C61C2211yescharacteristic
31#127×C61—24no—
32C2×C42×C61C2211yescharacteristic
33C24×C61C2312yes—
34C24×C61C2311yescharacteristic
35C24×C61C2311yescharacteristic
36C2×D4×C61—24no—
37C2×D4×C61—24no—
38C2×D4×C61—22no—
39C2×D4×C61—24no—
40C2×D4×C61—24no—
41C2×D4×C61—41no—
42C2×D4×C61—41no—
43C2×D4×C61—42no—
44C2×D4×C61—42no—
45C2×D4×C61—41no—
46C2×D4×C61—41no—
47C2×D4×C61D414yes—
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2312yes—
50C22×Dic61—22no—
51C22×Dic61—41no—
52C22×Dic61—41no—
53C22×Dic61—41no—
54C22×Dic61—42no—
55C22×Dic61C2312yes—
56C22×Dic61C2312yes—
57C22×Dic61C2312yes—
58C22×Dic61C2312yes—
59C42×C61—22no—
60C22⋊Dic61—22no—
61C22⋊Dic61—24no—
62C22⋊Dic61—41no—
63C22⋊Dic61—42no—
64C22⋊Dic61—42no—
65C22⋊Dic61—42no—
66C22⋊Dic61—42no—
67C22⋊Dic61—42no—
68#11758196—24no—
69#11758196—24no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61—21no—
73C23×C61—22no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61C2×D412yes—
86C23×C61C2×D412yes—
87C23×C61C2411yescharacteristic
88D4×C61—44no—
89D4×C61—48no—
90D4×C61—48no—
91D4×C61—44no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61#4114yes—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—44no—
111C2×Dic61—44no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—24no—
115C22×C61—24no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—42no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61C22×D411yescharacteristic
130C22×C61C2×#4112yes—
131C22×C61H(5,𝔽2)11yescharacteristic
132C22×C61H(5,𝔽2)11yescharacteristic
133C22×C61H(5,𝔽2)12yes—
134C4×C61—22no—
135C4×C61—24no—
136Dic61—42no—
137Dic61—42no—
138Dic61—42no—
139Dic61—42no—
140#2709—611nomaximal, Sylow
141C2×C61—42no—
142C2×C61—42no—
143C2×C61—82no—
144C2×C61#53411yescharacteristic
145C2×C61#54012yes—
146C2×C61#54612yes—
147C2×C61#55911yescharacteristic
148C2×C61#56011yescharacteristic
149C2×#127D6111yescharacteristic
150C2×#123—611no—
151#394—612no—
152#394—612no—
153#394—612no—
154#387—612no—
155#386—612no—
156#386—612no—
157#386—611no—
158C61#270911yescharacteristic, complemented, Sylow
159C22×D4C2×D6112yes—
160C22×D4C2×D6112yes—
161C22×D4C2×D6111yescharacteristic
162C22×D4C2×D6111yescharacteristic
163C23×C4—611no—
164C23×C4—611no—
165#127—24no—
166#123—1224no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—612no—
169C2×C22⋊C4—612no—
170C2×C22⋊C4—611no—
171C2×C22⋊C4—612no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—611no—
175C2×C22⋊C4—612no—
176C2×C22⋊C4—612no—
177C2×C42C2×D6111yescharacteristic
178#95—612no—
179#95—612no—
180#95—612no—
181#95—612no—
182C24C22×D6112yes—
183C24C22×D6111yescharacteristic
184C24C22×D6111yescharacteristic
185C2×D4—24no—
186C2×D4—24no—
187C2×D4—24no—
188C2×D4—24no—
189C2×D4—22no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4C22⋊D6114yes—
197C22×C4—612no—
198C22×C4—612no—
199C22×C4—612no—
200C22×C4—612no—
201C22×C4—1222no—
202C22×C4—2441no—
203C22×C4—2441no—
204C22×C4—2441no—
205C22×C4—2442no—
206C22×C4C22×D6112yes—
207C22×C4C22×D6111yescharacteristic
208C4⋊C4—1224no—
209C4⋊C4—1224no—
210C22⋊C4—1222no—
211C22⋊C4—1224no—
212C22⋊C4—2441no—
213C22⋊C4—2442no—
214C22⋊C4—2442no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C22⋊C4—2442no—
218C42—22no—
219C23—22no—
220C23—22no—
221C23—21no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23C2×C22⋊D6112yes—
235C23C2×C22⋊D6112yes—
236C23C23×D6111yescharacteristic
237D4—44no—
238D4—48no—
239D4—48no—
240D4—44no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—1222no—
246C2×C4—1222no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—2444no—
258C2×C4—2444no—
259C2×C4#1175822414yes—
260C2×C4C2×C22⋊D6112yes—
261C22—22no—
262C22—22no—
263C22—24no—
264C22—24no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—41no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22C22×C22⋊D6111yescharacteristic
279C22C2×#1175822412yes—
280C22#1451982211yescharacteristic
281C22#1451982212yes—
282C22#1451982211yescharacteristic
283C4—22no—
284C4—24no—
285C4—2442no—
286C4—2442no—
287C4—2442no—
288C4—2442no—
289C2—42no—
290C2—42no—
291C2—82no—
292C2#1684032111yescharacteristic
293C2#1684036612yes—
294C2#1684040612yes—
295C2#1684049811yescharacteristic
296C2#1684049911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#127×C61C2
hypercenterC2×#127D61
hypocenterC61#2709
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#14519758C2semidirect
2. #16839676C2semidirect
3. #16839676C2semidirect
4. #16839676C2semidirect
5. #16839646C2semidirect
6. #16839642C2semidirect
7. #16839642C2semidirect
8. #16839642C2semidirect
158. C61#2709semidirect