Finite Group Databasebeta

← #21449145

Subgroups — #21449145

Order 7808.

1116 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D61C211yesmaximal, characteristic
2C2×#14519761C211yesmaximal, characteristic, complemented
3C2×#14519758C211yesmaximal, characteristic, complemented
4C22×#11758198C211yesmaximal, characteristic, complemented
5#16839680C212yesmaximal, complemented
6#16839678C212yesmaximal, complemented
7#16839641C211yesmaximal, characteristic, complemented
8#16839636C212yesmaximal, complemented
9#16839617C212yesmaximal, complemented
10#16839617C211yesmaximal, characteristic, complemented
11C61×#386C211yesmaximal, characteristic, complemented
12C24×D61C2211yescharacteristic
13C24×D61C2211yescharacteristic
14C22×D244C2211yescharacteristic
15C22×C22⋊D61C2211yescharacteristic
16C22×C22⋊D61C2211yescharacteristic
17C2×D4×D61—24no—
18C2×D4×D61—24no—
19C2×D4×D61—24no—
20C23×Dic61C2211yescharacteristic, complemented
21C22×C4×D61C2211yescharacteristic
22#14519761—24no—
23#14519758—24no—
24C2×C4⋊Dic61C2212yescomplemented
25C2×#11758196C2212yescomplemented
26C2×C22⋊Dic61C2211yescharacteristic, complemented
27C2×C22⋊Dic61C2212yescomplemented
28C2×#11758198—24no—
29C2×#11758198C2212yes—
30C2×#11758198C2212yes—
31C2×#11758198C2212yescomplemented
32C2×#11758198C2212yescomplemented
33C2×#11758198C2212yescomplemented
34C2×#11758198C2212yescomplemented
35#14519684C2212yescomplemented
36C22×D4×C61C2211yescharacteristic
37C23×C4×C61C2211yescharacteristic, complemented
38C2×C22⋊C4×C61C2211yescharacteristic, complemented
39C2×C22⋊C4×C61C2212yescomplemented
40#95×C61C2212yescomplemented
41C24×C61C2311yescharacteristic
42C24×C61C2311yescharacteristic
43C23×D61—22no—
44C23×D61—22no—
45C23×D61—22no—
46C23×D61—22no—
47C23×D61—22no—
48C23×D61—24no—
49C23×D61—24no—
50C23×D61—42no—
51C23×D61—42no—
52C23×D61D414yes—
53C23×D61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C23×D61C2311yescharacteristic
56C2×D4×C61—22no—
57C2×D4×C61—22no—
58C2×D4×C61D414yes—
59C22×C4×C61—22no—
60C22×C4×C61—42no—
61C22×C4×C61C2312yes—
62C22×C4×C61C2312yes—
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—22no—
65C2×C22⋊D61—22no—
66C2×C22⋊D61—22no—
67C2×C22⋊D61—22no—
68C2×C22⋊D61—22no—
69C2×C22⋊D61D414yes—
70C22×Dic61—22no—
71C22×Dic61—22no—
72C22×Dic61—22no—
73C22×Dic61C2312yes—
74C22×Dic61C2312yes—
75C22×Dic61C2311yescharacteristic
76D4×D61—232no—
77C2×D244—22no—
78C2×D244—22no—
79C2×D244—22no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C22⋊C4×C61—22no—
84C22⋊C4×C61—42no—
85C22⋊Dic61—22no—
86C22⋊Dic61—24no—
87#11758198—24no—
88#11758198—24no—
89#11758198—24no—
90#11758198—24no—
91#11758198—42no—
92#11758198—42no—
93C4⋊Dic61—24no—
94#11758196—24no—
95C23×C61—22no—
96C23×C61—22no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—22no—
100C23×C61—22no—
101C23×C61C2×D412yes—
102C23×C61C2×D412yes—
103C23×C61C2×D412yes—
104C23×C61C2×D412yes—
105C23×C61C2411yescharacteristic
106C22×D61—21no—
107C22×D61—21no—
108C22×D61—22no—
109C22×D61—28no—
110C22×D61—28no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—22no—
116C22×D61—22no—
117C22×D61—22no—
118C22×D61—22no—
119C22×D61—28no—
120C22×D61—44no—
121C22×D61—48no—
122C22×D61—48no—
123C22×D61—48no—
124C22×D61—48no—
125C22×D61—44no—
126C22×D61—44no—
127C22×D61C2×D412yes—
128C22×D61C2×D412yes—
129C22×D61C2×D412yes—
130C22×D61#4114yes—
131D4×C61—28no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—22no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61—22no—
138C2×C4×C61—22no—
139C2×C4×C61—22no—
140C2×C4×C61—44no—
141C2×C4×C61C2×D412yes—
142C22⋊D61—28no—
143C22⋊D61—28no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—22no—
152C2×Dic61—44no—
153C2×Dic61C2×D412yes—
154D244—28no—
155C4×D61—28no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—24no—
159C22×C61—24no—
160C22×C61—22no—
161C22×C61—24no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—42no—
165C22×C61#12014yes—
166C22×C61C22×D411yescharacteristic
167C22×C61C22×D411yescharacteristic
168C22×C61C22×D411yescharacteristic
169C22×C61C2×#4112yes—
170C22×C61H(5,𝔽2)12yes—
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—24no—
174C2×D61—24no—
175C2×D61—22no—
176C2×D61—22no—
177C2×D61—22no—
178C2×D61—22no—
179C2×D61—24no—
180C2×D61—416no—
181C2×D61—416no—
182C2×D61—41no—
183C2×D61—41no—
184C2×D61—42no—
185C2×D61—42no—
186C2×D61—42no—
187C2×D61#12314yescomplemented
188C4×C61—22no—
189C4×C61—42no—
190C4×C61—42no—
191Dic61—22no—
192Dic61—42no—
193Dic61—42no—
194#2405—611nomaximal, Sylow
195C2×C61—24no—
196C2×C61—42no—
197C2×C61C2×#12011yescharacteristic
198C2×C61C2×#12311yescharacteristic
199C2×C61#53411yescharacteristic
200C2×C61#54612yes—
201C2×C61#54612yes—
202D61—24no—
203D61—42no—
204D61—42no—
205C23×D4—611no—
206C2×#123—611no—
207C2×#123—611no—
208C22×C22⋊C4—611no—
209#394—612no—
210#394—612no—
211#386—611no—
212#386D6111yescharacteristic, complemented
213#385—612no—
214#379—611no—
215#379—612no—
216C61#240511yescharacteristic, complemented, Sylow
217C25—611no—
218C25—611no—
219C22×D4—611no—
220C22×D4—611no—
221C22×D4—611no—
222C22×D4—1224no—
223C22×D4—1224no—
224C22×D4—1224no—
225C22×D4C2×D6111yescharacteristic
226C23×C4—611no—
227C23×C4—611no—
228C23×C4C2×D6111yescharacteristic, complemented
229#123—1224no—
230#123—1224no—
231C2×C4⋊C4—612no—
232C2×C4⋊C4—612no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—612no—
235C2×C22⋊C4—612no—
236C2×C22⋊C4—612no—
237C2×C22⋊C4—612no—
238C2×C22⋊C4—612no—
239C2×C22⋊C4—612no—
240C2×C22⋊C4—612no—
241C2×C22⋊C4—1224no—
242C2×C22⋊C4C2×D6111yescharacteristic, complemented
243C2×C22⋊C4C2×D6112yescomplemented
244#95—612no—
245#95C2×D6112yescomplemented
246C24—611no—
247C24—611no—
248C24—611no—
249C24—614no—
250C24—1222no—
251C24—1222no—
252C24—1224no—
253C24—1224no—
254C24—1222no—
255C24—1222no—
256C24—1222no—
257C24—2442no—
258C24—2442no—
259C24C22×D6111yescharacteristic
260C24C22×D6111yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—614no—
264C2×D4—1222no—
265C2×D4—1222no—
266C2×D4—1222no—
267C2×D4—12232no—
268C2×D4—1222no—
269C2×D4—1222no—
270C2×D4—1222no—
271C2×D4—1222no—
272C2×D4—1222no—
273C2×D4D24414yes—
274C22×C4—22no—
275C22×C4—42no—
276C22×C4—611no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1222no—
282C22×C4—1222no—
283C22×C4—1222no—
284C22×C4—1222no—
285C22×C4C22×D6112yes—
286C22×C4C22×D6112yes—
287C22×C4C22×D6111yescharacteristic
288C4⋊C4—1224no—
289C4⋊C4—1224no—
290C22⋊C4—22no—
291C22⋊C4—42no—
292C22⋊C4—1224no—
293C22⋊C4—1224no—
294C22⋊C4—1224no—
295C22⋊C4—1224no—
296C22⋊C4—1222no—
297C22⋊C4—1224no—
298C22⋊C4—2442no—
299C22⋊C4—2442no—
300C23—22no—
301C23—22no—
302C23—21no—
303C23—21no—
304C23—22no—
305C23—22no—
306C23—612no—
307C23—614no—
308C23—612no—
309C23—612no—
310C23—1228no—
311C23—1228no—
312C23—1221no—
313C23—1221no—
314C23—1222no—
315C23—1221no—
316C23—1221no—
317C23—1221no—
318C23—1221no—
319C23—1222no—
320C23—1222no—
321C23—1222no—
322C23—1222no—
323C23—1228no—
324C23—2444no—
325C23—2448no—
326C23—2448no—
327C23—2448no—
328C23—2444no—
329C23—2448no—
330C23—2444no—
331C23C2×D24412yes—
332C23C2×D24412yes—
333C23D4×D6112yes—
334C23D4×D6112yes—
335C23C23×D6111yescharacteristic
336D4—28no—
337D4—1228no—
338D4—1228no—
339D4—1228no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—44no—
349C2×C4—612no—
350C2×C4—1228no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—2444no—
360C2×C4C2×D24412yes—
361C22—22no—
362C22—22no—
363C22—24no—
364C22—24no—
365C22—22no—
366C22—24no—
367C22—41no—
368C22—41no—
369C22—42no—
370C22—614no—
371C22—1222no—
372C22—1222no—
373C22—1224no—
374C22—1224no—
375C22—1222no—
376C22—1222no—
377C22—1222no—
378C22—1222no—
379C22—1224no—
380C22—24416no—
381C22—24416no—
382C22—2441no—
383C22—2441no—
384C22—2442no—
385C22—2442no—
386C22—2442no—
387C22#1451974714yes—
388C22C2×D4×D6111yescharacteristic
389C22C2×D4×D6111yescharacteristic
390C22C22×D24411yescharacteristic
391C22#41×D6112yes—
392C22#1451982212yes—
393C4—22no—
394C4—42no—
395C4—42no—
396C4—1222no—
397C4—2442no—
398C4—2442no—
399C2—24no—
400C2—42no—
401C2—1224no—
402C2—2442no—
403C2—2442no—
404C2C2×#1451974711yescharacteristic
405C2#123×D6111yescharacteristic
406C2#1684032211yescharacteristic
407C2#1684040112yes—
408C2#1684040712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2405
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#14519761C2semidirect
3. C2×#14519758C2semidirect
4. C22×#11758198C2semidirect
5. #16839680C2semidirect
6. #16839678C2semidirect
7. #16839641C2semidirect
8. #16839636C2semidirect
9. #16839617C2semidirect
10. #16839617C2semidirect
11. C61×#386C2semidirect
20. C23×Dic61C22semidirect
24. C2×C4⋊Dic61C22semidirect
25. C2×#11758196C22semidirect
26. C2×C22⋊Dic61C22semidirect
27. C2×C22⋊Dic61C22semidirect
31. C2×#11758198C22semidirect
32. C2×#11758198C22semidirect
33. C2×#11758198C22semidirect
34. C2×#11758198C22semidirect
35. #14519684C22semidirect
37. C23×C4×C61C22semidirect
38. C2×C22⋊C4×C61C22semidirect
39. C2×C22⋊C4×C61C22semidirect
40. #95×C61C22semidirect
187. C2×D61#123semidirect
212. #386D61semidirect
216. C61#2405semidirect
228. C23×C4C2×D61semidirect
242. C2×C22⋊C4C2×D61semidirect
243. C2×C22⋊C4C2×D61semidirect
245. #95C2×D61semidirect