Finite Group Databasebeta

← #21458826

Subgroups — #21458826

Order 7808.

384 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840495C211yesmaximal, characteristic, complemented
2#16840494C211yesmaximal, characteristic, complemented
3#16840144C211yesmaximal, characteristic, complemented
4#16840143C211yesmaximal, characteristic, complemented
5#16840137C211yesmaximal, characteristic
6#16839980C211yesmaximal, characteristic, complemented
7#16839978C211yesmaximal, characteristic, complemented
8#16839975C211yesmaximal, characteristic, complemented
9#16839961C211yesmaximal, characteristic, complemented
10#16839960C211yesmaximal, characteristic, complemented
11#16839886C211yesmaximal, characteristic, complemented
12#16839854C211yesmaximal, characteristic, complemented
13C4×#11758199C211yesmaximal, characteristic, complemented
14#16839842C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758200C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23#14519773C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519766C2211yescharacteristic
26#14519765C2211yescharacteristic
27#14519764C2211yescharacteristic
28#14519763—21no—
29#14519763—21no—
30#14519761—21no—
31#14519760—21no—
32#14519759—21no—
33#14519759—21no—
34Q8×Dic61C2211yescharacteristic
35C4×Dic122C2211yescharacteristic
36#14519742C2211yescharacteristic
37C4×D244C2211yescharacteristic
38D4×Dic61C2211yescharacteristic
39#14519739C2211yescharacteristic
40C4×C22⋊D61—21no—
41#14519737—21no—
42#14519710C2211yescharacteristic
43#14519706C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519702C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519697C2211yescharacteristic
49C4×#92418C2211yescharacteristic
50C8×Dic61C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic
56C4⋊C8×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C22×Dic61—21no—
68C2×D244C2311yescharacteristic
69C2×D244C2311yescharacteristic
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×Dic122D411yescharacteristic
73C2×Dic122C2311yescharacteristic
74SD16×C61—41no—
75D8×C61—41no—
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61C2311yescharacteristic
79C22⋊C4×C61—21no—
80C22⋊C4×C61—21no—
81C22⋊C4×C61—21no—
82C42×C61C2311yescharacteristic
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85C22⋊Dic61—21no—
86#11758202—22no—
87#11758201—41no—
88#11758200—41no—
89#11758199—22no—
90#11758199—22no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61—21no—
105C4×Dic61C2311yescharacteristic
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109D488—41no—
110#11758190—41no—
111C23×C61—21no—
112C23×C61—21no—
113C22×D61—21no—
114C22×D61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—81no—
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2411yescharacteristic
127C22⋊D61—42no—
128C22⋊D61—42no—
129C22⋊D61—81no—
130C22⋊D61—81no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—81no—
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136C2×Dic61C2×D411yescharacteristic
137C2×Dic61C2×D411yescharacteristic
138D244—21no—
139D244—21no—
140D244—21no—
141D244—21no—
142C4×D61—81no—
143C4×D61—81no—
144Dic122—22no—
145Dic122—21no—
146Dic122—21no—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418#4112yes—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61C22×D411yescharacteristic
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—41no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61C2×#4111yescharacteristic
169C4×C61H(5,𝔽2)11yescharacteristic
170Dic61—21no—
171Dic61—21no—
172Dic61—21no—
173Dic61—41no—
174Dic61—41no—
175Dic61#13512yes—
176#3396—611nomaximal, Sylow
177C2×C61—81no—
178C2×C61—81no—
179C2×C61#55011yescharacteristic
180C2×C61C2×#13511yescharacteristic
181C2×C61#57611yescharacteristic
182D61—81no—
183D61—81no—
184#559—611no—
185#559—611no—
186#495—611no—
187#495—611no—
188#493—611no—
189#463—611no—
190#463—611no—
191#463—611no—
192#463D6111yescharacteristic, complemented
193#460—611no—
194#460—611no—
195C8×Q8—611no—
196C4×Q16—611no—
197C4×D8—611no—
198C4×D8—611no—
199C61#339611yescharacteristic, complemented, Sylow
200C2×Q16—611no—
201C2×SD16—611no—
202C2×SD16—611no—
203C2×SD16—611no—
204C2×SD16C2×D6111yescharacteristic
205C2×D8—611no—
206C2×D8—611no—
207C2×D8—611no—
208C2×D8C2×D6111yescharacteristic
209#127—611no—
210#127—611no—
211#124—611no—
212#124—611no—
213#124—611no—
214#124—1221no—
215#124—1221no—
216#124C2×D6111yescharacteristic
217#123—1221no—
218#123—1221no—
219#123—1221no—
220#123—1221no—
221C4×Q8—611no—
222C4×Q8—611no—
223C4×Q8—611no—
224C4×D4—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C4×D4—1221no—
229C4×D4C2×D6111yescharacteristic
230#107—611no—
231C4⋊C8—611no—
232C4⋊C8—611no—
233C4⋊C8C2×D6111yescharacteristic
234#103—611no—
235#103C2×D6111yescharacteristic
236#102—611no—
237#102—611no—
238#102—611no—
239#102C2×D6111yescharacteristic
240C4×C8—611no—
241C4×C8—611no—
242C4×C8—611no—
243C2×Q8—611no—
244C2×Q8—611no—
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—611no—
248C2×D4—1221no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4C22×D6111yescharacteristic
253C2×D4C22×D6111yescharacteristic
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258Q16—1222no—
259SD16—41no—
260SD16—2441no—
261SD16—2441no—
262SD16—2441no—
263D8—41no—
264D8—1222no—
265D8—1222no—
266D8—2441no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C4⋊C4—611no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4—1221no—
277C4⋊C4C22×D6111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C42—611no—
291C42—611no—
292C42—1221no—
293C42—1221no—
294C42C22×D6111yescharacteristic
295C23—21no—
296C23—21no—
297C23—1221no—
298C23—1221no—
299Q8—21no—
300Q8—21no—
301Q8—1222no—
302Q8—1221no—
303Q8—1221no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—1221no—
309D4—1221no—
310D4—1221no—
311D4—1221no—
312D4—4881no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—611no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4D4×D6111yescharacteristic
329C2×C4D4×D6111yescharacteristic
330C2×C4C23×D6111yescharacteristic
331C8—21no—
332C8—21no—
333C8—612no—
334C8—1221no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—612no—
353C4—1221no—
354C4—1221no—
355C4—1221no—
356C4—2441no—
357C4—2441no—
358C4#41×D6111yescharacteristic
359C4#1451982211yescharacteristic
360C2—81no—
361C2—81no—
362C2—4881no—
363C2—4881no—
364C2#1684043011yescharacteristic
365C2#135×D6111yescharacteristic
366C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3396
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840495C2semidirect
2. #16840494C2semidirect
3. #16840144C2semidirect
4. #16840143C2semidirect
6. #16839980C2semidirect
7. #16839978C2semidirect
8. #16839975C2semidirect
9. #16839961C2semidirect
10. #16839960C2semidirect
11. #16839886C2semidirect
12. #16839854C2semidirect
13. C4×#11758199C2semidirect
14. #16839842C2semidirect
15. C61×#463C2semidirect
192. #463D61semidirect
199. C61#3396semidirect