Finite Group Databasebeta

← #21457980

Subgroups — #21457980

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#16840477C211yesmaximal, characteristic, complemented
2#16840407C211yesmaximal, characteristic, complemented
3#16840122C211yesmaximal, characteristic, complemented
4#16840106C211yesmaximal, characteristic, complemented
5#16840088C211yesmaximal, characteristic, complemented
6#16840042C211yesmaximal, characteristic, complemented
7#16840007C211yesmaximal, characteristic, complemented
8#16839997C211yesmaximal, characteristic, complemented
9#16839977C211yesmaximal, characteristic, complemented
10#16839904C211yesmaximal, characteristic, complemented
11#16839894C211yesmaximal, characteristic, complemented
12#16839835C211yesmaximal, characteristic, complemented
13#16839765C211yesmaximal, characteristic, complemented
14#16839755C211yesmaximal, characteristic, complemented
15C61×#442C211yesmaximal, characteristic, complemented
16C2×#11758224C2211yescharacteristic
17C2×D4×D61C2211yescharacteristic
18C2×#11758200C2211yescharacteristic, complemented
19C2×#11758199C2211yescharacteristic
20C2×#11758189C2211yescharacteristic
21C2×C8×D61C2211yescharacteristic, complemented
22#14519777C2211yescharacteristic, complemented
23#14519765C2211yescharacteristic
24#14519763—21no—
25#14519763—21no—
26#14519761—21no—
27#14519757C2211yescharacteristic
28#14519752C2211yescharacteristic
29#14519751—21no—
30#14519751—21no—
31#14519748C2211yescharacteristic
32#14519748C2211yescharacteristic, complemented
33#14519747—21no—
34C4×D244C2211yescharacteristic
35#14519736—21no—
36#14519735C2211yescharacteristic
37#14519735C2211yescharacteristic, complemented
38C2×#11758198—21no—
39#14519710C2211yescharacteristic, complemented
40#14519710C2211yescharacteristic, complemented
41C4⋊#92418C2211yescharacteristic, complemented
42#14519702C2211yescharacteristic, complemented
43#14519702C2211yescharacteristic, complemented
44#14519700C2211yescharacteristic, complemented
45#14519699C2211yescharacteristic
46#14519699C2211yescharacteristic
47#14519698C2211yescharacteristic
48#14519698C2211yescharacteristic
49#14519697C2211yescharacteristic
50#14519689C2211yescharacteristic
51#14519689C2211yescharacteristic, complemented
52C2×D8×C61C2211yescharacteristic
53C4×D4×C61C2211yescharacteristic
54C4×D4×C61C2211yescharacteristic, complemented
55#106×C61C2211yescharacteristic, complemented
56#102×C61C2211yescharacteristic
57#102×C61C2211yescharacteristic, complemented
58#97×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61C2311yescharacteristic
61C2×D4×C61C2311yescharacteristic
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C2×C22⋊D61—21no—
65C2×C22⋊D61—21no—
66C2×C22⋊D61—21no—
67C2×C22⋊D61—21no—
68C22×Dic61—21no—
69#11758224—22no—
70#11758224—41no—
71D4×D61—22no—
72D4×D61—41no—
73C2×D244—21no—
74C2×D244D411yescharacteristic
75C2×D244C2311yescharacteristic
76C2×C4×D61C2311yescharacteristic
77C2×C4×D61C2311yescharacteristic
78C2×Dic122—21no—
79C2×Dic122C2311yescharacteristic
80D8×C61—22no—
81C2×C8×C61C2311yescharacteristic
82C2×C8×C61C2311yescharacteristic
83C4⋊C4×C61C2311yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C22⋊C4×C61—21no—
86C22⋊C4×C61—21no—
87C42×C61C2311yescharacteristic
88C22⋊Dic61—21no—
89C22⋊Dic61—21no—
90#11758200—41no—
91#11758199—41no—
92#11758198—21no—
93#11758198—21no—
94#11758198—21no—
95#11758198—21no—
96#11758198—21no—
97#11758198—21no—
98#11758198D411yescharacteristic
99#11758198D411yescharacteristic
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61D411yescharacteristic
103C4⋊Dic61C2311yescharacteristic
104C4⋊Dic61C2311yescharacteristic
105C4×Dic61—21no—
106C4×Dic61—21no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109#11758189—41no—
110C8×D61—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
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—21no—
122D4×C61#4112yes—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—42no—
126C2×C4×C61—81no—
127C2×C4×C61C2×D411yescharacteristic
128C2×C4×C61C2×D411yescharacteristic
129C2×C4×C61C2411yescharacteristic
130C22⋊D61—42no—
131C22⋊D61—42no—
132C22⋊D61—81no—
133C22⋊D61—81no—
134C2×Dic61—21no—
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—42no—
138C2×Dic61C2×D411yescharacteristic
139C2×Dic61C2×D411yescharacteristic
140D244—21no—
141D244—21no—
142D244—41no—
143D244—81no—
144C4×D61—21no—
145C4×D61—21no—
146C4×D61—21no—
147C4×D61—21no—
148Dic122—21no—
149Dic122—21no—
150Dic122—81no—
151C8×C61—21no—
152C8×C61—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—22no—
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—21no—
165C2×D61—21no—
166C2×D61—21no—
167C2×D61—21no—
168C2×D61—41no—
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#3319—611nomaximal, Sylow
184C2×C61—42no—
185C2×C61—81no—
186C2×C61#54611yescharacteristic
187C2×C61#57511yescharacteristic
188C2×C61#57611yescharacteristic
189D61—41no—
190D61—41no—
191D61—81no—
192#555—611no—
193#546—611no—
194#489—611no—
195#485—611no—
196#482—611no—
197#474—611no—
198#468—611no—
199#466—611no—
200#463—611no—
201#449—611no—
202#447—611no—
203#442D6111yescharacteristic, complemented
204#435—611no—
205#418—611no—
206#416—611no—
207C61#331911yescharacteristic, complemented, Sylow
208C2×#41—611no—
209C22×D4—611no—
210C2×SD16—611no—
211C2×D8—611no—
212C2×D8C2×D6111yescharacteristic
213C2×M16—611no—
214C22×C8—611no—
215C4⋊Q8—611no—
216#124—611no—
217#124—1221no—
218#124—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×D4C2×D6111yescharacteristic
229C4×D4C2×D6111yescharacteristic, complemented
230#117—611no—
231#117—611no—
232#117—1221no—
233C2×C22⋊C4—1221no—
234#107—611no—
235#107—611no—
236#106C2×D6111yescharacteristic, complemented
237C4⋊C8—611no—
238#103—611no—
239#103—611no—
240#103—611no—
241#102—611no—
242#102—611no—
243#102—611no—
244#102—611no—
245#102—611no—
246#102C2×D6111yescharacteristic
247#102C2×D6111yescharacteristic, complemented
248C22⋊C8—611no—
249C22⋊C8—611no—
250#97C2×D6111yescharacteristic, complemented
251C24—1221no—
252#41—1222no—
253#41—2441no—
254C2×Q8—611no—
255C2×Q8—1221no—
256C2×D4—611no—
257C2×D4—611no—
258C2×D4—1221no—
259C2×D4—1221no—
260C2×D4—1222no—
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—1221no—
264C2×D4—2441no—
265C2×D4C22×D6111yescharacteristic
266C2×D4C22×D6111yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—611no—
270C22×C4—611no—
271C22×C4—1221no—
272SD16—2441no—
273D8—22no—
274D8—2441no—
275M16—2441no—
276C2×C8—611no—
277C2×C8—611no—
278C2×C8—2441no—
279C2×C8C22×D6111yescharacteristic
280C2×C8C22×D6111yescharacteristic
281C4⋊C4—611no—
282C4⋊C4—611no—
283C4⋊C4—611no—
284C4⋊C4—1221no—
285C4⋊C4—1221no—
286C4⋊C4C22×D6111yescharacteristic
287C4⋊C4C22×D6111yescharacteristic
288C22⋊C4—21no—
289C22⋊C4—21no—
290C22⋊C4—611no—
291C22⋊C4—611no—
292C22⋊C4—1221no—
293C22⋊C4—1221no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4—1221no—
300C42—1221no—
301C42—1221no—
302C42C22×D6111yescharacteristic
303C23—21no—
304C23—21no—
305C23—611no—
306C23—611no—
307C23—1221no—
308C23—4881no—
309C23—2442no—
310C23—2442no—
311Q8—1221no—
312Q8—1221no—
313Q8—4881no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—1221no—
318D4—1221no—
319D4—4881no—
320D4—4881no—
321D4—4881no—
322D4—2441no—
323D4—2442no—
324D4—2442no—
325D4#1175822212yes—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—611no—
331C2×C4—611no—
332C2×C4—1221no—
333C2×C4—1221no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—1221no—
337C2×C4—1221no—
338C2×C4—1221no—
339C2×C4—2442no—
340C2×C4D4×D6111yescharacteristic
341C2×C4D4×D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—21no—
344C8—21no—
345C8—1221no—
346C8—1221no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—1221no—
354C22—1221no—
355C22—1221no—
356C22—1221no—
357C22—1221no—
358C22—1221no—
359C22—4884no—
360C22—2441no—
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—
373C4C2×#1175822211yescharacteristic
374C4#1451982311yescharacteristic
375C2—42no—
376C2—81no—
377C2—4881no—
378C2—2441no—
379C2—2441no—
380C2#1684040811yescharacteristic
381C2#1684055811yescharacteristic
382C2#1684056611yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#442C2
socleC22×C61C22×D4
hypercenter#442D61
hypocenterC61#3319
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #16840477C2semidirect
2. #16840407C2semidirect
3. #16840122C2semidirect
4. #16840106C2semidirect
5. #16840088C2semidirect
6. #16840042C2semidirect
7. #16840007C2semidirect
8. #16839997C2semidirect
9. #16839977C2semidirect
10. #16839904C2semidirect
11. #16839894C2semidirect
12. #16839835C2semidirect
13. #16839765C2semidirect
14. #16839755C2semidirect
15. C61×#442C2semidirect
18. C2×#11758200C22semidirect
21. C2×C8×D61C22semidirect
22. #14519777C22semidirect
32. #14519748C22semidirect
37. #14519735C22semidirect
39. #14519710C22semidirect
40. #14519710C22semidirect
41. C4⋊#92418C22semidirect
42. #14519702C22semidirect
43. #14519702C22semidirect
44. #14519700C22semidirect
51. #14519689C22semidirect
54. C4×D4×C61C22semidirect
55. #106×C61C22semidirect
57. #102×C61C22semidirect
58. #97×C61C22semidirect
203. #442D61semidirect
207. C61#3319semidirect
229. C4×D4C2×D61semidirect
236. #106C2×D61semidirect
247. #102C2×D61semidirect
250. #97C2×D61semidirect