Finite Group Databasebeta

← #21451596

Subgroups — #21451596

Order 7808.

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

normal subgroups only

This group has 702 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×#14519745C211yesmaximal, characteristic
2C22×#11758198C211yesmaximal, characteristic, complemented
3#16839691C212yesmaximal, complemented
4#16839689C212yesmaximal, complemented
5#16839678C212yesmaximal, complemented
6#16839677C212yesmaximal, complemented
7#16839642C211yesmaximal, characteristic, complemented
8#16839637C211yesmaximal, characteristic, complemented
9#16839635C211yesmaximal, characteristic, complemented
10#16839617C211yesmaximal, characteristic, complemented
11C61×#386C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C23×Dic61C2211yescharacteristic
16#14519745—24no—
17C2×C4⋊Dic61C2212yescomplemented
18C2×#11758196C2212yescomplemented
19C2×C22⋊Dic61C2211yescharacteristic
20C2×C22⋊Dic61C2211yescharacteristic
21C2×C22⋊Dic61C2212yescomplemented
22C2×#11758198—24no—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29#14519684C2212yescomplemented
30#14519684C2212yescomplemented
31#14519684C2212yescomplemented
32C22×D4×C61C2211yescharacteristic
33C23×C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yescomplemented
36#95×C61C2212yescomplemented
37C24×C61C2311yescharacteristic
38C24×C61C2311yescharacteristic
39C23×D61—22no—
40C23×D61—22no—
41C23×D61—42no—
42C23×D61—42no—
43C23×D61D414yes—
44C23×D61C2311yescharacteristic
45C23×D61C2311yescharacteristic
46C2×D4×C61—22no—
47C2×D4×C61—22no—
48C2×D4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—42no—
51C22×C4×C61C2311yescharacteristic
52C22×C4×C61C2312yes—
53C22×C4×C61C2312yes—
54C2×C22⋊D61—22no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—42no—
57C2×C22⋊D61—42no—
58C22×Dic61—22no—
59C22×Dic61—42no—
60C22×Dic61C2312yes—
61C22×Dic61C2311yescharacteristic
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2312yes—
64C22⋊C4×C61—22no—
65C22⋊C4×C61—42no—
66C22⋊Dic61—22no—
67C22⋊Dic61—22no—
68C22⋊Dic61—42no—
69#11758198—24no—
70#11758198—24no—
71#11758198—22no—
72#11758198—22no—
73#11758198—42no—
74#11758198—42no—
75C4⋊Dic61—42no—
76#11758196—42no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—21no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61C2×D412yes—
85C23×C61#4112yes—
86C23×C61#4112yes—
87C23×C61C2411yescharacteristic
88C22×D61—28no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—21no—
92C22×D61—21no—
93C22×D61—22no—
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—22no—
97C22×D61—44no—
98C22×D61—44no—
99C22×D61—48no—
100C22×D61—48no—
101C22×D61C2×D412yes—
102C22×D61C2×D412yes—
103D4×C61—44no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—22no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—22no—
110C2×C4×C61—22no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—44no—
114C22⋊D61—44no—
115C22⋊D61—44no—
116C2×Dic61—22no—
117C2×Dic61—21no—
118C2×Dic61—21no—
119C2×Dic61—22no—
120C2×Dic61—22no—
121C2×Dic61—22no—
122C2×Dic61—22no—
123C2×Dic61—22no—
124C2×Dic61—22no—
125C2×Dic61—22no—
126C2×Dic61—44no—
127C22×C61—22no—
128C22×C61—22no—
129C22×C61—24no—
130C22×C61—24no—
131C22×C61—41no—
132C22×C61—41no—
133C22×C61—41no—
134C22×C61—42no—
135C22×C61—42no—
136C22×C61#12314yes—
137C22×C61C22×D411yescharacteristic
138C22×C61C2×#4111yescharacteristic
139C22×C61C2×#4111yescharacteristic
140C22×C61H(5,𝔽2)12yes—
141C22×C61H(5,𝔽2)12yes—
142C2×D61—22no—
143C2×D61—22no—
144C2×D61—22no—
145C2×D61—22no—
146C2×D61—22no—
147C2×D61—22no—
148C2×D61—416no—
149C2×D61—42no—
150C2×D61—42no—
151C2×D61—42no—
152C2×D61—42no—
153C4×C61—41no—
154C4×C61—42no—
155C4×C61—42no—
156Dic61—42no—
157Dic61—41no—
158Dic61—41no—
159Dic61—42no—
160#2622—611nomaximal, Sylow
161C2×C61—24no—
162C2×C61—81no—
163C2×C61C2×#12311yescharacteristic
164C2×C61#53411yescharacteristic
165C2×C61#53411yescharacteristic
166C2×C61#53812yes—
167C2×C61#53812yes—
168D61—42no—
169D61—42no—
170C2×#120—611no—
171C22×C22⋊C4—611no—
172#397—612no—
173#397—612no—
174#394—612no—
175#394—612no—
176#386—611no—
177#386D6111yescharacteristic, complemented
178#385—611no—
179#385—611no—
180#379—611no—
181C61#262211yescharacteristic, complemented, Sylow
182C25—611no—
183C22×D4—611no—
184C22×D4—611no—
185C22×D4C2×D6111yescharacteristic
186C23×C4—611no—
187C23×C4C2×D6111yescharacteristic
188#120—1224no—
189C2×C4⋊C4—612no—
190C2×C4⋊C4—612no—
191C2×C22⋊C4—611no—
192C2×C22⋊C4—611no—
193C2×C22⋊C4—612no—
194C2×C22⋊C4—612no—
195C2×C22⋊C4—611no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—612no—
198C2×C22⋊C4—612no—
199C2×C22⋊C4—612no—
200C2×C22⋊C4—1224no—
201C2×C22⋊C4C2×D6111yescharacteristic
202C2×C22⋊C4C2×D6112yescomplemented
203#95—612no—
204#95—612no—
205#95—612no—
206#95C2×D6112yescomplemented
207C24—611no—
208C24—611no—
209C24—614no—
210C24—1222no—
211C24—1222no—
212C24—2442no—
213C24—2442no—
214C24C22×D6111yescharacteristic
215C24C22×D6111yescharacteristic
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—1222no—
220C2×D4—1222no—
221C2×D4—2442no—
222C2×D4—2442no—
223C22×C4—22no—
224C22×C4—42no—
225C22×C4—612no—
226C22×C4—612no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—1222no—
230C22×C4—2442no—
231C22×C4C22×D6111yescharacteristic
232C22×C4C22×D6112yes—
233C22×C4C22×D6112yes—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C22⋊C4—22no—
237C22⋊C4—42no—
238C22⋊C4—1224no—
239C22⋊C4—1224no—
240C22⋊C4—1222no—
241C22⋊C4—1222no—
242C22⋊C4—1222no—
243C22⋊C4—1222no—
244C22⋊C4—2442no—
245C22⋊C4—2442no—
246C22⋊C4—2442no—
247C23—22no—
248C23—22no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—22no—
253C23—22no—
254C23—612no—
255C23—612no—
256C23—1221no—
257C23—1221no—
258C23—1221no—
259C23—1221no—
260C23—1222no—
261C23—1222no—
262C23—1222no—
263C23—1222no—
264C23—1228no—
265C23—2444no—
266C23—2444no—
267C23—2448no—
268C23—2448no—
269C23#1175822212yes—
270C23D4×D6112yes—
271C23#1175822412yes—
272C23C23×D6111yescharacteristic
273D4—44no—
274D4—2444no—
275D4—2444no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—1222no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1222no—
290C2×C4—1222no—
291C2×C4—1222no—
292C2×C4—1222no—
293C2×C4—1222no—
294C2×C4—1222no—
295C2×C4—1222no—
296C2×C4—2444no—
297C22—22no—
298C22—22no—
299C22—24no—
300C22—24no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—42no—
305C22—42no—
306C22—1222no—
307C22—1222no—
308C22—1222no—
309C22—1222no—
310C22—1222no—
311C22—1222no—
312C22—24416no—
313C22—2442no—
314C22—2442no—
315C22—2442no—
316C22—2442no—
317C22#1451975914yes—
318C22C2×D4×D6111yescharacteristic
319C22C2×#1175822411yescharacteristic
320C22C2×#1175822211yescharacteristic
321C22#1451982212yes—
322C22#1451982312yes—
323C4—41no—
324C4—42no—
325C4—42no—
326C4—2441no—
327C4—2442no—
328C4—2441no—
329C4—2442no—
330C2—24no—
331C2—81no—
332C2—2442no—
333C2—2442no—
334C2C2×#1451975911yescharacteristic
335C2#1684032211yescharacteristic
336C2#1684032311yescharacteristic
337C2#1684034512yes—
338C2#1684034912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2622
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×#11758198C2semidirect
3. #16839691C2semidirect
4. #16839689C2semidirect
5. #16839678C2semidirect
6. #16839677C2semidirect
7. #16839642C2semidirect
8. #16839637C2semidirect
9. #16839635C2semidirect
10. #16839617C2semidirect
11. C61×#386C2semidirect
17. C2×C4⋊Dic61C22semidirect
18. C2×#11758196C22semidirect
21. C2×C22⋊Dic61C22semidirect
29. #14519684C22semidirect
30. #14519684C22semidirect
31. #14519684C22semidirect
35. C2×C22⋊C4×C61C22semidirect
36. #95×C61C22semidirect
177. #386D61semidirect
181. C61#2622semidirect
202. C2×C22⋊C4C2×D61semidirect
206. #95C2×D61semidirect