Finite Group Databasebeta

← #21436222

Subgroups — #21436222

Order 7552.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838092C211yesmaximal, characteristic, complemented
2#16837766C211yesmaximal, characteristic, complemented
3#16837723C211yesmaximal, characteristic, complemented
4#16837718C211yesmaximal, characteristic, complemented
5#16837709C211yesmaximal, characteristic, complemented
6#16837646C211yesmaximal, characteristic, complemented
7#16837629C211yesmaximal, characteristic, complemented
8#16837599C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837564C211yesmaximal, characteristic, complemented
11#16837507C211yesmaximal, characteristic, complemented
12#16837474C211yesmaximal, characteristic, complemented
13#16837403C211yesmaximal, characteristic, complemented
14#16837398C211yesmaximal, characteristic, complemented
15C59×#550C211yesmaximal, characteristic
16C2×#11745672C2211yescharacteristic
17C2×#11745670C2211yescharacteristic
18C2×#11745670C2211yescharacteristic
19C2×#11745664C2211yescharacteristic
20C22×C59⋊C8C2211yescharacteristic
21#14273720—21no—
22#14273719C2211yescharacteristic
23#14273717—21no—
24#14273708—21no—
25#14273706C2211yescharacteristic
26#14273706C2211yescharacteristic
27C4×Dic118C2211yescharacteristic
28#14273686C2211yescharacteristic
29#14273683—21no—
30C2×C4⋊Dic59C2211yescharacteristic
31#14273660C2211yescharacteristic
32#14273658C2211yescharacteristic
33#14273658C2211yescharacteristic
34C4⋊(C59⋊C8)C2211yescharacteristic
35#14273651C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273648C2211yescharacteristic
40#14273648C2211yescharacteristic
41#14273648C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44#14273648C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47#14273638C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C2×#41×C59C2211yescharacteristic
50#127×C59—21no—
51#127×C59C2211yescharacteristic
52#121×C59—21no—
53#121×C59—21no—
54#121×C59C2211yescharacteristic
55#121×C59C2211yescharacteristic
56C4×Q8×C59C2211yescharacteristic
57C4×D4×C59—21no—
58C4×D4×C59C2211yescharacteristic
59#41×C59—22no—
60#41×C59—22no—
61#41×C59—41no—
62#41×C59—41no—
63C2×Q8×C59C2311yescharacteristic
64C2×D4×C59—21no—
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—21no—
70C2×D4×C59D411yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C22×Dic59—21no—
78C2×Dic118C2311yescharacteristic
79C4⋊C4×C59—21no—
80C4⋊C4×C59D411yescharacteristic
81C4⋊C4×C59C2311yescharacteristic
82C22⋊C4×C59—21no—
83C22⋊C4×C59—21no—
84C22⋊C4×C59D411yescharacteristic
85C22⋊C4×C59D411yescharacteristic
86C42×C59—21no—
87C42×C59C2311yescharacteristic
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90C22⋊Dic59—21no—
91#11745672—22no—
92#11745670—41no—
93#11745670—41no—
94C4⋊Dic59—21no—
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97C4⋊Dic59C2311yescharacteristic
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103C4×Dic59—21no—
104C4×Dic59—21no—
105#11745664—41no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8C2311yescharacteristic
108C2×C59⋊C8C2311yescharacteristic
109C2×C59⋊C8C2311yescharacteristic
110C2×C59⋊C8C2311yescharacteristic
111C23×C59—21no—
112C23×C59—21no—
113C23×C59C2×D411yescharacteristic
114C23×C59C2×D411yescharacteristic
115Q8×C59—21no—
116Q8×C59#4112yes—
117D4×C59—21no—
118D4×C59—21no—
119D4×C59—21no—
120D4×C59—21no—
121D4×C59—41no—
122D4×C59—42no—
123D4×C59—42no—
124D4×C59—42no—
125D4×C59—81no—
126D4×C59—81no—
127D4×C59—81no—
128C2×C4×C59—21no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—42no—
135C2×C4×C59—42no—
136C2×C4×C59C2×D411yescharacteristic
137C2×C4×C59C2×D411yescharacteristic
138C2×C4×C59C2×D411yescharacteristic
139C2×C4×C59C2×D411yescharacteristic
140C2×C4×C59C2411yescharacteristic
141C2×Dic59—21no—
142C2×Dic59—21no—
143C2×Dic59—21no—
144C2×Dic59—21no—
145C2×Dic59—42no—
146Dic118—21no—
147Dic118—21no—
148C59⋊C8—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C59⋊C8—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—41no—
161C22×C59—41no—
162C22×C59—41no—
163C22×C59—41no—
164C22×C59C22×D411yescharacteristic
165C4×C59—21no—
166C4×C59—21no—
167C4×C59—22no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—41no—
171C4×C59C2×#4111yescharacteristic
172C4×C59H(5,𝔽2)11yescharacteristic
173Dic59—41no—
174Dic59—41no—
175Dic59—41no—
176Dic59—41no—
177#3317—591nomaximal, Sylow
178C2×C59—41no—
179C2×C59—41no—
180C2×C59—81no—
181C2×C59—81no—
182C2×C59#54611yescharacteristic
183C2×C59#57511yescharacteristic
184C2×C59#57711yescharacteristic
185#552—591no—
186#550D5911yescharacteristic
187#490—591no—
188#482—591no—
189#481—591no—
190#479—591no—
191#468—591no—
192#465—591no—
193#460—591no—
194#452—591no—
195#452—591no—
196#441—591no—
197#435—591no—
198#417—591no—
199#416—591no—
200C59#331711yescharacteristic, complemented, Sylow
201C2×#41C2×D5911yescharacteristic
202C2×#41C2×D5911yescharacteristic
203C2×Q16—591no—
204C2×SD16—591no—
205C2×SD16—591no—
206C2×M16—591no—
207C22×C8—591no—
208#127—21no—
209#127C2×D5911yescharacteristic
210#126—1181no—
211#125—591no—
212#125—1181no—
213#123—1181no—
214C22⋊Q8—591no—
215C22⋊Q8—591no—
216#121—21no—
217#121—21no—
218#121C2×D5911yescharacteristic
219#121C2×D5911yescharacteristic
220C4×Q8—591no—
221C4×Q8C2×D5911yescharacteristic
222C4×D4—21no—
223C4×D4C2×D5911yescharacteristic
224#117—591no—
225#117—1181no—
226C2×C4⋊C4—591no—
227#107—591no—
228#106—591no—
229#106—591no—
230C4⋊C8—591no—
231#103—591no—
232#103—591no—
233#103—591no—
234#103—591no—
235#102—591no—
236#102—591no—
237#102—591no—
238#102—591no—
239#102—591no—
240#102—591no—
241C22⋊C8—591no—
242C22⋊C8—591no—
243#97—591no—
244#41—22no—
245#41—22no—
246#41—41no—
247#41—41no—
248C2×Q8—591no—
249C2×Q8C22×D5911yescharacteristic
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4C22⋊D5911yescharacteristic
257C2×D4C22×D5911yescharacteristic
258C2×D4C22×D5911yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—1181no—
262C22×C4C22×D5911yescharacteristic
263C22×C4C22×D5911yescharacteristic
264Q16—1182no—
265SD16—2361no—
266SD16—2361no—
267M16—2361no—
268C2×C8—591no—
269C2×C8—591no—
270C2×C8—591no—
271C2×C8—591no—
272C2×C8—2361no—
273C4⋊C4—21no—
274C4⋊C4—591no—
275C4⋊C4—591no—
276C4⋊C4—591no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4—1181no—
280C4⋊C4—1181no—
281C4⋊C4—1181no—
282C4⋊C4—1181no—
283C4⋊C4C22⋊D5911yescharacteristic
284C4⋊C4C22×D5911yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C22⋊C4—1181no—
290C22⋊C4C22⋊D5911yescharacteristic
291C22⋊C4C22⋊D5911yescharacteristic
292C42—21no—
293C42—1181no—
294C42—1181no—
295C42C22×D5911yescharacteristic
296C23—21no—
297C23—21no—
298C23C2×C22⋊D5911yescharacteristic
299C23C2×C22⋊D5911yescharacteristic
300Q8—21no—
301Q8—1181no—
302Q8—1181no—
303Q8#1174568712yes—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—41no—
309D4—42no—
310D4—42no—
311D4—42no—
312D4—81no—
313D4—81no—
314D4—81no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—1181no—
324C2×C4—1181no—
325C2×C4—1181no—
326C2×C4—1181no—
327C2×C4—2362no—
328C2×C4C2×C22⋊D5911yescharacteristic
329C2×C4C2×C22⋊D5911yescharacteristic
330C2×C4C2×C22⋊D5911yescharacteristic
331C2×C4C2×C22⋊D5911yescharacteristic
332C2×C4C23×D5911yescharacteristic
333C8—1181no—
334C8—1181no—
335C8—1181no—
336C8—1181no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22C22×C22⋊D5911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—41no—
356C4—2361no—
357C4—2361no—
358C4—2361no—
359C4—2361no—
360C4C2×#1174568711yescharacteristic
361C4#1427377211yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—81no—
366C2#1683804611yescharacteristic
367C2#1683820011yescharacteristic
368C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#550C2
socleC22×C59C22×D4
hypercenter#550D59
hypocenterC59#3317
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #16838092C2semidirect
2. #16837766C2semidirect
3. #16837723C2semidirect
4. #16837718C2semidirect
5. #16837709C2semidirect
6. #16837646C2semidirect
7. #16837629C2semidirect
8. #16837599C2semidirect
9. #16837564C2semidirect
10. #16837564C2semidirect
11. #16837507C2semidirect
12. #16837474C2semidirect
13. #16837403C2semidirect
14. #16837398C2semidirect
200. C59#3317semidirect