Finite Group Databasebeta

← #21451703

Subgroups — #21451703

Order 7808.

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

normal subgroups only

This group has 620 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×#14519751C211yesmaximal, characteristic, complemented
2#16839701C211yesmaximal, characteristic, complemented
3#16839698C211yesmaximal, characteristic, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839677C212yesmaximal, complemented
6#16839671C211yesmaximal, characteristic, complemented
7#16839670C212yesmaximal, complemented
8#16839653C212yesmaximal, complemented
9#16839641C212yesmaximal, complemented
10#16839625C211yesmaximal, characteristic, complemented
11C2×C4×D4×C61C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C22⋊D61C2212yes—
15#14519751—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×#11758198C2212yes—
21C2×#11758198C2212yes—
22C2×#11758198C2212yes—
23C2×#11758198C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29C22×D4×C61C2211yescharacteristic
30C23×C4×C61C2211yescharacteristic
31C23×C4×C61C2211yescharacteristic
32C4×D4×C61—24no—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36C2×C42×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C24×C61C2311yescharacteristic
39C23×D61C2312yes—
40C2×D4×C61—22no—
41C2×D4×C61—22no—
42C2×D4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—42no—
45C22×C4×C61—42no—
46C22×C4×C61D414yescomplemented
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C22×C4×C61C2311yescharacteristic
51C22×C4×C61C2311yescharacteristic
52C2×C22⋊D61—24no—
53C2×C22⋊D61—24no—
54C2×C22⋊D61—42no—
55C2×C22⋊D61—42no—
56C2×C22⋊D61—42no—
57C2×C22⋊D61—42no—
58C22×Dic61C2312yes—
59C22×Dic61C2312yes—
60C22×Dic61C2312yes—
61C2×D244—22no—
62C2×D244—42no—
63C4⋊C4×C61—22no—
64C22⋊C4×C61—22no—
65C22⋊C4×C61—22no—
66C42×C61—22no—
67C22⋊Dic61—42no—
68C22⋊Dic61—42no—
69#11758198—24no—
70#11758198—24no—
71#11758198—42no—
72#11758198—42no—
73C4⋊Dic61—22no—
74#11758196—42no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—21no—
78C23×C61—21no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61C2×D412yes—
84C23×C61#4112yes—
85C23×C61C2411yescharacteristic
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—22no—
93D4×C61—28no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—44no—
103C2×C4×C61—44no—
104C2×C4×C61C2×D412yes—
105C2×C4×C61C2×D412yes—
106C2×C4×C61#4112yes—
107C22⋊D61—48no—
108C22⋊D61—48no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118D244—44no—
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—24no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61C22×D411yescharacteristic
130C22×C61C2×#4111yescharacteristic
131C22×C61C2×#4111yescharacteristic
132C22×C61H(5,𝔽2)12yes—
133C22×C61H(5,𝔽2)12yes—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C2×D61—42no—
140C2×D61—42no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—41no—
145C4×C61—41no—
146Dic61—42no—
147Dic61—42no—
148Dic61—42no—
149#2635—611nomaximal, Sylow
150C2×C61—42no—
151C2×C61—42no—
152C2×C61#52511yescharacteristic
153C2×C61#53411yescharacteristic
154C2×C61#53511yescharacteristic
155C2×C61#53812yes—
156C2×C61#54012yes—
157D61—82no—
158C2×#121—611no—
159C2×C4×D4D6111yescharacteristic, complemented
160#400—611no—
161#399—611no—
162#394—611no—
163#394—612no—
164#392—612no—
165#392—611no—
166#388—612no—
167#386—612no—
168#381—611no—
169C61#263511yescharacteristic, complemented, Sylow
170C22×D4—612no—
171C22×D4—612no—
172C22×D4—611no—
173C22×D4C2×D6111yescharacteristic
174C23×C4C2×D6111yescharacteristic
175C23×C4C2×D6111yescharacteristic
176#121—1224no—
177C4×D4—24no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—612no—
180C2×C4⋊C4C2×D6111yescharacteristic
181C2×C22⋊C4—612no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—612no—
187C2×C22⋊C4C2×D6111yescharacteristic
188C2×C22⋊C4C2×D6111yescharacteristic
189C2×C42C2×D6111yescharacteristic
190#95—612no—
191#95—611no—
192#95—611no—
193#95—612no—
194#95—612no—
195C24—612no—
196C24C22×D6111yescharacteristic
197C24C22×D6111yescharacteristic
198C2×D4—22no—
199C2×D4—22no—
200C2×D4—22no—
201C2×D4—1224no—
202C2×D4—1224no—
203C2×D4—1222no—
204C2×D4—2442no—
205C2×D4—2442no—
206C2×D4—2442no—
207C2×D4—2442no—
208C2×D4—2442no—
209C22×C4—22no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—612no—
213C22×C4—612no—
214C22×C4—612no—
215C22×C4C22⋊D6114yescomplemented
216C22×C4C22×D6111yescharacteristic
217C22×C4C22×D6111yescharacteristic
218C22×C4C22×D6111yescharacteristic
219C22×C4C22×D6111yescharacteristic
220C22×C4C22×D6111yescharacteristic
221C4⋊C4—22no—
222C4⋊C4—1222no—
223C4⋊C4—2442no—
224C22⋊C4—22no—
225C22⋊C4—22no—
226C22⋊C4—1224no—
227C22⋊C4—1224no—
228C22⋊C4—2442no—
229C22⋊C4—2442no—
230C22⋊C4—2442no—
231C22⋊C4—2442no—
232C42—22no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—1222no—
242C23—1222no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23—1222no—
247C23—1222no—
248C23#1175822212yes—
249C23C2×C22⋊D6112yes—
250C23C23×D6111yescharacteristic
251D4—28no—
252D4—2444no—
253D4—2448no—
254D4—2448no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—1222no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4#1175822212yes—
275C2×C4C2×C22⋊D6112yes—
276C2×C4C2×C22⋊D6112yes—
277C22—22no—
278C22—22no—
279C22—22no—
280C22—22no—
281C22—24no—
282C22—41no—
283C22—41no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22—2442no—
291C22—2442no—
292C22—2442no—
293C22—2442no—
294C22C22×C22⋊D6111yescharacteristic
295C22C2×#1175822211yescharacteristic
296C22C2×#1175822211yescharacteristic
297C22#1451982212yes—
298C22#1451982312yes—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—41no—
303C4—41no—
304C4—2442no—
305C4—2442no—
306C4—2442no—
307C2—42no—
308C2—42no—
309C2—4882no—
310C2#1684027311yescharacteristic
311C2#1684032111yescharacteristic
312C2#1684032611yescharacteristic
313C2#1684034512yes—
314C2#1684036312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×C4×D4×C61C2
hypercenterC2×C4×D4D61
hypocenterC61#2635
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#14519751C2semidirect
2. #16839701C2semidirect
3. #16839698C2semidirect
4. #16839679C2semidirect
5. #16839677C2semidirect
6. #16839671C2semidirect
7. #16839670C2semidirect
8. #16839653C2semidirect
9. #16839641C2semidirect
10. #16839625C2semidirect
11. C2×C4×D4×C61C2semidirect
46. C22×C4×C61D4semidirect
159. C2×C4×D4D61semidirect
169. C61#2635semidirect
215. C22×C4C22⋊D61semidirect