Finite Group Databasebeta

← #21456866

Subgroups — #21456866

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840363C211yesmaximal, characteristic, complemented
2#16840330C211yesmaximal, characteristic, complemented
3#16840148C211yesmaximal, characteristic, complemented
4#16840137C211yesmaximal, characteristic, complemented
5#16840125C211yesmaximal, characteristic, complemented
6#16840118C211yesmaximal, characteristic, complemented
7#16839974C211yesmaximal, characteristic, complemented
8#16839958C211yesmaximal, characteristic, complemented
9#16839957C211yesmaximal, characteristic, complemented
10#16839910C211yesmaximal, characteristic, complemented
11#16839906C211yesmaximal, characteristic, complemented
12#16839897C211yesmaximal, characteristic, complemented
13#16839894C211yesmaximal, characteristic, complemented
14#16839822C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758201C2211yescharacteristic, complemented
19C2×D488C2211yescharacteristic
20C2×D488C2211yescharacteristic, complemented
21C2×#11758199C2211yescharacteristic
22C2×#11758199C2211yescharacteristic
23C2×#11758199C2211yescharacteristic, complemented
24#14519774C2211yescharacteristic
25#14519773C2211yescharacteristic
26#14519773C2211yescharacteristic, complemented
27#14519768C2211yescharacteristic, complemented
28#14519766C2211yescharacteristic
29#14519760—21no—
30#14519759—21no—
31#14519752C2211yescharacteristic
32#14519751—21no—
33#14519750—21no—
34#14519750—21no—
35#14519750—21no—
36#14519748C2211yescharacteristic
37#14519747—21no—
38#14519747—21no—
39C4×D244C2211yescharacteristic, 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×SD16×C61C2211yescharacteristic, complemented
53C2×D8×C61C2211yescharacteristic
54#124×C61C2211yescharacteristic
55C4×D4×C61C2211yescharacteristic, complemented
56C4⋊C8×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70#11758226—41no—
71#11758226—41no—
72D4×D61—41no—
73D4×D61—41no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244—21no—
77C2×D244—21no—
78C2×D244C2311yescharacteristic
79C2×D244C2311yescharacteristic
80C2×D244C2311yescharacteristic
81C2×C4×D61—21no—
82C2×C4×D61—21no—
83C2×C4×D61C2311yescharacteristic
84SD16×C61—41no—
85D8×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C42×C61C2311yescharacteristic
93C22⋊Dic61—21no—
94#11758201—41no—
95#11758199—41no—
96#11758199—41no—
97#11758199—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198D411yescharacteristic
103#11758198D411yescharacteristic
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106#11758196—21no—
107#11758196D411yescharacteristic
108#11758196D411yescharacteristic
109C4×Dic61C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112D488—41no—
113D488—41no—
114C23×C61—21no—
115C23×C61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—42no—
120C22×D61—81no—
121C22×D61—81no—
122C22×D61C2×D411yescharacteristic
123Q8×C61—21no—
124Q8×C61—21no—
125D4×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—81no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—81no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C22⋊D61—81no—
141C2×Dic61—21no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—21no—
150D244—21no—
151D244—42no—
152D244—81no—
153D244—81no—
154D244—81no—
155C4×D61—21no—
156C4×D61—21no—
157C4×D61—42no—
158C4×D61—81no—
159C8×C61—21no—
160C8×C61—21no—
161#92418—21no—
162#92418—21no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61—41no—
168C22×C61—41no—
169C22×C61C22×D411yescharacteristic
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—41no—
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—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—41no—
186C4×C61—41no—
187C4×C61H(5,𝔽2)11yescharacteristic
188C4×C61H(5,𝔽2)11yescharacteristic
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—41no—
193#3220—611nomaximal, Sylow
194C2×C61—81no—
195C2×C61—81no—
196C2×C61#53511yescharacteristic
197C2×C61#57611yescharacteristic
198C2×C61#57611yescharacteristic
199D61—41no—
200D61—81no—
201D61—81no—
202D61—81no—
203#540—611no—
204#535—611no—
205#496—611no—
206#493—611no—
207#490—611no—
208#488—611no—
209#463—611no—
210#463D6111yescharacteristic, complemented
211#459—611no—
212#459—611no—
213#449—611no—
214#449—611no—
215#447—611no—
216#447—611no—
217#433—611no—
218C61#322011yescharacteristic, complemented, Sylow
219C2×#41—611no—
220C22×D4—611no—
221C2×SD16—611no—
222C2×SD16C2×D6111yescharacteristic, complemented
223C2×D8—611no—
224C2×D8—611no—
225C2×D8—611no—
226C2×D8—611no—
227C2×D8—611no—
228C2×D8C2×D6111yescharacteristic
229#127—611no—
230#127—611no—
231#127—611no—
232#125—611no—
233#124—611no—
234#124C2×D6111yescharacteristic
235#123—1221no—
236#123—1221no—
237#121—611no—
238#121—611no—
239#121—1221no—
240#121—1221no—
241#121—1221no—
242#121—1221no—
243#120—1221no—
244#120—1221no—
245C4×D4—611no—
246C4×D4C2×D6111yescharacteristic, complemented
247#117—611no—
248C4⋊C8—611no—
249C4⋊C8C2×D6111yescharacteristic, complemented
250#103—611no—
251#103C2×D6111yescharacteristic, complemented
252#102—611no—
253#102—611no—
254#102—611no—
255#102—611no—
256#102—611no—
257#102C2×D6111yescharacteristic
258C22⋊C8—611no—
259C22⋊C8—611no—
260#97—611no—
261C4×C8—611no—
262C24—1221no—
263#41—2441no—
264#41—2441no—
265C2×Q8C22×D6111yescharacteristic
266C2×D4—611no—
267C2×D4—611no—
268C2×D4—611no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C2×D4—1221no—
276C2×D4—1221no—
277C2×D4—1221no—
278C2×D4—1221no—
279C2×D4—2441no—
280C2×D4—2441no—
281C2×D4C22×D6111yescharacteristic
282C2×D4C22×D6111yescharacteristic
283C22×C4—21no—
284C22×C4—611no—
285C22×C4—1221no—
286C22×C4—1221no—
287SD16—41no—
288SD16—2441no—
289D8—41no—
290D8—2441no—
291D8—2441no—
292D8—2441no—
293D8—2441no—
294D8—2441no—
295C2×C8—611no—
296C2×C8—611no—
297C2×C8C22×D6111yescharacteristic
298C2×C8C22×D6111yescharacteristic
299C4⋊C4—611no—
300C4⋊C4—611no—
301C4⋊C4—611no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C4⋊C4C22×D6111yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—611no—
309C22⋊C4—611no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C22⋊C4—1221no—
314C22⋊C4—1221no—
315C42—611no—
316C42C22×D6111yescharacteristic
317C23—21no—
318C23—21no—
319C23—611no—
320C23—1221no—
321C23—1221no—
322C23—1221no—
323C23—4881no—
324C23—4881no—
325C23—2442no—
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—1221no—
333D4—1221no—
334D4—1221no—
335D4—1221no—
336D4—1221no—
337D4—1221no—
338D4—4881no—
339D4—4881no—
340D4—4881no—
341D4—4881no—
342D4—4881no—
343D4—4881no—
344D4—4881no—
345D4—4881no—
346D4—2442no—
347D4—2442no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—1221no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—4881no—
358C2×C4—2442no—
359C2×C4D4×D6111yescharacteristic
360C2×C4D4×D6111yescharacteristic
361C2×C4C23×D6111yescharacteristic
362C8—21no—
363C8—21no—
364C8—1221no—
365C8—1221no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—1221no—
373C22—1221no—
374C22—1221no—
375C22—4884no—
376C22—2441no—
377C22—2441no—
378C22—2441no—
379C22—2441no—
380C22—2441no—
381C22—2441no—
382C22—2441no—
383C22—2441no—
384C22—2441no—
385C22C2×D4×D6111yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—1221no—
391C4—1221no—
392C4—1221no—
393C4—2441no—
394C4#1451982211yescharacteristic
395C4#1451982311yescharacteristic
396C2—81no—
397C2—81no—
398C2—4881no—
399C2—4881no—
400C2—4881no—
401C2—2441no—
402C2#1684032811yescharacteristic
403C2#1684056411yescharacteristic
404C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3220
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #16840363C2semidirect
2. #16840330C2semidirect
3. #16840148C2semidirect
4. #16840137C2semidirect
5. #16840125C2semidirect
6. #16840118C2semidirect
7. #16839974C2semidirect
8. #16839958C2semidirect
9. #16839957C2semidirect
10. #16839910C2semidirect
11. #16839906C2semidirect
12. #16839897C2semidirect
13. #16839894C2semidirect
14. #16839822C2semidirect
15. C61×#463C2semidirect
18. C2×#11758201C22semidirect
20. C2×D488C22semidirect
23. C2×#11758199C22semidirect
26. #14519773C22semidirect
27. #14519768C22semidirect
39. C4×D244C22semidirect
41. C4⋊#92418C22semidirect
42. #14519701C22semidirect
44. #14519699C22semidirect
47. #14519697C22semidirect
50. #14519687C22semidirect
51. C8×Dic61C22semidirect
52. C2×SD16×C61C22semidirect
55. C4×D4×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #103×C61C22semidirect
210. #463D61semidirect
218. C61#3220semidirect
222. C2×SD16C2×D61semidirect
246. C4×D4C2×D61semidirect
249. C4⋊C8C2×D61semidirect
251. #103C2×D61semidirect