Finite Group Databasebeta

← #21453464

Subgroups — #21453464

Order 7808.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839704C211yesmaximal, characteristic, complemented
2#16839698C211yesmaximal, characteristic, complemented
3#16839696C211yesmaximal, characteristic, complemented
4#16839685C211yesmaximal, characteristic, complemented
5#16839685C211yesmaximal, characteristic, complemented
6#16839685C211yesmaximal, characteristic, complemented
7#16839665C211yesmaximal, characteristic
8#16839659C211yesmaximal, characteristic, complemented
9#16839645C211yesmaximal, characteristic, complemented
10#16839642C211yesmaximal, characteristic
11#16839635C211yesmaximal, characteristic, complemented
12#16839635C211yesmaximal, characteristic, complemented
13#16839634C211yesmaximal, characteristic, complemented
14#16839620C211yesmaximal, characteristic, complemented
15C61×#386C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×#11758196C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
32C2×C22⋊Dic61C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C4×Dic61C2211yescharacteristic
36#14519684C2211yescharacteristic
37#14519684C2211yescharacteristic
38#14519684C2211yescharacteristic
39#14519684C2211yescharacteristic
40#14519684C2211yescharacteristic
41#14519684C2211yescharacteristic
42#14519684C2211yescharacteristic
43#14519684C2211yescharacteristic
44C22×D4×C61C2211yescharacteristic
45C23×C4×C61C2211yescharacteristic
46C2×C22⋊C4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C24×C61C2311yescharacteristic
53C2×D4×C61—41no—
54C2×D4×C61—41no—
55C2×D4×C61Q814yes—
56C22×C4×C61—41no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×Dic61—22no—
65C22×Dic61—41no—
66C22×Dic61—41no—
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C22×Dic61C2311yescharacteristic
71C22×Dic61C2311yescharacteristic
72C22×Dic61C2311yescharacteristic
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C22⋊C4×C61—41no—
78C22⋊Dic61—22no—
79C22⋊Dic61—22no—
80C22⋊Dic61—22no—
81C22⋊Dic61—41no—
82C22⋊Dic61—41no—
83C22⋊Dic61—41no—
84C22⋊Dic61—41no—
85C4⋊Dic61—22no—
86C4⋊Dic61—41no—
87C4⋊Dic61—41no—
88#11758196—22no—
89#11758196—41no—
90#11758196—41no—
91#11758196—41no—
92#11758196—41no—
93#11758196—41no—
94#11758196—41no—
95#11758196—41no—
96C4×Dic61—41no—
97C23×C61—21no—
98C23×C61—21no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—21no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61C2×Q812yes—
110C23×C61C2×Q812yes—
111C23×C61C2411yescharacteristic
112D4×C61—44no—
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—21no—
126C2×C4×C61—21no—
127C2×C4×C61—44no—
128C2×C4×C61C2×Q812yes—
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—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—44no—
152C2×Dic61#4112yes—
153C2×Dic61#4112yes—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—22no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61C22×Q811yescharacteristic
169C22×C61C2×#4111yescharacteristic
170C22×C61C2×#4111yescharacteristic
171C22×C61H(5,𝔽2)11yescharacteristic
172C22×C61H(5,𝔽2)11yescharacteristic
173C22×C61H(5,𝔽2)11yescharacteristic
174C22×C61H(5,𝔽2)11yescharacteristic
175C4×C61—22no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61—41no—
180Dic61—22no—
181Dic61—22no—
182Dic61—41no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187Dic61—41no—
188#2780—611nomaximal, Sylow
189C2×C61—42no—
190C2×C61—42no—
191C2×C61#53811yescharacteristic
192C2×C61#54011yescharacteristic
193C2×C61#54311yescharacteristic
194C2×C61#55311yescharacteristic
195C2×C61#55411yescharacteristic
196C2×C61#55411yescharacteristic
197C2×C61#56011yescharacteristic
198#400—611no—
199#399—611no—
200#398—611no—
201#396—611no—
202#396—611no—
203#396—611no—
204#390—611no—
205#389—611no—
206#387—611no—
207#386—611no—
208#386D6111yescharacteristic
209#385—611no—
210#385—611no—
211#385—611no—
212#380—611no—
213C61#278011yescharacteristic, complemented, Sylow
214C22×D4C2×D6111yescharacteristic
215C23×C4—611no—
216C23×C4C2×D6111yescharacteristic
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—611no—
227C2×C4⋊C4—611no—
228C2×C22⋊C4—611no—
229C2×C22⋊C4—611no—
230C2×C22⋊C4—611no—
231C2×C22⋊C4—611no—
232C2×C22⋊C4—611no—
233C2×C22⋊C4—611no—
234C2×C22⋊C4—611no—
235C2×C22⋊C4C2×D6111yescharacteristic
236C2×C22⋊C4C2×D6111yescharacteristic
237C2×C22⋊C4C2×D6111yescharacteristic
238C2×C42—611no—
239#95—611no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—611no—
245#95—611no—
246#95—611no—
247#95C2×D6111yescharacteristic
248#95C2×D6111yescharacteristic
249C24C22×D6111yescharacteristic
250C24C22×D6111yescharacteristic
251C2×D4—41no—
252C2×D4—41no—
253C2×D4Dic12214yes—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—611no—
258C22×C4—611no—
259C22×C4—611no—
260C22×C4—611no—
261C22×C4—611no—
262C22×C4—611no—
263C22×C4—611no—
264C22×C4—611no—
265C22×C4—1222no—
266C22×C4—2441no—
267C22×C4—2441no—
268C22×C4C22×D6111yescharacteristic
269C22×C4C22×D6111yescharacteristic
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272C22×C4C22×D6111yescharacteristic
273C4⋊C4—1222no—
274C4⋊C4—1222no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—1222no—
288C22⋊C4—1222no—
289C22⋊C4—1222no—
290C22⋊C4—2441no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C42—2441no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23C2×Dic12212yes—
308C23C2×Dic12212yes—
309C23C23×D6111yescharacteristic
310D4—44no—
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—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—44no—
326C2×C4—612no—
327C2×C4—612no—
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—1221no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—2444no—
351C2×C4C2×Dic12212yes—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22C22×Dic12211yescharacteristic
367C22#41×D6111yescharacteristic
368C22#41×D6111yescharacteristic
369C22#1451982211yescharacteristic
370C22#1451982211yescharacteristic
371C22#1451982211yescharacteristic
372C22#1451982211yescharacteristic
373C4—22no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—1222no—
379C4—1222no—
380C4—2441no—
381C4—2441no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4—2441no—
386C2—42no—
387C2—42no—
388C2#1684034411yescharacteristic
389C2#1684036211yescharacteristic
390C2#1684038811yescharacteristic
391C2#1684045711yescharacteristic
392C2#1684047111yescharacteristic
393C2#1684047111yescharacteristic
394C2#1684050111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#386C2
hypercenter#386D61
hypocenterC61#2780
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839698C2semidirect
3. #16839696C2semidirect
4. #16839685C2semidirect
5. #16839685C2semidirect
6. #16839685C2semidirect
8. #16839659C2semidirect
9. #16839645C2semidirect
11. #16839635C2semidirect
12. #16839635C2semidirect
13. #16839634C2semidirect
14. #16839620C2semidirect
213. C61#2780semidirect