Finite Group Databasebeta

← #21452182

Subgroups — #21452182

Order 7808.

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

normal subgroups only

This group has 668 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×#14519759C212yesmaximal, complemented
2C2×#14519750C212yesmaximal, complemented
3#16839685C212yesmaximal, complemented
4#16839678C212yesmaximal, complemented
5#16839670C212yesmaximal, complemented
6#16839664C211yesmaximal, characteristic, complemented
7#16839660C211yesmaximal, characteristic, complemented
8#16839633C212yesmaximal, complemented
9C61×#390C211yesmaximal, characteristic, complemented
10C22×D244C2211yescharacteristic
11C22×C22⋊D61C2212yes—
12C22×C22⋊D61C2212yes—
13C22×C4×D61C2212yes—
14#14519759—28no—
15#14519750—28no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×#11758198C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26#14519684C2212yes—
27#14519684C2212yes—
28C22×D4×C61C2211yescharacteristic
29C2×C4⋊C4×C61C2211yescharacteristic
30C2×C22⋊C4×C61C2212yes—
31C2×C22⋊C4×C61C2212yes—
32C2×C42×C61C2211yescharacteristic
33C24×C61C2312yes—
34C23×D61C2312yes—
35C2×D4×C61—22no—
36C2×D4×C61—41no—
37C2×D4×C61—41no—
38C22×C4×C61C2312yes—
39C22×C4×C61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C2×C22⋊D61—24no—
45C2×C22⋊D61—42no—
46C2×C22⋊D61—42no—
47C2×C22⋊D61—42no—
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2312yes—
51C2×D244—41no—
52C2×D244—41no—
53C2×D244D414yescomplemented
54C2×C4×D61—24no—
55C2×C4×D61—24no—
56C2×C4×D61—42no—
57C4⋊C4×C61—41no—
58C22⋊C4×C61—24no—
59C22⋊C4×C61—24no—
60C42×C61—41no—
61C22⋊Dic61—24no—
62C22⋊Dic61—42no—
63#11758198—24no—
64#11758198—24no—
65#11758198—24no—
66C4⋊Dic61—41no—
67C4⋊Dic61—41no—
68C4⋊Dic61D414yescomplemented
69#11758196—24no—
70#11758196—24no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61C2411yescharacteristic
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61C2×D414yes—
86D4×C61—44no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C2×C4×C61C2×D412yes—
98C2×C4×C61#4112yes—
99C22⋊D61—48no—
100C22⋊D61—48no—
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×Dic61C2×D414yes—
110D244—44no—
111C4×D61—48no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61C22×D411yescharacteristic
120C22×C61C22×D411yescharacteristic
121C22×C61C2×#4111yescharacteristic
122C22×C61H(5,𝔽2)11yescharacteristic
123C22×C61H(5,𝔽2)11yescharacteristic
124C22×C61H(5,𝔽2)11yescharacteristic
125C22×C612−1+411yescharacteristic
126C2×D61—24no—
127C2×D61—24no—
128C2×D61—24no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C4×C61—22no—
134C4×C61—22no—
135C4×C61—22no—
136C4×C61—42no—
137Dic61—24no—
138Dic61—42no—
139Dic61—42no—
140#2682—611nomaximal, Sylow
141C2×C61—82no—
142C2×C61#53411yescharacteristic
143C2×C61#53711yescharacteristic
144C2×C61#53811yescharacteristic
145C2×C61D4211yescharacteristic
146C2×C61#54711yescharacteristic
147C2×C61#55011yescharacteristic
148C2×C61#56211yescharacteristic
149D61—44no—
150C2×#123—612no—
151C2×#121—612no—
152#396—612no—
153#394—612no—
154#392—612no—
155#390—611no—
156#390D6111yescharacteristic, complemented
157#389—611no—
158#385—612no—
159C61#268211yescharacteristic, complemented, Sylow
160C22×D4—612no—
161C22×D4—612no—
162C22×D4—611no—
163C22×D4C2×D6111yescharacteristic
164C23×C4—612no—
165#123—1228no—
166#121—1228no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4—612no—
169C2×C4⋊C4—612no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4C2×D6111yescharacteristic
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—612no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4C2×D6112yes—
179C2×C22⋊C4C2×D6112yes—
180C2×C42C2×D6111yescharacteristic
181#95—612no—
182#95—612no—
183C24—612no—
184C24C22×D6112yes—
185C2×D4—22no—
186C2×D4—41no—
187C2×D4—41no—
188C2×D4—614no—
189C2×D4—1224no—
190C2×D4—1224no—
191C2×D4—1224no—
192C2×D4—2441no—
193C2×D4—2441no—
194C2×D4—2442no—
195C2×D4—2442no—
196C2×D4—2442no—
197C22×C4—612no—
198C22×C4—612no—
199C22×C4—612no—
200C22×C4—1224no—
201C22×C4—1224no—
202C22×C4—2442no—
203C22×C4C22×D6112yes—
204C22×C4C22×D6111yescharacteristic
205C22×C4C22×D6111yescharacteristic
206C22×C4C22×D6111yescharacteristic
207C4⋊C4—41no—
208C4⋊C4—614no—
209C4⋊C4—1224no—
210C4⋊C4—1224no—
211C4⋊C4—2441no—
212C4⋊C4—2441no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—1224no—
216C22⋊C4—1224no—
217C22⋊C4—1224no—
218C22⋊C4—1224no—
219C22⋊C4—2442no—
220C42—41no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—614no—
229C23—1222no—
230C23—1222no—
231C23—1222no—
232C23—1222no—
233C23—1222no—
234C23—1222no—
235C23C23×D6111yescharacteristic
236D4—44no—
237D4—2444no—
238D4—2448no—
239D4—2448no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—614no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—2448no—
259C2×C4#1175822212yes—
260C2×C4D4×D6112yes—
261C2×C4D4×D6112yes—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—42no—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—1224no—
270C22—1224no—
271C22—1224no—
272C22—2442no—
273C22—2442no—
274C22—2442no—
275C22—2442no—
276C22C2×D4×D6111yescharacteristic
277C22C2×D4×D6111yescharacteristic
278C22C2×#1175822211yescharacteristic
279C22#1451982211yescharacteristic
280C22#1451982211yescharacteristic
281C22#1451982311yescharacteristic
282C22#1451982411yescharacteristic
283C4—22no—
284C4—22no—
285C4—22no—
286C4—42no—
287C4—1224no—
288C4—2442no—
289C4—2442no—
290C2—82no—
291C2—2444no—
292C2#1684032011yescharacteristic
293C2#1684033911yescharacteristic
294C2#1684035011yescharacteristic
295C2#1684039711yescharacteristic
296C2#1684041711yescharacteristic
297C2#1684043311yescharacteristic
298C2#1684050611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2682
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519759C2semidirect
2. C2×#14519750C2semidirect
3. #16839685C2semidirect
4. #16839678C2semidirect
5. #16839670C2semidirect
6. #16839664C2semidirect
7. #16839660C2semidirect
8. #16839633C2semidirect
9. C61×#390C2semidirect
53. C2×D244D4semidirect
68. C4⋊Dic61D4semidirect
156. #390D61semidirect
159. C61#2682semidirect