Finite Group Databasebeta

← #21456064

Subgroups — #21456064

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#16840368C211yesmaximal, characteristic, complemented
2#16840234C211yesmaximal, characteristic, complemented
3#16840089C211yesmaximal, characteristic, complemented
4#16840088C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16839958C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839897C211yesmaximal, characteristic, complemented
9#16839897C211yesmaximal, characteristic, complemented
10#16839873C211yesmaximal, characteristic, complemented
11#16839871C211yesmaximal, characteristic, complemented
12#16839844C211yesmaximal, characteristic, complemented
13#16839842C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#478C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×D488C2211yescharacteristic
18C2×D488C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21#14519774C2211yescharacteristic, complemented
22#14519762—21no—
23#14519762—21no—
24#14519752—21no—
25#14519752—21no—
26#14519752C2211yescharacteristic
27#14519752C2211yescharacteristic
28C4×D244C2211yescharacteristic
29D4×Dic61C2211yescharacteristic
30#14519739C2211yescharacteristic
31#14519739C2211yescharacteristic, complemented
32#14519739C2211yescharacteristic, complemented
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519735C2211yescharacteristic
36#14519734C2211yescharacteristic
37C2×#11758198—21no—
38C22⋊C4×D61—21no—
39#14519710C2211yescharacteristic, complemented
40#14519708C2211yescharacteristic, complemented
41C4⋊#92418C2211yescharacteristic, complemented
42#14519699C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic, complemented
44#14519697C2211yescharacteristic
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52#125×C61C2211yescharacteristic, complemented
53C4×D4×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C22×Dic61—21no—
64D4×D61—22no—
65D4×D61—22no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244—21no—
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
72C2×D244C2311yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C42×C61C2311yescharacteristic
87C22⋊Dic61—21no—
88#11758199—22no—
89#11758199—22no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198D411yescharacteristic
98#11758198D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106D488—22no—
107D488—22no—
108C23×C61—21no—
109C22×D61—21no—
110C22×D61—24no—
111C22×D61—21no—
112C22×D61—21no—
113C22×D61—81no—
114C22×D61—81no—
115C22×D61C2×D411yescharacteristic
116D4×C61—21no—
117D4×C61#4112yes—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—81no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2411yescharacteristic
125C22⋊D61—24no—
126C2×Dic61—21no—
127C2×Dic61—81no—
128C2×Dic61C2×D411yescharacteristic
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131D244—21no—
132D244—21no—
133D244—21no—
134D244—21no—
135D244—21no—
136D244—81no—
137D244—81no—
138D244—81no—
139D244—81no—
140D244#4112yes—
141C4×D61—21no—
142C4×D61—21no—
143C4×D61—81no—
144C4×D61—81no—
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×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—22no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61—41no—
173C4×C61C2×#4111yescharacteristic
174C4×C61C2×#4111yescharacteristic
175Dic61—21no—
176Dic61—21no—
177Dic61—21no—
178Dic61—41no—
179#3122—611nomaximal, Sylow
180C2×C61—42no—
181C2×C61#52511yescharacteristic
182C2×C61#57611yescharacteristic
183C2×C61#57611yescharacteristic
184D61—41no—
185D61—42no—
186D61—81no—
187D61—81no—
188#540—611no—
189#518—611no—
190#482—611no—
191#482—611no—
192#478—611no—
193#478D6111yescharacteristic, complemented
194#459—611no—
195#459—611no—
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×D8—611no—
208C2×D8—611no—
209#127—611no—
210#125C2×D6111yescharacteristic, complemented
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#107C2×D6111yescharacteristic, complemented
231#106—611no—
232#106C2×D6111yescharacteristic, complemented
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
242#102C2×D6111yescharacteristic
243C22⋊C8—611no—
244C22⋊C8—611no—
245#97—611no—
246C4×C8—611no—
247C24—1221no—
248C2×D4—611no—
249C2×D4—611no—
250C2×D4—611no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4—1221no—
254C2×D4—1222no—
255C2×D4—1222no—
256C2×D4—1221no—
257C2×D4—1221no—
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—1222no—
267D8—1222no—
268D8—1222no—
269D8—1222no—
270C2×C8—611no—
271C2×C8—611no—
272C2×C8C22×D6111yescharacteristic
273C2×C8C22×D6111yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4C22×D6111yescharacteristic
280C4⋊C4C22×D6111yescharacteristic
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—611no—
298C23—1224no—
299C23—1221no—
300C23—1221no—
301C23—1221no—
302C23—4881no—
303C23—4881no—
304D4—21no—
305D4—612no—
306D4—1224no—
307D4—1221no—
308D4—1221no—
309D4—1221no—
310D4—1221no—
311D4—1221no—
312D4—4881no—
313D4—4881no—
314D4—4881no—
315D4—4881no—
316D4#1175822612yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
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—1221no—
343C22—1222no—
344C22—1221no—
345C22—1221no—
346C22—4884no—
347C22—2441no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—1221no—
362C4—1221no—
363C4—1221no—
364C4—2441no—
365C4#41×D6111yescharacteristic
366C4C2×#1175822611yescharacteristic
367C2—42no—
368C2—4881no—
369C2—4881no—
370C2—2441no—
371C2—2442no—
372C2#1684027511yescharacteristic
373C2#1684056411yescharacteristic
374C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#478C2
socleC22×C61C22×D4
hypercenter#478D61
hypocenterC61#3122
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #16840368C2semidirect
2. #16840234C2semidirect
3. #16840089C2semidirect
4. #16840088C2semidirect
5. #16840059C2semidirect
6. #16839958C2semidirect
7. #16839957C2semidirect
8. #16839897C2semidirect
9. #16839897C2semidirect
10. #16839873C2semidirect
11. #16839871C2semidirect
12. #16839844C2semidirect
13. #16839842C2semidirect
14. #16839822C2semidirect
15. C61×#478C2semidirect
21. #14519774C22semidirect
31. #14519739C22semidirect
32. #14519739C22semidirect
39. #14519710C22semidirect
40. #14519708C22semidirect
41. C4⋊#92418C22semidirect
42. #14519699C22semidirect
43. #14519699C22semidirect
46. #14519697C22semidirect
47. #14519697C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
52. #125×C61C22semidirect
54. #107×C61C22semidirect
55. #106×C61C22semidirect
56. C4⋊C8×C61C22semidirect
193. #478D61semidirect
203. C61#3122semidirect
210. #125C2×D61semidirect
230. #107C2×D61semidirect
232. #106C2×D61semidirect
234. C4⋊C8C2×D61semidirect