Finite Group Databasebeta

← #21458014

Subgroups — #21458014

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#16840408C211yesmaximal, characteristic, complemented
2#16840119C211yesmaximal, characteristic, complemented
3#16840103C211yesmaximal, characteristic, complemented
4#16840075C211yesmaximal, characteristic, complemented
5#16840059C211yesmaximal, characteristic, complemented
6#16840013C211yesmaximal, characteristic, complemented
7#16840006C211yesmaximal, characteristic, complemented
8#16839977C211yesmaximal, characteristic, complemented
9#16839905C211yesmaximal, characteristic, complemented
10#16839895C211yesmaximal, characteristic, complemented
11C4×#11758199C211yesmaximal, characteristic, complemented
12#16839840C211yesmaximal, characteristic, complemented
13#16839766C211yesmaximal, characteristic, complemented
14#16839761C211yesmaximal, characteristic, complemented
15C61×#553C211yesmaximal, characteristic, complemented
16C2×#11758222C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C2×#11758200C2211yescharacteristic, complemented
19C2×#11758199C2211yescharacteristic
20C2×#11758199C2211yescharacteristic
21C2×#11758194C2211yescharacteristic
22C2×#11758194C2211yescharacteristic, complemented
23#14519765C2211yescharacteristic
24#14519762—21no—
25#14519756C2211yescharacteristic
26#14519751C2211yescharacteristic
27#14519750—21no—
28#14519745—21no—
29C4×D244C2211yescharacteristic
30C22⋊C4×D61—21no—
31#14519710C2211yescharacteristic, complemented
32#14519710C2211yescharacteristic, complemented
33#14519708C2211yescharacteristic, complemented
34C4⋊#92418C2211yescharacteristic, complemented
35#14519700C2211yescharacteristic, complemented
36#14519700C2211yescharacteristic, complemented
37#14519700C2211yescharacteristic, complemented
38#14519698C2211yescharacteristic, complemented
39#14519697C2211yescharacteristic
40#14519697C2211yescharacteristic
41#14519697C2211yescharacteristic
42#14519697C2211yescharacteristic
43#14519697C2211yescharacteristic
44#14519697C2211yescharacteristic
45C22⋊#92418C2211yescharacteristic
46C22⋊#92418C2211yescharacteristic, complemented
47C4×#92418C2211yescharacteristic, complemented
48#126×C61—21no—
49#125×C61C2211yescharacteristic, complemented
50#123×C61—21no—
51#121×C61—21no—
52#121×C61C2211yescharacteristic
53#121×C61C2211yescharacteristic, complemented
54C4×D4×C61—21no—
55C4×D4×C61C2211yescharacteristic
56C4×D4×C61C2211yescharacteristic, complemented
57#117×C61C2211yescharacteristic
58C2×C4⋊C4×C61C2211yescharacteristic, complemented
59C23×D61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61D411yescharacteristic
63C2×D4×C61C2311yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C2311yescharacteristic
67C22×C4×C61C2311yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70#11758222—22no—
71#11758222—41no—
72C2×D244—22no—
73C2×D244—21no—
74C2×D244—41no—
75C2×D244C2311yescharacteristic
76C2×D244C2311yescharacteristic
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×Dic122C2311yescharacteristic
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61D411yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C22⋊C4×C61—21no—
88C22⋊C4×C61—21no—
89C22⋊C4×C61—21no—
90C22⋊C4×C61—21no—
91C22⋊C4×C61D411yescharacteristic
92C22⋊C4×C61D411yescharacteristic
93C42×C61—21no—
94C42×C61C2311yescharacteristic
95C22⋊Dic61—21no—
96#11758200—41no—
97#11758199—22no—
98#11758199—41no—
99#11758198—21no—
100#11758198—21no—
101#11758198—21no—
102#11758198—21no—
103C4⋊Dic61C2311yescharacteristic
104#11758196—21no—
105#11758194—41no—
106#11758194—41no—
107C2×#92418C2311yescharacteristic
108C2×#92418C2311yescharacteristic
109C2×#92418C2311yescharacteristic
110C2×#92418C2311yescharacteristic
111C23×C61—21no—
112C23×C61C2×D411yescharacteristic
113C23×C61C2×D411yescharacteristic
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—81no—
119D4×C61—21no—
120D4×C61—21no—
121D4×C61—41no—
122D4×C61—42no—
123D4×C61—81no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2411yescharacteristic
138C22⋊D61—42no—
139C22⋊D61—81no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142D244—21no—
143D244—21no—
144D244—21no—
145D244—42no—
146D244#4112yes—
147C4×D61—42no—
148C4×D61—81no—
149Dic122—21no—
150Dic122—21no—
151#92418—21no—
152#92418—21no—
153#92418—21no—
154#92418—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—21no—
158C22×C61—21no—
159C22×C61—21no—
160C22×C61—21no—
161C22×C61—41no—
162C22×C61—41no—
163C22×C61—41no—
164C22×C61C22×D411yescharacteristic
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C2×D61—41no—
169C2×D61—41no—
170C2×D61—41no—
171C2×D61—84no—
172C4×C61—21no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—41no—
177C4×C61—41no—
178C4×C61—41no—
179C4×C61C2×#4111yescharacteristic
180C4×C61H(5,𝔽2)11yescharacteristic
181Dic61—41no—
182Dic61—41no—
183#3322—611nomaximal, Sylow
184C2×C61—41no—
185C2×C61—41no—
186C2×C61—81no—
187C2×C61#54611yescharacteristic
188C2×C61#57511yescharacteristic
189C2×C61#57611yescharacteristic
190D61—42no—
191D61—81no—
192#553D6111yescharacteristic, complemented
193#546—611no—
194#488—611no—
195#485—611no—
196#480—611no—
197#478—611no—
198#469—611no—
199#468—611no—
200#463—611no—
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×SD16—611no—
211C2×D8—611no—
212C2×D8—611no—
213C2×M16—611no—
214C2×M16—611no—
215#126—21no—
216#125C2×D6111yescharacteristic, complemented
217#124—611no—
218#123—21no—
219#123—1221no—
220C22⋊Q8—611no—
221#121—21no—
222#121—611no—
223#121—1221no—
224#121C2×D6111yescharacteristic
225#121C2×D6111yescharacteristic, complemented
226#120—1221no—
227C4×D4—21no—
228C4×D4—611no—
229C4×D4C2×D6111yescharacteristic
230C4×D4C2×D6111yescharacteristic, complemented
231#117C2×D6111yescharacteristic
232C2×C4⋊C4C2×D6111yescharacteristic, complemented
233C2×C22⋊C4—1221no—
234#107—611no—
235#107—611no—
236#106—611no—
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#102—611no—
247#102—611no—
248C22⋊C8—611no—
249C22⋊C8—611no—
250C4×C8—611no—
251C24—1221no—
252#41—1222no—
253#41—2441no—
254C2×Q8—611no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—611no—
258C2×D4—611no—
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—21no—
268C22×C4—1221no—
269C22×C4—1221no—
270C22×C4C22×D6111yescharacteristic
271C22×C4C22×D6111yescharacteristic
272SD16—2441no—
273D8—1222no—
274D8—2441no—
275M16—2441no—
276M16—2441no—
277C2×C8—611no—
278C2×C8—611no—
279C2×C8—611no—
280C2×C8—611no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—611no—
285C4⋊C4—1221no—
286C4⋊C4C22⋊D6111yescharacteristic
287C4⋊C4C22×D6111yescharacteristic
288C4⋊C4C22×D6111yescharacteristic
289C4⋊C4C22×D6111yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—1221no—
295C22⋊C4—1221no—
296C22⋊C4—1221no—
297C22⋊C4—1221no—
298C22⋊C4—1221no—
299C22⋊C4C22⋊D6111yescharacteristic
300C22⋊C4C22⋊D6111yescharacteristic
301C42—21no—
302C42C22×D6111yescharacteristic
303C23—21no—
304C23—1221no—
305C23—1221no—
306C23—4881no—
307C23—2442no—
308C23—2442no—
309C23C2×C22⋊D6111yescharacteristic
310C23C2×C22⋊D6111yescharacteristic
311Q8—1221no—
312Q8—1221no—
313D4—21no—
314D4—21no—
315D4—41no—
316D4—42no—
317D4—81no—
318D4—612no—
319D4—1221no—
320D4—1221no—
321D4—1221no—
322D4—4881no—
323D4—2442no—
324D4—2442no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4C2×C22⋊D6111yescharacteristic
339C2×C4C2×C22⋊D6111yescharacteristic
340C2×C4C2×C22⋊D6111yescharacteristic
341C2×C4C2×C22⋊D6111yescharacteristic
342C2×C4C23×D6111yescharacteristic
343C8—1221no—
344C8—1221no—
345C8—1221no—
346C8—1221no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—1222no—
357C22—4884no—
358C22—2441no—
359C22—2441no—
360C22—2441no—
361C22—2441no—
362C22—2441no—
363C22C22×C22⋊D6111yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—2441no—
372C4—2441no—
373C4#41×D6111yescharacteristic
374C4#1451982311yescharacteristic
375C2—41no—
376C2—41no—
377C2—81no—
378C2—4881no—
379C2—2442no—
380C2#1684040011yescharacteristic
381C2#1684056011yescharacteristic
382C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#553C2
socleC22×C61C22×D4
hypercenter#553D61
hypocenterC61#3322
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #16840408C2semidirect
2. #16840119C2semidirect
3. #16840103C2semidirect
4. #16840075C2semidirect
5. #16840059C2semidirect
6. #16840013C2semidirect
7. #16840006C2semidirect
8. #16839977C2semidirect
9. #16839905C2semidirect
10. #16839895C2semidirect
11. C4×#11758199C2semidirect
12. #16839840C2semidirect
13. #16839766C2semidirect
14. #16839761C2semidirect
15. C61×#553C2semidirect
18. C2×#11758200C22semidirect
22. C2×#11758194C22semidirect
31. #14519710C22semidirect
32. #14519710C22semidirect
33. #14519708C22semidirect
34. C4⋊#92418C22semidirect
35. #14519700C22semidirect
36. #14519700C22semidirect
37. #14519700C22semidirect
38. #14519698C22semidirect
46. C22⋊#92418C22semidirect
47. C4×#92418C22semidirect
49. #125×C61C22semidirect
53. #121×C61C22semidirect
56. C4×D4×C61C22semidirect
58. C2×C4⋊C4×C61C22semidirect
192. #553D61semidirect
207. C61#3322semidirect
216. #125C2×D61semidirect
225. #121C2×D61semidirect
230. C4×D4C2×D61semidirect
232. C2×C4⋊C4C2×D61semidirect