Finite Group Databasebeta

← #21451952

Subgroups — #21451952

Order 7808.

598 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519762C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3#16839688C211yesmaximal, characteristic, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839679C212yesmaximal, complemented
6#16839672C212yesmaximal, complemented
7#16839672C211yesmaximal, characteristic, complemented
8#16839663C212yesmaximal, complemented
9#16839651C212yesmaximal, complemented
10#16839609C211yesmaximal, characteristic, complemented
11C61×#398C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×D244C2211yescharacteristic
15C22×D244C2212yes—
16C22×C4×D61C2211yescharacteristic
17#14519762—24no—
18#14519752—24no—
19C2×#11758196C2211yescharacteristic
20C2×#11758198C2211yescharacteristic
21C2×#11758198C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×C4×Dic61C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C23×D61C2312yes—
39C23×D61C2311yescharacteristic
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×D244—24no—
49C2×D244—22no—
50C2×D244—22no—
51C2×D244—24no—
52C2×D244—42no—
53C2×D244—42no—
54C2×D244—42no—
55C2×D244—42no—
56C2×D244—42no—
57C2×D244—42no—
58C2×C4×D61—42no—
59C2×C4×D61D414yescomplemented
60C4⋊C4×C61—22no—
61C4⋊C4×C61—22no—
62C4⋊C4×C61—42no—
63#11758198—22no—
64#11758198—22no—
65#11758198—24no—
66#11758198—24no—
67#11758198—24no—
68#11758198—22no—
69#11758198—42no—
70#11758198—42no—
71#11758198—42no—
72#11758196—22no—
73C4×Dic61—42no—
74C23×C61C2411yescharacteristic
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—21no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—21no—
91C22×D61C2×D412yes—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—21no—
102C2×C4×C61—22no—
103C2×C4×C61C2×D412yes—
104C2×C4×C61#4114yes—
105C2×Dic61—22no—
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61C2×D412yes—
112D244—44no—
113D244—48no—
114D244—44no—
115D244—48no—
116C4×D61—44no—
117C22×C61C22×D411yescharacteristic
118C22×C61C2×#4112yes—
119C22×C61H(5,𝔽2)11yescharacteristic
120C22×C61H(5,𝔽2)12yes—
121C22×C61H(5,𝔽2)11yescharacteristic
122C2×D61—22no—
123C2×D61—22no—
124C2×D61—22no—
125C2×D61—42no—
126C2×D61—42no—
127C2×D61—41no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—41no—
131C2×D61—42no—
132C2×D61—41no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61—42no—
139C4×C61—22no—
140C4×C61—24no—
141C4×C61—41no—
142C4×C61—42no—
143C4×C61—41no—
144Dic61—22no—
145Dic61—41no—
146Dic61—42no—
147#2661—611nomaximal, Sylow
148C2×C61#53211yescharacteristic
149C2×C61#53411yescharacteristic
150C2×C61#53511yescharacteristic
151C2×C61#53812yes—
152C2×C61#54012yes—
153D61—42no—
154D61—82no—
155D61—81no—
156C2×#123—611no—
157C2×#121—611no—
158#398D6111yescharacteristic, complemented
159#397—611no—
160#394—611no—
161#394—612no—
162#392—611no—
163#392—612no—
164#390—612no—
165#388—612no—
166C4×C22⋊C4—611no—
167C61#266111yescharacteristic, complemented, Sylow
168C22×D4—612no—
169C22×D4—611no—
170C22×D4—611no—
171C22×D4—612no—
172C23×C4—611no—
173#123—1224no—
174#121—1224no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4C2×D6111yescharacteristic
177C2×C4⋊C4C2×D6111yescharacteristic
178C2×C4⋊C4C2×D6112yes—
179C2×C22⋊C4—612no—
180C2×C22⋊C4—611no—
181C2×C22⋊C4—611no—
182C2×C22⋊C4—611no—
183C2×C22⋊C4—612no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—612no—
187C2×C22⋊C4—612no—
188C2×C42—612no—
189#95—611no—
190#95—612no—
191#95C2×D6111yescharacteristic
192#95C2×D6112yes—
193C24—611no—
194C24—611no—
195C24—612no—
196C2×D4—1224no—
197C2×D4—1222no—
198C2×D4—1222no—
199C2×D4—1224no—
200C2×D4—2442no—
201C2×D4—2442no—
202C2×D4—2442no—
203C2×D4—2442no—
204C2×D4—2442no—
205C2×D4—2442no—
206C22×C4—611no—
207C22×C4—614no—
208C22×C4—612no—
209C22×C4—611no—
210C22×C4—2442no—
211C22×C4C22×D6112yes—
212C22×C4C22×D6111yescharacteristic
213C22×C4C22×D6111yescharacteristic
214C22×C4C22×D6111yescharacteristic
215C22×C4C22×D6112yes—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—42no—
219C4⋊C4—1222no—
220C22⋊C4—1224no—
221C22⋊C4—1222no—
222C22⋊C4—1222no—
223C22⋊C4—1222no—
224C22⋊C4—1224no—
225C22⋊C4—1224no—
226C22⋊C4—2442no—
227C22⋊C4—2442no—
228C22⋊C4—2442no—
229C42—2442no—
230C23—612no—
231C23—1222no—
232C23—1221no—
233C23—1222no—
234C23—1221no—
235C23—1221no—
236C23—1222no—
237C23—1222no—
238C23—1222no—
239C23—1222no—
240C23—1222no—
241C23—1221no—
242C23—1221no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23—1222no—
247C23C23×D6111yescharacteristic
248D4—2444no—
249D4—2448no—
250D4—2444no—
251D4—2448no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—612no—
264C2×C4—1222no—
265C2×C4—1221no—
266C2×C4—1222no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—2444no—
271C2×C4D4×D6112yes—
272C2×C4#1175822614yes—
273C22—1222no—
274C22—1222no—
275C22—1222no—
276C22—2441no—
277C22—2442no—
278C22—2442no—
279C22—2441no—
280C22—2442no—
281C22—2441no—
282C22—2442no—
283C22—2442no—
284C22—2442no—
285C22—2442no—
286C22—2442no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22C2×D4×D6111yescharacteristic
291C22C2×#1175822612yes—
292C22#1451982211yescharacteristic
293C22#1451982312yes—
294C22#1451982311yescharacteristic
295C4—22no—
296C4—24no—
297C4—41no—
298C4—41no—
299C4—42no—
300C4—1222no—
301C4—2441no—
302C4—2442no—
303C2—4882no—
304C2—4881no—
305C2—2442no—
306C2#1684031311yescharacteristic
307C2#1684032311yescharacteristic
308C2#1684032811yescharacteristic
309C2#1684035212yes—
310C2#1684036812yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#398C2
hypercenter#398D61
hypocenterC61#2661
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
2. C2×#14519752C2semidirect
3. #16839688C2semidirect
4. #16839679C2semidirect
5. #16839679C2semidirect
6. #16839672C2semidirect
7. #16839672C2semidirect
8. #16839663C2semidirect
9. #16839651C2semidirect
10. #16839609C2semidirect
11. C61×#398C2semidirect
59. C2×C4×D61D4semidirect
158. #398D61semidirect
167. C61#2661semidirect