Finite Group Databasebeta

← #21451848

Subgroups — #21451848

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839698C211yesmaximal, characteristic, complemented
2#16839696C211yesmaximal, characteristic, complemented
3#16839693C211yesmaximal, characteristic, complemented
4#16839691C211yesmaximal, characteristic, complemented
5#16839687C211yesmaximal, characteristic, complemented
6#16839684C211yesmaximal, characteristic, complemented
7#16839677C211yesmaximal, characteristic
8#16839677C211yesmaximal, characteristic
9#16839662C211yesmaximal, characteristic
10#16839654C211yesmaximal, characteristic, complemented
11#16839653C211yesmaximal, characteristic, complemented
12#16839650C211yesmaximal, characteristic, complemented
13#16839649C211yesmaximal, characteristic, complemented
14C4×#11758196C211yesmaximal, characteristic, complemented
15C61×#388C211yesmaximal, characteristic, complemented
16C22×C22⋊D61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×C4×Dic61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
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
48C2×C42×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—41no—
61C2×C22⋊D61—41no—
62C22×Dic61C2311yescharacteristic
63C22×Dic61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C4⋊C4×C61—41no—
70C22⋊C4×C61—22no—
71C22⋊C4×C61—41no—
72C22⋊C4×C61—41no—
73C42×C61—41no—
74C22⋊Dic61—22no—
75C22⋊Dic61—41no—
76C22⋊Dic61—41no—
77#11758198—22no—
78#11758198—22no—
79#11758198—41no—
80#11758198—41no—
81#11758198—41no—
82#11758198—41no—
83C4⋊Dic61—41no—
84C4⋊Dic61—41no—
85#11758196—22no—
86#11758196—22no—
87#11758196—22no—
88#11758196—41no—
89#11758196—41no—
90#11758196—41no—
91C4×Dic61—22no—
92C4×Dic61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61C2411yescharacteristic
101C22×D61—21no—
102C22×D61—21no—
103C22×D61—21no—
104C22×D61—21no—
105C22×D61—21no—
106C22×D61—21no—
107C22×D61—21no—
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#4112yes—
147C2×Dic61#4112yes—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61C2×#4111yescharacteristic
156C22×C61C2×#4111yescharacteristic
157C22×C61C2×#4111yescharacteristic
158C22×C61H(5,𝔽2)11yescharacteristic
159C22×C61H(5,𝔽2)11yescharacteristic
160C22×C61H(5,𝔽2)11yescharacteristic
161C22×C612−1+411yescharacteristic
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C4×C61—22no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61—41no—
174C4×C61—41no—
175Dic61—22no—
176Dic61—22no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180Dic61—41no—
181Dic61—41no—
182#2651—611nomaximal, Sylow
183C2×C61—81no—
184C2×C61#52911yescharacteristic
185C2×C61#53811yescharacteristic
186C2×C61#53911yescharacteristic
187C2×C61#54011yescharacteristic
188C2×C61#54011yescharacteristic
189C2×C61#54211yescharacteristic
190C2×C61#54211yescharacteristic
191D61—81no—
192#399—611no—
193#398—611no—
194#398—611no—
195#397—611no—
196#397—611no—
197#396—611no—
198#394—611no—
199#394—611no—
200#390—611no—
201#388—611no—
202#388—611no—
203#388—611no—
204#388D6111yescharacteristic, complemented
205#387—611no—
206C4×C4⋊C4—611no—
207C61#265111yescharacteristic, complemented, Sylow
208C22×D4—611no—
209C2×C4⋊C4—611no—
210C2×C4⋊C4—611no—
211C2×C4⋊C4—611no—
212C2×C4⋊C4—611no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—611no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4C2×D6111yescharacteristic
218C2×C22⋊C4—611no—
219C2×C22⋊C4—611no—
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—
231C2×C42—611no—
232C2×C42C2×D6111yescharacteristic
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#95C2×D6111yescharacteristic
242#95C2×D6111yescharacteristic
243C24—611no—
244C24C22×D6111yescharacteristic
245C2×D4—1222no—
246C2×D4—2441no—
247C2×D4—2441no—
248C22×C4—611no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
255C22×C4C22×D6111yescharacteristic
256C22×C4C22×D6111yescharacteristic
257C22×C4C22×D6111yescharacteristic
258C22×C4C22×D6111yescharacteristic
259C22×C4C22×D6111yescharacteristic
260C22×C4C22×D6111yescharacteristic
261C4⋊C4—41no—
262C4⋊C4—1222no—
263C4⋊C4—1222no—
264C4⋊C4—1222no—
265C4⋊C4—2441no—
266C4⋊C4—2441no—
267C4⋊C4—2441no—
268C4⋊C4—2441no—
269C4⋊C4—2441no—
270C22⋊C4—22no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—1222no—
274C22⋊C4—1222no—
275C22⋊C4—1222no—
276C22⋊C4—2441no—
277C22⋊C4—2441no—
278C22⋊C4—2441no—
279C22⋊C4—2441no—
280C22⋊C4—2441no—
281C22⋊C4—2441no—
282C42—41no—
283C42—1222no—
284C42—2441no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—1221no—
293C23—1221no—
294C23—1221no—
295C23—1221no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299C23C23×D6111yescharacteristic
300D4—2444no—
301C2×C4—21no—
302C2×C4—21no—
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—612no—
319C2×C4—612no—
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#1175822212yes—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—2441no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22#41×D6111yescharacteristic
355C22#41×D6111yescharacteristic
356C22C2×#1175822211yescharacteristic
357C22#1451982211yescharacteristic
358C22#1451982211yescharacteristic
359C22#1451982311yescharacteristic
360C22#1451982411yescharacteristic
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—1222no—
368C4—1222no—
369C4—2441no—
370C4—2441no—
371C4—2441no—
372C4—2441no—
373C4—2441no—
374C2—81no—
375C2—4881no—
376C2#1684029011yescharacteristic
377C2#1684034411yescharacteristic
378C2#1684035411yescharacteristic
379C2#1684036311yescharacteristic
380C2#1684036411yescharacteristic
381C2#1684037611yescharacteristic
382C2#1684037811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#388C2
hypercenter#388D61
hypocenterC61#2651
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #16839698C2semidirect
2. #16839696C2semidirect
3. #16839693C2semidirect
4. #16839691C2semidirect
5. #16839687C2semidirect
6. #16839684C2semidirect
10. #16839654C2semidirect
11. #16839653C2semidirect
12. #16839650C2semidirect
13. #16839649C2semidirect
14. C4×#11758196C2semidirect
15. C61×#388C2semidirect
204. #388D61semidirect
207. C61#2651semidirect