Finite Group Databasebeta

← #21450722

Subgroups — #21450722

Order 7808.

732 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519752C211yesmaximal, characteristic, complemented
2C2×#14519751C211yesmaximal, characteristic, complemented
3C2×#14519739C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D61C211yesmaximal, characteristic, complemented
5#16839691C212yesmaximal, complemented
6#16839671C212yesmaximal, complemented
7#16839640C212yesmaximal, complemented
8#16839638C212yesmaximal, complemented
9#16839627C211yesmaximal, characteristic, complemented
10#16839619C211yesmaximal, characteristic, complemented
11C61×#380C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C22×D244C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C22×C22⋊D61C2212yes—
16C22×C4×D61C2211yescharacteristic
17C22×C4×D61C2212yes—
18#14519752—24no—
19#14519751—24no—
20#14519739—24no—
21C4×C22⋊D61—24no—
22C2×C4⋊Dic61C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2212yes—
30C2×C4×Dic61C2211yescharacteristic
31#14519684C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34C23×C4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2211yescharacteristic
36C2×C4⋊C4×C61C2211yescharacteristic
37C2×C22⋊C4×C61C2212yes—
38#95×C61C2212yes—
39C24×C61C2311yescharacteristic
40C23×D61C2312yes—
41C23×D61C2311yescharacteristic
42C22×C4×C61—22no—
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61C2312yes—
46C22×C4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2311yescharacteristic
49C2×C22⋊D61—22no—
50C2×C22⋊D61—22no—
51C2×C22⋊D61—24no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—22no—
54C2×C22⋊D61—42no—
55C22×Dic61C2311yescharacteristic
56C22×Dic61C2312yes—
57C22×Dic61C2311yescharacteristic
58C22×Dic61C2311yescharacteristic
59C2×D244—22no—
60C2×D244—22no—
61C2×D244—24no—
62C2×D244—24no—
63C2×D244—42no—
64C2×D244D414yescomplemented
65C2×C4×D61—22no—
66C2×C4×D61—22no—
67C2×C4×D61—22no—
68C2×C4×D61—24no—
69C2×C4×D61—42no—
70C2×C4×D61—42no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—22no—
73C22⋊C4×C61—42no—
74C22⋊Dic61—22no—
75#11758198—24no—
76#11758198—24no—
77#11758198—22no—
78#11758198—24no—
79#11758198—42no—
80C4⋊Dic61—22no—
81#11758196—22no—
82C4×Dic61D414yescomplemented
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—21no—
88C23×C61—21no—
89C23×C61#4112yes—
90C23×C61C2411yescharacteristic
91C22×D61—22no—
92C22×D61—21no—
93C22×D61—21no—
94C22×D61—21no—
95C22×D61—22no—
96C22×D61—22no—
97C22×D61—21no—
98C22×D61—22no—
99C22×D61—21no—
100C22×D61—22no—
101C22×D61—22no—
102C22×D61—21no—
103C22×D61C2×D414yes—
104C22×D61#4112yes—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—22no—
110C2×C4×C61—21no—
111C2×C4×C61—22no—
112C2×C4×C61—22no—
113C2×C4×C61—22no—
114C2×C4×C61—44no—
115C2×C4×C61C2×D412yes—
116C2×C4×C61C2×D412yes—
117C2×C4×C61#4112yes—
118C22⋊D61—28no—
119C22⋊D61—48no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—22no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—22no—
129C2×Dic61—22no—
130C2×Dic61C2×D412yes—
131C2×Dic61C2×D412yes—
132D244—28no—
133D244—48no—
134C4×D61—48no—
135C4×D61—44no—
136C22×C61—22no—
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61—41no—
143C22×C61C22×D411yescharacteristic
144C22×C61C22×D411yescharacteristic
145C22×C61C2×#4111yescharacteristic
146C22×C61C2×#4111yescharacteristic
147C22×C61C2×#4111yescharacteristic
148C22×C61H(5,𝔽2)11yescharacteristic
149C22×C61H(5,𝔽2)11yescharacteristic
150C2×D61—24no—
151C2×D61—22no—
152C2×D61—22no—
153C2×D61—24no—
154C2×D61—24no—
155C2×D61—22no—
156C2×D61—41no—
157C2×D61—42no—
158C2×D61—42no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—42no—
162C2×D61—41no—
163C2×D61—42no—
164C4×C61—41no—
165C4×C61—42no—
166C4×C61—42no—
167C4×C61#12114yes—
168Dic61—22no—
169Dic61—22no—
170Dic61—41no—
171Dic61—42no—
172#2535—611nomaximal, Sylow
173C2×C61—42no—
174C2×C61C2×#12111yescharacteristic
175C2×C61#52511yescharacteristic
176C2×C61#53511yescharacteristic
177C2×C61#54611yescharacteristic
178C2×C61#54611yescharacteristic
179C2×C61#55311yescharacteristic
180C2×C61#55311yescharacteristic
181D61—44no—
182D61—42no—
183C2×#121—611no—
184C2×#121—611no—
185C2×C4×D4—611no—
186C2×C4×D4—611no—
187#397—612no—
188#392—612no—
189#386—612no—
190#386—612no—
191#382—611no—
192#380—611no—
193#380D6111yescharacteristic, complemented
194C61#253511yescharacteristic, complemented, Sylow
195C22×D4—611no—
196C22×D4—612no—
197C22×D4—611no—
198C22×D4—612no—
199C23×C4—611no—
200C23×C4—612no—
201C23×C4C2×D6111yescharacteristic
202#121—1224no—
203#121—1224no—
204C4×D4—1224no—
205C4×D4—1224no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—611no—
208C2×C4⋊C4C2×D6111yescharacteristic
209C2×C4⋊C4C2×D6111yescharacteristic
210C2×C22⋊C4—611no—
211C2×C22⋊C4—611no—
212C2×C22⋊C4—612no—
213C2×C22⋊C4—612no—
214C2×C22⋊C4—612no—
215C2×C22⋊C4—612no—
216C2×C22⋊C4C2×D6112yes—
217C2×C42—611no—
218#95—612no—
219#95—612no—
220#95—612no—
221#95C2×D6112yes—
222C24—612no—
223C24—611no—
224C24C22×D6111yescharacteristic
225C2×D4—614no—
226C2×D4—1224no—
227C2×D4—1224no—
228C2×D4—1222no—
229C2×D4—1222no—
230C2×D4—1222no—
231C2×D4—1224no—
232C2×D4—1224no—
233C2×D4—1222no—
234C2×D4—1222no—
235C2×D4—2442no—
236C2×D4—2442no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—611no—
241C22×C4—611no—
242C22×C4—612no—
243C22×C4—611no—
244C22×C4—1224no—
245C22×C4—1222no—
246C22×C4—1222no—
247C22×C4—1222no—
248C22×C4—2442no—
249C22×C4—2442no—
250C22×C4C22×D6112yes—
251C22×C4C22×D6112yes—
252C22×C4C22×D6111yescharacteristic
253C22×C4C22×D6111yescharacteristic
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—1222no—
257C4⋊C4—1222no—
258C22⋊C4—42no—
259C22⋊C4—1224no—
260C22⋊C4—1222no—
261C22⋊C4—1224no—
262C22⋊C4—1224no—
263C22⋊C4—1222no—
264C22⋊C4—2442no—
265C42—614no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—614no—
273C23—612no—
274C23—1222no—
275C23—1221no—
276C23—1221no—
277C23—1222no—
278C23—1221no—
279C23—1222no—
280C23—1221no—
281C23—1222no—
282C23—1222no—
283C23—1221no—
284C23—1221no—
285C23—1222no—
286C23#1175822612yes—
287C23C23×D6111yescharacteristic
288D4—1228no—
289D4—1228no—
290D4—2448no—
291D4—2448no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—22no—
301C2×C4—44no—
302C2×C4—612no—
303C2×C4—612no—
304C2×C4—1221no—
305C2×C4—1221no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1222no—
311C2×C4—1221no—
312C2×C4—1222no—
313C2×C4—1222no—
314C2×C4—2448no—
315C2×C4—2444no—
316C2×C4#1175822212yes—
317C2×C4D4×D6112yes—
318C2×C4D4×D6112yes—
319C22—22no—
320C22—22no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—1222no—
327C22—1224no—
328C22—1222no—
329C22—1224no—
330C22—1222no—
331C22—1224no—
332C22—2442no—
333C22—2441no—
334C22—2442no—
335C22—2441no—
336C22—2442no—
337C22—2442no—
338C22—2441no—
339C22—2441no—
340C22C2×D4×D6111yescharacteristic
341C22C2×D4×D6111yescharacteristic
342C22#41×D6111yescharacteristic
343C22C2×#1175822211yescharacteristic
344C22C2×#1175822611yescharacteristic
345C22#1451982211yescharacteristic
346C22#1451982311yescharacteristic
347C4—41no—
348C4—42no—
349C4—42no—
350C4—1222no—
351C4—1222no—
352C4—2441no—
353C4—2442no—
354C4#1451975014yes—
355C2—42no—
356C2—2442no—
357C2—2444no—
358C2C2×#1451975011yescharacteristic
359C2#1684027511yescharacteristic
360C2#1684032811yescharacteristic
361C2#1684040311yescharacteristic
362C2#1684040911yescharacteristic
363C2#1684045611yescharacteristic
364C2#1684046011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#380C2
hypercenter#380D61
hypocenterC61#2535
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#14519752C2semidirect
2. C2×#14519751C2semidirect
3. C2×#14519739C2semidirect
4. C2×C4×C22⋊D61C2semidirect
5. #16839691C2semidirect
6. #16839671C2semidirect
7. #16839640C2semidirect
8. #16839638C2semidirect
9. #16839627C2semidirect
10. #16839619C2semidirect
11. C61×#380C2semidirect
64. C2×D244D4semidirect
82. C4×Dic61D4semidirect
193. #380D61semidirect
194. C61#2535semidirect