Finite Group Databasebeta

← #21457630

Subgroups — #21457630

Order 7808.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840413C211yesmaximal, characteristic, complemented
2#16840396C211yesmaximal, characteristic, complemented
3#16840107C211yesmaximal, characteristic, complemented
4#16840077C211yesmaximal, characteristic, complemented
5#16840041C211yesmaximal, characteristic, complemented
6#16839999C211yesmaximal, characteristic, complemented
7#16839996C211yesmaximal, characteristic, complemented
8#16839956C211yesmaximal, characteristic, complemented
9#16839898C211yesmaximal, characteristic, complemented
10#16839897C211yesmaximal, characteristic, complemented
11#16839844C211yesmaximal, characteristic, complemented
12#16839825C211yesmaximal, characteristic, complemented
13C2×#14519697C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#480C211yesmaximal, characteristic, complemented
16C2×#11758222—21no—
17C22×D244C2211yescharacteristic
18C2×D4×D61—21no—
19C2×D4×D61C2211yescharacteristic
20C2×D488C2211yescharacteristic
21C2×D488C2211yescharacteristic, complemented
22C2×#11758199C2211yescharacteristic, complemented
23C22×#92418C2211yescharacteristic, complemented
24C2×C8×D61C2211yescharacteristic, complemented
25#14519776C2211yescharacteristic, complemented
26#14519773C2211yescharacteristic
27#14519762—21no—
28#14519760—21no—
29#14519755—21no—
30#14519752C2211yescharacteristic
31#14519752C2211yescharacteristic, complemented
32#14519751C2211yescharacteristic, complemented
33#14519750—21no—
34#14519747—21no—
35#14519745—21no—
36#14519739C2211yescharacteristic
37#14519739C2211yescharacteristic, complemented
38C4×C22⋊D61C2211yescharacteristic
39C4⋊C4×D61C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519699C2211yescharacteristic
43#14519699C2211yescharacteristic, complemented
44#14519698C2211yescharacteristic, complemented
45#14519697C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic, complemented
49#14519697C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52#121×C61C2211yescharacteristic
53C2×C4⋊C4×C61C2211yescharacteristic, complemented
54#107×C61C2211yescharacteristic, complemented
55#107×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61—21no—
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70D4×D61—22no—
71D4×D61—41no—
72D4×D61—44no—
73#11758222—44no—
74C2×D244—22no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244—41no—
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×D244C2311yescharacteristic
82C2×C4×D61—21no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61C2311yescharacteristic
86C2×Dic122—21no—
87C2×C8×C61C2311yescharacteristic
88C2×C8×C61C2311yescharacteristic
89C4⋊C4×C61—21no—
90C4⋊C4×C61C2311yescharacteristic
91C4⋊C4×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C22⋊C4×C61—21no—
94C22⋊Dic61D411yescharacteristic
95#11758199—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198D411yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196D411yescharacteristic
106C4×Dic61C2311yescharacteristic
107C2×#92418—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110D488—22no—
111D488—41no—
112C8×D61—41no—
113C23×C61—21no—
114C23×C61C2×D411yescharacteristic
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61C2×D411yescharacteristic
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—42no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—42no—
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—81no—
140C22⋊D61D814yescomplemented
141C2×Dic61—21no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—21no—
150D244—42no—
151D244—42no—
152D244—42no—
153D244#4112yescomplemented
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—42no—
157C4×D61—42no—
158C4×D61—42no—
159Dic122—42no—
160C8×C61—21no—
161C8×C61—21no—
162#92418—21no—
163#92418—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61C2×D812yes—
170C22×C61C22×D411yescharacteristic
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—22no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C2×D61—41no—
181C2×D61—41no—
182C2×D61—84no—
183C2×D61—84no—
184C2×D61C2×D812yes—
185C4×C61—21no—
186C4×C61—41no—
187C4×C61—41no—
188C4×C61—41no—
189C4×C61C2×#4111yescharacteristic
190C4×C61H(5,𝔽2)11yescharacteristic
191Dic61—21no—
192Dic61—21no—
193Dic61—41no—
194Dic61C2×D812yes—
195#3294—611nomaximal, Sylow
196C2×C61—22no—
197C2×C61—81no—
198C2×C61#54611yescharacteristic
199C2×C61C22×D811yescharacteristic
200C2×C61#57711yescharacteristic
201D61—22no—
202D61—42no—
203D61—81no—
204D61—81no—
205#547—611no—
206D42—611no—
207#486—611no—
208#480—611no—
209#480D6111yescharacteristic, complemented
210#474—611no—
211#466—611no—
212#466—611no—
213#459—611no—
214#447—611no—
215#447—611no—
216C4×D8—611no—
217C8×D4—611no—
218C2×#102—611no—
219C2×#102—611no—
220C61#329411yescharacteristic, complemented, Sylow
221C2×#41—1221no—
222C22×D4—611no—
223C22×D4—611no—
224C22×D4—1221no—
225C2×D8—611no—
226C2×D8—611no—
227C2×D8—611no—
228C22×C8—611no—
229C22×C8—611no—
230C4⋊Q8—611no—
231#127—611no—
232#123—1221no—
233#123—1221no—
234C22⋊Q8—1221no—
235#121—611no—
236#121—611no—
237#121—611no—
238#121—1221no—
239#121C2×D6111yescharacteristic
240#120—1221no—
241#120—1221no—
242C4×D4—611no—
243C4×D4—611no—
244C4×D4—611no—
245C2×C4⋊C4—611no—
246C2×C4⋊C4C2×D6111yescharacteristic, complemented
247#107—611no—
248#107C2×D6111yescharacteristic, complemented
249#107C2×D6111yescharacteristic, complemented
250C4⋊C8—611no—
251#102—611no—
252#102—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102—611no—
258#102—611no—
259#102C2×D6111yescharacteristic, complemented
260#102C2×D6111yescharacteristic, complemented
261C22⋊C8—611no—
262C22⋊C8C2×D6111yescharacteristic, complemented
263C4×C8—611no—
264C24—1221no—
265C24—1221no—
266#41—2444no—
267C2×Q8—1221no—
268C2×D4—21no—
269C2×D4—611no—
270C2×D4—611no—
271C2×D4—611no—
272C2×D4—611no—
273C2×D4—1222no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—1222no—
280C2×D4—1221no—
281C2×D4—1221no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2444no—
285C2×D4C22×D6111yescharacteristic
286C22×C4—21no—
287C22×C4—611no—
288C22×C4—1221no—
289C22×C4—1221no—
290C22×C4—1221no—
291C22×C4C22×D6111yescharacteristic
292D8—1222no—
293D8—2441no—
294D8—2441no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8—2441no—
298C2×C8—2441no—
299C2×C8C22×D6111yescharacteristic
300C2×C8C22×D6111yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—611no—
303C4⋊C4—611no—
304C4⋊C4—1221no—
305C4⋊C4—1221no—
306C4⋊C4C22×D6111yescharacteristic
307C4⋊C4C22×D6111yescharacteristic
308C4⋊C4C22×D6111yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—611no—
311C22⋊C4—611no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C42—611no—
318C23—21no—
319C23—611no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—4881no—
324C23—4881no—
325C23—2442no—
326C23—2442no—
327C23—2442no—
328C23—2442no—
329C23D4×D6111yescharacteristic
330Q8—2442no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—614no—
335D4—612no—
336D4—1221no—
337D4—1221no—
338D4—1221no—
339D4—1221no—
340D4—1221no—
341D4—4881no—
342D4—2442no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346D4—2442no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—611no—
355C2×C4—611no—
356C2×C4—611no—
357C2×C4—1221no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4D4×D6111yescharacteristic
364C2×C4C23×D6111yescharacteristic
365C8—21no—
366C8—21no—
367C8—1221no—
368C8—1221no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—612no—
375C22—1221no—
376C22—1221no—
377C22—1222no—
378C22—4884no—
379C22—4884no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22—2441no—
386C22—2441no—
387C22—2441no—
388C22D8×D6112yes—
389C22C2×D4×D6111yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—612no—
395C4—1221no—
396C4—1221no—
397C4—2441no—
398C4#41×D6111yescharacteristic
399C4#1451982311yescharacteristic
400C2—22no—
401C2—81no—
402C2—1222no—
403C2—4881no—
404C2—4881no—
405C2—2442no—
406C2#1684040411yescharacteristic
407C2C2×D8×D6111yescharacteristic
408C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3294
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #16840413C2semidirect
2. #16840396C2semidirect
3. #16840107C2semidirect
4. #16840077C2semidirect
5. #16840041C2semidirect
6. #16839999C2semidirect
7. #16839996C2semidirect
8. #16839956C2semidirect
9. #16839898C2semidirect
10. #16839897C2semidirect
11. #16839844C2semidirect
12. #16839825C2semidirect
13. C2×#14519697C2semidirect
14. #102×D61C2semidirect
15. C61×#480C2semidirect
21. C2×D488C22semidirect
22. C2×#11758199C22semidirect
23. C22×#92418C22semidirect
24. C2×C8×D61C22semidirect
25. #14519776C22semidirect
31. #14519752C22semidirect
32. #14519751C22semidirect
37. #14519739C22semidirect
39. C4⋊C4×D61C22semidirect
40. #14519710C22semidirect
41. #14519706C22semidirect
43. #14519699C22semidirect
44. #14519698C22semidirect
47. #14519697C22semidirect
48. #14519697C22semidirect
49. #14519697C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
53. C2×C4⋊C4×C61C22semidirect
54. #107×C61C22semidirect
55. #107×C61C22semidirect
56. #102×C61C22semidirect
57. #102×C61C22semidirect
58. C22⋊C8×C61C22semidirect
140. C22⋊D61D8semidirect
153. D244#41semidirect
209. #480D61semidirect
220. C61#3294semidirect
246. C2×C4⋊C4C2×D61semidirect
248. #107C2×D61semidirect
249. #107C2×D61semidirect
259. #102C2×D61semidirect
260. #102C2×D61semidirect
262. C22⋊C8C2×D61semidirect