Finite Group Databasebeta

← #21458111

Subgroups — #21458111

Order 7808.

386 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840475C211yesmaximal, characteristic
2#16840425C211yesmaximal, characteristic, complemented
3#16840111C211yesmaximal, characteristic, complemented
4#16840106C211yesmaximal, characteristic, complemented
5#16840056C211yesmaximal, characteristic, complemented
6#16840010C211yesmaximal, characteristic, complemented
7#16840009C211yesmaximal, characteristic, complemented
8#16839966C211yesmaximal, characteristic, complemented
9#16839903C211yesmaximal, characteristic, complemented
10#16839902C211yesmaximal, characteristic, complemented
11#16839849C211yesmaximal, characteristic, complemented
12#16839837C211yesmaximal, characteristic, complemented
13#16839770C211yesmaximal, characteristic, complemented
14#16839769C211yesmaximal, characteristic, complemented
15C61×#485C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C2×Q8×D61C2211yescharacteristic
18C2×#11758190C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758201C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C2×#11758189C2211yescharacteristic
23#14519776—21no—
24#14519776C2211yescharacteristic
25#14519775C2211yescharacteristic
26#14519765—21no—
27#14519763—21no—
28#14519757C2211yescharacteristic
29#14519755—21no—
30#14519754—21no—
31#14519752C2211yescharacteristic
32#14519751C2211yescharacteristic
33#14519750—21no—
34#14519742C2211yescharacteristic
35#14519739C2211yescharacteristic
36C4×C22⋊D61C2211yescharacteristic
37#14519737—21no—
38#14519735C2211yescharacteristic
39#14519734—21no—
40#14519710C2211yescharacteristic
41#14519706C2211yescharacteristic
42#14519702C2211yescharacteristic
43#14519702C2211yescharacteristic
44#14519701C2211yescharacteristic
45#14519700C2211yescharacteristic
46#14519700C2211yescharacteristic
47#14519700C2211yescharacteristic
48#14519700C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51C8×Dic61C2211yescharacteristic
52C22⋊Q8×C61C2211yescharacteristic
53#117×C61C2211yescharacteristic
54#107×C61C2211yescharacteristic
55#106×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic
57#103×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic
59C2×Q8×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×C22⋊D61D411yescharacteristic
63C22×Dic61—21no—
64Q8×D61—22no—
65Q8×D61—41no—
66C2×D244—21no—
67C2×D244C2311yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61C2311yescharacteristic
71C2×Dic122—22no—
72C2×Dic122—21no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—41no—
76C2×Dic122C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61C2311yescharacteristic
82C4⋊C4×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C42×C61—21no—
87C22⋊Dic61D411yescharacteristic
88#11758201—41no—
89#11758198—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198D411yescharacteristic
95C4⋊Dic61—21no—
96C4⋊Dic61C2311yescharacteristic
97#11758196—21no—
98#11758196—21no—
99#11758196—21no—
100#11758196—21no—
101#11758196D411yescharacteristic
102C4×Dic61—21no—
103C4×Dic61—21no—
104C4×Dic61C2311yescharacteristic
105#11758194—41no—
106C2×#92418C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108#11758190—22no—
109#11758190—41no—
110#11758189—41no—
111C23×C61C2×D411yescharacteristic
112C22×D61—21no—
113C22×D61C2×D411yescharacteristic
114Q8×C61—21no—
115Q8×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×D411yescharacteristic
123C2×C4×C61C2411yescharacteristic
124C22⋊D61—22no—
125C22⋊D61—81no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—42no—
130C2×Dic61C2×D411yescharacteristic
131C2×Dic61C2×D411yescharacteristic
132C2×Dic61C2×D411yescharacteristic
133D244—21no—
134D244—21no—
135D244—81no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—42no—
139C4×D61—42no—
140Dic122—21no—
141Dic122—21no—
142Dic122—21no—
143Dic122—42no—
144Dic122—42no—
145Dic122—81no—
146Dic122#4112yes—
147C8×C61—21no—
148C8×C61—21no—
149#92418—21no—
150#92418—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61C22×D411yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C4×C61—21no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61H(5,𝔽2)11yescharacteristic
168Dic61—22no—
169Dic61—21no—
170Dic61—21no—
171Dic61—41no—
172Dic61—41no—
173Dic61#13712yes—
174#3329—611nomaximal, Sylow
175C2×C61—41no—
176C2×C61#54611yescharacteristic
177C2×C61C2×#13711yescharacteristic
178C2×C61#57711yescharacteristic
179D61—41no—
180D61—81no—
181#555—611no—
182D4×Q8—611no—
183#487—611no—
184#485—611no—
185#485D6111yescharacteristic, complemented
186#477—611no—
187#468—611no—
188#468—611no—
189#461—611no—
190#448—611no—
191#448—611no—
192C4×SD16—611no—
193#436—611no—
194#419—611no—
195#419—611no—
196C61#332911yescharacteristic, complemented, Sylow
197C22×Q8—611no—
198C22×Q8—611no—
199C2×SD16—611no—
200C2×SD16—611no—
201C2×SD16—611no—
202C2×M16—611no—
203C2×M16—611no—
204C4⋊Q8—611no—
205C4⋊Q8—611no—
206C4⋊Q8—1221no—
207#124—1221no—
208#124—1221no—
209C22⋊Q8—611no—
210C22⋊Q8—1221no—
211C22⋊Q8—1221no—
212C22⋊Q8C2×D6111yescharacteristic
213#121—611no—
214#121—611no—
215#121—1221no—
216C4×Q8—611no—
217C4×D4—611no—
218C4×D4—611no—
219C4×D4—1221no—
220#117—611no—
221#117—1221no—
222#117C2×D6111yescharacteristic
223#107—611no—
224#107C2×D6111yescharacteristic
225#106C2×D6111yescharacteristic
226C4⋊C8—611no—
227#103—611no—
228#103—611no—
229#103—611no—
230#103—611no—
231#103—611no—
232#103—611no—
233#103—611no—
234#103C2×D6111yescharacteristic
235#103C2×D6111yescharacteristic
236#102—611no—
237C22⋊C8—611no—
238C22⋊C8C2×D6111yescharacteristic
239C4×C8—611no—
240C2×Q8—611no—
241C2×Q8—611no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—1222no—
245C2×Q8—1221no—
246C2×Q8—1222no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8C22×D6111yescharacteristic
250C2×D4—611no—
251C2×D4—611no—
252C2×D4—1221no—
253C2×D4—1221no—
254C22×C4—611no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4C22×D6111yescharacteristic
259SD16—1222no—
260SD16—2441no—
261SD16—2441no—
262M16—2441no—
263M16—2441no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8C22×D6111yescharacteristic
267C2×C8C22×D6111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—611no—
270C4⋊C4—611no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4C22×D6111yescharacteristic
277C4⋊C4C22×D6111yescharacteristic
278C4⋊C4C22×D6111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—611no—
282C22⋊C4—611no—
283C22⋊C4—1221no—
284C22⋊C4—1221no—
285C22⋊C4—1221no—
286C22⋊C4—1221no—
287C22⋊C4—1221no—
288C42—21no—
289C42—611no—
290C42—1221no—
291C42—1221no—
292C23—611no—
293C23—1221no—
294C23D4×D6111yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—612no—
298Q8—1221no—
299Q8—1221no—
300Q8—1221no—
301Q8—4881no—
302Q8—2442no—
303Q8—2442no—
304D4—1222no—
305D4—1221no—
306D4—1221no—
307D4—4881no—
308D4—4881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—611no—
316C2×C4—611no—
317C2×C4—611no—
318C2×C4—1221no—
319C2×C4—1221no—
320C2×C4—1221no—
321C2×C4—1221no—
322C2×C4—1221no—
323C2×C4—2442no—
324C2×C4—2442no—
325C2×C4—2442no—
326C2×C4D4×D6111yescharacteristic
327C2×C4C23×D6111yescharacteristic
328C8—21no—
329C8—21no—
330C8—1221no—
331C8—1221no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—1221no—
336C22—1221no—
337C22—1221no—
338C22—2441no—
339C22—2441no—
340C22—2441no—
341C22C2×D4×D6111yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—612no—
348C4—1221no—
349C4—1221no—
350C4—1222no—
351C4—2441no—
352C4—2441no—
353C4#41×D6111yescharacteristic
354C4#1451982311yescharacteristic
355C2—41no—
356C2—4881no—
357C2—2441no—
358C2#1684040411yescharacteristic
359C2#137×D6111yescharacteristic
360C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#485C2
socleC22×C61C22×D4
hypercenter#485D61
hypocenterC61#3329
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #16840425C2semidirect
3. #16840111C2semidirect
4. #16840106C2semidirect
5. #16840056C2semidirect
6. #16840010C2semidirect
7. #16840009C2semidirect
8. #16839966C2semidirect
9. #16839903C2semidirect
10. #16839902C2semidirect
11. #16839849C2semidirect
12. #16839837C2semidirect
13. #16839770C2semidirect
14. #16839769C2semidirect
15. C61×#485C2semidirect
185. #485D61semidirect
196. C61#3329semidirect