Finite Group Databasebeta

← #21458840

Subgroups — #21458840

Order 7808.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840484C211yesmaximal, characteristic, complemented
2#16840433C211yesmaximal, characteristic, complemented
3#16840151C211yesmaximal, characteristic, complemented
4#16840148C211yesmaximal, characteristic, complemented
5#16840133C211yesmaximal, characteristic, complemented
6#16839980C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839966C211yesmaximal, characteristic, complemented
9#16839962C211yesmaximal, characteristic, complemented
10#16839961C211yesmaximal, characteristic, complemented
11#16839956C211yesmaximal, characteristic, complemented
12#16839890C211yesmaximal, characteristic, complemented
13#16839861C211yesmaximal, characteristic, complemented
14#16839844C211yesmaximal, characteristic, complemented
15C61×#440C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C2×#11758190C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758201C2211yescharacteristic
22C2×D488C2211yescharacteristic
23C2×D488C2211yescharacteristic
24C2×#11758199C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519774C2211yescharacteristic
27#14519773C2211yescharacteristic
28#14519773C2211yescharacteristic
29#14519772—21no—
30#14519771—21no—
31#14519766C2211yescharacteristic
32#14519765C2211yescharacteristic
33#14519755—21no—
34#14519751—21no—
35#14519750—21no—
36#14519750—21no—
37C4×Dic122C2211yescharacteristic
38#14519742C2211yescharacteristic
39#14519739C2211yescharacteristic
40#14519739C2211yescharacteristic
41#14519739C2211yescharacteristic
42#14519734—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×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66#11758222—44no—
67C2×D244—21no—
68C2×D244—21no—
69C2×D244C2311yescharacteristic
70C2×D244C2311yescharacteristic
71C2×D244C2311yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—21no—
75C2×Dic122D411yescharacteristic
76C2×Dic122C2311yescharacteristic
77SD16×C61—22no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C22⋊C4×C61—21no—
84C42×C61—21no—
85C42×C61C2311yescharacteristic
86#11758201—41no—
87#11758201—41no—
88#11758200—41no—
89#11758199—41no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61D411yescharacteristic
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196D411yescharacteristic
102#11758196D411yescharacteristic
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105C4×Dic61C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108D488—22no—
109D488—41no—
110#11758190—22no—
111#11758190—41no—
112C23×C61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116Q8×C61—21no—
117Q8×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—42no—
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×Dic61C2×D411yescharacteristic
133C2×Dic61C2×D411yescharacteristic
134C2×Dic61C2×D411yescharacteristic
135C2×Dic61C2×D411yescharacteristic
136D244—21no—
137D244—21no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—21no—
142D244—42no—
143D244—81no—
144C4×D61—42no—
145C4×D61—42no—
146C4×D61—42no—
147Dic122—22no—
148Dic122—21no—
149Dic122—21no—
150C8×C61—21no—
151C8×C61#4112yescomplemented
152#92418—21no—
153#92418—21no—
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—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61—41no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—21no—
175Dic61—21no—
176Dic61—21no—
177Dic61—41no—
178Dic61AGL(1,ℤ/8)12yes—
179#3397—611nomaximal, Sylow
180C2×C61—81no—
181C2×C61#55011yescharacteristic
182C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
183C2×C61#57711yescharacteristic
184D61—81no—
185D61—81no—
186D61—81no—
187#556—611no—
188#550—611no—
189#496—611no—
190#496—611no—
191#492—611no—
192#463—611no—
193#463—611no—
194#461—611no—
195#460—611no—
196#460—611no—
197#459—611no—
198#446—611no—
199#440—611no—
200#440D6111yescharacteristic, complemented
201C4×D8—611no—
202C61#339711yescharacteristic, complemented, Sylow
203C2×#41—1221no—
204C2×SD16—611no—
205C2×SD16—611no—
206C2×SD16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×SD16C2×D6111yescharacteristic
210C2×D8—611no—
211C2×D8—611no—
212C2×D8—611no—
213C4⋊Q8—611no—
214#127—611no—
215#127—611no—
216#127—611no—
217#126—1221no—
218#126—1221no—
219#124—611no—
220#124—611no—
221C22⋊Q8—1221no—
222#121—1221no—
223#121—1221no—
224#121—1221no—
225C4×Q8—611no—
226C4×Q8—611no—
227C4×Q8C2×D6111yescharacteristic
228C4×D4—611no—
229C4×D4—611no—
230C4×D4—611no—
231C4×D4C2×D6111yescharacteristic
232#117—1221no—
233#107C2×D6111yescharacteristic
234C4⋊C8—611no—
235C4⋊C8—611no—
236C4⋊C8—611no—
237#103—611no—
238#103C2×D6111yescharacteristic
239#102—611no—
240#102—611no—
241#102—611no—
242#102C2×D6111yescharacteristic
243#97—611no—
244#97C2×D6111yescharacteristic
245C4×C8—611no—
246#41—2444no—
247C2×Q8—611no—
248C2×Q8—611no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—611no—
251C2×D4—611no—
252C2×D4—611no—
253C2×D4—1221no—
254C2×D4—1221no—
255C2×D4—1221no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4C22×D6111yescharacteristic
260C22×C4—21no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264SD16—22no—
265SD16—1222no—
266SD16—2441no—
267SD16—2441no—
268SD16—2441no—
269SD16—2441no—
270D8—1222no—
271D8—2441no—
272D8—2441no—
273C2×C8—611no—
274C2×C8—611no—
275C2×C8C22×D6111yescharacteristic
276C2×C8C22×D6111yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—611no—
279C4⋊C4—611no—
280C4⋊C4—611no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4C22×D6111yescharacteristic
285C4⋊C4C22×D6111yescharacteristic
286C22⋊C4—21no—
287C22⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C42—21no—
295C42—611no—
296C42—611no—
297C42—1221no—
298C42C22×D6111yescharacteristic
299C23—21no—
300C23—1221no—
301C23—1221no—
302C23—1221no—
303Q8—21no—
304Q8—21no—
305Q8—1222no—
306Q8—1221no—
307Q8—1221no—
308D4—21no—
309D4—21no—
310D4—1221no—
311D4—1221no—
312D4—1221no—
313D4—1221no—
314D4—1221no—
315D4—1221no—
316D4—4881no—
317D4—4881no—
318D4—4881no—
319D4—2442no—
320D4—2442no—
321D4—2442no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—1221no—
331C2×C4—2442no—
332C2×C4—2442no—
333C2×C4—2442no—
334C2×C4D4×D6111yescharacteristic
335C2×C4D4×D6111yescharacteristic
336C2×C4C23×D6111yescharacteristic
337C8—21no—
338C8—1221no—
339C8—1221no—
340C8#1175822212yescomplemented
341C22—41no—
342C22—41no—
343C22—41no—
344C22—2441no—
345C22—2441no—
346C22—2441no—
347C22—2441no—
348C22—2441no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22C2×D4×D6111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—612no—
360C4—1221no—
361C4—1221no—
362C4—1221no—
363C4—2441no—
364C4C2×#1175822211yescharacteristic
365C4#1451982311yescharacteristic
366C2—81no—
367C2—4881no—
368C2—4881no—
369C2—4881no—
370C2#1684043311yescharacteristic
371C2AGL(1,ℤ/8)×D6111yescharacteristic
372C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#440C2
socleC22×C61C22×D4
hypercenter#440D61
hypocenterC61#3397
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. #16840484C2semidirect
2. #16840433C2semidirect
3. #16840151C2semidirect
4. #16840148C2semidirect
5. #16840133C2semidirect
6. #16839980C2semidirect
7. #16839977C2semidirect
8. #16839966C2semidirect
9. #16839962C2semidirect
10. #16839961C2semidirect
11. #16839956C2semidirect
12. #16839890C2semidirect
13. #16839861C2semidirect
14. #16839844C2semidirect
15. C61×#440C2semidirect
151. C8×C61#41semidirect
200. #440D61semidirect
202. C61#3397semidirect
340. C8#11758222semidirect