Finite Group Databasebeta

← #21457842

Subgroups — #21457842

Order 7808.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840452C211yesmaximal, characteristic, complemented
2D4×D244C211yesmaximal, characteristic
3#16840127C211yesmaximal, characteristic, complemented
4#16840087C211yesmaximal, characteristic, complemented
5#16840076C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16840008C211yesmaximal, characteristic, complemented
8#16839991C211yesmaximal, characteristic, complemented
9#16839963C211yesmaximal, characteristic, complemented
10#16839915C211yesmaximal, characteristic, complemented
11#16839915C211yesmaximal, characteristic, complemented
12#16839864C211yesmaximal, characteristic, complemented
13#16839768C211yesmaximal, characteristic, complemented
14C2×#14519699C211yesmaximal, characteristic, complemented
15C61×#435C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×D4×D61—21no—
19C2×#11758190C2211yescharacteristic
20C2×#11758190C2211yescharacteristic, complemented
21C2×#11758190C2211yescharacteristic, complemented
22#14519774C2211yescharacteristic
23#14519770—21no—
24#14519769C2211yescharacteristic, complemented
25#14519767—21no—
26#14519758—21no—
27#14519756C2211yescharacteristic, complemented
28#14519756C2211yescharacteristic, complemented
29#14519752—21no—
30#14519751C2211yescharacteristic
31#14519751C2211yescharacteristic
32#14519747—21no—
33#14519747—21no—
34C4×Dic122C2211yescharacteristic, complemented
35C4×D244C2211yescharacteristic
36#14519736C2211yescharacteristic, complemented
37#14519733—21no—
38C2×C4⋊Dic61C2211yescharacteristic, complemented
39#14519711C2211yescharacteristic, complemented
40#14519711C2211yescharacteristic, complemented
41#14519709C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic, complemented
47#14519699C2211yescharacteristic, complemented
48#14519699C2211yescharacteristic, complemented
49#14519699C2211yescharacteristic, complemented
50#14519699C2211yescharacteristic, complemented
51#14519699C2211yescharacteristic, complemented
52C2×M16×C61C2211yescharacteristic, complemented
53C22×C8×C61C2211yescharacteristic, complemented
54C4×D4×C61C2211yescharacteristic
55C4⋊C8×C61C2211yescharacteristic, complemented
56C22⋊C8×C61C2211yescharacteristic, complemented
57C22⋊C8×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×D4×C61D411yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C22×Dic61—21no—
67D4×D61—44no—
68C2×D244—22no—
69C2×D244—22no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244—21no—
73C2×D244—21no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244C2311yescharacteristic
77C2×D244C2311yescharacteristic
78C2×D244C2311yescharacteristic
79C2×C4×D61—21no—
80C2×Dic122C2311yescharacteristic
81M16×C61—41no—
82C2×C8×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C2×C8×C61C2311yescharacteristic
86C2×C8×C61C2311yescharacteristic
87C4⋊C4×C61D411yescharacteristic
88C22⋊C4×C61D411yescharacteristic
89C22⋊C4×C61D411yescharacteristic
90C42×C61C2311yescharacteristic
91C22⋊Dic61—21no—
92C22⋊Dic61—21no—
93C22⋊Dic61—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97C4⋊Dic61—21no—
98C4⋊Dic61C2311yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106#11758196—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109#11758190—22no—
110#11758190—41no—
111#11758190—41no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—42no—
118C22×D61—42no—
119C22×D61—42no—
120C22×D61—42no—
121C22×D61—81no—
122C22×D61—81no—
123D4×C61—22no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2×D411yescharacteristic
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2411yescharacteristic
133C22⋊D61—42no—
134C22⋊D61—42no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61—21no—
139C2×Dic61—21no—
140C2×Dic61—42no—
141D244—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—21no—
146D244—42no—
147D244—42no—
148D244—42no—
149D244—81no—
150D244#4112yes—
151C4×D61—42no—
152Dic122—21no—
153Dic122—21no—
154C8×C61—21no—
155C8×C61—21no—
156C8×C61—21no—
157C8×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—21no—
162C22×C61—21no—
163C22×C61AGL(1,ℤ/8)12yes—
164C22×C61C22×D411yescharacteristic
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—41no—
172C2×D61—41no—
173C2×D61—41no—
174C2×D61—84no—
175C2×D61—84no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61C2×#4111yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—41no—
183Dic61—41no—
184Dic61—41no—
185Dic61—41no—
186Dic61—41no—
187#3310—611nomaximal, Sylow
188C2×C61—22no—
189C2×C61—41no—
190C2×C61#54611yescharacteristic
191C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C61#57711yescharacteristic
193D61—42no—
194D61—81no—
195D61—81no—
196#552—611no—
197D42—611no—
198#490—611no—
199#482—611no—
200#480—611no—
201#478—611no—
202#468—611no—
203#465—611no—
204#460—611no—
205#450—611no—
206#450—611no—
207#440—611no—
208#435D6111yescharacteristic, complemented
209#418—611no—
210C2×#102—611no—
211C61#331011yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—611no—
214C22×D4—1221no—
215C2×SD16—611no—
216C2×SD16—611no—
217C2×SD16—611no—
218C2×M16C2×D6111yescharacteristic, complemented
219C22×C8C2×D6111yescharacteristic, complemented
220#127—611no—
221#126—1221no—
222#125—611no—
223#125—1221no—
224#123—1221no—
225C22⋊Q8—611no—
226C22⋊Q8—611no—
227#121—611no—
228#121—611no—
229#121—1221no—
230#120—1221no—
231#120—1221no—
232C4×Q8—611no—
233C4×D4—611no—
234C4×D4C2×D6111yescharacteristic
235#117—611no—
236#117—1221no—
237C2×C4⋊C4—611no—
238#107—611no—
239#107—611no—
240#106—611no—
241C4⋊C8C2×D6111yescharacteristic, complemented
242#103—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102—611no—
248#102—611no—
249#102—611no—
250#102—611no—
251#102—611no—
252C22⋊C8C2×D6111yescharacteristic, complemented
253C22⋊C8C2×D6111yescharacteristic, complemented
254#97C2×D6111yescharacteristic, complemented
255C24—1221no—
256C24—1221no—
257C2×Q8—611no—
258C2×D4—611no—
259C2×D4—611no—
260C2×D4—611no—
261C2×D4—1222no—
262C2×D4—1222no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1221no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2444no—
272C2×D4D24411yescharacteristic
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4C22×D6111yescharacteristic
276C22×C4C22×D6111yescharacteristic
277SD16—1222no—
278SD16—2441no—
279SD16—2441no—
280M16—41no—
281C2×C8—41no—
282C2×C8C22×D6111yescharacteristic
283C2×C8C22×D6111yescharacteristic
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4D24411yescharacteristic
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4D24411yescharacteristic
304C22⋊C4D24411yescharacteristic
305C42—1221no—
306C42—1221no—
307C42C22×D6111yescharacteristic
308C23—1221no—
309C23—1221no—
310C23—1221no—
311C23—4881no—
312C23—4881no—
313C23—2442no—
314C23—2442no—
315C23—2442no—
316C23—2442no—
317C23C2×D24411yescharacteristic
318C23C2×D24411yescharacteristic
319Q8—1221no—
320Q8—1221no—
321D4—22no—
322D4—612no—
323D4—1221no—
324D4—1221no—
325D4—1221no—
326D4—1221no—
327D4—1221no—
328D4—4881no—
329D4—2442no—
330D4—2442no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—1221no—
339C2×C4—1221no—
340C2×C4—1221no—
341C2×C4—1221no—
342C2×C4—1221no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4C2×D24411yescharacteristic
346C2×C4C2×D24411yescharacteristic
347C2×C4C2×D24411yescharacteristic
348C2×C4C2×D24411yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—1222no—
360C22—4884no—
361C22—4884no—
362C22—2441no—
363C22—2441no—
364C22—2441no—
365C22—2441no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22#1451980512yes—
371C22C22×D24411yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—2441no—
377C4—2441no—
378C4—2441no—
379C4—2441no—
380C4—2441no—
381C4#41×D6111yescharacteristic
382C4#1451982211yescharacteristic
383C2—22no—
384C2—41no—
385C2—4881no—
386C2—4881no—
387C2—2442no—
388C2#1684040711yescharacteristic
389C2C2×#1451980511yescharacteristic
390C2#1684057411yescharacteristic
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#435C2
socleC22×C61C22×D4
hypercenter#435D61
hypocenterC61#3310
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16840452C2semidirect
3. #16840127C2semidirect
4. #16840087C2semidirect
5. #16840076C2semidirect
6. #16840063C2semidirect
7. #16840008C2semidirect
8. #16839991C2semidirect
9. #16839963C2semidirect
10. #16839915C2semidirect
11. #16839915C2semidirect
12. #16839864C2semidirect
13. #16839768C2semidirect
14. C2×#14519699C2semidirect
15. C61×#435C2semidirect
20. C2×#11758190C22semidirect
21. C2×#11758190C22semidirect
24. #14519769C22semidirect
27. #14519756C22semidirect
28. #14519756C22semidirect
34. C4×Dic122C22semidirect
36. #14519736C22semidirect
38. C2×C4⋊Dic61C22semidirect
39. #14519711C22semidirect
40. #14519711C22semidirect
41. #14519709C22semidirect
42. #14519702C22semidirect
46. #14519699C22semidirect
47. #14519699C22semidirect
48. #14519699C22semidirect
49. #14519699C22semidirect
50. #14519699C22semidirect
51. #14519699C22semidirect
52. C2×M16×C61C22semidirect
53. C22×C8×C61C22semidirect
55. C4⋊C8×C61C22semidirect
56. C22⋊C8×C61C22semidirect
57. C22⋊C8×C61C22semidirect
58. #97×C61C22semidirect
208. #435D61semidirect
211. C61#3310semidirect
218. C2×M16C2×D61semidirect
219. C22×C8C2×D61semidirect
241. C4⋊C8C2×D61semidirect
252. C22⋊C8C2×D61semidirect
253. C22⋊C8C2×D61semidirect
254. #97C2×D61semidirect