Finite Group Databasebeta

← #21449170

Subgroups — #21449170

Order 7808.

1232 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1232 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14519750C212yesmaximal, complemented
3C2×#14519747C212yesmaximal, complemented
4C2×#14519739C211yesmaximal, characteristic, complemented
5#16839679C211yesmaximal, characteristic, complemented
6#16839672C211yesmaximal, characteristic, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839662C212yesmaximal, complemented
9#16839621C211yesmaximal, characteristic, complemented
10#16839617C212yesmaximal, complemented
11C61×#394C211yesmaximal, characteristic, complemented
12C24×D61C2212yes—
13C22×D244C2211yescharacteristic
14C22×D244C2211yescharacteristic
15C22×D244C2212yescomplemented
16C22×C22⋊D61C2212yes—
17C22×C22⋊D61C2212yescomplemented
18C2×D4×D61—28no—
19C2×D4×D61—24no—
20C22×C4×D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic, complemented
22#14519750—28no—
23#14519747—28no—
24#14519739—24no—
25C2×#11758196C2212yescomplemented
26C2×C22⋊Dic61C2212yescomplemented
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2212yes—
29C2×#11758198C2211yescharacteristic, complemented
30C2×#11758198C2212yescomplemented
31C2×#11758198C2212yescomplemented
32C2×#11758198C2212yescomplemented
33C2×C4×Dic61C2211yescharacteristic, complemented
34#14519684C2211yescharacteristic, complemented
35C22×D4×C61C2211yescharacteristic
36C2×C4⋊C4×C61C2211yescharacteristic, complemented
37C2×C22⋊C4×C61C2212yescomplemented
38C2×C22⋊C4×C61C2212yescomplemented
39#95×C61C2211yescharacteristic, complemented
40C24×C61C2312yes—
41C23×D61—24no—
42C23×D61—24no—
43C23×D61—24no—
44C23×D61—24no—
45C23×D61—24no—
46C23×D61—42no—
47C23×D61—42no—
48C23×D61C2312yes—
49C23×D61C2311yescharacteristic
50C23×D61C2311yescharacteristic
51C2×D4×C61—24no—
52C2×D4×C61—22no—
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2312yes—
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C2×C22⋊D61—24no—
58C2×C22⋊D61—24no—
59C2×C22⋊D61—24no—
60C2×C22⋊D61—24no—
61C2×C22⋊D61—42no—
62C2×C22⋊D61D418yescomplemented
63C22×Dic61C2312yes—
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66D4×D61—232no—
67C2×D244—24no—
68C2×D244—22no—
69C2×D244—22no—
70C2×D244—22no—
71C2×D244—24no—
72C2×D244—24no—
73C2×D244—42no—
74C2×D244D414yescomplemented
75C2×C4×D61—24no—
76C2×C4×D61—22no—
77C2×C4×D61—24no—
78C2×C4×D61D414yescomplemented
79C4⋊C4×C61—22no—
80C22⋊C4×C61—24no—
81C22⋊C4×C61—24no—
82C22⋊Dic61—42no—
83#11758198—22no—
84#11758198—24no—
85#11758198—24no—
86#11758198—22no—
87#11758198—24no—
88#11758198—42no—
89#11758196—24no—
90C4×Dic61—22no—
91C23×C61—22no—
92C23×C61—22no—
93C23×C61—22no—
94C23×C61—22no—
95C23×C61—22no—
96C23×C61—22no—
97C23×C61C2×D414yes—
98C23×C61C2411yescharacteristic
99C22×D61—22no—
100C22×D61—22no—
101C22×D61—216no—
102C22×D61—21no—
103C22×D61—22no—
104C22×D61—22no—
105C22×D61—22no—
106C22×D61—22no—
107C22×D61—21no—
108C22×D61—22no—
109C22×D61—22no—
110C22×D61—22no—
111C22×D61—22no—
112C22×D61—48no—
113C22×D61—48no—
114C22×D61—48no—
115C22×D61—48no—
116C22×D61—48no—
117C22×D61—48no—
118C22×D61C2×D414yes—
119C22×D61C2×D412yes—
120C22×D61C2×D412yes—
121C22×D61C2×D412yescomplemented
122C22×D61#4112yes—
123D4×C61—28no—
124C2×C4×C61—21no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61C2×D412yes—
133C2×C4×C61C2×D412yescomplemented
134C22⋊D61—216no—
135C22⋊D61—48no—
136C2×Dic61—21no—
137C2×Dic61—22no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—22no—
141C2×Dic61C2×D412yes—
142C2×Dic61C2×D414yes—
143D244—28no—
144D244—28no—
145D244—48no—
146C4×D61—28no—
147C4×D61—44no—
148C22×C61—24no—
149C22×C61—24no—
150C22×C61—24no—
151C22×C61—42no—
152C22×C61—42no—
153C22×C61—42no—
154C22×C61—42no—
155C22×C61C22×D411yescharacteristic
156C22×C61C22×D412yes—
157C22×C61C22×D411yescharacteristic
158C22×C61C2×#4111yescharacteristic
159C22×C61H(5,𝔽2)12yes—
160C2×D61—22no—
161C2×D61—22no—
162C2×D61—24no—
163C2×D61—24no—
164C2×D61—24no—
165C2×D61—22no—
166C2×D61—24no—
167C2×D61—24no—
168C2×D61—24no—
169C2×D61—432no—
170C2×D61—41no—
171C2×D61—42no—
172C2×D61—41no—
173C2×D61—42no—
174C2×D61—42no—
175C2×D61—42no—
176C2×D61—42no—
177C2×D61#12114yescomplemented
178C4×C61—22no—
179C4×C61—22no—
180C4×C61—41no—
181C4×C61—42no—
182Dic61—41no—
183Dic61—42no—
184Dic61#12014yescomplemented
185#2408—611nomaximal, Sylow
186C2×C61—44no—
187C2×C61C2×#12011yescharacteristic
188C2×C61C2×#12111yescharacteristic
189C2×C61#53511yescharacteristic
190C2×C61D4212yes—
191C2×C61#54612yes—
192D61—24no—
193D61—42no—
194D61—44no—
195C23×D4—611no—
196C2×#121—612no—
197C2×#120—612no—
198C2×C4×D4—611no—
199#394—611no—
200#394D6111yescharacteristic, complemented
201#392—611no—
202#392—611no—
203#390—612no—
204#380—611no—
205#379—612no—
206C61#240811yescharacteristic, complemented, Sylow
207C25—612no—
208C22×D4—612no—
209C22×D4—612no—
210C22×D4—611no—
211C22×D4—611no—
212C22×D4—612no—
213C22×D4—1224no—
214C22×D4—1228no—
215C22×D4C2×D6111yescharacteristic
216C23×C4—611no—
217C23×C4—611no—
218#121—1228no—
219#120—1228no—
220C4×D4—1224no—
221C2×C4⋊C4—612no—
222C2×C4⋊C4C2×D6111yescharacteristic, complemented
223C2×C22⋊C4—611no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—612no—
226C2×C22⋊C4—612no—
227C2×C22⋊C4—612no—
228C2×C22⋊C4—612no—
229C2×C22⋊C4—612no—
230C2×C22⋊C4C2×D6112yescomplemented
231C2×C22⋊C4C2×D6112yescomplemented
232C2×C42—611no—
233#95—611no—
234#95C2×D6111yescharacteristic, complemented
235C24—611no—
236C24—612no—
237C24—611no—
238C24—1224no—
239C24—1224no—
240C24—1224no—
241C24—1224no—
242C24—1224no—
243C24—2442no—
244C24—2442no—
245C24C22×D6112yes—
246C2×D4—24no—
247C2×D4—22no—
248C2×D4—618no—
249C2×D4—614no—
250C2×D4—1222no—
251C2×D4—1224no—
252C2×D4—1222no—
253C2×D4—1224no—
254C2×D4—1224no—
255C2×D4—1224no—
256C2×D4—1224no—
257C2×D4—12232no—
258C2×D4—1224no—
259C2×D4—1224no—
260C2×D4—1222no—
261C2×D4—2442no—
262C2×D4—2442no—
263C22×C4—611no—
264C22×C4—614no—
265C22×C4—612no—
266C22×C4—611no—
267C22×C4—1224no—
268C22×C4—1222no—
269C22×C4—1224no—
270C22×C4C22×D6112yes—
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273C22×C4C22×D6111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—1224no—
276C22⋊C4—24no—
277C22⋊C4—24no—
278C22⋊C4—1222no—
279C22⋊C4—1224no—
280C22⋊C4—1224no—
281C22⋊C4—1222no—
282C22⋊C4—1224no—
283C22⋊C4—2442no—
284C22⋊C4—2442no—
285C42—1222no—
286C23—22no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—612no—
293C23—612no—
294C23—612no—
295C23—614no—
296C23—612no—
297C23—12216no—
298C23—1222no—
299C23—1222no—
300C23—1221no—
301C23—1222no—
302C23—1222no—
303C23—1222no—
304C23—1222no—
305C23—1221no—
306C23—1222no—
307C23—1222no—
308C23—1222no—
309C23—1222no—
310C23—2448no—
311C23—2448no—
312C23—2448no—
313C23—2448no—
314C23—2448no—
315C23—2448no—
316C23D4×D6114yes—
317C23C23×D6111yescharacteristic
318D4—28no—
319D4—1228no—
320D4—1228no—
321D4—12216no—
322D4—2448no—
323D4—2448no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—612no—
333C2×C4—614no—
334C2×C4—1228no—
335C2×C4—1221no—
336C2×C4—1222no—
337C2×C4—1222no—
338C2×C4—1222no—
339C2×C4—1222no—
340C2×C4—2444no—
341C2×C4D4×D6112yes—
342C2×C4D4×D6112yescomplemented
343C22—24no—
344C22—24no—
345C22—24no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—42no—
350C22—614no—
351C22—1222no—
352C22—1222no—
353C22—1224no—
354C22—1224no—
355C22—1224no—
356C22—1222no—
357C22—1224no—
358C22—1224no—
359C22—1224no—
360C22—24432no—
361C22—2441no—
362C22—2442no—
363C22—2441no—
364C22—2442no—
365C22—2442no—
366C22—2442no—
367C22—2442no—
368C22C2×D4×D6111yescharacteristic
369C22C2×D4×D6112yes—
370C22C2×D4×D6111yescharacteristic
371C22#41×D6111yescharacteristic
372C22#1451982312yes—
373C4—22no—
374C4—22no—
375C4—41no—
376C4—42no—
377C4—614no—
378C4—2441no—
379C4—2442no—
380C2—44no—
381C2—1224no—
382C2—2444no—
383C2—2442no—
384C2#120×D6111yescharacteristic
385C2#121×D6111yescharacteristic
386C2#1684033011yescharacteristic
387C2#1684039612yes—
388C2#1684040412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2408
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C22×D4×D61C2semidirect
2. C2×#14519750C2semidirect
3. C2×#14519747C2semidirect
4. C2×#14519739C2semidirect
5. #16839679C2semidirect
6. #16839672C2semidirect
7. #16839670C2semidirect
8. #16839662C2semidirect
9. #16839621C2semidirect
10. #16839617C2semidirect
11. C61×#394C2semidirect
15. C22×D244C22semidirect
17. C22×C22⋊D61C22semidirect
21. C22×C4×D61C22semidirect
25. C2×#11758196C22semidirect
26. C2×C22⋊Dic61C22semidirect
29. C2×#11758198C22semidirect
30. C2×#11758198C22semidirect
31. C2×#11758198C22semidirect
32. C2×#11758198C22semidirect
33. C2×C4×Dic61C22semidirect
34. #14519684C22semidirect
36. C2×C4⋊C4×C61C22semidirect
37. C2×C22⋊C4×C61C22semidirect
38. C2×C22⋊C4×C61C22semidirect
39. #95×C61C22semidirect
62. C2×C22⋊D61D4semidirect
74. C2×D244D4semidirect
78. C2×C4×D61D4semidirect
121. C22×D61C2×D4semidirect
133. C2×C4×C61C2×D4semidirect
177. C2×D61#121semidirect
184. Dic61#120semidirect
200. #394D61semidirect
206. C61#2408semidirect
222. C2×C4⋊C4C2×D61semidirect
230. C2×C22⋊C4C2×D61semidirect
231. C2×C22⋊C4C2×D61semidirect
234. #95C2×D61semidirect
342. C2×C4D4×D61semidirect