Finite Group Databasebeta

← #21456060

Subgroups — #21456060

Order 7808.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840366C211yesmaximal, characteristic, complemented
2#16840234C211yesmaximal, characteristic, complemented
3#16840085C211yesmaximal, characteristic, complemented
4#16840084C211yesmaximal, characteristic, complemented
5#16840063C211yesmaximal, characteristic, complemented
6#16840062C211yesmaximal, characteristic, complemented
7#16839954C211yesmaximal, characteristic, complemented
8#16839894C211yesmaximal, characteristic, complemented
9#16839894C211yesmaximal, characteristic, complemented
10#16839874C211yesmaximal, characteristic, complemented
11#16839871C211yesmaximal, characteristic, complemented
12D8×Dic61C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#459C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758199C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19#14519769C2211yescharacteristic, complemented
20#14519758—21no—
21#14519758—21no—
22#14519749—21no—
23#14519749—21no—
24#14519748C2211yescharacteristic
25#14519748C2211yescharacteristic
26C4×D244C2211yescharacteristic
27D4×Dic61C2211yescharacteristic
28D4×Dic61C2211yescharacteristic, complemented
29D4×Dic61C2211yescharacteristic, complemented
30#14519739C2211yescharacteristic
31C4×C22⋊D61—21no—
32#14519737—21no—
33#14519735C2211yescharacteristic
34#14519734C2211yescharacteristic
35C2×#11758198—21no—
36C22⋊C4×D61—21no—
37#14519711C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519709C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41C4⋊#92418C2211yescharacteristic, complemented
42#14519699C2211yescharacteristic
43#14519699C2211yescharacteristic
44#14519698C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54#127×C61C2211yescharacteristic, complemented
55C4×D4×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C22×Dic61—21no—
72D4×D61—22no—
73D4×D61—22no—
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78D8×C61—22no—
79D8×C61—22no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758199—22no—
91#11758199—22no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198D411yescharacteristic
96#11758198D411yescharacteristic
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196D411yescharacteristic
103#11758196D411yescharacteristic
104C4×Dic61—21no—
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C22×D61—21no—
112C22×D61—24no—
113C22×D61—81no—
114C22×D61—81no—
115C22×D61C2×D411yescharacteristic
116D4×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—81no—
122D4×C61—81no—
123D4×C61#4112yes—
124C2×C4×C61—21no—
125C2×C4×C61—81no—
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2411yescharacteristic
129C22⋊D61—24no—
130C22⋊D61—81no—
131C22⋊D61—81no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—81no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244#4112yes—
143C4×D61—21no—
144C4×D61—21no—
145C4×D61—81no—
146C4×D61—81no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—22no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C22×D411yescharacteristic
161C2×D61—21no—
162C2×D61—22no—
163C2×D61—21no—
164C2×D61—21no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61C2×#4111yescharacteristic
172C4×C61C2×#4111yescharacteristic
173Dic61—21no—
174Dic61—21no—
175Dic61—21no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179#3122—611nomaximal, Sylow
180C2×C61—42no—
181C2×C61—81no—
182C2×C61—81no—
183C2×C61#52511yescharacteristic
184C2×C61#57611yescharacteristic
185C2×C61#57611yescharacteristic
186D61—41no—
187D61—42no—
188#540—611no—
189#518—611no—
190#482—611no—
191#482—611no—
192#478—611no—
193#478—611no—
194#459—611no—
195#459D6111yescharacteristic, complemented
196#447—611no—
197#447—611no—
198#442—611no—
199#442—611no—
200C4×D8—611no—
201C4×D8—611no—
202#433—611no—
203C61#312211yescharacteristic, complemented, Sylow
204C22×D4—611no—
205C2×D8—611no—
206C2×D8—611no—
207C2×D8C2×D6111yescharacteristic
208C2×D8C2×D6111yescharacteristic
209#127C2×D6111yescharacteristic, complemented
210#125—611no—
211#123—1221no—
212#123—1221no—
213#121—611no—
214#121—611no—
215#121—1221no—
216#121—1221no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—611no—
220C4×D4—611no—
221C4×D4—611no—
222C4×D4—1221no—
223C4×D4—1221no—
224C4×D4C2×D6111yescharacteristic
225#117—611no—
226#117—611no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229#107—611no—
230#107—611no—
231#106—611no—
232#106—611no—
233C4⋊C8—611no—
234C4⋊C8C2×D6111yescharacteristic, complemented
235#102—611no—
236#102—611no—
237#102—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102C2×D6111yescharacteristic, complemented
242#102C2×D6111yescharacteristic, complemented
243C22⋊C8—611no—
244C22⋊C8—611no—
245#97—611no—
246C4×C8—611no—
247C24—1221no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4—1222no—
253C2×D4—1222no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4C22×D6111yescharacteristic
257C2×D4C22×D6111yescharacteristic
258C2×D4C22×D6111yescharacteristic
259C22×C4—21no—
260C22×C4—611no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266D8—22no—
267D8—22no—
268D8—1222no—
269D8—1222no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8C22×D6111yescharacteristic
273C2×C8C22×D6111yescharacteristic
274C4⋊C4—611no—
275C4⋊C4—611no—
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4—1221no—
280C4⋊C4—1221no—
281C4⋊C4C22×D6111yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—611no—
284C22⋊C4—611no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—611no—
294C42—1221no—
295C42C22×D6111yescharacteristic
296C23—21no—
297C23—21no—
298C23—21no—
299C23—611no—
300C23—1224no—
301C23—1221no—
302C23—4881no—
303C23—4881no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—612no—
312D4—1224no—
313D4—1221no—
314D4—4881no—
315D4—4881no—
316D4#1175822412yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—1221no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4D4×D6111yescharacteristic
333C2×C4D4×D6111yescharacteristic
334C2×C4C23×D6111yescharacteristic
335C8—21no—
336C8—21no—
337C8—1221no—
338C8—1221no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—1221no—
349C22—1222no—
350C22—1221no—
351C22—1221no—
352C22—4884no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—1221no—
360C4—1221no—
361C4—1221no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C4#41×D6111yescharacteristic
366C4C2×#1175822411yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—2441no—
371C2—2442no—
372C2#1684027211yescharacteristic
373C2#1684056311yescharacteristic
374C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#459C2
socleC22×C61C22×D4
hypercenter#459D61
hypocenterC61#3122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16840366C2semidirect
2. #16840234C2semidirect
3. #16840085C2semidirect
4. #16840084C2semidirect
5. #16840063C2semidirect
6. #16840062C2semidirect
7. #16839954C2semidirect
8. #16839894C2semidirect
9. #16839894C2semidirect
10. #16839874C2semidirect
11. #16839871C2semidirect
12. D8×Dic61C2semidirect
13. #16839842C2semidirect
14. #16839822C2semidirect
15. C61×#459C2semidirect
19. #14519769C22semidirect
28. D4×Dic61C22semidirect
29. D4×Dic61C22semidirect
37. #14519711C22semidirect
38. #14519710C22semidirect
39. #14519709C22semidirect
40. #14519708C22semidirect
41. C4⋊#92418C22semidirect
46. #14519698C22semidirect
47. #14519698C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
54. #127×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #102×C61C22semidirect
58. #102×C61C22semidirect
195. #459D61semidirect
203. C61#3122semidirect
209. #127C2×D61semidirect
234. C4⋊C8C2×D61semidirect
241. #102C2×D61semidirect
242. #102C2×D61semidirect