Finite Group Databasebeta

← #21453044

Subgroups — #21453044

Order 7808.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16839704C211yesmaximal, characteristic, complemented
2#16839690C211yesmaximal, characteristic, complemented
3#16839687C211yesmaximal, characteristic, complemented
4#16839685C211yesmaximal, characteristic, complemented
5#16839676C211yesmaximal, characteristic, complemented
6#16839665C211yesmaximal, characteristic, complemented
7#16839650C211yesmaximal, characteristic, complemented
8#16839642C211yesmaximal, characteristic, complemented
9#16839642C211yesmaximal, characteristic, complemented
10#16839642C211yesmaximal, characteristic, complemented
11#16839642C211yesmaximal, characteristic, complemented
12#16839637C211yesmaximal, characteristic, complemented
13#16839629C211yesmaximal, characteristic, complemented
14#16839623C211yesmaximal, characteristic, complemented
15C61×#392C211yesmaximal, characteristic
16C23×Dic61C2211yescharacteristic
17C23×Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2211yescharacteristic
19C2×C4⋊Dic61C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2211yescharacteristic
24C2×C22⋊Dic61C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C22⋊Dic61C2211yescharacteristic
28C2×C22⋊Dic61C2211yescharacteristic
29C2×C22⋊Dic61C2211yescharacteristic
30C2×C22⋊Dic61C2211yescharacteristic
31C2×C22⋊Dic61C2211yescharacteristic
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
44C22×D4×C61C2211yescharacteristic
45C22×D4×C61C2211yescharacteristic
46C22×D4×C61C2211yescharacteristic
47C2×C22⋊C4×C61C2211yescharacteristic
48C2×C22⋊C4×C61C2211yescharacteristic
49C2×C22⋊C4×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51C24×C61C2311yescharacteristic
52C24×C61C2311yescharacteristic
53C24×C61C2311yescharacteristic
54C2×D4×C61—22no—
55C2×D4×C61—22no—
56C2×D4×C61—22no—
57C2×D4×C61—22no—
58C2×D4×C61—22no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C2×D4×C61—41no—
62C2×D4×C61—41no—
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C22×C4×C61C2311yescharacteristic
67C22×Dic61—22no—
68C22×Dic61—41no—
69C22×Dic61—41no—
70C22×Dic61—41no—
71C22×Dic61—41no—
72C22×Dic61—41no—
73C22×Dic61C2311yescharacteristic
74C22×Dic61C2311yescharacteristic
75C22×Dic61C2311yescharacteristic
76C22×Dic61C2311yescharacteristic
77C22×Dic61C2311yescharacteristic
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22⋊C4×C61—22no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊Dic61—22no—
85C22⋊Dic61—41no—
86C22⋊Dic61—41no—
87C22⋊Dic61—41no—
88C22⋊Dic61—41no—
89C22⋊Dic61—41no—
90C22⋊Dic61—41no—
91C22⋊Dic61—41no—
92C22⋊Dic61—41no—
93C22⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—41no—
96#11758196—41no—
97#11758196—41no—
98C4×Dic61—22no—
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×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61#4112yes—
119C23×C61#4112yes—
120C23×C61C2411yescharacteristic
121D4×C61—44no—
122D4×C61—44no—
123D4×C61—44no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61#4112yes—
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—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—44no—
161C2×Dic61—44no—
162C22×C61—22no—
163C22×C61—22no—
164C22×C61—22no—
165C22×C61—22no—
166C22×C61—22no—
167C22×C61—22no—
168C22×C61—41no—
169C22×C61—41no—
170C22×C61—41no—
171C22×C61—41no—
172C22×C61—41no—
173C22×C61—41no—
174C22×C61—41no—
175C22×C61—41no—
176C22×C61—41no—
177C22×C61—41no—
178C22×C61—41no—
179C22×C61—41no—
180C22×C61—41no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61C2×#4111yescharacteristic
184C22×C61C2×#4111yescharacteristic
185C22×C61C2×#4111yescharacteristic
186C22×C61H(5,𝔽2)11yescharacteristic
187C22×C61H(5,𝔽2)11yescharacteristic
188C22×C61H(5,𝔽2)11yescharacteristic
189C22×C61H(5,𝔽2)11yescharacteristic
190C4×C61—22no—
191C4×C61—41no—
192C4×C61—41no—
193C4×C61—41no—
194Dic61—41no—
195Dic61—41no—
196Dic61—41no—
197Dic61—41no—
198Dic61—41no—
199Dic61—41no—
200Dic61—41no—
201Dic61—41no—
202#2749—611nomaximal, Sylow
203C2×C61—42no—
204C2×C61—42no—
205C2×C61—81no—
206C2×C61#53811yescharacteristic
207C2×C61#53811yescharacteristic
208C2×C61#54011yescharacteristic
209C2×C61#55111yescharacteristic
210C2×C61#55111yescharacteristic
211C2×C61#55311yescharacteristic
212C2×C61#56011yescharacteristic
213#400—611no—
214#397—611no—
215#397—611no—
216#396—611no—
217#394—611no—
218#392D6111yescharacteristic
219#390—611no—
220#388—611no—
221#386—611no—
222#386—611no—
223#386—611no—
224#386—611no—
225#385—611no—
226#383—611no—
227#381—611no—
228C61#274911yescharacteristic, complemented, Sylow
229C22×D4C2×D6111yescharacteristic
230C22×D4C2×D6111yescharacteristic
231C22×D4C2×D6111yescharacteristic
232C23×C4—611no—
233C23×C4—611no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—611no—
238C2×C22⋊C4—611no—
239C2×C22⋊C4—611no—
240C2×C22⋊C4—611no—
241C2×C22⋊C4—611no—
242C2×C22⋊C4—611no—
243C2×C22⋊C4—611no—
244C2×C22⋊C4—611no—
245C2×C22⋊C4—611no—
246C2×C22⋊C4—611no—
247C2×C22⋊C4—611no—
248C2×C22⋊C4C2×D6111yescharacteristic
249C2×C22⋊C4C2×D6111yescharacteristic
250C2×C22⋊C4C2×D6111yescharacteristic
251C2×C42—611no—
252#95—611no—
253#95—611no—
254#95—611no—
255#95—611no—
256#95—611no—
257#95—611no—
258#95—611no—
259#95—611no—
260#95—611no—
261#95—611no—
262#95—611no—
263#95C2×D6111yescharacteristic
264C24C22×D6111yescharacteristic
265C24C22×D6111yescharacteristic
266C24C22×D6111yescharacteristic
267C2×D4—22no—
268C2×D4—22no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—1222no—
285C22×C4—2441no—
286C22×C4—2441no—
287C22×C4—2441no—
288C22×C4—2441no—
289C22×C4—2441no—
290C22×C4C22×D6111yescharacteristic
291C22×C4C22×D6111yescharacteristic
292C22×C4C22×D6111yescharacteristic
293C22×C4C22×D6111yescharacteristic
294C4⋊C4—2441no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C22⋊C4—22no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—1222no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C22⋊C4—2441no—
305C22⋊C4—2441no—
306C22⋊C4—2441no—
307C22⋊C4—2441no—
308C22⋊C4—2441no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C42—1222no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23#1175822412yes—
332C23#1175822412yes—
333C23C23×D6111yescharacteristic
334D4—44no—
335D4—44no—
336D4—44no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—1221no—
349C2×C4—1221no—
350C2×C4—1221no—
351C2×C4—1221no—
352C2×C4—1221no—
353C2×C4—1221no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1221no—
364C2×C4—1221no—
365C2×C4—1221no—
366C2×C4—1221no—
367C2×C4—1221no—
368C2×C4—1221no—
369C2×C4—1221no—
370C2×C4—1221no—
371C2×C4—1221no—
372C2×C4—2444no—
373C2×C4—2444no—
374C2×C4#1175822412yes—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—22no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22C2×#1175822411yescharacteristic
397C22C2×#1175822411yescharacteristic
398C22C2×#1175822411yescharacteristic
399C22#1451982211yescharacteristic
400C22#1451982211yescharacteristic
401C22#1451982211yescharacteristic
402C22#1451982311yescharacteristic
403C4—22no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—2441no—
408C4—2441no—
409C4—2441no—
410C4—2441no—
411C4—2441no—
412C4—2441no—
413C4—2441no—
414C4—2441no—
415C2—42no—
416C2—42no—
417C2—81no—
418C2#1684034711yescharacteristic
419C2#1684034911yescharacteristic
420C2#1684036611yescharacteristic
421C2#1684044311yescharacteristic
422C2#1684044311yescharacteristic
423C2#1684046411yescharacteristic
424C2#1684050011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2749
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #16839704C2semidirect
2. #16839690C2semidirect
3. #16839687C2semidirect
4. #16839685C2semidirect
5. #16839676C2semidirect
6. #16839665C2semidirect
7. #16839650C2semidirect
8. #16839642C2semidirect
9. #16839642C2semidirect
10. #16839642C2semidirect
11. #16839642C2semidirect
12. #16839637C2semidirect
13. #16839629C2semidirect
14. #16839623C2semidirect
228. C61#2749semidirect