Finite Group Databasebeta

← #21458045

Subgroups — #21458045

Order 7808.

448 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#16840483C211yesmaximal, characteristic, complemented
2#16840396C211yesmaximal, characteristic
3#16840107C211yesmaximal, characteristic, complemented
4#16840089C211yesmaximal, characteristic, complemented
5#16840083C211yesmaximal, characteristic, complemented
6#16840041C211yesmaximal, characteristic, complemented
7#16840011C211yesmaximal, characteristic, complemented
8#16839960C211yesmaximal, characteristic, complemented
9#16839912C211yesmaximal, characteristic, complemented
10#16839911C211yesmaximal, characteristic, complemented
11#16839847C211yesmaximal, characteristic, complemented
12#16839838C211yesmaximal, characteristic, complemented
13#16839768C211yesmaximal, characteristic, complemented
14#16839765C211yesmaximal, characteristic, complemented
15C61×#468C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C2×D4×D61—21no—
18C2×D4×D61C2211yescharacteristic
19C2×#11758201C2211yescharacteristic
20C2×#11758201C2211yescharacteristic, complemented
21C2×#11758189C2211yescharacteristic, complemented
22#14519776C2211yescharacteristic, complemented
23#14519773C2211yescharacteristic
24#14519772—21no—
25#14519770—21no—
26#14519763—21no—
27#14519753C2211yescharacteristic, complemented
28#14519752C2211yescharacteristic
29#14519750—21no—
30#14519747—21no—
31#14519745—21no—
32Q8×Dic61C2211yescharacteristic, complemented
33#14519742—21no—
34#14519739C2211yescharacteristic
35C4×C22⋊D61C2211yescharacteristic
36#14519736C2211yescharacteristic, complemented
37#14519735C2211yescharacteristic, complemented
38#14519710C2211yescharacteristic, complemented
39#14519708C2211yescharacteristic, complemented
40#14519706C2211yescharacteristic, complemented
41#14519699C2211yescharacteristic
42#14519699C2211yescharacteristic
43#14519699C2211yescharacteristic, complemented
44#14519699C2211yescharacteristic, complemented
45#14519698C2211yescharacteristic, complemented
46#14519698C2211yescharacteristic, complemented
47#14519697C2211yescharacteristic
48#14519697C2211yescharacteristic, complemented
49C22⋊#92418C2211yescharacteristic, complemented
50#14519689C2211yescharacteristic, complemented
51C8×Dic61C2211yescharacteristic, complemented
52C2×SD16×C61C2211yescharacteristic, complemented
53C2×M16×C61C2211yescharacteristic, complemented
54C22⋊Q8×C61C2211yescharacteristic, complemented
55#121×C61C2211yescharacteristic
56#107×C61C2211yescharacteristic, complemented
57#103×C61C2211yescharacteristic, complemented
58#102×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C23×D61—21no—
61C2×Q8×C61C2311yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C2×C22⋊D61D411yescharacteristic
69D4×D61—22no—
70D4×D61—41no—
71D4×D61—44no—
72C2×D244—22no—
73C2×D244—21no—
74C2×D244—21no—
75C2×D244—41no—
76C2×D244C2311yescharacteristic
77C2×D244C2311yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61C2311yescharacteristic
80C2×Dic122—21no—
81SD16×C61—41no—
82M16×C61—41no—
83C2×C8×C61C2311yescharacteristic
84C2×C8×C61C2311yescharacteristic
85C4⋊C4×C61—21no—
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61D411yescharacteristic
92#11758201—22no—
93#11758201—41no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99C4⋊Dic61—21no—
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196D411yescharacteristic
105C4×Dic61—21no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111#11758189—41no—
112C23×C61—21no—
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—42no—
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—42no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—22no—
136C22⋊D61—42no—
137C22⋊D61—42no—
138C22⋊D61—81no—
139C2×Dic61—21no—
140C2×Dic61—21no—
141C2×Dic61C2×D411yescharacteristic
142C2×Dic61C2×D411yescharacteristic
143C2×Dic61C2×D411yescharacteristic
144D244—21no—
145D244—21no—
146D244—21no—
147D244—42no—
148D244—42no—
149D244#4112yes—
150C4×D61—21no—
151C4×D61—21no—
152C4×D61—42no—
153Dic122—42no—
154C8×C61—21no—
155C8×C61—21no—
156#92418—21no—
157#92418—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—21no—
166C2×D61—22no—
167C2×D61—21no—
168C2×D61—21no—
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—41no—
178C4×C61—41no—
179C4×C61—41no—
180C4×C61C2×#4111yescharacteristic
181C4×C61H(5,𝔽2)11yescharacteristic
182Dic61—21no—
183Dic61—21no—
184Dic61—41no—
185Dic61—41no—
186Dic61AGL(1,ℤ/8)12yes—
187#3324—611nomaximal, Sylow
188C2×C61—41no—
189C2×C61—81no—
190C2×C61#54611yescharacteristic
191C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
192C2×C61#57711yescharacteristic
193D61—41no—
194D61—42no—
195D61—81no—
196#556—611no—
197D42—611no—
198#486—611no—
199#482—611no—
200#482—611no—
201#474—611no—
202#468—611no—
203#468D6111yescharacteristic, complemented
204#460—611no—
205#450—611no—
206#450—611no—
207C4×SD16—611no—
208#436—611no—
209#418—611no—
210#418—611no—
211C61#332411yescharacteristic, complemented, Sylow
212C22×D4—611no—
213C22×D4—611no—
214C22×D4—1221no—
215C2×SD16—611no—
216C2×SD16—611no—
217C2×SD16C2×D6111yescharacteristic, complemented
218C2×M16—611no—
219C2×M16C2×D6111yescharacteristic, complemented
220C4⋊Q8—611no—
221#127—611no—
222#126—1221no—
223#126—1221no—
224#124—1221no—
225C22⋊Q8—611no—
226C22⋊Q8C2×D6111yescharacteristic, complemented
227#121—611no—
228#121—1221no—
229#121C2×D6111yescharacteristic
230#120—1221no—
231#120—1221no—
232C4×Q8—611no—
233C4×Q8—1221no—
234C4×D4—611no—
235C4×D4—611no—
236#117—611no—
237#117—611no—
238#107—611no—
239#107C2×D6111yescharacteristic, complemented
240#106—611no—
241C4⋊C8—611no—
242#103C2×D6111yescharacteristic, complemented
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#102C2×D6111yescharacteristic, complemented
252C22⋊C8—611no—
253C22⋊C8—611no—
254C4×C8—611no—
255C24—1221no—
256C24—1221no—
257C2×Q8—1221no—
258C2×Q8C22×D6111yescharacteristic
259C2×D4—21no—
260C2×D4—611no—
261C2×D4—611no—
262C2×D4—611no—
263C2×D4—1222no—
264C2×D4—1221no—
265C2×D4—1221no—
266C2×D4—1221no—
267C2×D4—1221no—
268C2×D4—1222no—
269C2×D4—1221no—
270C2×D4—2441no—
271C2×D4—2441no—
272C2×D4—2444no—
273C2×D4C22×D6111yescharacteristic
274C22×C4—611no—
275C22×C4—1221no—
276C22×C4C22×D6111yescharacteristic
277SD16—41no—
278SD16—1222no—
279SD16—2441no—
280M16—41no—
281M16—2441no—
282C2×C8—611no—
283C2×C8—611no—
284C2×C8C22×D6111yescharacteristic
285C2×C8C22×D6111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—611no—
288C4⋊C4—611no—
289C4⋊C4—611no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4C22×D6111yescharacteristic
294C4⋊C4C22×D6111yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—611no—
298C22⋊C4—611no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C22⋊C4—1221no—
302C22⋊C4—1221no—
303C22⋊C4—1221no—
304C42—611no—
305C42—1221no—
306C42—1221no—
307C42—1221no—
308C23—21no—
309C23—611no—
310C23—1221no—
311C23—1221no—
312C23—4881no—
313C23—4881no—
314C23—2442no—
315C23—2442no—
316C23—2442no—
317C23—2442no—
318C23D4×D6111yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—2442no—
322D4—21no—
323D4—21no—
324D4—42no—
325D4—612no—
326D4—1222no—
327D4—1221no—
328D4—1221no—
329D4—1221no—
330D4—4881no—
331D4—2442no—
332D4—2442no—
333D4—2442no—
334D4—2442no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—2442no—
348C2×C4D4×D6111yescharacteristic
349C2×C4C23×D6111yescharacteristic
350C8—21no—
351C8—21no—
352C8—1221no—
353C8—1221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—1221no—
361C22—1221no—
362C22—1221no—
363C22—1222no—
364C22—4884no—
365C22—4884no—
366C22—2441no—
367C22—2441no—
368C22—2441no—
369C22—2441no—
370C22—2441no—
371C22C2×D4×D6111yescharacteristic
372C4—21no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—612no—
377C4—1221no—
378C4—1221no—
379C4—2441no—
380C4—2441no—
381C4#41×D6111yescharacteristic
382C4#1451982211yescharacteristic
383C2—41no—
384C2—81no—
385C2—4881no—
386C2—2441no—
387C2—2442no—
388C2#1684040111yescharacteristic
389C2AGL(1,ℤ/8)×D6111yescharacteristic
390C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#468C2
socleC22×C61C22×D4
hypercenter#468D61
hypocenterC61#3324
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #16840483C2semidirect
3. #16840107C2semidirect
4. #16840089C2semidirect
5. #16840083C2semidirect
6. #16840041C2semidirect
7. #16840011C2semidirect
8. #16839960C2semidirect
9. #16839912C2semidirect
10. #16839911C2semidirect
11. #16839847C2semidirect
12. #16839838C2semidirect
13. #16839768C2semidirect
14. #16839765C2semidirect
15. C61×#468C2semidirect
20. C2×#11758201C22semidirect
21. C2×#11758189C22semidirect
22. #14519776C22semidirect
27. #14519753C22semidirect
32. Q8×Dic61C22semidirect
36. #14519736C22semidirect
37. #14519735C22semidirect
38. #14519710C22semidirect
39. #14519708C22semidirect
40. #14519706C22semidirect
43. #14519699C22semidirect
44. #14519699C22semidirect
45. #14519698C22semidirect
46. #14519698C22semidirect
48. #14519697C22semidirect
49. C22⋊#92418C22semidirect
50. #14519689C22semidirect
51. C8×Dic61C22semidirect
52. C2×SD16×C61C22semidirect
53. C2×M16×C61C22semidirect
54. C22⋊Q8×C61C22semidirect
56. #107×C61C22semidirect
57. #103×C61C22semidirect
58. #102×C61C22semidirect
203. #468D61semidirect
211. C61#3324semidirect
217. C2×SD16C2×D61semidirect
219. C2×M16C2×D61semidirect
226. C22⋊Q8C2×D61semidirect
239. #107C2×D61semidirect
242. #103C2×D61semidirect
251. #102C2×D61semidirect