Finite Group Databasebeta

← #21436302

Subgroups — #21436302

Order 7552.

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#16838102C211yesmaximal, characteristic, complemented
2#16838047C211yesmaximal, characteristic, complemented
3#16837757C211yesmaximal, characteristic, complemented
4#16837745C211yesmaximal, characteristic, complemented
5#16837717C211yesmaximal, characteristic, complemented
6#16837702C211yesmaximal, characteristic, complemented
7#16837654C211yesmaximal, characteristic, complemented
8#16837647C211yesmaximal, characteristic, complemented
9#16837617C211yesmaximal, characteristic, complemented
10#16837544C211yesmaximal, characteristic, complemented
11#16837534C211yesmaximal, characteristic, complemented
12#16837481C211yesmaximal, characteristic, complemented
13#16837405C211yesmaximal, characteristic, complemented
14#16837400C211yesmaximal, characteristic, complemented
15C4×D8×C59C211yesmaximal, characteristic, complemented
16C2×#11745687C2211yescharacteristic
17C2×D4×D59C2211yescharacteristic
18C2×#11745670C2211yescharacteristic, complemented
19C2×#11745669C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×#11745659C2211yescharacteristic, complemented
22#14273720—21no—
23#14273719C2211yescharacteristic, complemented
24#14273715C2211yescharacteristic
25#14273711—21no—
26#14273710—21no—
27#14273707C2211yescharacteristic
28#14273702C2211yescharacteristic
29#14273701—21no—
30#14273700—21no—
31#14273698C2211yescharacteristic
32#14273698C2211yescharacteristic, complemented
33#14273697—21no—
34C4×D236C2211yescharacteristic
35C4×C22⋊D59—21no—
36#14273685C2211yescharacteristic
37C4⋊C4×D59C2211yescharacteristic, complemented
38C2×(C2×D59)⋊C4—21no—
39#14273660C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273652C2211yescharacteristic, complemented
43#14273652C2211yescharacteristic, complemented
44#14273650C2211yescharacteristic, complemented
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic, complemented
52C2×D8×C59C2211yescharacteristic
53C4×D4×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic, complemented
55#107×C59C2211yescharacteristic, complemented
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic, complemented
58C4×C8×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×D4×C59C2311yescharacteristic
61C2×D4×C59C2311yescharacteristic
62C22×C4×C59—21no—
63C22×C4×C59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C22×Dic59—21no—
69#11745687—22no—
70#11745687—41no—
71D4×D59—22no—
72D4×D59—41no—
73C2×D236—21no—
74C2×D236D411yescharacteristic
75C2×D236C2311yescharacteristic
76C2×C4×D59—21no—
77C2×C4×D59C2311yescharacteristic
78C2×C4×D59C2311yescharacteristic
79C2×Dic118C2311yescharacteristic
80D8×C59—22no—
81C2×C8×C59C2311yescharacteristic
82C2×C8×C59C2311yescharacteristic
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C22⋊C4×C59—21no—
86C22⋊C4×C59—21no—
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90#11745670—41no—
91#11745669—41no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4D411yescharacteristic
98(C2×D59)⋊C4D411yescharacteristic
99C4⋊Dic59—21no—
100C4⋊Dic59D411yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745659—41no—
110#11745659—41no—
111C23×C59—21no—
112C23×C59—21no—
113C22×D59—21no—
114C22×D59—42no—
115C22×D59—42no—
116C22×D59—81no—
117C22×D59C2×D411yescharacteristic
118C22×D59C2×D411yescharacteristic
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—21no—
122D4×C59#4112yes—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—81no—
126C2×C4×C59—81no—
127C2×C4×C59C2×D411yescharacteristic
128C2×C4×C59C2×D411yescharacteristic
129C2×C4×C59C2411yescharacteristic
130C22⋊D59—42no—
131C22⋊D59—42no—
132C22⋊D59—42no—
133C22⋊D59—81no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—42no—
138C2×Dic59C2×D411yescharacteristic
139C2×Dic59C2×D411yescharacteristic
140D236—21no—
141D236—21no—
142D236—41no—
143D236—81no—
144C4×D59—21no—
145C4×D59—21no—
146C4×D59—21no—
147C4×D59—21no—
148C4×D59—81no—
149Dic118—21no—
150Dic118—21no—
151C8×C59—21no—
152C8×C59—21no—
153C59⋊C8—21no—
154C59⋊C8—21no—
155C22×C59—22no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59C22×D411yescharacteristic
162C2×D59—21no—
163C2×D59—21no—
164C2×D59—21no—
165C2×D59—21no—
166C2×D59—21no—
167C2×D59—21no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C2×D59—84no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59C2×#4111yescharacteristic
177C4×C59H(5,𝔽2)11yescharacteristic
178Dic59—21no—
179Dic59—21no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3322—591nomaximal, Sylow
184C2×C59—42no—
185C2×C59—81no—
186C2×C59#54611yescharacteristic
187C2×C59#57511yescharacteristic
188C2×C59#57611yescharacteristic
189D59—41no—
190D59—41no—
191D59—81no—
192#553—591no—
193#546—591no—
194#488—591no—
195#485—591no—
196#480—591no—
197#478—591no—
198#469—591no—
199#468—591no—
200#463—591no—
201#449—591no—
202#447—591no—
203C4×D8D5911yescharacteristic, complemented
204#436—591no—
205#418—591no—
206#417—591no—
207C59#332211yescharacteristic, complemented, Sylow
208C2×#41—591no—
209C22×D4—591no—
210C2×SD16—591no—
211C2×D8—591no—
212C2×D8C2×D5911yescharacteristic
213C2×M16—591no—
214C2×M16—591no—
215#126—1181no—
216#125—591no—
217#124—591no—
218#123—1181no—
219#123—1181no—
220C22⋊Q8—591no—
221#121—591no—
222#121—591no—
223#121—591no—
224#121—1181no—
225#121—1181no—
226#120—1181no—
227C4×D4—591no—
228C4×D4—1181no—
229C4×D4C2×D5911yescharacteristic
230C4×D4C2×D5911yescharacteristic, complemented
231#117—591no—
232C2×C4⋊C4—591no—
233C2×C22⋊C4—1181no—
234#107—591no—
235#107C2×D5911yescharacteristic, complemented
236#106—591no—
237C4⋊C8—591no—
238#103—591no—
239#103—591no—
240#103—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102C2×D5911yescharacteristic
247#102C2×D5911yescharacteristic, complemented
248C22⋊C8—591no—
249C22⋊C8—591no—
250C4×C8C2×D5911yescharacteristic, complemented
251C24—1181no—
252#41—1182no—
253#41—2361no—
254C2×Q8—591no—
255C2×D4—591no—
256C2×D4—591no—
257C2×D4—1181no—
258C2×D4—1181no—
259C2×D4—1182no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—2361no—
264C2×D4C22×D5911yescharacteristic
265C2×D4C22×D5911yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—591no—
269C22×C4—591no—
270C22×C4—1181no—
271C22×C4—1181no—
272SD16—2361no—
273D8—22no—
274D8—2361no—
275M16—2361no—
276M16—2361no—
277C2×C8—591no—
278C2×C8—591no—
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C4⋊C4—591no—
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—1181no—
285C4⋊C4—1181no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4C22×D5911yescharacteristic
289C4⋊C4C22×D5911yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—591no—
293C22⋊C4—591no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4—1181no—
298C22⋊C4—1181no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C42—1181no—
302C42C22×D5911yescharacteristic
303C23—21no—
304C23—21no—
305C23—591no—
306C23—591no—
307C23—1181no—
308C23—4721no—
309C23—2362no—
310C23—2362no—
311Q8—1181no—
312Q8—1181no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—1181no—
317D4—1181no—
318D4—4721no—
319D4—4721no—
320D4—2361no—
321D4—2362no—
322D4—2362no—
323D4—2362no—
324D4#1174568512yes—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—591no—
330C2×C4—591no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—1181no—
334C2×C4—1181no—
335C2×C4—1181no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—4721no—
339C2×C4—2362no—
340C2×C4D4×D5911yescharacteristic
341C2×C4D4×D5911yescharacteristic
342C2×C4C23×D5911yescharacteristic
343C8—21no—
344C8—21no—
345C8—1181no—
346C8—1181no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—1181no—
354C22—1181no—
355C22—1181no—
356C22—1181no—
357C22—1181no—
358C22—1181no—
359C22—4724no—
360C22—2361no—
361C22—2361no—
362C22—2361no—
363C22C2×D4×D5911yescharacteristic
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—1181no—
369C4—1181no—
370C4—2361no—
371C4—2361no—
372C4—2361no—
373C4C2×#1174568511yescharacteristic
374C4#1427377311yescharacteristic
375C2—42no—
376C2—81no—
377C2—4721no—
378C2—2361no—
379C2—2361no—
380C2#1683804811yescharacteristic
381C2#1683819911yescharacteristic
382C2#1683820311yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC4×D8×C59C2
socleC22×C59C22×D4
hypercenterC4×D8D59
hypocenterC59#3322
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #16838102C2semidirect
2. #16838047C2semidirect
3. #16837757C2semidirect
4. #16837745C2semidirect
5. #16837717C2semidirect
6. #16837702C2semidirect
7. #16837654C2semidirect
8. #16837647C2semidirect
9. #16837617C2semidirect
10. #16837544C2semidirect
11. #16837534C2semidirect
12. #16837481C2semidirect
13. #16837405C2semidirect
14. #16837400C2semidirect
15. C4×D8×C59C2semidirect
18. C2×#11745670C22semidirect
21. C2×#11745659C22semidirect
23. #14273719C22semidirect
32. #14273698C22semidirect
37. C4⋊C4×D59C22semidirect
39. #14273660C22semidirect
40. #14273658C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273652C22semidirect
43. #14273652C22semidirect
44. #14273650C22semidirect
51. (C2×D59)⋊C8C22semidirect
54. C4×D4×C59C22semidirect
55. #107×C59C22semidirect
57. #102×C59C22semidirect
58. C4×C8×C59C22semidirect
203. C4×D8D59semidirect
207. C59#3322semidirect
230. C4×D4C2×D59semidirect
235. #107C2×D59semidirect
247. #102C2×D59semidirect
250. C4×C8C2×D59semidirect