Finite Group Databasebeta

← #21456096

Subgroups — #21456096

Order 7808.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840383C211yesmaximal, characteristic, complemented
2#16840092C211yesmaximal, characteristic, complemented
3#16840080C211yesmaximal, characteristic, complemented
4#16840052C211yesmaximal, characteristic, complemented
5#16840047C211yesmaximal, characteristic, complemented
6#16839984C211yesmaximal, characteristic, complemented
7#16839977C211yesmaximal, characteristic, complemented
8#16839924C211yesmaximal, characteristic, complemented
9#16839907C211yesmaximal, characteristic
10#16839872C211yesmaximal, characteristic, complemented
11#16839867C211yesmaximal, characteristic, complemented
12C4×#11758201C211yesmaximal, characteristic, complemented
13C4×#11758200C211yesmaximal, characteristic, complemented
14#16839823C211yesmaximal, characteristic, complemented
15C61×#520C211yesmaximal, characteristic, complemented
16C2×#11758202C2211yescharacteristic
17C2×#11758200C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758199C2211yescharacteristic
20#14519777C2211yescharacteristic
21#14519772—21no—
22#14519765C2211yescharacteristic
23#14519763—21no—
24#14519759—21no—
25#14519756C2211yescharacteristic
26#14519755—21no—
27#14519751C2211yescharacteristic
28C4×Dic122C2211yescharacteristic
29C4×D244C2211yescharacteristic
30#14519708C2211yescharacteristic
31#14519708C2211yescharacteristic
32#14519708C2211yescharacteristic
33#14519708C2211yescharacteristic
34C4⋊#92418C2211yescharacteristic
35C4⋊#92418C2211yescharacteristic
36#14519701C2211yescharacteristic
37#14519701C2211yescharacteristic
38#14519700C2211yescharacteristic
39#14519700C2211yescharacteristic
40#14519698C2211yescharacteristic
41#14519698C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44C22⋊#92418C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46#14519688C2211yescharacteristic
47C4×#92418C2211yescharacteristic
48C2×#41×C61C2211yescharacteristic
49C4×Q8×C61C2211yescharacteristic
50C4×Q8×C61C2211yescharacteristic
51C4×D4×C61—21no—
52C4×D4×C61—21no—
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55#117×C61—21no—
56#117×C61C2211yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—22no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61C2311yescharacteristic
69C2×C22⋊D61—21no—
70C2×D244C2311yescharacteristic
71C2×C4×D61—21no—
72C2×Dic122—21no—
73C2×Dic122C2311yescharacteristic
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—21no—
77C4⋊C4×C61D411yescharacteristic
78C4⋊C4×C61D411yescharacteristic
79C4⋊C4×C61C2311yescharacteristic
80C4⋊C4×C61C2311yescharacteristic
81C22⋊C4×C61—21no—
82C22⋊C4×C61—21no—
83C22⋊C4×C61D411yescharacteristic
84C22⋊C4×C61D411yescharacteristic
85C42×C61—21no—
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90#11758202—22no—
91#11758201—22no—
92#11758200—22no—
93#11758199—22no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103C4×Dic61—21no—
104C2×#92418C2311yescharacteristic
105C2×#92418C2311yescharacteristic
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—21no—
111Q8×C61—21no—
112Q8×C61#4112yes—
113D4×C61—24no—
114D4×C61—21no—
115D4×C61#4112yes—
116C2×C4×C61—24no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—81no—
123C2×C4×C61—81no—
124C2×C4×C61—81no—
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—81no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135D244—21no—
136D244—21no—
137C4×D61—81no—
138Dic122—21no—
139Dic122—21no—
140Dic122—81no—
141#92418—21no—
142#92418—21no—
143#92418—21no—
144#92418—21no—
145C22×C61—21no—
146C22×C61—22no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61C22×D411yescharacteristic
152C2×D61—41no—
153C2×D61—41no—
154C2×D61—41no—
155C4×C61—21no—
156C4×C61—22no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61C2×#4111yescharacteristic
164C4×C61C2×#4111yescharacteristic
165Dic61—41no—
166Dic61—41no—
167Dic61—41no—
168#3125—611nomaximal, Sylow
169C2×C61—41no—
170C2×C61—42no—
171C2×C61#52511yescharacteristic
172C2×C61#57711yescharacteristic
173C2×C61#57711yescharacteristic
174D61—81no—
175#542—611no—
176#520D6111yescharacteristic, complemented
177#483—611no—
178#481—611no—
179#476—611no—
180#475—611no—
181#464—611no—
182#463—611no—
183#452—611no—
184#449—611no—
185#442—611no—
186#441—611no—
187C4×SD16—611no—
188C4×SD16—611no—
189#433—611no—
190C61#312511yescharacteristic, complemented, Sylow
191C2×#41C2×D6111yescharacteristic
192C2×Q16—611no—
193C2×SD16—611no—
194C2×SD16—611no—
195C2×D8—611no—
196C4⋊Q8—611no—
197#126—1221no—
198#124—611no—
199#124—1221no—
200#123—1221no—
201C22⋊Q8—611no—
202C22⋊Q8—1221no—
203#121—611no—
204C4×Q8—611no—
205C4×Q8C2×D6111yescharacteristic
206C4×Q8C2×D6111yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4—611no—
210C4×D4C2×D6111yescharacteristic
211C4×D4C2×D6111yescharacteristic
212#117—21no—
213#117C2×D6111yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C2×D6111yescharacteristic
216#106—611no—
217#106—611no—
218#106—611no—
219#106—611no—
220C4⋊C8—611no—
221C4⋊C8—611no—
222#103—611no—
223#103—611no—
224#103—611no—
225#103—611no—
226#102—611no—
227#102—611no—
228#102—611no—
229#102—611no—
230C22⋊C8—611no—
231C22⋊C8—611no—
232#97—611no—
233C4×C8—611no—
234#41—22no—
235#41—22no—
236C2×Q8—611no—
237C2×Q8—1221no—
238C2×Q8C22×D6111yescharacteristic
239C2×D4—21no—
240C2×D4—611no—
241C2×D4—1221no—
242C2×D4C22×D6111yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—1221no—
248C22×C4C22×D6111yescharacteristic
249Q16—1222no—
250SD16—1222no—
251SD16—1222no—
252D8—1222no—
253C2×C8—611no—
254C2×C8—611no—
255C2×C8—611no—
256C2×C8—611no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—611no—
261C4⋊C4—611no—
262C4⋊C4—1221no—
263C4⋊C4—1221no—
264C4⋊C4—1221no—
265C4⋊C4C22⋊D6111yescharacteristic
266C4⋊C4C22⋊D6111yescharacteristic
267C4⋊C4C22×D6111yescharacteristic
268C4⋊C4C22×D6111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—1221no—
272C22⋊C4—1221no—
273C22⋊C4—1221no—
274C22⋊C4—1221no—
275C22⋊C4—1221no—
276C22⋊C4C22⋊D6111yescharacteristic
277C22⋊C4C22⋊D6111yescharacteristic
278C42—21no—
279C42—21no—
280C42—1221no—
281C42C22×D6111yescharacteristic
282C42C22×D6111yescharacteristic
283C23—21no—
284C23—1221no—
285C23C2×C22⋊D6111yescharacteristic
286Q8—21no—
287Q8—1221no—
288Q8—1221no—
289Q8—4881no—
290Q8#1175822212yes—
291D4—24no—
292D4—21no—
293D4—1221no—
294D4—1221no—
295D4—4881no—
296D4#1175822212yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—4881no—
310C2×C4C2×C22⋊D6111yescharacteristic
311C2×C4C2×C22⋊D6111yescharacteristic
312C2×C4C2×C22⋊D6111yescharacteristic
313C2×C4C2×C22⋊D6111yescharacteristic
314C2×C4C2×C22⋊D6111yescharacteristic
315C2×C4C23×D6111yescharacteristic
316C8—1221no—
317C8—1221no—
318C8—1221no—
319C8—1221no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—2441no—
327C22—2441no—
328C22—2441no—
329C22C22×C22⋊D6111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—2441no—
339C4—2441no—
340C4—2441no—
341C4C2×#1175822211yescharacteristic
342C4C2×#1175822211yescharacteristic
343C2—41no—
344C2—42no—
345C2—4881no—
346C2#1684027311yescharacteristic
347C2#1684057011yescharacteristic
348C2#1684057311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#520C2
socleC22×C61C22×D4
hypercenter#520D61
hypocenterC61#3125
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #16840383C2semidirect
2. #16840092C2semidirect
3. #16840080C2semidirect
4. #16840052C2semidirect
5. #16840047C2semidirect
6. #16839984C2semidirect
7. #16839977C2semidirect
8. #16839924C2semidirect
10. #16839872C2semidirect
11. #16839867C2semidirect
12. C4×#11758201C2semidirect
13. C4×#11758200C2semidirect
14. #16839823C2semidirect
15. C61×#520C2semidirect
176. #520D61semidirect
190. C61#3125semidirect