Finite Group Databasebeta

← #21449144

Subgroups — #21449144

Order 7808.

1116 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C23×C22⋊D61C211yesmaximal, characteristic
2C2×#14519759C212yesmaximal, complemented
3C2×C22⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839678C212yesmaximal, complemented
5#16839677C212yesmaximal, complemented
6#16839638C212yesmaximal, complemented
7#16839637C211yesmaximal, characteristic, complemented
8#16839634C211yesmaximal, characteristic, complemented
9#16839618C211yesmaximal, characteristic, complemented
10#16839617C211yesmaximal, characteristic, complemented
11C61×#379C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C22×C22⋊D61—24no—
14C22×C22⋊D61—28no—
15C22×C22⋊D61C2212yes—
16C22×C22⋊D61C2212yes—
17C23×Dic61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic, complemented
19C22×C4×D61C2211yescharacteristic, complemented
20#14519759—28no—
21C2×C4⋊Dic61C2212yescomplemented
22C2×#11758196C2212yescomplemented
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2212yescomplemented
26C2×C22⋊Dic61C2212yescomplemented
27C2×#11758198C2211yescharacteristic, complemented
28C2×#11758198C2211yescharacteristic, complemented
29C2×#11758198C2212yescomplemented
30C2×#11758198C2212yescomplemented
31C22⋊C4×D61—24no—
32#14519684C2212yescomplemented
33#14519684C2212yescomplemented
34C25×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2212yescomplemented
38C2×C22⋊C4×C61C2212yescomplemented
39C24×C61—24no—
40C24×C61—22no—
41C24×C61—22no—
42C24×C61—22no—
43C24×C61—42no—
44C24×C61C2312yes—
45C24×C61C2311yescharacteristic
46C23×D61—22no—
47C23×D61—22no—
48C23×D61—24no—
49C23×D61—42no—
50C23×D61D414yes—
51C23×D61C2311yescharacteristic
52C23×D61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2312yes—
56C2×C22⋊D61—232no—
57C2×C22⋊D61—24no—
58C2×C22⋊D61—24no—
59C2×C22⋊D61—24no—
60C2×C22⋊D61—24no—
61C2×C22⋊D61—24no—
62C2×C22⋊D61D418yes—
63C22×Dic61—22no—
64C22×Dic61—24no—
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2312yes—
68C22×Dic61C2312yes—
69C2×C4×D61—22no—
70C2×C4×D61—22no—
71C2×C4×D61—24no—
72C2×C4×D61—42no—
73C22⋊C4×C61—22no—
74C22⋊C4×C61—24no—
75C22⋊C4×C61—22no—
76C22⋊C4×C61—42no—
77C22⋊Dic61—22no—
78C22⋊Dic61—24no—
79C22⋊Dic61—22no—
80C22⋊Dic61—42no—
81#11758198—22no—
82#11758198—22no—
83#11758198—24no—
84#11758198—42no—
85C4⋊Dic61—24no—
86#11758196—24no—
87C23×C61—22no—
88C23×C61—22no—
89C23×C61—28no—
90C23×C61—22no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61—22no—
95C23×C61—22no—
96C23×C61—48no—
97C23×C61—48no—
98C23×C61—44no—
99C23×C61—44no—
100C23×C61C2×D414yes—
101C23×C61C2×D412yes—
102C23×C61#4112yes—
103C23×C61#4112yes—
104C23×C61C2411yescharacteristic
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—22no—
108C22×D61—28no—
109C22×D61—22no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—22no—
113C22×D61—28no—
114C22×D61—44no—
115C22×D61—48no—
116C22×D61—48no—
117C22×D61C2×D412yes—
118C22×D61C2×D414yes—
119C22×D61C2×D412yes—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C22⋊D61—216no—
128C22⋊D61—216no—
129C2×Dic61—28no—
130C2×Dic61—22no—
131C2×Dic61—22no—
132C2×Dic61—22no—
133C2×Dic61—22no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—22no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61C2×D414yes—
140C4×D61—44no—
141C4×D61—44no—
142C22×C61—22no—
143C22×C61—22no—
144C22×C61—24no—
145C22×C61—24no—
146C22×C61—24no—
147C22×C61—24no—
148C22×C61—24no—
149C22×C61—416no—
150C22×C61—42no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61#12314yescomplemented
155C22×C61C22×D411yescharacteristic
156C22×C61C22×D412yes—
157C22×C61C2×#4111yescharacteristic
158C22×C61C2×#4111yescharacteristic
159C22×C61H(5,𝔽2)12yes—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—24no—
163C2×D61—24no—
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—416no—
168C2×D61—42no—
169C2×D61—42no—
170C2×D61#12014yes—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—42no—
174Dic61—24no—
175Dic61—41no—
176Dic61—41no—
177Dic61—42no—
178#2405—611nomaximal, Sylow
179C2×C61—24no—
180C2×C61—44no—
181C2×C61C2×#12011yescharacteristic
182C2×C61C2×#12311yescharacteristic
183C2×C61#53411yescharacteristic
184C2×C61#54612yes—
185C2×C61#54612yes—
186D61—24no—
187D61—42no—
188C23×D4—611no—
189C2×#123—612no—
190C22×C22⋊C4—611no—
191#394—612no—
192#394—612no—
193#386—612no—
194#385—611no—
195#385—611no—
196#379—611no—
197#379—611no—
198#379D6111yescharacteristic, complemented
199C61#240511yescharacteristic, complemented, Sylow
200C25—611no—
201C25C2×D6111yescharacteristic
202C22×D4—612no—
203C22×D4—612no—
204C22×D4—1228no—
205C22×D4—1224no—
206C23×C4—611no—
207C23×C4—611no—
208C23×C4—611no—
209#123—1228no—
210C2×C4⋊C4—612no—
211C2×C4⋊C4—612no—
212C2×C22⋊C4—611no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4—611no—
215C2×C22⋊C4—611no—
216C2×C22⋊C4—611no—
217C2×C22⋊C4—612no—
218C2×C22⋊C4—612no—
219C2×C22⋊C4—612no—
220C2×C22⋊C4—1224no—
221C2×C22⋊C4C2×D6111yescharacteristic
222C2×C22⋊C4C2×D6111yescharacteristic
223C2×C22⋊C4C2×D6112yescomplemented
224C2×C22⋊C4C2×D6112yescomplemented
225#95—612no—
226#95—612no—
227C24—24no—
228C24—22no—
229C24—22no—
230C24—22no—
231C24—42no—
232C24—611no—
233C24—611no—
234C24—614no—
235C24—1224no—
236C24—1222no—
237C24—1222no—
238C24—2442no—
239C24C22×D6112yes—
240C24C22×D6111yescharacteristic
241C2×D4—618no—
242C2×D4—1224no—
243C2×D4—1224no—
244C2×D4—1224no—
245C2×D4—1224no—
246C2×D4—12232no—
247C2×D4—1224no—
248C22×C4—612no—
249C22×C4—611no—
250C22×C4—612no—
251C22×C4—611no—
252C22×C4—1222no—
253C22×C4—1222no—
254C22×C4—1224no—
255C22×C4—1224no—
256C22×C4—1222no—
257C22×C4—2442no—
258C22×C4C22×D6111yescharacteristic
259C22×C4C22×D6112yes—
260C22×C4C22×D6111yescharacteristic
261C4⋊C4—1224no—
262C4⋊C4—1224no—
263C22⋊C4—22no—
264C22⋊C4—24no—
265C22⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—1222no—
268C22⋊C4—1222no—
269C22⋊C4—1224no—
270C22⋊C4—1222no—
271C22⋊C4—1222no—
272C22⋊C4—1224no—
273C22⋊C4—2442no—
274C22⋊C4—2442no—
275C23—22no—
276C23—22no—
277C23—28no—
278C23—22no—
279C23—22no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—22no—
284C23—48no—
285C23—48no—
286C23—44no—
287C23—44no—
288C23—614no—
289C23—612no—
290C23—612no—
291C23—1228no—
292C23—1221no—
293C23—1221no—
294C23—1222no—
295C23—1222no—
296C23—1221no—
297C23—1221no—
298C23—1222no—
299C23—1228no—
300C23—2444no—
301C23—2448no—
302C23—2448no—
303C23#1175822212yes—
304C23D4×D6114yes—
305C23D4×D6112yes—
306C23#1175822412yes—
307C23C23×D6111yescharacteristic
308D4—12216no—
309D4—12216no—
310C2×C4—22no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—614no—
318C2×C4—1228no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1222no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1222no—
325C2×C4—1222no—
326C2×C4—1222no—
327C2×C4—1222no—
328C2×C4—2444no—
329C2×C4—2444no—
330C22—22no—
331C22—22no—
332C22—24no—
333C22—24no—
334C22—24no—
335C22—24no—
336C22—24no—
337C22—416no—
338C22—42no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—614no—
343C22—1222no—
344C22—1222no—
345C22—1224no—
346C22—1224no—
347C22—1222no—
348C22—1222no—
349C22—1222no—
350C22—24416no—
351C22—2442no—
352C22—2442no—
353C22#1451975914yescomplemented
354C22C2×D4×D6111yescharacteristic
355C22C2×D4×D6112yes—
356C22C2×#1175822411yescharacteristic
357C22C2×#1175822211yescharacteristic
358C22#1451982212yes—
359C4—41no—
360C4—41no—
361C4—42no—
362C4—1224no—
363C4—2441no—
364C4—2441no—
365C4—2442no—
366C2—24no—
367C2—44no—
368C2—1224no—
369C2—2442no—
370C2#120×D6111yescharacteristic
371C2C2×#1451975911yescharacteristic
372C2#1684032211yescharacteristic
373C2#1684039912yes—
374C2#1684040212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#379C2
hypercenter#379D61
hypocenterC61#2405
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#14519759C2semidirect
3. C2×C22⋊C4×D61C2semidirect
4. #16839678C2semidirect
5. #16839677C2semidirect
6. #16839638C2semidirect
7. #16839637C2semidirect
8. #16839634C2semidirect
9. #16839618C2semidirect
10. #16839617C2semidirect
11. C61×#379C2semidirect
18. C22×C4×D61C22semidirect
19. C22×C4×D61C22semidirect
21. C2×C4⋊Dic61C22semidirect
22. C2×#11758196C22semidirect
25. C2×C22⋊Dic61C22semidirect
26. C2×C22⋊Dic61C22semidirect
27. C2×#11758198C22semidirect
28. C2×#11758198C22semidirect
29. C2×#11758198C22semidirect
30. C2×#11758198C22semidirect
32. #14519684C22semidirect
33. #14519684C22semidirect
37. C2×C22⋊C4×C61C22semidirect
38. C2×C22⋊C4×C61C22semidirect
154. C22×C61#123semidirect
198. #379D61semidirect
199. C61#2405semidirect
223. C2×C22⋊C4C2×D61semidirect
224. C2×C22⋊C4C2×D61semidirect
353. C22#14519759semidirect