Finite Group Databasebeta

← #21456906

Subgroups — #21456906

Order 7808.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840381C211yesmaximal, characteristic, complemented
2#16840330C211yesmaximal, characteristic, complemented
3#16840152C211yesmaximal, characteristic, complemented
4#16840121C211yesmaximal, characteristic, complemented
5#16840109C211yesmaximal, characteristic, complemented
6#16839986C211yesmaximal, characteristic, complemented
7#16839979C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839955C211yesmaximal, characteristic, complemented
10#16839923C211yesmaximal, characteristic, complemented
11#16839911C211yesmaximal, characteristic, complemented
12#16839906C211yesmaximal, characteristic, complemented
13#16839894C211yesmaximal, characteristic, complemented
14#16839821C211yesmaximal, characteristic, complemented
15C61×#495C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758201C2211yescharacteristic
19C2×#11758201C2211yescharacteristic, complemented
20C2×#11758199C2211yescharacteristic
21C2×#11758199C2211yescharacteristic, complemented
22#14519777C2211yescharacteristic, complemented
23#14519774C2211yescharacteristic
24#14519773C2211yescharacteristic
25#14519770—21no—
26#14519766C2211yescharacteristic
27#14519763—21no—
28#14519761—21no—
29#14519754—21no—
30#14519753C2211yescharacteristic
31#14519750—21no—
32#14519750—21no—
33#14519748C2211yescharacteristic
34#14519747—21no—
35#14519747—21no—
36Q8×Dic61C2211yescharacteristic, complemented
37D4×Dic61C2211yescharacteristic, complemented
38#14519734C2211yescharacteristic
39#14519706C2211yescharacteristic, complemented
40#14519706C2211yescharacteristic, complemented
41#14519701C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519688C2211yescharacteristic, complemented
52C2×Q16×C61C2211yescharacteristic, complemented
53C2×SD16×C61C2211yescharacteristic
54C2×SD16×C61C2211yescharacteristic, complemented
55C2×D8×C61C2211yescharacteristic
56#124×C61C2211yescharacteristic
57#124×C61C2211yescharacteristic, complemented
58C4×C8×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61C2311yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69#11758226—41no—
70#11758226—41no—
71D4×D61—41no—
72D4×D61—41no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244C2311yescharacteristic
77C2×D244C2311yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81Q16×C61—41no—
82SD16×C61—41no—
83SD16×C61—41no—
84D8×C61—41no—
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C42×C61C2311yescharacteristic
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758201—41no—
95#11758201—41no—
96#11758199—41no—
97#11758199—41no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198D411yescharacteristic
102#11758198D411yescharacteristic
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61C2311yescharacteristic
106C4⋊Dic61C2311yescharacteristic
107#11758196—21no—
108#11758196D411yescharacteristic
109#11758196D411yescharacteristic
110C4×Dic61—21no—
111C4×Dic61C2311yescharacteristic
112C2×#92418C2311yescharacteristic
113C2×#92418C2311yescharacteristic
114C23×C61—21no—
115C23×C61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—42no—
119C22×D61—81no—
120C22×D61—81no—
121C22×D61C2×D411yescharacteristic
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—21no—
129D4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—42no—
136C22⋊D61—81no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61—81no—
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—21no—
146D244—21no—
147D244—21no—
148D244—21no—
149D244—42no—
150D244—81no—
151D244—81no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—42no—
155Dic122—81no—
156C8×C61—21no—
157C8×C61—21no—
158#92418—21no—
159#92418—21no—
160C22×C61—41no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61C22×D411yescharacteristic
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—84no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61H(5,𝔽2)11yescharacteristic
182C4×C61H(5,𝔽2)11yescharacteristic
183Dic61—21no—
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188#3224—611nomaximal, Sylow
189C2×C61—81no—
190C2×C61—81no—
191C2×C61#53511yescharacteristic
192C2×C61#57611yescharacteristic
193C2×C61#57711yescharacteristic
194D61—41no—
195D61—81no—
196D61—81no—
197#542—611no—
198#535—611no—
199#496—611no—
200#495D6111yescharacteristic, complemented
201#489—611no—
202#486—611no—
203#464—611no—
204#463—611no—
205#460—611no—
206#459—611no—
207#452—611no—
208#450—611no—
209#449—611no—
210#447—611no—
211#433—611no—
212C61#322411yescharacteristic, complemented, Sylow
213C2×#41—611no—
214C22×D4—611no—
215C2×Q16C2×D6111yescharacteristic, complemented
216C2×SD16—611no—
217C2×SD16—611no—
218C2×SD16C2×D6111yescharacteristic
219C2×SD16C2×D6111yescharacteristic, complemented
220C2×D8—611no—
221C2×D8—611no—
222C2×D8C2×D6111yescharacteristic
223C4⋊Q8—611no—
224#127—611no—
225#127—611no—
226#126—1221no—
227#124—611no—
228#124—1221no—
229#124C2×D6111yescharacteristic
230#124C2×D6111yescharacteristic, complemented
231#123—1221no—
232C22⋊Q8—611no—
233C22⋊Q8—1221no—
234#121—611no—
235#121—1221no—
236#121—1221no—
237#120—1221no—
238#120—1221no—
239C4×Q8—611no—
240C4×D4—611no—
241#117—611no—
242C4⋊C8—611no—
243C4⋊C8—611no—
244#103—611no—
245#103—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252C22⋊C8—611no—
253C22⋊C8—611no—
254#97—611no—
255C4×C8C2×D6111yescharacteristic, complemented
256C24—1221no—
257#41—2441no—
258#41—2441no—
259C2×Q8—1221no—
260C2×Q8C22×D6111yescharacteristic
261C2×Q8C22×D6111yescharacteristic
262C2×D4—611no—
263C2×D4—611no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—2441no—
272C2×D4—2441no—
273C2×D4C22×D6111yescharacteristic
274C2×D4C22×D6111yescharacteristic
275C22×C4—611no—
276C22×C4—1221no—
277C22×C4—1221no—
278Q16—41no—
279SD16—41no—
280SD16—41no—
281SD16—2441no—
282SD16—2441no—
283D8—41no—
284D8—2441no—
285D8—2441no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8C22×D6111yescharacteristic
289C2×C8C22×D6111yescharacteristic
290C4⋊C4—611no—
291C4⋊C4—611no—
292C4⋊C4—611no—
293C4⋊C4—611no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—1221no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—611no—
302C22⋊C4—611no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C42—611no—
309C42—1221no—
310C42C22×D6111yescharacteristic
311C23—21no—
312C23—21no—
313C23—611no—
314C23—1221no—
315C23—1221no—
316C23—4881no—
317C23—4881no—
318C23—2442no—
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—4881no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—1221no—
329D4—1221no—
330D4—1221no—
331D4—1221no—
332D4—4881no—
333D4—4881no—
334D4—4881no—
335D4—4881no—
336D4—4881no—
337D4—2442no—
338D4—2442no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—4881no—
349C2×C4—2442no—
350C2×C4D4×D6111yescharacteristic
351C2×C4D4×D6111yescharacteristic
352C2×C4C23×D6111yescharacteristic
353C8—21no—
354C8—21no—
355C8—1221no—
356C8—1221no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—1221no—
364C22—1221no—
365C22—1221no—
366C22—4884no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22—2441no—
372C22—2441no—
373C22C2×D4×D6111yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—1221no—
379C4—1221no—
380C4—1221no—
381C4—2441no—
382C4—2441no—
383C4#1451982211yescharacteristic
384C4#1451982211yescharacteristic
385C2—81no—
386C2—81no—
387C2—4881no—
388C2—4881no—
389C2—2441no—
390C2#1684032511yescharacteristic
391C2#1684056411yescharacteristic
392C2#1684056911yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#495C2
socleC22×C61C22×D4
hypercenter#495D61
hypocenterC61#3224
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #16840381C2semidirect
2. #16840330C2semidirect
3. #16840152C2semidirect
4. #16840121C2semidirect
5. #16840109C2semidirect
6. #16839986C2semidirect
7. #16839979C2semidirect
8. #16839960C2semidirect
9. #16839955C2semidirect
10. #16839923C2semidirect
11. #16839911C2semidirect
12. #16839906C2semidirect
13. #16839894C2semidirect
14. #16839821C2semidirect
15. C61×#495C2semidirect
19. C2×#11758201C22semidirect
21. C2×#11758199C22semidirect
22. #14519777C22semidirect
36. Q8×Dic61C22semidirect
37. D4×Dic61C22semidirect
39. #14519706C22semidirect
40. #14519706C22semidirect
41. #14519701C22semidirect
42. #14519701C22semidirect
45. #14519699C22semidirect
46. #14519699C22semidirect
51. #14519688C22semidirect
52. C2×Q16×C61C22semidirect
54. C2×SD16×C61C22semidirect
57. #124×C61C22semidirect
58. C4×C8×C61C22semidirect
200. #495D61semidirect
212. C61#3224semidirect
215. C2×Q16C2×D61semidirect
219. C2×SD16C2×D61semidirect
230. #124C2×D61semidirect
255. C4×C8C2×D61semidirect