Finite Group Databasebeta

← #21453010

Subgroups — #21453010

Order 7808.

448 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61⋊#401C211yesmaximal, characteristic, complemented
2#16839704C211yesmaximal, characteristic, complemented
3#16839699C211yesmaximal, characteristic, complemented
4#16839694C211yesmaximal, characteristic, complemented
5#16839677C211yesmaximal, characteristic
6#16839655C211yesmaximal, characteristic, complemented
7#16839654C211yesmaximal, characteristic, complemented
8#16839648C211yesmaximal, characteristic, complemented
9#16839639C211yesmaximal, characteristic
10#16839638C211yesmaximal, characteristic
11#16839637C211yesmaximal, characteristic, complemented
12#16839637C211yesmaximal, characteristic, complemented
13#16839624C211yesmaximal, characteristic, complemented
14#16839619C211yesmaximal, characteristic, complemented
15C61×#397C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18C22×C4×D61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×C4⋊Dic61C2211yescharacteristic
21C2×C4⋊Dic61C2211yescharacteristic
22C2×C4⋊Dic61C2211yescharacteristic
23C2×C4⋊Dic61C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×C4×Dic61C2211yescharacteristic
33#14519684C2211yescharacteristic
34#14519684C2211yescharacteristic
35#14519684C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44C2×C4⋊C4×C61C2211yescharacteristic
45C2×C22⋊C4×C61C2211yescharacteristic
46C2×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48#95×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C23×D61C2311yescharacteristic
53C22×C4×C61C2311yescharacteristic
54C22×C4×C61C2311yescharacteristic
55C22×C4×C61C2311yescharacteristic
56C22×C4×C61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C2×C22⋊D61—22no—
60C2×C22⋊D61—22no—
61C2×C22⋊D61—41no—
62C22×Dic61—41no—
63C22×Dic61—41no—
64C22×Dic61—41no—
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C2×C4×D61—22no—
73C2×C4×D61—22no—
74C2×C4×D61—41no—
75C4⋊C4×C61—22no—
76C22⋊C4×C61—22no—
77C22⋊C4×C61—22no—
78C22⋊C4×C61—22no—
79C22⋊Dic61—41no—
80C22⋊Dic61—41no—
81#11758198—22no—
82#11758198—41no—
83#11758198—41no—
84#11758198—41no—
85#11758198—41no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89C4⋊Dic61—41no—
90C4⋊Dic61—41no—
91#11758196—41no—
92C4×Dic61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61#4112yes—
100C23×C61C2411yescharacteristic
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61#4112yes—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61#4112yes—
126C22⋊D61—44no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—44no—
149C4×D61—44no—
150C22×C61—22no—
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C2×#4111yescharacteristic
158C22×C61C2×#4111yescharacteristic
159C22×C61C2×#4111yescharacteristic
160C22×C61H(5,𝔽2)11yescharacteristic
161C22×C61H(5,𝔽2)11yescharacteristic
162C22×C61H(5,𝔽2)11yescharacteristic
163C22×C612−1+411yescharacteristic
164C2×D61—22no—
165C2×D61—22no—
166C2×D61—22no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C4×C61—22no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61—41no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183Dic61—41no—
184#2746—611nomaximal, Sylow
185C2×C61—42no—
186C2×C61#53911yescharacteristic
187C2×C61#53911yescharacteristic
188C2×C61#54211yescharacteristic
189C2×C61#55111yescharacteristic
190C2×C61#55111yescharacteristic
191C2×C61#55311yescharacteristic
192C2×C61#56011yescharacteristic
193D61—42no—
194#401—611no—
195#400—611no—
196#399—611no—
197#398—611no—
198#397D6111yescharacteristic, complemented
199#394—611no—
200#388—611no—
201#388—611no—
202#387—611no—
203#386—611no—
204#386—611no—
205#385—611no—
206#385—611no—
207#381—611no—
208#380—611no—
209C61#274611yescharacteristic, complemented, Sylow
210C22×D4—611no—
211C23×C4—611no—
212C23×C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4C2×D6111yescharacteristic
220C2×C22⋊C4—611no—
221C2×C22⋊C4—611no—
222C2×C22⋊C4—611no—
223C2×C22⋊C4—611no—
224C2×C22⋊C4—611no—
225C2×C22⋊C4—611no—
226C2×C22⋊C4—611no—
227C2×C22⋊C4C2×D6111yescharacteristic
228C2×C22⋊C4C2×D6111yescharacteristic
229C2×C22⋊C4C2×D6111yescharacteristic
230C2×C42—611no—
231#95—611no—
232#95—611no—
233#95—611no—
234#95—611no—
235#95—611no—
236#95—611no—
237#95—611no—
238#95—611no—
239#95—611no—
240#95—611no—
241#95—611no—
242#95C2×D6111yescharacteristic
243#95C2×D6111yescharacteristic
244#95C2×D6111yescharacteristic
245C24—611no—
246C24C22×D6111yescharacteristic
247C2×D4—1222no—
248C2×D4—1222no—
249C2×D4—2441no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4—611no—
256C22×C4—611no—
257C22×C4—1222no—
258C22×C4—1222no—
259C22×C4—2441no—
260C22×C4—2441no—
261C22×C4—2441no—
262C22×C4—2441no—
263C22×C4C22×D6111yescharacteristic
264C22×C4C22×D6111yescharacteristic
265C22×C4C22×D6111yescharacteristic
266C22×C4C22×D6111yescharacteristic
267C22×C4C22×D6111yescharacteristic
268C22×C4C22×D6111yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—2441no—
271C4⋊C4—2441no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—1222no—
280C22⋊C4—2441no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C42—2441no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—612no—
294C23—1221no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23—1221no—
300C23#1175822412yes—
301C23C23×D6111yescharacteristic
302D4—2444no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—2444no—
342C2×C4—2444no—
343C2×C4#1175822412yes—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1222no—
352C22—1222no—
353C22—1222no—
354C22—2441no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22#41×D6111yescharacteristic
359C22C2×#1175822411yescharacteristic
360C22C2×#1175822411yescharacteristic
361C22#1451982311yescharacteristic
362C22#1451982311yescharacteristic
363C22#1451982311yescharacteristic
364C22#1451982411yescharacteristic
365C4—22no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—2441no—
372C4—2441no—
373C4—2441no—
374C4—2441no—
375C4—2441no—
376C4—2441no—
377C4—2441no—
378C2—42no—
379C2—2442no—
380C2#1684035311yescharacteristic
381C2#1684035611yescharacteristic
382C2#1684038111yescharacteristic
383C2#1684043511yescharacteristic
384C2#1684043511yescharacteristic
385C2#1684046411yescharacteristic
386C2#1684050311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2746
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C61⋊#401C2semidirect
2. #16839704C2semidirect
3. #16839699C2semidirect
4. #16839694C2semidirect
6. #16839655C2semidirect
7. #16839654C2semidirect
8. #16839648C2semidirect
11. #16839637C2semidirect
12. #16839637C2semidirect
13. #16839624C2semidirect
14. #16839619C2semidirect
15. C61×#397C2semidirect
198. #397D61semidirect
209. C61#2746semidirect