Finite Group Databasebeta

← #21458027

Subgroups — #21458027

Order 7808.

414 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840462C211yesmaximal, characteristic, complemented
2#16840405C211yesmaximal, characteristic, complemented
3#16840116C211yesmaximal, characteristic, complemented
4#16840101C211yesmaximal, characteristic, complemented
5#16840074C211yesmaximal, characteristic, complemented
6#16840063C211yesmaximal, characteristic, complemented
7#16840012C211yesmaximal, characteristic, complemented
8#16840005C211yesmaximal, characteristic, complemented
9#16839906C211yesmaximal, characteristic, complemented
10#16839894C211yesmaximal, characteristic, complemented
11C4×#11758199C211yesmaximal, characteristic, complemented
12#16839839C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839762C211yesmaximal, characteristic, complemented
15C61×#463C211yesmaximal, characteristic, complemented
16C2×#11758226C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758199C2211yescharacteristic
19C2×#11758189C2211yescharacteristic
20C2×#11758189C2211yescharacteristic, complemented
21#14519770—21no—
22#14519769C2211yescharacteristic, complemented
23#14519760—21no—
24#14519759—21no—
25#14519753C2211yescharacteristic
26#14519750—21no—
27#14519750—21no—
28#14519748C2211yescharacteristic
29#14519748C2211yescharacteristic
30#14519748C2211yescharacteristic, complemented
31#14519747—21no—
32C4×D244C2211yescharacteristic
33C4×D244C2211yescharacteristic
34C4×C22⋊D61—21no—
35#14519735C2211yescharacteristic
36C4⋊C4×D61C2211yescharacteristic, complemented
37C22⋊C4×D61—21no—
38#14519711C2211yescharacteristic, complemented
39#14519710C2211yescharacteristic, complemented
40#14519709C2211yescharacteristic, complemented
41#14519701C2211yescharacteristic, complemented
42#14519701C2211yescharacteristic, complemented
43#14519699C2211yescharacteristic
44#14519699C2211yescharacteristic
45#14519698C2211yescharacteristic
46#14519698C2211yescharacteristic
47#14519698C2211yescharacteristic, complemented
48#14519697C2211yescharacteristic
49#14519689C2211yescharacteristic
50#14519689C2211yescharacteristic, complemented
51C4×#92418C2211yescharacteristic, 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—
68#11758226—22no—
69#11758226—41no—
70D4×D61—22no—
71D4×D61—41no—
72C2×D244—21no—
73C2×D244D411yescharacteristic
74C2×D244C2311yescharacteristic
75C2×C4×D61—21no—
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61C2311yescharacteristic
79C2×C4×D61C2311yescharacteristic
80SD16×C61—41no—
81D8×C61—41no—
82C2×C8×C61C2311yescharacteristic
83C2×C8×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—21no—
88C42×C61C2311yescharacteristic
89C22⋊Dic61—21no—
90C22⋊Dic61—21no—
91C22⋊Dic61—21no—
92#11758199—22no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198D411yescharacteristic
97#11758198D411yescharacteristic
98C4⋊Dic61D411yescharacteristic
99C4⋊Dic61C2311yescharacteristic
100C4⋊Dic61C2311yescharacteristic
101C4⋊Dic61C2311yescharacteristic
102#11758196—21no—
103#11758196—21no—
104#11758196—21no—
105#11758196—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758189—41no—
110#11758189—41no—
111C23×C61—21no—
112C23×C61—21no—
113C22×D61—21no—
114C22×D61—42no—
115C22×D61—42no—
116C22×D61—81no—
117C22×D61C2×D411yescharacteristic
118C22×D61C2×D411yescharacteristic
119Q8×C61—21no—
120Q8×C61—21no—
121D4×C61—21no—
122D4×C61—21no—
123D4×C61—21no—
124D4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—81no—
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2×D411yescharacteristic
130C2×C4×C61C2411yescharacteristic
131C22⋊D61—42no—
132C22⋊D61—42no—
133C22⋊D61—81no—
134C22⋊D61—81no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—21no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140D244—21no—
141D244—41no—
142D244—42no—
143D244#4112yes—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148C4×D61—42no—
149C4×D61—81no—
150C4×D61—81no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61C22×D411yescharacteristic
162C2×D61—21no—
163C2×D61—21no—
164C2×D61—22no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—21no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—84no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—41no—
175C4×C61—41no—
176C4×C61C2×#4111yescharacteristic
177C4×C61H(5,𝔽2)11yescharacteristic
178Dic61—21no—
179Dic61—21no—
180Dic61—41no—
181Dic61—41no—
182Dic61—41no—
183#3322—611nomaximal, Sylow
184C2×C61—81no—
185C2×C61—81no—
186C2×C61#54611yescharacteristic
187C2×C61#57511yescharacteristic
188C2×C61#57611yescharacteristic
189D61—41no—
190D61—41no—
191D61—42no—
192#553—611no—
193#546—611no—
194#488—611no—
195#485—611no—
196#480—611no—
197#478—611no—
198#469—611no—
199#468—611no—
200#463D6111yescharacteristic, complemented
201#449—611no—
202#447—611no—
203C4×D8—611no—
204#436—611no—
205#418—611no—
206#417—611no—
207C61#332211yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C22×D4—611no—
210C2×SD16C2×D6111yescharacteristic, complemented
211C2×D8—611no—
212C2×D8C2×D6111yescharacteristic
213C2×M16—611no—
214C2×M16—611no—
215#126—1221no—
216#125—611no—
217#124C2×D6111yescharacteristic
218#123—1221no—
219#123—1221no—
220C22⋊Q8—611no—
221#121—611no—
222#121—611no—
223#121—611no—
224#121—1221no—
225#121—1221no—
226#120—1221no—
227C4×D4—611no—
228C4×D4—611no—
229C4×D4—1221no—
230C4×D4C2×D6111yescharacteristic, complemented
231#117—611no—
232C2×C4⋊C4—611no—
233C2×C22⋊C4—1221no—
234#107—611no—
235#107—611no—
236#106—611no—
237C4⋊C8C2×D6111yescharacteristic, complemented
238#103—611no—
239#103—611no—
240#103C2×D6111yescharacteristic, complemented
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102—611no—
247#102C2×D6111yescharacteristic
248C22⋊C8—611no—
249C22⋊C8—611no—
250C4×C8—611no—
251C24—1221no—
252#41—1222no—
253#41—2441no—
254C2×Q8C22×D6111yescharacteristic
255C2×D4—611no—
256C2×D4—611no—
257C2×D4—1221no—
258C2×D4—1221no—
259C2×D4—1222no—
260C2×D4—1221no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—2441no—
264C2×D4C22×D6111yescharacteristic
265C2×D4C22×D6111yescharacteristic
266C22×C4—21no—
267C22×C4—611no—
268C22×C4—611no—
269C22×C4—1221no—
270C22×C4—1221no—
271C22×C4—1221no—
272SD16—41no—
273D8—41no—
274D8—1222no—
275M16—2441no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—611no—
285C4⋊C4—1221no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C4⋊C4—1221no—
289C4⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—611no—
294C22⋊C4—611no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C22⋊C4—1221no—
301C42—1221no—
302C42C22×D6111yescharacteristic
303C23—21no—
304C23—21no—
305C23—611no—
306C23—611no—
307C23—1221no—
308C23—4881no—
309C23—2442no—
310C23—2442no—
311Q8—21no—
312Q8—21no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—612no—
318D4—1221no—
319D4—4881no—
320D4—4881no—
321D4—2441no—
322D4—2442no—
323D4—2442no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—611no—
329C2×C4—611no—
330C2×C4—1221no—
331C2×C4—1221no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—4881no—
338C2×C4—4881no—
339C2×C4—2442no—
340C2×C4D4×D6111yescharacteristic
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—1221no—
354C22—1221no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—1222no—
360C22—4884no—
361C22—2441no—
362C22—2441no—
363C22C2×D4×D6111yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—1221no—
369C4—1221no—
370C4—2441no—
371C4—2441no—
372C4—2441no—
373C4#41×D6111yescharacteristic
374C4#1451982211yescharacteristic
375C2—81no—
376C2—81no—
377C2—2441no—
378C2—2441no—
379C2—2442no—
380C2#1684040911yescharacteristic
381C2#1684055911yescharacteristic
382C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#463C2
socleC22×C61C22×D4
hypercenter#463D61
hypocenterC61#3322
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. #16840462C2semidirect
2. #16840405C2semidirect
3. #16840116C2semidirect
4. #16840101C2semidirect
5. #16840074C2semidirect
6. #16840063C2semidirect
7. #16840012C2semidirect
8. #16840005C2semidirect
9. #16839906C2semidirect
10. #16839894C2semidirect
11. C4×#11758199C2semidirect
12. #16839839C2semidirect
13. #16839765C2semidirect
14. #16839762C2semidirect
15. C61×#463C2semidirect
20. C2×#11758189C22semidirect
22. #14519769C22semidirect
30. #14519748C22semidirect
36. C4⋊C4×D61C22semidirect
38. #14519711C22semidirect
39. #14519710C22semidirect
40. #14519709C22semidirect
41. #14519701C22semidirect
42. #14519701C22semidirect
47. #14519698C22semidirect
50. #14519689C22semidirect
51. C4×#92418C22semidirect
52. C2×SD16×C61C22semidirect
55. C4×D4×C61C22semidirect
56. C4⋊C8×C61C22semidirect
57. #103×C61C22semidirect
200. #463D61semidirect
207. C61#3322semidirect
210. C2×SD16C2×D61semidirect
230. C4×D4C2×D61semidirect
237. C4⋊C8C2×D61semidirect
240. #103C2×D61semidirect