Finite Group Databasebeta

← #21457896

Subgroups — #21457896

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#16840467C211yesmaximal, characteristic, complemented
2#16840406C211yesmaximal, characteristic
3#16840120C211yesmaximal, characteristic, complemented
4#16840097C211yesmaximal, characteristic, complemented
5#16840074C211yesmaximal, characteristic, complemented
6#16840040C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic, complemented
8#16840003C211yesmaximal, characteristic, complemented
9#16839983C211yesmaximal, characteristic, complemented
10#16839925C211yesmaximal, characteristic, complemented
11#16839913C211yesmaximal, characteristic, complemented
12#16839859C211yesmaximal, characteristic, complemented
13#16839833C211yesmaximal, characteristic, complemented
14#16839760C211yesmaximal, characteristic, complemented
15C2×#102×C61C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×Dic244C2211yescharacteristic, complemented
18C2×#11758200C2211yescharacteristic
19C2×#11758200C2211yescharacteristic
20C2×#11758189C2211yescharacteristic, complemented
21#14519776C2211yescharacteristic, complemented
22#14519767—21no—
23#14519764C2211yescharacteristic
24#14519758—21no—
25#14519757C2211yescharacteristic, complemented
26#14519756—21no—
27#14519756C2211yescharacteristic
28#14519756C2211yescharacteristic
29#14519755—21no—
30#14519749—21no—
31#14519748C2211yescharacteristic
32#14519746—21no—
33#14519742C2211yescharacteristic, complemented
34D4×Dic61C2211yescharacteristic
35C4×C22⋊D61—21no—
36C4×C22⋊D61C2211yescharacteristic
37C4⋊C4×D61C2211yescharacteristic, complemented
38C2×C22⋊Dic61—21no—
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519710C2211yescharacteristic, complemented
42#14519706C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519702C2211yescharacteristic, complemented
45#14519700C2211yescharacteristic, complemented
46#14519700C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51#14519687C2211yescharacteristic, complemented
52C22×D4×C61C2211yescharacteristic
53C22×C8×C61C2211yescharacteristic
54C2×C4⋊C4×C61C2211yescharacteristic
55#102×C61C2211yescharacteristic
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic
58#102×C61C2211yescharacteristic
59C24×C61—21no—
60C2×D4×C61—22no—
61C2×D4×C61—21no—
62C2×D4×C61—41no—
63C2×D4×C61C2311yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72#11758224—22no—
73#11758224—41no—
74C2×C4×D61—21no—
75C2×C4×D61C2311yescharacteristic
76C2×Dic122—21no—
77C2×Dic122C2311yescharacteristic
78C2×Dic122C2311yescharacteristic
79C2×C8×C61—41no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊Dic61—21no—
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61D411yescharacteristic
92#11758200—22no—
93#11758200—41no—
94#11758198—21no—
95#11758198D411yescharacteristic
96C4⋊Dic61—21no—
97C4⋊Dic61C2311yescharacteristic
98C4⋊Dic61C2311yescharacteristic
99#11758196—21no—
100#11758196—21no—
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61C2311yescharacteristic
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109Dic244—41no—
110#11758189—41no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—42no—
114C23×C61—42no—
115C23×C61—81no—
116C23×C61C2×D411yescharacteristic
117C22×D61C2×D411yescharacteristic
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—42no—
122D4×C61#4112yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—22no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C2×Dic61—21no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61—81no—
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141C2×Dic61C2×D411yescharacteristic
142C4×D61—21no—
143C4×D61—21no—
144C4×D61—81no—
145Dic122—21no—
146Dic122—21no—
147Dic122—21no—
148Dic122—21no—
149Dic122—81no—
150C8×C61—21no—
151C8×C61—21no—
152#92418—21no—
153#92418—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—22no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—84no—
163C22×C61#13712yes—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C4×C61—21no—
169C4×C61—41no—
170C4×C61—41no—
171C4×C61C2×#4111yescharacteristic
172C4×C61H(5,𝔽2)11yescharacteristic
173Dic61—21no—
174Dic61—21no—
175Dic61—21no—
176Dic61—41no—
177Dic61—41no—
178Dic61—41no—
179Dic61—41no—
180#3314—611nomaximal, Sylow
181C2×C61—22no—
182C2×C61—42no—
183C2×C61—81no—
184C2×C61#54611yescharacteristic
185C2×C61C2×#13711yescharacteristic
186C2×C61#57611yescharacteristic
187D61—41no—
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#435—611no—
201#417—611no—
202C2×#102D6111yescharacteristic, complemented
203C61#331411yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C22×D4C2×D6111yescharacteristic
206C2×Q16—611no—
207C2×SD16—611no—
208C2×SD16—611no—
209C2×M16—611no—
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—611no—
226C4×D4—1221no—
227C2×C4⋊C4—611no—
228C2×C4⋊C4C2×D6111yescharacteristic
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#103—611no—
238#102—611no—
239#102—611no—
240#102C2×D6111yescharacteristic
241#102C2×D6111yescharacteristic
242#102C2×D6111yescharacteristic
243#102C2×D6111yescharacteristic
244C22⋊C8—611no—
245C22⋊C8—611no—
246#97—611no—
247C24—21no—
248#41—1222no—
249#41—2441no—
250C2×Q8—611no—
251C2×Q8—611no—
252C2×Q8—1221no—
253C2×D4—22no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4—611no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4C22×D6111yescharacteristic
260C2×D4C22×D6111yescharacteristic
261C22×C4—21no—
262C22×C4—611no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4C22×D6111yescharacteristic
267Q16—2441no—
268SD16—1222no—
269SD16—2441no—
270M16—2441no—
271C2×C8—41no—
272C2×C8—611no—
273C2×C8—611no—
274C2×C8C22×D6111yescharacteristic
275C2×C8C22×D6111yescharacteristic
276C4⋊C4—21no—
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⋊C4C22×D6111yescharacteristic
287C4⋊C4C22×D6111yescharacteristic
288C22⋊C4—611no—
289C22⋊C4—611no—
290C22⋊C4—1221no—
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—21no—
301C23—42no—
302C23—42no—
303C23—81no—
304C23—611no—
305C23D4×D6111yescharacteristic
306Q8—1221no—
307Q8—1221no—
308Q8—1221no—
309Q8—1221no—
310Q8—4881no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—1222no—
316D4—4881no—
317D4—2442no—
318D4#1175822212yes—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
324C2×C4—611no—
325C2×C4—611no—
326C2×C4—611no—
327C2×C4—1221no—
328C2×C4—1221no—
329C2×C4—1221no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—4881no—
334C2×C4—4881no—
335C2×C4—2442no—
336C2×C4D4×D6111yescharacteristic
337C2×C4C23×D6111yescharacteristic
338C8—21no—
339C8—21no—
340C8—1221no—
341C8—1221no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22#1451980612yes—
355C22C2×D4×D6111yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—1221no—
360C4—1221no—
361C4—1221no—
362C4—2441no—
363C4—2441no—
364C4—2441no—
365C4—2441no—
366C4C2×#1175822211yescharacteristic
367C4#1451982211yescharacteristic
368C2—22no—
369C2—42no—
370C2—81no—
371C2—2441no—
372C2#1684040211yescharacteristic
373C2C2×#1451980611yescharacteristic
374C2#1684056311yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#102×C61C2
socleC22×C61C22×D4
hypercenterC2×#102D61
hypocenterC61#3314
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #16840467C2semidirect
3. #16840120C2semidirect
4. #16840097C2semidirect
5. #16840074C2semidirect
6. #16840040C2semidirect
7. #16840007C2semidirect
8. #16840003C2semidirect
9. #16839983C2semidirect
10. #16839925C2semidirect
11. #16839913C2semidirect
12. #16839859C2semidirect
13. #16839833C2semidirect
14. #16839760C2semidirect
15. C2×#102×C61C2semidirect
17. C2×Dic244C22semidirect
20. C2×#11758189C22semidirect
21. #14519776C22semidirect
25. #14519757C22semidirect
33. #14519742C22semidirect
37. C4⋊C4×D61C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519710C22semidirect
42. #14519706C22semidirect
43. #14519702C22semidirect
44. #14519702C22semidirect
45. #14519700C22semidirect
46. #14519700C22semidirect
50. #14519689C22semidirect
51. #14519687C22semidirect
202. C2×#102D61semidirect
203. C61#3314semidirect