Finite Group Databasebeta

← #21456611

Subgroups — #21456611

Order 7808.

424 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840275C211yesmaximal, characteristic, complemented
2#16840269C211yesmaximal, characteristic, complemented
3#16840101C211yesmaximal, characteristic, complemented
4#16840100C211yesmaximal, characteristic, complemented
5#16840087C211yesmaximal, characteristic, complemented
6#16840084C211yesmaximal, characteristic, complemented
7#16840000C211yesmaximal, characteristic, complemented
8#16839997C211yesmaximal, characteristic, complemented
9#16839994C211yesmaximal, characteristic, complemented
10#16839988C211yesmaximal, characteristic, complemented
11#16839923C211yesmaximal, characteristic, complemented
12#16839907C211yesmaximal, characteristic, complemented
13#16839906C211yesmaximal, characteristic, complemented
14C22⋊C8×D61C211yesmaximal, characteristic, complemented
15C61×#452C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C2×#11758201C2211yescharacteristic, complemented
19C2×#11758199C2211yescharacteristic, complemented
20C2×C8×D61C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic
22#14519762—21no—
23#14519758—21no—
24#14519753C2211yescharacteristic
25#14519753C2211yescharacteristic
26#14519753C2211yescharacteristic
27#14519752C2211yescharacteristic
28#14519751C2211yescharacteristic
29#14519748C2211yescharacteristic
30#14519748C2211yescharacteristic
31#14519747—21no—
32#14519745—21no—
33#14519739—21no—
34C4×C22⋊D61—21no—
35C4×C22⋊D61—21no—
36#14519737—21no—
37#14519736C2211yescharacteristic
38#14519735C2211yescharacteristic
39#14519711C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519708C2211yescharacteristic, complemented
43#14519701C2211yescharacteristic, complemented
44#14519701C2211yescharacteristic, complemented
45#14519701C2211yescharacteristic, complemented
46#14519699C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic, complemented
48#14519698C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic
52C2×#41×C61C2211yescharacteristic
53C2×Q16×C61C2211yescharacteristic, complemented
54C2×SD16×C61C2211yescharacteristic, complemented
55C22⋊Q8×C61C2211yescharacteristic
56#103×C61C2211yescharacteristic, complemented
57#102×C61C2211yescharacteristic, complemented
58C22⋊C8×C61C2211yescharacteristic
59C23×D61D411yescharacteristic
60#41×C61—41no—
61#41×C61—41no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61C2311yescharacteristic
66C22×C4×C61—21no—
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—21no—
71C22×Dic61D411yescharacteristic
72#11758226—41no—
73#11758226—41no—
74C2×D244—21no—
75C2×D244—21no—
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61D411yescharacteristic
81C2×C4×D61D411yescharacteristic
82C2×C4×D61C2311yescharacteristic
83C2×C4×D61C2311yescharacteristic
84Q16×C61—41no—
85SD16×C61—41no—
86C2×C8×C61C2311yescharacteristic
87C2×C8×C61C2311yescharacteristic
88C4⋊C4×C61—21no—
89C4⋊C4×C61C2311yescharacteristic
90C22⋊C4×C61—21no—
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758201—41no—
95#11758199—41no—
96#11758198—21no—
97#11758198—21no—
98#11758198—21no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102C4⋊Dic61C2311yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105#11758196—21no—
106#11758196—21no—
107#11758196—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C2×#92418C2311yescharacteristic
111C2×#92418C2311yescharacteristic
112C8×D61—41no—
113C8×D61—41no—
114C23×C61—21no—
115C23×C61C2×D411yescharacteristic
116C22×D61—22no—
117C22×D61—21no—
118C22×D61—41no—
119C22×D61—41no—
120C22×D61C2×D411yescharacteristic
121C22×D61C2×D411yescharacteristic
122Q8×C61—21no—
123Q8×C61—21no—
124Q8×C61—21no—
125Q8×C61—21no—
126D4×C61—21no—
127D4×C61—21no—
128D4×C61—42no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—21no—
134C2×C4×C61—42no—
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—42no—
138C22⋊D61—42no—
139C22⋊D61—42no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—41no—
144C2×Dic61C2×D411yescharacteristic
145C2×Dic61C2×D411yescharacteristic
146D244—21no—
147D244—21no—
148D244—42no—
149D244—42no—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—21no—
153C4×D61—21no—
154C4×D61—41no—
155C4×D61—41no—
156C4×D61—42no—
157C8×C61—21no—
158C8×C61—21no—
159#92418—21no—
160#92418—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61C22×D411yescharacteristic
168C2×D61—21no—
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—21no—
173C2×D61—44no—
174C2×D61—41no—
175C2×D61—41no—
176C2×D61—41no—
177C2×D61#13512yes—
178C4×C61—21no—
179C4×C61—41no—
180C4×C61—41no—
181C4×C61—41no—
182C4×C61H(5,𝔽2)11yescharacteristic
183C4×C61H(5,𝔽2)11yescharacteristic
184Dic61—21no—
185Dic61—21no—
186Dic61—41no—
187Dic61—41no—
188Dic61—41no—
189#3191—611nomaximal, Sylow
190C2×C61—41no—
191C2×C61—81no—
192C2×C61#53411yescharacteristic
193C2×C61C2×#13511yescharacteristic
194C2×C61#57511yescharacteristic
195D61—22no—
196D61—41no—
197D61—81no—
198#525—611no—
199#525—611no—
200#485—611no—
201#485—611no—
202#482—611no—
203#482—611no—
204#467—611no—
205#466—611no—
206#465—611no—
207#465—611no—
208#452—611no—
209#452D6111yescharacteristic, complemented
210#449—611no—
211#449—611no—
212C2×C22⋊C8—611no—
213C61#319111yescharacteristic, complemented, Sylow
214C2×#41—611no—
215C2×#41C2×D6111yescharacteristic
216C23×C4—611no—
217C2×Q16C2×D6111yescharacteristic, complemented
218C2×SD16—611no—
219C2×SD16C2×D6111yescharacteristic, complemented
220C2×D8—611no—
221C22×C8—611no—
222C22×C8—611no—
223#123—1221no—
224#123—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—611no—
227C22⋊Q8—611no—
228C22⋊Q8C2×D6111yescharacteristic
229#121—611no—
230#121—611no—
231#121—611no—
232#121—611no—
233#120—1221no—
234#120—1221no—
235C4×D4—1221no—
236C4×D4—1221no—
237C4×D4—1221no—
238C4×D4—1221no—
239#117—611no—
240#117—611no—
241#107—611no—
242#107—611no—
243#106—611no—
244#106—611no—
245#103—611no—
246#103—611no—
247#103—611no—
248#103C2×D6111yescharacteristic, complemented
249#102—611no—
250#102—611no—
251#102—611no—
252#102C2×D6111yescharacteristic, complemented
253C22⋊C8—611no—
254C22⋊C8—611no—
255C22⋊C8—611no—
256C22⋊C8C2×D6111yescharacteristic
257C24—611no—
258#41—41no—
259#41—41no—
260#41—2441no—
261#41—2441no—
262C2×Q8C22×D6111yescharacteristic
263C2×Q8C22×D6111yescharacteristic
264C2×D4—21no—
265C2×D4—611no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4C22×D6111yescharacteristic
272C22×C4—21no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—1221no—
279C22×C4—2441no—
280C22×C4—2441no—
281C22×C4C22×D6111yescharacteristic
282Q16—41no—
283SD16—41no—
284SD16—2441no—
285D8—2441no—
286C2×C8—611no—
287C2×C8—611no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8C22×D6111yescharacteristic
291C2×C8C22×D6111yescharacteristic
292C4⋊C4—21no—
293C4⋊C4—611no—
294C4⋊C4—611no—
295C4⋊C4—611no—
296C4⋊C4—1221no—
297C4⋊C4—1221no—
298C4⋊C4—1221no—
299C4⋊C4C22×D6111yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C22⋊C4—1221no—
305C22⋊C4—1221no—
306C22⋊C4—1221no—
307C22⋊C4—1221no—
308C22⋊C4—1221no—
309C22⋊C4—1221no—
310C42—1221no—
311C42—1221no—
312C23—21no—
313C23—611no—
314C23—611no—
315C23—1222no—
316C23—1221no—
317C23—2441no—
318C23—2441no—
319C23D4×D6111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—21no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—1221no—
328D4—1221no—
329D4—2442no—
330D4—2442no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4D4×D6111yescharacteristic
354C2×C4C23×D6111yescharacteristic
355C8—21no—
356C8—21no—
357C8—1221no—
358C8—1221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—612no—
366C22—1221no—
367C22—1221no—
368C22—1221no—
369C22—1221no—
370C22—1221no—
371C22—2444no—
372C22—2441no—
373C22—2441no—
374C22—2441no—
375C22C2×D4×D6111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—1221no—
381C4—1221no—
382C4—2441no—
383C4—2441no—
384C4—2441no—
385C4#1451982211yescharacteristic
386C4#1451982211yescharacteristic
387C2—41no—
388C2—81no—
389C2—1222no—
390C2—4881no—
391C2—2441no—
392C2#1684032211yescharacteristic
393C2#135×D6111yescharacteristic
394C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#452C2
socleC22×C61C22×D4
hypercenter#452D61
hypocenterC61#3191
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #16840275C2semidirect
2. #16840269C2semidirect
3. #16840101C2semidirect
4. #16840100C2semidirect
5. #16840087C2semidirect
6. #16840084C2semidirect
7. #16840000C2semidirect
8. #16839997C2semidirect
9. #16839994C2semidirect
10. #16839988C2semidirect
11. #16839923C2semidirect
12. #16839907C2semidirect
13. #16839906C2semidirect
14. C22⋊C8×D61C2semidirect
15. C61×#452C2semidirect
18. C2×#11758201C22semidirect
19. C2×#11758199C22semidirect
39. #14519711C22semidirect
40. #14519710C22semidirect
41. #14519709C22semidirect
42. #14519708C22semidirect
43. #14519701C22semidirect
44. #14519701C22semidirect
45. #14519701C22semidirect
46. #14519699C22semidirect
47. #14519699C22semidirect
48. #14519698C22semidirect
53. C2×Q16×C61C22semidirect
54. C2×SD16×C61C22semidirect
56. #103×C61C22semidirect
57. #102×C61C22semidirect
209. #452D61semidirect
213. C61#3191semidirect
217. C2×Q16C2×D61semidirect
219. C2×SD16C2×D61semidirect
248. #103C2×D61semidirect
252. #102C2×D61semidirect