Finite Group Databasebeta

← #21456888

Subgroups — #21456888

Order 7808.

396 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840370C211yesmaximal, characteristic, complemented
2#16840330C211yesmaximal, characteristic
3#16840155C211yesmaximal, characteristic, complemented
4#16840133C211yesmaximal, characteristic, complemented
5#16840125C211yesmaximal, characteristic, complemented
6#16840118C211yesmaximal, characteristic, complemented
7#16839981C211yesmaximal, characteristic, complemented
8#16839963C211yesmaximal, characteristic, complemented
9#16839962C211yesmaximal, characteristic, complemented
10#16839927C211yesmaximal, characteristic, complemented
11#16839923C211yesmaximal, characteristic, complemented
12#16839914C211yesmaximal, characteristic, complemented
13#16839911C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#464C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758202C2211yescharacteristic, complemented
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758200C2211yescharacteristic
22C2×#11758201C2211yescharacteristic
23C2×#11758201C2211yescharacteristic, complemented
24#14519775C2211yescharacteristic, complemented
25#14519774C2211yescharacteristic
26#14519773C2211yescharacteristic
27#14519772—21no—
28#14519771—21no—
29#14519769—21no—
30#14519768C2211yescharacteristic, complemented
31#14519767—21no—
32#14519766C2211yescharacteristic
33#14519757C2211yescharacteristic
34#14519753C2211yescharacteristic
35#14519750—21no—
36#14519750—21no—
37#14519747—21no—
38#14519747—21no—
39C4×Dic122C2211yescharacteristic, complemented
40#14519734C2211yescharacteristic
41C4⋊#92418C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic
46#14519697C2211yescharacteristic
47#14519697C2211yescharacteristic, complemented
48#14519689C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519687C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×Q8×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×C22⋊D61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66#11758226—41no—
67#11758226—41no—
68D4×D61—41no—
69D4×D61—41no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244C2311yescharacteristic
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61C2311yescharacteristic
77C2×Dic122C2311yescharacteristic
78Q16×C61—41no—
79SD16×C61—41no—
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61C2311yescharacteristic
84C22⋊C4×C61—21no—
85C22⋊C4×C61—21no—
86C42×C61—21no—
87C42×C61C2311yescharacteristic
88#11758202—41no—
89#11758201—41no—
90#11758201—41no—
91#11758200—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97#11758198D411yescharacteristic
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101#11758196—21no—
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196D411yescharacteristic
107#11758196D411yescharacteristic
108C4×Dic61—21no—
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112#11758190—41no—
113#11758190—41no—
114C23×C61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—42no—
118C22×D61—81no—
119C22×D61—81no—
120C22×D61C2×D411yescharacteristic
121Q8×C61—21no—
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—42no—
134C22⋊D61—81no—
135C22⋊D61—81no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140C2×Dic61C2×D411yescharacteristic
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—42no—
146D244—81no—
147D244—81no—
148C4×D61—21no—
149C4×D61—21no—
150C4×D61—42no—
151Dic122—21no—
152Dic122—21no—
153C8×C61—21no—
154C8×C61—21no—
155#92418—21no—
156#92418—21no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61C22×D411yescharacteristic
161C2×D61—21no—
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—41no—
165C2×D61—41no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—84no—
171C4×C61—21no—
172C4×C61—21no—
173C4×C61—41no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61H(5,𝔽2)11yescharacteristic
177C4×C61H(5,𝔽2)11yescharacteristic
178Dic61—21no—
179Dic61—21no—
180Dic61—21no—
181Dic61—41no—
182Dic61—41no—
183#3222—611nomaximal, Sylow
184C2×C61—81no—
185C2×C61#53511yescharacteristic
186C2×C61#57711yescharacteristic
187C2×C61#57711yescharacteristic
188D61—41no—
189D61—81no—
190D61—81no—
191#541—611no—
192#535—611no—
193#497—611no—
194#492—611no—
195#490—611no—
196#488—611no—
197#464—611no—
198#464D6111yescharacteristic, complemented
199#460—611no—
200#460—611no—
201#452—611no—
202#452—611no—
203#450—611no—
204#450—611no—
205#433—611no—
206C61#322211yescharacteristic, complemented, Sylow
207C2×#41—611no—
208C22×D4—611no—
209C2×Q16—611no—
210C2×Q16C2×D6111yescharacteristic, complemented
211C2×SD16—611no—
212C2×SD16—611no—
213C2×SD16—611no—
214C2×SD16—611no—
215C2×SD16—611no—
216C2×SD16C2×D6111yescharacteristic
217C4⋊Q8—611no—
218#127—611no—
219#127—611no—
220#126—1221no—
221#126—1221no—
222#125—611no—
223#125—1221no—
224#125—1221no—
225#124—611no—
226#124C2×D6111yescharacteristic
227C22⋊Q8—611no—
228C22⋊Q8—611no—
229#121—1221no—
230#121—1221no—
231#120—1221no—
232#120—1221no—
233C4×Q8—611no—
234C4×Q8C2×D6111yescharacteristic, complemented
235#117—611no—
236C4⋊C8—611no—
237C4⋊C8C2×D6111yescharacteristic, complemented
238#103—611no—
239#103C2×D6111yescharacteristic, complemented
240#102—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102C2×D6111yescharacteristic
246C22⋊C8—611no—
247C22⋊C8—611no—
248#97—611no—
249C4×C8—611no—
250C24—1221no—
251#41—2441no—
252#41—2441no—
253C2×Q8—611no—
254C2×Q8C22×D6111yescharacteristic
255C2×Q8C22×D6111yescharacteristic
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—2441no—
265C2×D4—2441no—
266C2×D4C22×D6111yescharacteristic
267C22×C4—611no—
268C22×C4—1221no—
269Q16—41no—
270Q16—2441no—
271SD16—41no—
272SD16—2441no—
273SD16—2441no—
274SD16—2441no—
275SD16—2441no—
276SD16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4C22×D6111yescharacteristic
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—611no—
296C22⋊C4—611no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C42—21no—
302C42—611no—
303C42—1221no—
304C42C22×D6111yescharacteristic
305C23—21no—
306C23—611no—
307C23—1221no—
308C23—1221no—
309C23—4881no—
310C23—4881no—
311C23—2442no—
312Q8—21no—
313Q8—21no—
314Q8—21no—
315Q8—21no—
316Q8—1221no—
317Q8—1221no—
318D4—21no—
319D4—21no—
320D4—1221no—
321D4—1221no—
322D4—1221no—
323D4—1221no—
324D4—4881no—
325D4—4881no—
326D4—4881no—
327D4—4881no—
328D4—2442no—
329D4—2442no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—611no—
334C2×C4—611no—
335C2×C4—611no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—2442no—
341C2×C4D4×D6111yescharacteristic
342C2×C4D4×D6111yescharacteristic
343C2×C4C23×D6111yescharacteristic
344C8—21no—
345C8—21no—
346C8—1221no—
347C8—1221no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—1221no—
352C22—1221no—
353C22—1221no—
354C22—4884no—
355C22—2441no—
356C22—2441no—
357C22—2441no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22C2×D4×D6111yescharacteristic
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—1221no—
368C4—1221no—
369C4—1221no—
370C4—2441no—
371C4—2441no—
372C4#1451982211yescharacteristic
373C4#1451982311yescharacteristic
374C2—81no—
375C2—4881no—
376C2—4881no—
377C2—2441no—
378C2#1684032811yescharacteristic
379C2#1684056911yescharacteristic
380C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#464C2
socleC22×C61C22×D4
hypercenter#464D61
hypocenterC61#3222
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #16840370C2semidirect
3. #16840155C2semidirect
4. #16840133C2semidirect
5. #16840125C2semidirect
6. #16840118C2semidirect
7. #16839981C2semidirect
8. #16839963C2semidirect
9. #16839962C2semidirect
10. #16839927C2semidirect
11. #16839923C2semidirect
12. #16839914C2semidirect
13. #16839911C2semidirect
14. #16839822C2semidirect
15. C61×#464C2semidirect
18. C2×#11758202C22semidirect
20. C2×#11758190C22semidirect
23. C2×#11758201C22semidirect
24. #14519775C22semidirect
30. #14519768C22semidirect
39. C4×Dic122C22semidirect
41. C4⋊#92418C22semidirect
42. #14519701C22semidirect
44. #14519699C22semidirect
47. #14519697C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
52. C2×Q16×C61C22semidirect
55. C4×Q8×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #103×C61C22semidirect
198. #464D61semidirect
206. C61#3222semidirect
210. C2×Q16C2×D61semidirect
234. C4×Q8C2×D61semidirect
237. C4⋊C8C2×D61semidirect
239. #103C2×D61semidirect