Finite Group Databasebeta

← #21449451

Subgroups — #21449451

Order 7808.

1348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 181 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
1C22×D4×D61C211yesmaximal, characteristic, complemented
2C2×#14519773C212yesmaximal, complemented
3C2×#14519750C211yesmaximal, characteristic, complemented
4C2×#14519747C212yesmaximal, complemented
5C2×#14519745C212yesmaximal, complemented
6#16839672C211yesmaximal, characteristic, complemented
7#16839671C211yesmaximal, characteristic, complemented
8#16839670C211yesmaximal, characteristic, complemented
9#16839662C212yesmaximal, complemented
10#16839609C211yesmaximal, characteristic, complemented
11C61×#392C211yesmaximal, characteristic, complemented
12C24×D61C2212yes—
13C22×D244C2211yescharacteristic
14C22×D244C2211yescharacteristic
15C22×D244C2212yescomplemented
16C22×C22⋊D61C2211yescharacteristic
17C22×C22⋊D61C2212yes—
18C22×C22⋊D61C2211yescharacteristic, complemented
19C22×C22⋊D61C2212yescomplemented
20C22×C22⋊D61C2212yescomplemented
21C2×D4×D61—28no—
22C2×D4×D61—24no—
23C22×C4×D61C2211yescharacteristic
24#14519773—28no—
25#14519750—24no—
26#14519747—28no—
27#14519745—28no—
28C2×#11758196C2211yescharacteristic, complemented
29C2×C22⋊Dic61C2212yescomplemented
30C2×#11758198C2212yes—
31C2×#11758198C2212yescomplemented
32C2×#11758198C2212yescomplemented
33C2×#11758198C2211yescharacteristic, complemented
34C2×C4×Dic61C2212yescomplemented
35#14519684C2211yescharacteristic, complemented
36C22×D4×C61C2211yescharacteristic
37C22×D4×C61C2212yescomplemented
38C2×C22⋊C4×C61C2212yescomplemented
39C2×C22⋊C4×C61C2211yescharacteristic, complemented
40#95×C61C2211yescharacteristic, complemented
41C24×C61C2311yescharacteristic
42C24×C61C2312yes—
43C23×D61—24no—
44C23×D61—24no—
45C23×D61—24no—
46C23×D61—24no—
47C23×D61—24no—
48C23×D61—42no—
49C23×D61—42no—
50C23×D61C2311yescharacteristic
51C23×D61C2312yes—
52C23×D61C2311yescharacteristic
53C2×D4×C61—24no—
54C2×D4×C61—24no—
55C2×D4×C61—22no—
56C2×D4×C61—24no—
57C2×D4×C61—42no—
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2312yes—
61C2×C22⋊D61—24no—
62C2×C22⋊D61—24no—
63C2×C22⋊D61—22no—
64C2×C22⋊D61—24no—
65C2×C22⋊D61—24no—
66C2×C22⋊D61—24no—
67C2×C22⋊D61—22no—
68C2×C22⋊D61—24no—
69C2×C22⋊D61—24no—
70C2×C22⋊D61—24no—
71C2×C22⋊D61—42no—
72C2×C22⋊D61—42no—
73C2×C22⋊D61D418yescomplemented
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2312yes—
76C22×Dic61C2311yescharacteristic
77D4×D61—232no—
78C2×D244—24no—
79C2×D244—22no—
80C2×D244—24no—
81C2×D244—22no—
82C2×D244—24no—
83C2×D244—24no—
84C2×D244—42no—
85C2×C4×D61—24no—
86C2×C4×D61D414yescomplemented
87C22⋊C4×C61—22no—
88C22⋊C4×C61—24no—
89C22⋊Dic61—24no—
90#11758198—22no—
91#11758198—24no—
92#11758198—24no—
93#11758198D418yescomplemented
94#11758196—22no—
95C4×Dic61—24no—
96C23×C61—22no—
97C23×C61—22no—
98C23×C61—22no—
99C23×C61—22no—
100C23×C61—22no—
101C23×C61—22no—
102C23×C61—21no—
103C23×C61—22no—
104C23×C61—22no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61C2×D414yes—
108C23×C61C2411yescharacteristic
109C22×D61—22no—
110C22×D61—21no—
111C22×D61—21no—
112C22×D61—216no—
113C22×D61—22no—
114C22×D61—22no—
115C22×D61—22no—
116C22×D61—22no—
117C22×D61—22no—
118C22×D61—22no—
119C22×D61—21no—
120C22×D61—22no—
121C22×D61—22no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—48no—
125C22×D61—48no—
126C22×D61—48no—
127C22×D61—48no—
128C22×D61—48no—
129C22×D61—48no—
130C22×D61C2×D414yes—
131C22×D61C2×D414yes—
132C22×D61C2×D412yes—
133D4×C61—28no—
134D4×C61—48no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—21no—
139C2×C4×C61—22no—
140C2×C4×C61C2×D412yes—
141C2×C4×C61C2×D414yescomplemented
142C22⋊D61—216no—
143C22⋊D61—48no—
144C22⋊D61—48no—
145C22⋊D61—44no—
146C22⋊D61—44no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—21no—
150C2×Dic61—22no—
151C2×Dic61C2×D414yes—
152C2×Dic61C2×D412yes—
153C2×Dic61C2×D414yescomplemented
154D244—28no—
155D244—48no—
156D244—44no—
157C4×D61—28no—
158C22×C61—24no—
159C22×C61—24no—
160C22×C61—24no—
161C22×C61—42no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—42no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—42no—
169C22×C61—42no—
170C22×C61C22×D411yescharacteristic
171C22×C61C22×D412yes—
172C22×C61C22×D412yes—
173C22×C61H(5,𝔽2)11yescharacteristic
174C22×C61H(5,𝔽2)11yescharacteristic
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—24no—
178C2×D61—24no—
179C2×D61—24no—
180C2×D61—24no—
181C2×D61—24no—
182C2×D61—432no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61—41no—
188C2×D61—41no—
189C2×D61—41no—
190C2×D61—42no—
191C2×D61—42no—
192C2×D61#12714yescomplemented
193C4×C61—22no—
194C4×C61—24no—
195C4×C61—41no—
196Dic61—24no—
197Dic61—41no—
198Dic61#12014yescomplemented
199#2433—611nomaximal, Sylow
200C2×C61—44no—
201C2×C61—81no—
202C2×C61C2×#12011yescharacteristic
203C2×C61C2×#12711yescharacteristic
204C2×C61#53511yescharacteristic
205C2×C61D4212yes—
206C2×C61D4212yes—
207D61—24no—
208D61—44no—
209D61—81no—
210C23×D4—611no—
211C2×#127—612no—
212C2×#121—611no—
213C2×#120—612no—
214C2×#120—612no—
215#392—611no—
216#392—611no—
217#392—611no—
218#392D6111yescharacteristic, complemented
219#390—612no—
220C4×C22⋊C4—611no—
221C61#243311yescharacteristic, complemented, Sylow
222C25—612no—
223C22×D4—612no—
224C22×D4—611no—
225C22×D4—611no—
226C22×D4—612no—
227C22×D4—612no—
228C22×D4—611no—
229C22×D4—611no—
230C22×D4—612no—
231C22×D4—1224no—
232C22×D4—1228no—
233C22×D4C2×D6111yescharacteristic
234C22×D4C2×D6112yescomplemented
235C23×C4—611no—
236#127—1228no—
237#121—1224no—
238#120—1228no—
239#120—1228no—
240C2×C4⋊C4—611no—
241C2×C22⋊C4—612no—
242C2×C22⋊C4—612no—
243C2×C22⋊C4—612no—
244C2×C22⋊C4—612no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4C2×D6112yescomplemented
247C2×C22⋊C4C2×D6111yescharacteristic, complemented
248C2×C42—612no—
249#95—611no—
250#95C2×D6111yescharacteristic, complemented
251C24—611no—
252C24—612no—
253C24—611no—
254C24—1224no—
255C24—1224no—
256C24—1224no—
257C24—1224no—
258C24—1224no—
259C24—2442no—
260C24—2442no—
261C24C22×D6111yescharacteristic
262C24C22×D6112yes—
263C2×D4—24no—
264C2×D4—24no—
265C2×D4—22no—
266C2×D4—24no—
267C2×D4—42no—
268C2×D4—618no—
269C2×D4—1224no—
270C2×D4—1224no—
271C2×D4—1222no—
272C2×D4—1224no—
273C2×D4—1224no—
274C2×D4—1224no—
275C2×D4—1224no—
276C2×D4—1224no—
277C2×D4—1222no—
278C2×D4—1224no—
279C2×D4—12232no—
280C2×D4—1224no—
281C2×D4—1222no—
282C2×D4—1224no—
283C2×D4—1224no—
284C2×D4—1222no—
285C2×D4—1224no—
286C2×D4—2442no—
287C2×D4—2442no—
288C2×D4—2442no—
289C22×C4—611no—
290C22×C4—612no—
291C22×C4—614no—
292C22×C4—611no—
293C22×C4—1224no—
294C22×C4C22×D6111yescharacteristic
295C22×C4C22×D6111yescharacteristic
296C22×C4C22×D6112yes—
297C4⋊C4—1222no—
298C22⋊C4—22no—
299C22⋊C4—24no—
300C22⋊C4—618no—
301C22⋊C4—1224no—
302C22⋊C4—1224no—
303C22⋊C4—1222no—
304C22⋊C4—1224no—
305C42—1224no—
306C23—22no—
307C23—22no—
308C23—22no—
309C23—22no—
310C23—22no—
311C23—22no—
312C23—21no—
313C23—22no—
314C23—22no—
315C23—21no—
316C23—21no—
317C23—614no—
318C23—612no—
319C23—614no—
320C23—12216no—
321C23—1222no—
322C23—1221no—
323C23—1221no—
324C23—1222no—
325C23—1222no—
326C23—1222no—
327C23—1222no—
328C23—1222no—
329C23—1222no—
330C23—1221no—
331C23—1222no—
332C23—1222no—
333C23—1221no—
334C23—1221no—
335C23—2448no—
336C23—2448no—
337C23—2448no—
338C23—2448no—
339C23—2448no—
340C23—2448no—
341C23D4×D6114yes—
342C23C23×D6111yescharacteristic
343D4—28no—
344D4—48no—
345D4—1228no—
346D4—12216no—
347D4—2448no—
348D4—2444no—
349D4—2444no—
350D4—2448no—
351D4—2448no—
352D4—2444no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—21no—
358C2×C4—614no—
359C2×C4—612no—
360C2×C4—614no—
361C2×C4—1228no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1222no—
365C2×C4—1221no—
366C2×C4D4×D6112yes—
367C2×C4D4×D6114yescomplemented
368C22—24no—
369C22—24no—
370C22—24no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—42no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—42no—
379C22—42no—
380C22—614no—
381C22—1222no—
382C22—1222no—
383C22—1224no—
384C22—1224no—
385C22—1224no—
386C22—1224no—
387C22—1224no—
388C22—24432no—
389C22—2441no—
390C22—2441no—
391C22—2441no—
392C22—2442no—
393C22—2442no—
394C22—2442no—
395C22—2442no—
396C22—2442no—
397C22—2442no—
398C22C2×D4×D6111yescharacteristic
399C22C2×D4×D6112yes—
400C22C2×D4×D6112yes—
401C22#1451982211yescharacteristic
402C22#1451982311yescharacteristic
403C4—22no—
404C4—24no—
405C4—41no—
406C4—614no—
407C4—1224no—
408C4—2441no—
409C2—44no—
410C2—81no—
411C2—1224no—
412C2—4881no—
413C2—2444no—
414C2#120×D6111yescharacteristic
415C2#127×D6111yescharacteristic
416C2#1684032811yescharacteristic
417C2#1684039412yes—
418C2#1684039612yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2433
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D61C2semidirect
2. C2×#14519773C2semidirect
3. C2×#14519750C2semidirect
4. C2×#14519747C2semidirect
5. C2×#14519745C2semidirect
6. #16839672C2semidirect
7. #16839671C2semidirect
8. #16839670C2semidirect
9. #16839662C2semidirect
10. #16839609C2semidirect
11. C61×#392C2semidirect
15. C22×D244C22semidirect
18. C22×C22⋊D61C22semidirect
19. C22×C22⋊D61C22semidirect
20. C22×C22⋊D61C22semidirect
28. C2×#11758196C22semidirect
29. C2×C22⋊Dic61C22semidirect
31. C2×#11758198C22semidirect
32. C2×#11758198C22semidirect
33. C2×#11758198C22semidirect
34. C2×C4×Dic61C22semidirect
35. #14519684C22semidirect
37. C22×D4×C61C22semidirect
38. C2×C22⋊C4×C61C22semidirect
39. C2×C22⋊C4×C61C22semidirect
40. #95×C61C22semidirect
73. C2×C22⋊D61D4semidirect
86. C2×C4×D61D4semidirect
93. #11758198D4semidirect
141. C2×C4×C61C2×D4semidirect
153. C2×Dic61C2×D4semidirect
192. C2×D61#127semidirect
198. Dic61#120semidirect
218. #392D61semidirect
221. C61#2433semidirect
234. C22×D4C2×D61semidirect
246. C2×C22⋊C4C2×D61semidirect
247. C2×C22⋊C4C2×D61semidirect
250. #95C2×D61semidirect
367. C2×C4D4×D61semidirect