Finite Group Databasebeta

← #21458908

Subgroups — #21458908

Order 7808.

380 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#16840497C211yesmaximal, characteristic, complemented
2#16840495C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840148C211yesmaximal, characteristic, complemented
5#16840143C211yesmaximal, characteristic, complemented
6#16839987C211yesmaximal, characteristic, complemented
7#16839984C211yesmaximal, characteristic, complemented
8#16839980C211yesmaximal, characteristic, complemented
9#16839976C211yesmaximal, characteristic, complemented
10#16839957C211yesmaximal, characteristic, complemented
11#16839956C211yesmaximal, characteristic, complemented
12#16839890C211yesmaximal, characteristic, complemented
13#16839861C211yesmaximal, characteristic, complemented
14#16839844C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×D488C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic
24#14519774C2211yescharacteristic
25#14519773C2211yescharacteristic
26#14519766C2211yescharacteristic
27#14519766C2211yescharacteristic
28#14519765—21no—
29#14519765C2211yescharacteristic
30#14519764C2211yescharacteristic
31#14519763—21no—
32#14519762—21no—
33#14519762—21no—
34#14519760—21no—
35#14519759—21no—
36C4×Dic122C2211yescharacteristic
37#14519742C2211yescharacteristic
38C4×D244—21no—
39#14519739C2211yescharacteristic
40#14519739C2211yescharacteristic
41#14519739C2211yescharacteristic
42C4×C22⋊D61—21no—
43C4⋊#92418C2211yescharacteristic
44#14519706C2211yescharacteristic
45#14519706C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519687C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C2×SD16×C61C2211yescharacteristic
53C4×Q8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#107×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C2×D4×C61C2311yescharacteristic
61C22×C4×C61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C2×D244—21no—
65C2×D244—21no—
66C2×D244C2311yescharacteristic
67C2×D244C2311yescharacteristic
68C2×D244C2311yescharacteristic
69C2×C4×D61—21no—
70C2×C4×D61—21no—
71C2×C4×D61—21no—
72C2×Dic122D411yescharacteristic
73C2×Dic122C2311yescharacteristic
74SD16×C61—22no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C4⋊C4×C61—21no—
78C4⋊C4×C61C2311yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C22⋊C4×C61—21no—
81C42×C61—21no—
82C42×C61C2311yescharacteristic
83C22⋊Dic61—21no—
84C22⋊Dic61—21no—
85#11758202—41no—
86#11758201—41no—
87#11758199—41no—
88#11758199—41no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61D411yescharacteristic
99#11758196—21no—
100#11758196D411yescharacteristic
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61C2311yescharacteristic
104C4×Dic61C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107D488—22no—
108D488—41no—
109#11758190—22no—
110#11758190—41no—
111C23×C61—21no—
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115Q8×C61—21no—
116Q8×C61—21no—
117D4×C61—21no—
118D4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—81no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2411yescharacteristic
126C22⋊D61—42no—
127C22⋊D61—81no—
128C2×Dic61—21no—
129C2×Dic61C2×D411yescharacteristic
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—21no—
136D244—21no—
137D244—21no—
138D244—21no—
139D244—42no—
140D244—81no—
141C4×D61—81no—
142C4×D61—81no—
143C4×D61—81no—
144Dic122—21no—
145Dic122—21no—
146Dic122—41no—
147C8×C61—21no—
148C8×C61#4112yes—
149#92418—21no—
150#92418—21no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C2×D61—41no—
156C2×D61—41no—
157C2×D61—41no—
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×C61—41no—
169C4×C61C2×#4111yescharacteristic
170C4×C61H(5,𝔽2)11yescharacteristic
171Dic61—21no—
172Dic61—21no—
173Dic61—21no—
174Dic61—21no—
175Dic61—41no—
176#3403—611nomaximal, Sylow
177C2×C61—81no—
178C2×C61#55011yescharacteristic
179C2×C61#57511yescharacteristic
180C2×C61#57611yescharacteristic
181D61—81no—
182D61—81no—
183D61—81no—
184#559—611no—
185#559—611no—
186#496—611no—
187#496—611no—
188#495—611no—
189#464—611no—
190#464—611no—
191#463—611no—
192#463—611no—
193#459—611no—
194#459—611no—
195#446—611no—
196#440—611no—
197#440D6111yescharacteristic, complemented
198C4×D8—611no—
199C61#340311yescharacteristic, 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×D8—611no—
209#127—611no—
210#127—611no—
211#124—611no—
212#124—611no—
213#124—611no—
214#124—611no—
215#124—1221no—
216#124—1221no—
217#123—1221no—
218#123—1221no—
219#123—1221no—
220#123—1221no—
221C4×Q8—611no—
222C4×Q8—611no—
223C4×Q8C2×D6111yescharacteristic
224C4×D4—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C4×D4—1221no—
229C4×D4C2×D6111yescharacteristic
230#107C2×D6111yescharacteristic
231C4⋊C8—611no—
232C4⋊C8—611no—
233C4⋊C8—611no—
234#103—611no—
235#103C2×D6111yescharacteristic
236#102—611no—
237#102—611no—
238#102—611no—
239#102C2×D6111yescharacteristic
240#97—611no—
241#97C2×D6111yescharacteristic
242C4×C8—611no—
243C2×Q8—611no—
244C2×Q8—611no—
245C2×Q8C22×D6111yescharacteristic
246C2×D4—611no—
247C2×D4—611no—
248C2×D4—611no—
249C2×D4—1221no—
250C2×D4—1221no—
251C2×D4—1221no—
252C2×D4—1221no—
253C2×D4C22×D6111yescharacteristic
254C22×C4—21no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258Q16—2441no—
259SD16—22no—
260SD16—1222no—
261SD16—2441no—
262SD16—2441no—
263D8—1222no—
264D8—2441no—
265D8—2441no—
266D8—2441no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8C22×D6111yescharacteristic
270C2×C8C22×D6111yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—611no—
273C4⋊C4—611no—
274C4⋊C4—611no—
275C4⋊C4—1221no—
276C4⋊C4C22×D6111yescharacteristic
277C4⋊C4C22×D6111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
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—21no—
291C42—611no—
292C42—611no—
293C42—1221no—
294C42C22×D6111yescharacteristic
295C23—21no—
296C23—1221no—
297C23—1221no—
298C23—1221no—
299Q8—21no—
300Q8—21no—
301Q8—1221no—
302Q8—1221no—
303Q8—2441no—
304D4—21no—
305D4—21no—
306D4—1221no—
307D4—1221no—
308D4—1221no—
309D4—1221no—
310D4—1221no—
311D4—1221no—
312D4—4881no—
313D4—4881no—
314D4—2442no—
315D4—2442no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—611no—
321C2×C4—611no—
322C2×C4—611no—
323C2×C4—611no—
324C2×C4—1221no—
325C2×C4—4881no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4D4×D6111yescharacteristic
329C2×C4D4×D6111yescharacteristic
330C2×C4C23×D6111yescharacteristic
331C8—21no—
332C8—1221no—
333C8—1221no—
334C8#1175822212yes—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22—2441no—
342C22—2441no—
343C22—2441no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22C2×D4×D6111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—1221no—
354C4—1221no—
355C4—1221no—
356C4—1221no—
357C4—2441no—
358C4C2×#1175822211yescharacteristic
359C4#1451982311yescharacteristic
360C2—81no—
361C2—4881no—
362C2—4881no—
363C2—4881no—
364C2#1684043311yescharacteristic
365C2#1684056111yescharacteristic
366C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3403
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #16840497C2semidirect
2. #16840495C2semidirect
3. #16840151C2semidirect
4. #16840148C2semidirect
5. #16840143C2semidirect
6. #16839987C2semidirect
7. #16839984C2semidirect
8. #16839980C2semidirect
9. #16839976C2semidirect
10. #16839957C2semidirect
11. #16839956C2semidirect
12. #16839890C2semidirect
13. #16839861C2semidirect
14. #16839844C2semidirect
15. C61×#440C2semidirect
197. #440D61semidirect
199. C61#3403semidirect