Finite Group Databasebeta

← #21457893

Subgroups — #21457893

Order 7808.

410 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840470C211yesmaximal, characteristic, complemented
2#16840400C211yesmaximal, characteristic
3#16840123C211yesmaximal, characteristic, complemented
4#16840096C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16840010C211yesmaximal, characteristic, complemented
8#16840000C211yesmaximal, characteristic, complemented
9#16839986C211yesmaximal, characteristic, complemented
10#16839911C211yesmaximal, characteristic, complemented
11#16839863C211yesmaximal, characteristic, complemented
12#16839836C211yesmaximal, characteristic, complemented
13#16839763C211yesmaximal, characteristic, complemented
14#102×D61C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×D4×D61C2211yescharacteristic
17C2×#11758201C2211yescharacteristic
18C2×#11758194C2211yescharacteristic, complemented
19C2×C8×D61C2211yescharacteristic
20#14519776C2211yescharacteristic, complemented
21#14519767—21no—
22#14519766C2211yescharacteristic
23#14519760—21no—
24#14519757—21no—
25#14519754—21no—
26#14519753C2211yescharacteristic
27#14519753C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519749—21no—
30#14519745—21no—
31Q8×Dic61C2211yescharacteristic, complemented
32D4×Dic61C2211yescharacteristic
33C4×C22⋊D61C2211yescharacteristic
34#14519737—21no—
35C2×C4⋊Dic61C2211yescharacteristic, complemented
36C4⋊C4×D61C2211yescharacteristic
37C2×#11758198—21no—
38#14519711C2211yescharacteristic, complemented
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519706C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519687C2211yescharacteristic, complemented
52C2×#41×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic
55C22⋊Q8×C61C2211yescharacteristic, complemented
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic
58C22⋊C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60#41×C61—22no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61D411yescharacteristic
71C22×Dic61—21no—
72C22×Dic61—21no—
73D4×D61—22no—
74D4×D61—41no—
75C2×D244C2311yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—21no—
79Q16×C61—41no—
80SD16×C61—22no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61—21no—
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊Dic61—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⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107#11758194—41no—
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C8×D61—41no—
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—81no—
117C22×D61C2×D411yescharacteristic
118Q8×C61—21no—
119Q8×C61—21no—
120Q8×C61—21no—
121Q8×C61—21no—
122D4×C61—21no—
123D4×C61—42no—
124D4×C61#4112yes—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—42no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—22no—
134C22⋊D61—42no—
135C22⋊D61—81no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—81no—
149Dic122—81no—
150C8×C61—21no—
151C8×C61—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—22no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C22×D411yescharacteristic
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—84no—
167C2×D61#13712yes—
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—
178Dic61—41no—
179Dic61—41no—
180#3314—611nomaximal, Sylow
181C2×C61—42no—
182C2×C61—41no—
183C2×C61#54611yescharacteristic
184C2×C61C2×#13711yescharacteristic
185C2×C61#57611yescharacteristic
186D61—22no—
187D61—81no—
188#554—611no—
189#546—611no—
190#489—611no—
191#484—611no—
192#480—611no—
193#474—611no—
194#468—611no—
195#467—611no—
196#464—611no—
197#452D6111yescharacteristic, complemented
198#450—611no—
199#440—611no—
200#435—611no—
201#417—611no—
202C2×#102—611no—
203C61#331411yescharacteristic, complemented, Sylow
204C2×#41C2×D6111yescharacteristic
205C22×D4—611no—
206C2×Q16C2×D6111yescharacteristic, complemented
207C2×SD16—611no—
208C2×SD16C2×D6111yescharacteristic
209C2×M16—611no—
210C22×C8—611no—
211C4⋊Q8—611no—
212#125—1221no—
213#124—611no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8—611no—
217C22⋊Q8—1221no—
218C22⋊Q8—1221no—
219C22⋊Q8C2×D6111yescharacteristic, complemented
220#121—611no—
221#121—1221no—
222#120—1221no—
223C4×Q8—611no—
224C4×D4—611no—
225C4×D4—611no—
226C4×D4—1221no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C22⋊C4—1221no—
230#107—611no—
231#107—611no—
232#107—611no—
233C4⋊C8—611no—
234#103—611no—
235#103—611no—
236#103—611no—
237#103C2×D6111yescharacteristic, complemented
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102C2×D6111yescharacteristic
244C22⋊C8—611no—
245C22⋊C8C2×D6111yescharacteristic, complemented
246#97—611no—
247C24—1221no—
248#41—22no—
249#41—41no—
250C2×Q8—1221no—
251C2×Q8C22×D6111yescharacteristic
252C2×Q8C22×D6111yescharacteristic
253C2×D4—21no—
254C2×D4—611no—
255C2×D4—611no—
256C2×D4—1221no—
257C2×D4—1222no—
258C2×D4—1221no—
259C2×D4—2441no—
260C2×D4C22×D6111yescharacteristic
261C22×C4—21no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4C22×D6111yescharacteristic
267Q16—41no—
268SD16—22no—
269SD16—2441no—
270M16—2441no—
271C2×C8—611no—
272C2×C8—611no—
273C2×C8—2441no—
274C2×C8C22×D6111yescharacteristic
275C2×C8C22×D6111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4—611no—
280C4⋊C4—611no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4C22×D6111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—611no—
290C22⋊C4—611no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C42—611no—
298C42—1221no—
299C23—21no—
300C23—611no—
301C23—1221no—
302C23—4881no—
303C23—2442no—
304C23—2442no—
305C23D4×D6111yescharacteristic
306Q8—21no—
307Q8—21no—
308Q8—21no—
309Q8—21no—
310Q8—4881no—
311D4—21no—
312D4—42no—
313D4—1222no—
314D4—1221no—
315D4—1221no—
316D4—4881no—
317D4—2442no—
318D4#1175822412yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—611no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4D4×D6111yescharacteristic
337C2×C4C23×D6111yescharacteristic
338C8—21no—
339C8—21no—
340C8—1221no—
341C8—1221no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—612no—
349C22—1221no—
350C22—1221no—
351C22—4884no—
352C22—2441no—
353C22—2441no—
354C22—2441no—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—1221no—
361C4—1221no—
362C4—1221no—
363C4—2441no—
364C4—2441no—
365C4—2441no—
366C4C2×#1175822411yescharacteristic
367C4#1451982211yescharacteristic
368C2—41no—
369C2—42no—
370C2—1222no—
371C2—4881no—
372C2#1684039911yescharacteristic
373C2#137×D6111yescharacteristic
374C2#1684056411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3314
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16840470C2semidirect
3. #16840123C2semidirect
4. #16840096C2semidirect
5. #16840076C2semidirect
6. #16840040C2semidirect
7. #16840010C2semidirect
8. #16840000C2semidirect
9. #16839986C2semidirect
10. #16839911C2semidirect
11. #16839863C2semidirect
12. #16839836C2semidirect
13. #16839763C2semidirect
14. #102×D61C2semidirect
15. C61×#452C2semidirect
18. C2×#11758194C22semidirect
20. #14519776C22semidirect
31. Q8×Dic61C22semidirect
35. C2×C4⋊Dic61C22semidirect
38. #14519711C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519706C22semidirect
42. #14519701C22semidirect
43. #14519701C22semidirect
44. #14519701C22semidirect
51. #14519687C22semidirect
53. C2×Q16×C61C22semidirect
55. C22⋊Q8×C61C22semidirect
56. #103×C61C22semidirect
58. C22⋊C8×C61C22semidirect
197. #452D61semidirect
203. C61#3314semidirect
206. C2×Q16C2×D61semidirect
219. C22⋊Q8C2×D61semidirect
237. #103C2×D61semidirect
245. C22⋊C8C2×D61semidirect