Finite Group Databasebeta

← #21436167

Subgroups — #21436167

Order 7552.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838125C211yesmaximal, characteristic, complemented
2#16838064C211yesmaximal, characteristic
3#16837762C211yesmaximal, characteristic, complemented
4#16837746C211yesmaximal, characteristic, complemented
5#16837728C211yesmaximal, characteristic, complemented
6#16837697C211yesmaximal, characteristic, complemented
7#16837651C211yesmaximal, characteristic, complemented
8#16837642C211yesmaximal, characteristic, complemented
9#16837624C211yesmaximal, characteristic, complemented
10#16837563C211yesmaximal, characteristic, complemented
11#16837556C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837409C211yesmaximal, characteristic, complemented
14#16837397C211yesmaximal, characteristic, complemented
15C59×#441C211yesmaximal, characteristic, complemented
16C2×#11745689C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745659C2211yescharacteristic
21C2×C8×D59C2211yescharacteristic
22#14273727C2211yescharacteristic
23#14273722—21no—
24#14273722—21no—
25#14273715—21no—
26#14273715—21no—
27#14273715C2211yescharacteristic
28#14273707—21no—
29#14273707C2211yescharacteristic
30#14273703C2211yescharacteristic
31#14273703C2211yescharacteristic
32#14273702—21no—
33#14273702C2211yescharacteristic
34C4×Dic118—21no—
35C4×D236—21no—
36C4×D236C2211yescharacteristic
37#14273685C2211yescharacteristic
38#14273685C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273660C2211yescharacteristic
41C4⋊(C59⋊C8)C2211yescharacteristic
42#14273652C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273651C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273649C2211yescharacteristic
48#14273649C2211yescharacteristic
49#14273647C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C2×Q16×C59C2211yescharacteristic
53C4×Q8×C59C2211yescharacteristic
54C4×Q8×C59C2211yescharacteristic
55#106×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61#11745689—22no—
62#11745689—41no—
63Q8×D59—22no—
64Q8×D59—41no—
65C2×D236—21no—
66C2×D236—21no—
67C2×D236D411yescharacteristic
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59C2311yescharacteristic
72C2×C4×D59C2311yescharacteristic
73C2×Dic118—21no—
74C2×Dic118—21no—
75C2×Dic118C2311yescharacteristic
76Q16×C59—22no—
77C2×C8×C59C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59C2311yescharacteristic
82C4⋊C4×C59C2311yescharacteristic
83C42×C59—21no—
84C42×C59—21no—
85C42×C59C2311yescharacteristic
86#11745672—41no—
87#11745671—41no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93(C2×D59)⋊C4—21no—
94(C2×D59)⋊C4—21no—
95(C2×D59)⋊C4—21no—
96(C2×D59)⋊C4D411yescharacteristic
97(C2×D59)⋊C4D411yescharacteristic
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59D411yescharacteristic
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105C4×Dic59—21no—
106C4×Dic59—21no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109#11745659—41no—
110C8×D59—41no—
111C22×D59—21no—
112C22×D59C2×D411yescharacteristic
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59#4112yes—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59C2×D411yescharacteristic
123C2×C4×C59C2×D411yescharacteristic
124C2×C4×C59C2411yescharacteristic
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59C2×D411yescharacteristic
129C2×Dic59C2×D411yescharacteristic
130D236—21no—
131D236—21no—
132D236—41no—
133D236—42no—
134D236—42no—
135C4×D59—21no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—21no—
139C4×D59—42no—
140C4×D59—42no—
141Dic118—21no—
142Dic118—21no—
143Dic118—42no—
144Dic118—42no—
145C8×C59—21no—
146C8×C59—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C22×C59C22×D411yescharacteristic
150C2×D59—21no—
151C2×D59—21no—
152C2×D59—21no—
153C2×D59—21no—
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—41no—
157C2×D59—41no—
158C2×D59—41no—
159C4×C59—22no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—41no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59C2×#4111yescharacteristic
166C4×C59H(5,𝔽2)11yescharacteristic
167Dic59—21no—
168Dic59—21no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172#3313—591nomaximal, Sylow
173C2×C59#54611yescharacteristic
174C2×C59#57511yescharacteristic
175C2×C59#57811yescharacteristic
176D59—41no—
177D59—41no—
178D59—81no—
179#556—591no—
180#548—591no—
181#489—591no—
182#485—591no—
183#482—591no—
184#477—591no—
185#468—591no—
186#467—591no—
187#464—591no—
188#452—591no—
189#451—591no—
190#441D5911yescharacteristic, complemented
191#435—591no—
192#419—591no—
193#416—591no—
194C59#331311yescharacteristic, complemented, Sylow
195C2×#41—591no—
196C22×Q8—591no—
197C2×Q16—591no—
198C2×Q16C2×D5911yescharacteristic
199C2×SD16—591no—
200C2×M16—591no—
201C22×C8—591no—
202C4⋊Q8—591no—
203#126—1181no—
204#126—1181no—
205#124—591no—
206#124—1181no—
207#124—1181no—
208C22⋊Q8—591no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212#121—591no—
213#121—1181no—
214C4×Q8—1181no—
215C4×Q8C2×D5911yescharacteristic
216C4×Q8C2×D5911yescharacteristic
217C4×D4—591no—
218C4×D4—1181no—
219#117—591no—
220#117—591no—
221#107—591no—
222#107—591no—
223#106C2×D5911yescharacteristic
224C4⋊C8—591no—
225#103—591no—
226#103—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103C2×D5911yescharacteristic
231#103C2×D5911yescharacteristic
232#102—591no—
233#102—591no—
234#102—591no—
235C22⋊C8—591no—
236C22⋊C8—591no—
237#97C2×D5911yescharacteristic
238#41—1182no—
239#41—2361no—
240C2×Q8—591no—
241C2×Q8—1181no—
242C2×Q8—1181no—
243C2×Q8—1182no—
244C2×Q8—2361no—
245C2×Q8C22×D5911yescharacteristic
246C2×Q8C22×D5911yescharacteristic
247C2×D4—591no—
248C2×D4—591no—
249C2×D4—1181no—
250C2×D4—1181no—
251C22×C4—591no—
252C22×C4—591no—
253C22×C4—1181no—
254C22×C4—1181no—
255Q16—22no—
256Q16—2361no—
257SD16—2361no—
258M16—2361no—
259C2×C8—591no—
260C2×C8—591no—
261C2×C8—2361no—
262C2×C8C22×D5911yescharacteristic
263C2×C8C22×D5911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—591no—
267C4⋊C4—591no—
268C4⋊C4—591no—
269C4⋊C4—1181no—
270C4⋊C4—1181no—
271C4⋊C4—1181no—
272C4⋊C4—1181no—
273C4⋊C4C22×D5911yescharacteristic
274C4⋊C4C22×D5911yescharacteristic
275C22⋊C4—591no—
276C22⋊C4—591no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C22⋊C4—1181no—
280C22⋊C4—1181no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C42—21no—
286C42—21no—
287C42—1181no—
288C42—1181no—
289C42C22×D5911yescharacteristic
290C23—591no—
291C23—591no—
292C23—1181no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—1181no—
297Q8—1181no—
298Q8—2362no—
299Q8—2362no—
300Q8#1174568512yes—
301D4—1181no—
302D4—1181no—
303D4—2361no—
304D4—2362no—
305D4—2362no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—591no—
311C2×C4—591no—
312C2×C4—1181no—
313C2×C4—1181no—
314C2×C4—1181no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—2362no—
320C2×C4—2362no—
321C2×C4D4×D5911yescharacteristic
322C2×C4D4×D5911yescharacteristic
323C2×C4C23×D5911yescharacteristic
324C8—21no—
325C8—21no—
326C8—1181no—
327C8—1181no—
328C22—1181no—
329C22—1181no—
330C22—1181no—
331C22—1181no—
332C22—1181no—
333C22—1181no—
334C22—2361no—
335C22—2361no—
336C22—2361no—
337C22C2×D4×D5911yescharacteristic
338C4—21no—
339C4—21no—
340C4—22no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—1181no—
345C4—1181no—
346C4—2361no—
347C4—2361no—
348C4—2361no—
349C4C2×#1174568511yescharacteristic
350C4#1427377311yescharacteristic
351C2—4721no—
352C2—2361no—
353C2—2361no—
354C2#1683804811yescharacteristic
355C2#1683820111yescharacteristic
356C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#441C2
socleC22×C59C22×D4
hypercenter#441D59
hypocenterC59#3313
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #16838125C2semidirect
3. #16837762C2semidirect
4. #16837746C2semidirect
5. #16837728C2semidirect
6. #16837697C2semidirect
7. #16837651C2semidirect
8. #16837642C2semidirect
9. #16837624C2semidirect
10. #16837563C2semidirect
11. #16837556C2semidirect
12. #16837475C2semidirect
13. #16837409C2semidirect
14. #16837397C2semidirect
15. C59×#441C2semidirect
190. #441D59semidirect
194. C59#3313semidirect