Finite Group Databasebeta

← #21436104

Subgroups — #21436104

Order 7552.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838098C211yesmaximal, characteristic, complemented
2#16838073C211yesmaximal, characteristic, complemented
3#16837767C211yesmaximal, characteristic, complemented
4#16837727C211yesmaximal, characteristic, complemented
5#16837716C211yesmaximal, characteristic, complemented
6#16837710C211yesmaximal, characteristic, complemented
7#16837655C211yesmaximal, characteristic, complemented
8#16837638C211yesmaximal, characteristic, complemented
9#16837598C211yesmaximal, characteristic, complemented
10#16837549C211yesmaximal, characteristic, complemented
11#16837549C211yesmaximal, characteristic, complemented
12#16837504C211yesmaximal, characteristic, complemented
13#16837404C211yesmaximal, characteristic, complemented
14#16837399C211yesmaximal, characteristic, complemented
15C59×#435C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745685C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×D472C2211yescharacteristic
20C2×D472C2211yescharacteristic
21#14273724C2211yescharacteristic
22#14273723—21no—
23#14273722—21no—
24#14273719C2211yescharacteristic
25#14273709—21no—
26#14273701C2211yescharacteristic
27#14273701C2211yescharacteristic
28#14273701C2211yescharacteristic
29#14273701C2211yescharacteristic
30#14273700—21no—
31#14273700—21no—
32#14273699—21no—
33C4×Dic118C2211yescharacteristic
34C4×D236C2211yescharacteristic
35#14273689—21no—
36(C22⋊D59)⋊C4—21no—
37#14273686C2211yescharacteristic
38C2×C4⋊Dic59C2211yescharacteristic
39#14273661C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273649C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273649C2211yescharacteristic
50#14273649C2211yescharacteristic
51#14273649C2211yescharacteristic
52C2×M16×C59C2211yescharacteristic
53C22×C8×C59C2211yescharacteristic
54C4×D4×C59C2211yescharacteristic
55C4⋊C8×C59C2211yescharacteristic
56C22⋊C8×C59C2211yescharacteristic
57C22⋊C8×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×D4×C59D411yescharacteristic
60C22×C4×C59C2311yescharacteristic
61C22×C4×C59C2311yescharacteristic
62C2×C22⋊D59—21no—
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59—21no—
66C2×C22⋊D59—21no—
67C2×C22⋊D59—21no—
68C22×Dic59—21no—
69#11745685—22no—
70#11745685—22no—
71#11745685—41no—
72#11745685—41no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236C2311yescharacteristic
76C2×D236C2311yescharacteristic
77C2×D236C2311yescharacteristic
78C2×C4×D59—21no—
79C2×C4×D59—21no—
80C2×C4×D59—21no—
81C2×Dic118C2311yescharacteristic
82M16×C59—41no—
83C2×C8×C59—41no—
84C2×C8×C59C2311yescharacteristic
85C2×C8×C59C2311yescharacteristic
86C2×C8×C59C2311yescharacteristic
87C2×C8×C59C2311yescharacteristic
88C4⋊C4×C59D411yescharacteristic
89C22⋊C4×C59D411yescharacteristic
90C22⋊C4×C59D411yescharacteristic
91C42×C59C2311yescharacteristic
92C22⋊Dic59—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4—21no—
97(C2×D59)⋊C4—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59C2311yescharacteristic
100C4⋊Dic59C2311yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106C4×Dic59—21no—
107C4×Dic59—21no—
108D472—41no—
109D472—41no—
110#11745660—22no—
111C23×C59C2×D411yescharacteristic
112C23×C59C2×D411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—21no—
116D4×C59—41no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2411yescharacteristic
126C22⋊D59—42no—
127C22⋊D59—42no—
128C22⋊D59—42no—
129C22⋊D59—81no—
130C22⋊D59—81no—
131C22⋊D59—81no—
132C2×Dic59—21no—
133C2×Dic59—21no—
134C2×Dic59—21no—
135C2×Dic59—21no—
136C2×Dic59—21no—
137C2×Dic59—81no—
138D236—21no—
139D236—21no—
140D236—21no—
141D236—21no—
142D236—21no—
143D236—21no—
144D236—42no—
145D236—81no—
146C4×D59—42no—
147C4×D59—42no—
148C4×D59—81no—
149Dic118—21no—
150Dic118#4112yes—
151C8×C59—21no—
152C8×C59—21no—
153C8×C59—21no—
154C8×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59C22×D411yescharacteristic
162C2×D59—41no—
163C2×D59—41no—
164C2×D59—41no—
165C2×D59—41no—
166C2×D59—41no—
167C2×D59—41no—
168C2×D59—41no—
169C2×D59—41no—
170C2×D59—41no—
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—21no—
175C4×C59C2×#4111yescharacteristic
176C4×C59H(5,𝔽2)11yescharacteristic
177Dic59—22no—
178Dic59—41no—
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182#3309—591nomaximal, Sylow
183C2×C59—41no—
184C2×C59—41no—
185C2×C59#54611yescharacteristic
186C2×C59#57511yescharacteristic
187C2×C59#57611yescharacteristic
188D59—81no—
189D59—81no—
190D59—81no—
191#553—591no—
192#550—591no—
193#490—591no—
194#482—591no—
195#480—591no—
196#479—591no—
197#469—591no—
198#466—591no—
199#459—591no—
200#449—591no—
201#449—591no—
202#440—591no—
203#435D5911yescharacteristic, complemented
204#417—591no—
205#416—591no—
206C59#330911yescharacteristic, complemented, Sylow
207C2×#41—591no—
208C2×#41—591no—
209C2×SD16—591no—
210C2×D8—591no—
211C2×D8—591no—
212C2×M16C2×D5911yescharacteristic
213C22×C8C2×D5911yescharacteristic
214#127—591no—
215#127—1181no—
216#126—1181no—
217#125—591no—
218#123—1181no—
219#121—591no—
220#121—591no—
221#121—591no—
222#121—591no—
223#121—1181no—
224#121—1181no—
225#121—1181no—
226C4×Q8—591no—
227C4×D4—591no—
228C4×D4—1181no—
229C4×D4—1181no—
230C4×D4C2×D5911yescharacteristic
231#117—591no—
232C2×C4⋊C4—591no—
233#107—591no—
234#107—591no—
235#106—591no—
236C4⋊C8C2×D5911yescharacteristic
237#103—591no—
238#103—591no—
239#103—591no—
240#102—591no—
241#102—591no—
242#102—591no—
243#102—591no—
244#102—591no—
245#102—591no—
246#102—591no—
247C22⋊C8C2×D5911yescharacteristic
248C22⋊C8C2×D5911yescharacteristic
249#97C2×D5911yescharacteristic
250#41—1182no—
251#41—1182no—
252#41—2361no—
253#41—2361no—
254C2×Q8—591no—
255C2×D4—591no—
256C2×D4—591no—
257C2×D4—591no—
258C2×D4—1181no—
259C2×D4—1181no—
260C2×D4—1181no—
261C2×D4—1181no—
262C2×D4—1181no—
263C2×D4—1181no—
264C2×D4—1181no—
265C2×D4—1181no—
266C2×D4D23611yescharacteristic
267C22×C4—1181no—
268C22×C4—1181no—
269C22×C4—1181no—
270C22×C4—1181no—
271C22×C4C22×D5911yescharacteristic
272C22×C4C22×D5911yescharacteristic
273SD16—1182no—
274D8—2361no—
275D8—2361no—
276M16—41no—
277C2×C8—41no—
278C2×C8C22×D5911yescharacteristic
279C2×C8C22×D5911yescharacteristic
280C2×C8C22×D5911yescharacteristic
281C2×C8C22×D5911yescharacteristic
282C4⋊C4—591no—
283C4⋊C4—591no—
284C4⋊C4—591no—
285C4⋊C4—591no—
286C4⋊C4—1181no—
287C4⋊C4—1181no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C4⋊C4D23611yescharacteristic
291C22⋊C4—1181no—
292C22⋊C4—1181no—
293C22⋊C4—1181no—
294C22⋊C4—1181no—
295C22⋊C4—1181no—
296C22⋊C4—1181no—
297C22⋊C4D23611yescharacteristic
298C22⋊C4D23611yescharacteristic
299C42—1181no—
300C42—1181no—
301C42C22×D5911yescharacteristic
302C23—1181no—
303C23—1181no—
304C23—1181no—
305C23C2×D23611yescharacteristic
306C23C2×D23611yescharacteristic
307Q8—592no—
308Q8—1181no—
309D4—41no—
310D4—1181no—
311D4—1181no—
312D4—1181no—
313D4—1181no—
314D4—1181no—
315D4—1181no—
316D4—4721no—
317D4—4721no—
318D4—4721no—
319D4—4721no—
320D4—2362no—
321D4—2362no—
322D4—2362no—
323D4—2362no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—1181no—
329C2×C4—1181no—
330C2×C4—1181no—
331C2×C4—1181no—
332C2×C4—1181no—
333C2×C4—4721no—
334C2×C4—4721no—
335C2×C4—2362no—
336C2×C4—2362no—
337C2×C4C2×D23611yescharacteristic
338C2×C4C2×D23611yescharacteristic
339C2×C4C2×D23611yescharacteristic
340C2×C4C2×D23611yescharacteristic
341C2×C4C23×D5911yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—2361no—
353C22—2361no—
354C22—2361no—
355C22—2361no—
356C22—2361no—
357C22—2361no—
358C22—2361no—
359C22—2361no—
360C22—2361no—
361C22C22×D23611yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—1182no—
367C4—2361no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4#41×D5911yescharacteristic
372C4#1427377211yescharacteristic
373C2—41no—
374C2—41no—
375C2—4721no—
376C2—4721no—
377C2—4721no—
378C2#1683804711yescharacteristic
379C2#1683820211yescharacteristic
380C2#1683820711yescharacteristic
subgroupG/H
centerC22C22×D236
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#435C2
socleC22×C59C22×D4
hypercenter#435D59
hypocenterC59#3309
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #16838098C2semidirect
2. #16838073C2semidirect
3. #16837767C2semidirect
4. #16837727C2semidirect
5. #16837716C2semidirect
6. #16837710C2semidirect
7. #16837655C2semidirect
8. #16837638C2semidirect
9. #16837598C2semidirect
10. #16837549C2semidirect
11. #16837549C2semidirect
12. #16837504C2semidirect
13. #16837404C2semidirect
14. #16837399C2semidirect
15. C59×#435C2semidirect
203. #435D59semidirect
206. C59#3309semidirect