Finite Group Databasebeta

← #21457902

Subgroups — #21457902

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#16840469C211yesmaximal, characteristic, complemented
2#16840408C211yesmaximal, characteristic
3#16840122C211yesmaximal, characteristic, complemented
4#16840098C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840043C211yesmaximal, characteristic, complemented
7#16840008C211yesmaximal, characteristic, complemented
8#16840003C211yesmaximal, characteristic, complemented
9#16839985C211yesmaximal, characteristic, complemented
10#16839926C211yesmaximal, characteristic, complemented
11#16839915C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839764C211yesmaximal, characteristic, complemented
14C2×#14519699C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×Dic244C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic
21#14519777C2211yescharacteristic, complemented
22#14519768—21no—
23#14519765C2211yescharacteristic
24#14519762—21no—
25#14519756C2211yescharacteristic
26#14519756C2211yescharacteristic
27#14519756C2211yescharacteristic, complemented
28#14519754—21no—
29#14519754—21no—
30#14519751C2211yescharacteristic
31#14519750—21no—
32#14519745—21no—
33C4×Dic122C2211yescharacteristic, complemented
34C4×D244C2211yescharacteristic
35D4×Dic61—21no—
36C2×C4⋊Dic61C2211yescharacteristic
37C2×C4⋊Dic61C2211yescharacteristic, complemented
38C22⋊C4×D61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519711C2211yescharacteristic, complemented
41#14519711C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519702C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic
47#14519699C2211yescharacteristic
48#14519699C2211yescharacteristic
49#14519699C2211yescharacteristic
50#14519699C2211yescharacteristic
51#14519699C2211yescharacteristic
52C2×M16×C61C2211yescharacteristic, complemented
53C22×C8×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic, complemented
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61D411yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C22×Dic61—21no—
66C22×Dic61—21no—
67#11758222—22no—
68#11758222—41no—
69C2×D244—22no—
70C2×D244—21no—
71C2×D244—41no—
72C2×D244C2311yescharacteristic
73C2×D244C2311yescharacteristic
74C2×C4×D61—21no—
75C2×C4×D61—21no—
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79M16×C61—41no—
80C2×C8×C61—41no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61D411yescharacteristic
86C22⋊C4×C61D411yescharacteristic
87C22⋊C4×C61D411yescharacteristic
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102C4⋊Dic61C2311yescharacteristic
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108Dic244—41no—
109#11758190—22no—
110#11758190—41no—
111C23×C61C2×D411yescharacteristic
112C23×C61C2×D411yescharacteristic
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61—81no—
118D4×C61—22no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61C2×D411yescharacteristic
124C2×C4×C61C2×D411yescharacteristic
125C2×C4×C61C2×D411yescharacteristic
126C2×C4×C61C2×D411yescharacteristic
127C2×C4×C61C2411yescharacteristic
128C22⋊D61—42no—
129C22⋊D61—81no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—21no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—81no—
137C2×Dic61—81no—
138D244—21no—
139D244—21no—
140D244—21no—
141D244—42no—
142D244#4112yes—
143C4×D61—42no—
144C4×D61—81no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148Dic122—21no—
149Dic122—81no—
150C8×C61—21no—
151C8×C61—21no—
152C8×C61—21no—
153C8×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61#13712yes—
160C22×C61C22×D411yescharacteristic
161C2×D61—22no—
162C2×D61—41no—
163C2×D61—41no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—84no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61C2×#4111yescharacteristic
173C4×C61H(5,𝔽2)11yescharacteristic
174Dic61—41no—
175Dic61—41no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180#3314—611nomaximal, Sylow
181C2×C61—22no—
182C2×C61—41no—
183C2×C61#54611yescharacteristic
184C2×C61C2×#13711yescharacteristic
185C2×C61#57611yescharacteristic
186D61—42no—
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#452—611no—
198#450—611no—
199#440—611no—
200#435D6111yescharacteristic, complemented
201#417—611no—
202C2×#102—611no—
203C61#331411yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C22×D4—611no—
206C2×Q16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×M16C2×D6111yescharacteristic, complemented
210C22×C8C2×D6111yescharacteristic
211C4⋊Q8—611no—
212#125—1221no—
213#124—611no—
214#123—1221no—
215C22⋊Q8—611no—
216C22⋊Q8—611no—
217C22⋊Q8—611no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220#121—611no—
221#121—1221no—
222#120—1221no—
223C4×Q8—611no—
224C4×D4—611no—
225C4×D4—1221no—
226C4×D4C2×D6111yescharacteristic
227C2×C4⋊C4—611no—
228C2×C4⋊C4—611no—
229C2×C22⋊C4—1221no—
230#107—611no—
231#107—611no—
232#107—611no—
233C4⋊C8C2×D6111yescharacteristic, complemented
234#103—611no—
235#103—611no—
236#103—611no—
237#103—611no—
238#102—611no—
239#102—611no—
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244C22⋊C8C2×D6111yescharacteristic
245C22⋊C8C2×D6111yescharacteristic, complemented
246#97C2×D6111yescharacteristic, complemented
247C24—1221no—
248#41—1222no—
249#41—2441no—
250C2×Q8—611no—
251C2×Q8—611no—
252C2×Q8—1221no—
253C2×D4—611no—
254C2×D4—611no—
255C2×D4—1222no—
256C2×D4—1221no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—2441no—
260C2×D4D24411yescharacteristic
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4C22×D6111yescharacteristic
266C22×C4C22×D6111yescharacteristic
267Q16—2441no—
268SD16—1222no—
269SD16—2441no—
270M16—41no—
271C2×C8—41no—
272C2×C8C22×D6111yescharacteristic
273C2×C8C22×D6111yescharacteristic
274C2×C8C22×D6111yescharacteristic
275C2×C8C22×D6111yescharacteristic
276C4⋊C4—611no—
277C4⋊C4—611no—
278C4⋊C4—611no—
279C4⋊C4—611no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4D24411yescharacteristic
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4D24411yescharacteristic
296C22⋊C4D24411yescharacteristic
297C42—1221no—
298C42C22×D6111yescharacteristic
299C23—1221no—
300C23—1221no—
301C23—4881no—
302C23—2442no—
303C23—2442no—
304C23C2×D24411yescharacteristic
305C23C2×D24411yescharacteristic
306Q8—1221no—
307Q8—1221no—
308Q8—1221no—
309Q8—1221no—
310Q8—4881no—
311D4—22no—
312D4—612no—
313D4—1221no—
314D4—1221no—
315D4—1221no—
316D4—4881no—
317D4—2442no—
318D4—2442no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—1221no—
324C2×C4—1221no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—4881no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—2442no—
333C2×C4C2×D24411yescharacteristic
334C2×C4C2×D24411yescharacteristic
335C2×C4C2×D24411yescharacteristic
336C2×C4C2×D24411yescharacteristic
337C2×C4C23×D6111yescharacteristic
338C8—21no—
339C8—21no—
340C8—21no—
341C8—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—1222no—
348C22—4884no—
349C22—2441no—
350C22—2441no—
351C22—2441no—
352C22—2441no—
353C22—2441no—
354C22#1451981012yes—
355C22C22×D24411yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—2441no—
361C4—2441no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C4—2441no—
366C4#41×D6111yescharacteristic
367C4#1451982211yescharacteristic
368C2—22no—
369C2—41no—
370C2—4881no—
371C2—2442no—
372C2#1684040711yescharacteristic
373C2C2×#1451981011yescharacteristic
374C2#1684056711yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3314
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16840469C2semidirect
3. #16840122C2semidirect
4. #16840098C2semidirect
5. #16840076C2semidirect
6. #16840043C2semidirect
7. #16840008C2semidirect
8. #16840003C2semidirect
9. #16839985C2semidirect
10. #16839926C2semidirect
11. #16839915C2semidirect
12. #16839864C2semidirect
13. #16839764C2semidirect
14. C2×#14519699C2semidirect
15. C61×#435C2semidirect
18. C2×Dic244C22semidirect
21. #14519777C22semidirect
27. #14519756C22semidirect
33. C4×Dic122C22semidirect
37. C2×C4⋊Dic61C22semidirect
39. #14519711C22semidirect
40. #14519711C22semidirect
41. #14519711C22semidirect
42. #14519702C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
45. #14519702C22semidirect
52. C2×M16×C61C22semidirect
55. C4⋊C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. #97×C61C22semidirect
200. #435D61semidirect
203. C61#3314semidirect
209. C2×M16C2×D61semidirect
233. C4⋊C8C2×D61semidirect
245. C22⋊C8C2×D61semidirect
246. #97C2×D61semidirect