Finite Group Databasebeta

← #21451673

Subgroups — #21451673

Order 7808.

628 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14519763C211yesmaximal, characteristic, complemented
2C2×#14519739C211yesmaximal, characteristic, complemented
3#16839688C211yesmaximal, characteristic, complemented
4#16839675C212yesmaximal, complemented
5#16839672C211yesmaximal, characteristic, complemented
6#16839671C212yesmaximal, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839640C212yesmaximal, complemented
9#16839638C212yesmaximal, complemented
10#16839629C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×D244C2211yescharacteristic
14C22×D244C2212yes—
15C22×C22⋊D61C2211yescharacteristic
16C22×C22⋊D61C2212yes—
17C22×C4×D61C2212yes—
18#14519763—24no—
19#14519739—24no—
20C2×C22⋊Dic61C2211yescharacteristic
21C2×#11758198C2211yescharacteristic
22C2×#11758198C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C23×D61C2312yes—
40C22×C4×C61C2312yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—24no—
45C2×C22⋊D61—22no—
46C2×C22⋊D61—42no—
47C2×C22⋊D61—42no—
48C2×C22⋊D61—42no—
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C2×D244—24no—
54C2×D244—22no—
55C2×D244—24no—
56C2×D244—42no—
57C2×D244—42no—
58C2×C4×D61—24no—
59C2×C4×D61—42no—
60C2×C4×D61—42no—
61C2×Dic122—22no—
62C2×Dic122—42no—
63C4⋊C4×C61—22no—
64C22⋊C4×C61—22no—
65C22⋊C4×C61—42no—
66C22⋊Dic61—22no—
67#11758198—22no—
68#11758198—24no—
69#11758198—22no—
70#11758198—42no—
71#11758198—42no—
72#11758198—42no—
73C4×Dic61D414yescomplemented
74C23×C61—21no—
75C23×C61—22no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—21no—
79C23×C61C2411yescharacteristic
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—21no—
87C22×D61—22no—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—22no—
91C22×D61#4114yes—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61C2×D412yes—
102C22⋊D61—44no—
103C22⋊D61—48no—
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61C2×D412yes—
113C2×Dic61C2×D412yes—
114D244—28no—
115D244—48no—
116C4×D61—48no—
117Dic122—44no—
118C22×C61—41no—
119C22×C61—41no—
120C22×C61—41no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61C22×D411yescharacteristic
124C22×C61C2×#4112yes—
125C22×C61H(5,𝔽2)11yescharacteristic
126C22×C61H(5,𝔽2)11yescharacteristic
127C22×C61H(5,𝔽2)12yes—
128C2×D61—24no—
129C2×D61—24no—
130C2×D61—24no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—42no—
139C2×D61—42no—
140C4×C61—22no—
141C4×C61—41no—
142C4×C61—42no—
143C4×C61—42no—
144Dic61—22no—
145Dic61—22no—
146Dic61—41no—
147Dic61—42no—
148#2631—611nomaximal, Sylow
149C2×C61—81no—
150C2×C61#52511yescharacteristic
151C2×C61#53511yescharacteristic
152C2×C61#53511yescharacteristic
153C2×C61#53812yes—
154C2×C61#53812yes—
155D61—44no—
156D61—81no—
157C2×#124—611no—
158C2×C4×D4—611no—
159#397—611no—
160#397D6111yescharacteristic, complemented
161#393—612no—
162#392—612no—
163#392—611no—
164#392—611no—
165#386—612no—
166#386—612no—
167#383—611no—
168C61#263111yescharacteristic, complemented, Sylow
169C22×Q8—611no—
170C22×D4—611no—
171C22×D4—612no—
172C22×D4—611no—
173C22×D4—612no—
174C23×C4—612no—
175#124—1224no—
176C4×D4—1224no—
177C2×C4⋊C4C2×D6111yescharacteristic
178C2×C22⋊C4—611no—
179C2×C22⋊C4—612no—
180C2×C22⋊C4—611no—
181C2×C22⋊C4—611no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4C2×D6111yescharacteristic
186C2×C22⋊C4C2×D6112yes—
187C2×C42—611no—
188#95—612no—
189#95—612no—
190#95—611no—
191#95—612no—
192#95C2×D6111yescharacteristic
193#95C2×D6112yes—
194C24—612no—
195C24—611no—
196C24C22×D6111yescharacteristic
197C2×Q8—1222no—
198C2×Q8—2442no—
199C2×D4—1224no—
200C2×D4—1224no—
201C2×D4—1222no—
202C2×D4—1224no—
203C2×D4—1222no—
204C2×D4—2442no—
205C2×D4—2442no—
206C2×D4—2442no—
207C2×D4—2442no—
208C2×D4—2442no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—612no—
212C22×C4—611no—
213C22×C4—1224no—
214C22×C4—2442no—
215C22×C4—2442no—
216C22×C4C22×D6112yes—
217C22×C4C22×D6112yes—
218C22×C4C22×D6111yescharacteristic
219C22×C4C22×D6111yescharacteristic
220C4⋊C4—22no—
221C22⋊C4—22no—
222C22⋊C4—42no—
223C22⋊C4—1224no—
224C22⋊C4—1222no—
225C22⋊C4—1222no—
226C22⋊C4—1222no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C22⋊C4—2442no—
230C42—614no—
231C23—21no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23—22no—
236C23—614no—
237C23—1222no—
238C23—1222no—
239C23—1222no—
240C23—1222no—
241C23—1222no—
242C23—1222no—
243C23—1221no—
244C23—1222no—
245C23—1221no—
246C23—1221no—
247C23—1222no—
248C23C23×D6111yescharacteristic
249Q8—2444no—
250D4—1228no—
251D4—2448no—
252D4—2444no—
253D4—2448no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—612no—
264C2×C4—612no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—2448no—
274C2×C4D4×D6112yes—
275C22—41no—
276C22—41no—
277C22—41no—
278C22—42no—
279C22—42no—
280C22—1224no—
281C22—1224no—
282C22—1224no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22—2442no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22—2442no—
291C22—2442no—
292C22C2×D4×D6111yescharacteristic
293C22#41×D6112yes—
294C22#1451982211yescharacteristic
295C22#1451982311yescharacteristic
296C22#1451982312yes—
297C4—22no—
298C4—42no—
299C4—41no—
300C4—42no—
301C4—1222no—
302C4—1222no—
303C4—2441no—
304C4—2442no—
305C2—81no—
306C2—4881no—
307C2—2444no—
308C2#1684027011yescharacteristic
309C2#1684032811yescharacteristic
310C2#1684033011yescharacteristic
311C2#1684034812yes—
312C2#1684035112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2631
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14519763C2semidirect
2. C2×#14519739C2semidirect
3. #16839688C2semidirect
4. #16839675C2semidirect
5. #16839672C2semidirect
6. #16839671C2semidirect
7. #16839671C2semidirect
8. #16839640C2semidirect
9. #16839638C2semidirect
10. #16839629C2semidirect
11. C61×#397C2semidirect
73. C4×Dic61D4semidirect
160. #397D61semidirect
168. C61#2631semidirect