Finite Group Databasebeta

← #21434972

Subgroups — #21434972

Order 7552.

390 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#16837973C211yesmaximal, characteristic, complemented
2#16837740C211yesmaximal, characteristic, complemented
3#16837737C211yesmaximal, characteristic, complemented
4#16837732C211yesmaximal, characteristic, complemented
5#16837723C211yesmaximal, characteristic, complemented
6#16837658C211yesmaximal, characteristic, complemented
7#16837646C211yesmaximal, characteristic, complemented
8#16837641C211yesmaximal, characteristic, complemented
9#16837629C211yesmaximal, characteristic, complemented
10#16837564C211yesmaximal, characteristic, complemented
11#16837564C211yesmaximal, characteristic, complemented
12#16837557C211yesmaximal, characteristic, complemented
13#16837540C211yesmaximal, characteristic, complemented
14#16837369C211yesmaximal, characteristic, complemented
15C59×#537C211yesmaximal, characteristic
16C22×Dic118C2211yescharacteristic
17C2×#11745672C2211yescharacteristic
18C2×#11745672C2211yescharacteristic
19C2×#11745670C2211yescharacteristic
20C2×#11745670C2211yescharacteristic
21C2×#11745664C2211yescharacteristic
22C22×C59⋊C8C2211yescharacteristic
23#14273725—21no—
24#14273714—21no—
25#14273708—21no—
26#14273708—21no—
27#14273706C2211yescharacteristic
28#14273706C2211yescharacteristic
29#14273706C2211yescharacteristic
30#14273706C2211yescharacteristic
31#14273686C2211yescharacteristic
32#14273660C2211yescharacteristic
33#14273660C2211yescharacteristic
34#14273658C2211yescharacteristic
35#14273658C2211yescharacteristic
36#14273651C2211yescharacteristic
37#14273651C2211yescharacteristic
38#14273650C2211yescharacteristic
39#14273650C2211yescharacteristic
40#14273650C2211yescharacteristic
41#14273650C2211yescharacteristic
42#14273648C2211yescharacteristic
43#14273648C2211yescharacteristic
44C22⋊(C59⋊C8)C2211yescharacteristic
45C22⋊(C59⋊C8)C2211yescharacteristic
46C22⋊(C59⋊C8)C2211yescharacteristic
47C22⋊(C59⋊C8)C2211yescharacteristic
48C2×#41×C59C2211yescharacteristic
49C2×#41×C59C2211yescharacteristic
50C22⋊Q8×C59—21no—
51C22⋊Q8×C59C2211yescharacteristic
52C22⋊Q8×C59C2211yescharacteristic
53#121×C59—21no—
54#121×C59—21no—
55#121×C59—21no—
56#121×C59C2211yescharacteristic
57#121×C59C2211yescharacteristic
58C2×C4⋊C4×C59C2211yescharacteristic
59#41×C59—41no—
60#41×C59—41no—
61#41×C59—41no—
62#41×C59—41no—
63C2×Q8×C59D411yescharacteristic
64C2×Q8×C59C2311yescharacteristic
65C2×D4×C59—21no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59D411yescharacteristic
69C2×D4×C59D411yescharacteristic
70C2×D4×C59D411yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59C2311yescharacteristic
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C22×Dic59—21no—
78C2×Dic118—21no—
79C2×Dic118—41no—
80C2×Dic118—41no—
81C2×Dic118C2311yescharacteristic
82C2×Dic118C2311yescharacteristic
83C4⋊C4×C59—21no—
84C4⋊C4×C59—21no—
85C4⋊C4×C59—21no—
86C4⋊C4×C59C2311yescharacteristic
87C4⋊C4×C59C2311yescharacteristic
88C22⋊C4×C59—21no—
89C22⋊C4×C59—21no—
90C22⋊C4×C59—21no—
91C22⋊C4×C59—21no—
92C22⋊Dic59—21no—
93C22⋊Dic59—21no—
94C22⋊Dic59—21no—
95C22⋊Dic59—21no—
96C22⋊Dic59—21no—
97#11745672—41no—
98#11745672—41no—
99#11745670—41no—
100#11745670—41no—
101C4⋊Dic59C2311yescharacteristic
102C4⋊Dic59C2311yescharacteristic
103Dic59⋊C4—21no—
104Dic59⋊C4—21no—
105Dic59⋊C4—21no—
106Dic59⋊C4—21no—
107C4×Dic59—21no—
108#11745664—41no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8C2311yescharacteristic
111C2×C59⋊C8C2311yescharacteristic
112C2×C59⋊C8C2311yescharacteristic
113C2×C59⋊C8C2311yescharacteristic
114C23×C59—21no—
115C23×C59C2×D411yescharacteristic
116C23×C59C2×D411yescharacteristic
117C23×C59C2×D411yescharacteristic
118Q8×C59—21no—
119Q8×C59—21no—
120Q8×C59—41no—
121D4×C59—21no—
122D4×C59—21no—
123D4×C59—41no—
124D4×C59—41no—
125D4×C59—41no—
126D4×C59—42no—
127D4×C59—81no—
128D4×C59—81no—
129C2×C4×C59—21no—
130C2×C4×C59—21no—
131C2×C4×C59—21no—
132C2×C4×C59—21no—
133C2×C4×C59—21no—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—42no—
139C2×C4×C59—81no—
140C2×C4×C59C2×D411yescharacteristic
141C2×C4×C59C2×D411yescharacteristic
142C2×C4×C59C2×D411yescharacteristic
143C2×C4×C59C2411yescharacteristic
144C2×Dic59—21no—
145C2×Dic59—21no—
146C2×Dic59—21no—
147C2×Dic59—21no—
148C2×Dic59—42no—
149Dic118—21no—
150Dic118—21no—
151Dic118—21no—
152Dic118—21no—
153Dic118—42no—
154C59⋊C8—21no—
155C59⋊C8—21no—
156C59⋊C8—21no—
157C59⋊C8—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—41no—
168C22×C59—41no—
169C22×C59—41no—
170C22×C59C22×D411yescharacteristic
171C4×C59—21no—
172C4×C59—21no—
173C4×C59—21no—
174C4×C59—41no—
175C4×C59—41no—
176C4×C59—41no—
177C4×C59H(5,𝔽2)11yescharacteristic
178C4×C59H(5,𝔽2)11yescharacteristic
179Dic59—41no—
180Dic59—41no—
181Dic59—41no—
182Dic59—41no—
183#3201—591nomaximal, Sylow
184C2×C59—41no—
185C2×C59—41no—
186C2×C59—41no—
187C2×C59—81no—
188C2×C59#53411yescharacteristic
189C2×C59#57711yescharacteristic
190C2×C59#57811yescharacteristic
191#537D5911yescharacteristic
192#536—591no—
193#485—591no—
194#484—591no—
195#483—591no—
196#482—591no—
197#470—591no—
198#468—591no—
199#467—591no—
200#465—591no—
201#452—591no—
202#452—591no—
203#451—591no—
204#448—591no—
205#408—591no—
206C59#320111yescharacteristic, complemented, Sylow
207C2×#41C2×D5911yescharacteristic
208C2×#41C2×D5911yescharacteristic
209C22×Q8—591no—
210C2×Q16—591no—
211C2×Q16—591no—
212C2×SD16—591no—
213C2×SD16—591no—
214C2×M16—591no—
215C22×C8—591no—
216C4⋊Q8—1181no—
217#124—1181no—
218#123—1181no—
219#123—1181no—
220C22⋊Q8—21no—
221C22⋊Q8—591no—
222C22⋊Q8—591no—
223C22⋊Q8—591no—
224C22⋊Q8—591no—
225C22⋊Q8C2×D5911yescharacteristic
226C22⋊Q8C2×D5911yescharacteristic
227#121—21no—
228#121—21no—
229#121—21no—
230#121C2×D5911yescharacteristic
231#121C2×D5911yescharacteristic
232#117—591no—
233C2×C4⋊C4C2×D5911yescharacteristic
234#107—591no—
235#107—591no—
236#106—591no—
237#106—591no—
238#103—591no—
239#103—591no—
240#103—591no—
241#103—591no—
242#103—591no—
243#103—591no—
244#102—591no—
245#102—591no—
246C22⋊C8—591no—
247C22⋊C8—591no—
248C22⋊C8—591no—
249C22⋊C8—591no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—591no—
255C2×Q8—591no—
256C2×Q8—1181no—
257C2×Q8—2361no—
258C2×Q8—2361no—
259C2×Q8C22⋊D5911yescharacteristic
260C2×Q8C22×D5911yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4C22⋊D5911yescharacteristic
265C2×D4C22⋊D5911yescharacteristic
266C2×D4C22⋊D5911yescharacteristic
267C2×D4C22×D5911yescharacteristic
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—1181no—
271C22×C4C22×D5911yescharacteristic
272C22×C4C22×D5911yescharacteristic
273C22×C4C22×D5911yescharacteristic
274Q16—2361no—
275Q16—2361no—
276SD16—2361no—
277SD16—2361no—
278M16—2361no—
279C2×C8—591no—
280C2×C8—591no—
281C2×C8—591no—
282C2×C8—591no—
283C2×C8—2361no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—591no—
288C4⋊C4—591no—
289C4⋊C4—1181no—
290C4⋊C4—1181no—
291C4⋊C4—1181no—
292C4⋊C4—1181no—
293C4⋊C4C22×D5911yescharacteristic
294C4⋊C4C22×D5911yescharacteristic
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—1181no—
300C22⋊C4—1181no—
301C22⋊C4—1181no—
302C22⋊C4—1181no—
303C22⋊C4—1181no—
304C42—1181no—
305C23—21no—
306C23C2×C22⋊D5911yescharacteristic
307C23C2×C22⋊D5911yescharacteristic
308C23C2×C22⋊D5911yescharacteristic
309Q8—21no—
310Q8—21no—
311Q8—41no—
312Q8—1181no—
313Q8—1181no—
314Q8—1181no—
315Q8—1181no—
316Q8—2362no—
317D4—21no—
318D4—21no—
319D4—41no—
320D4—41no—
321D4—41no—
322D4—42no—
323D4—81no—
324D4—81no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—1181no—
337C2×C4—1181no—
338C2×C4—1181no—
339C2×C4—1181no—
340C2×C4—2362no—
341C2×C4C2×C22⋊D5911yescharacteristic
342C2×C4C2×C22⋊D5911yescharacteristic
343C2×C4C2×C22⋊D5911yescharacteristic
344C2×C4C23×D5911yescharacteristic
345C8—1181no—
346C8—1181no—
347C8—1181no—
348C8—1181no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×C22⋊D5911yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—2361no—
369C4—2361no—
370C4—2361no—
371C4—2361no—
372C4#1427377211yescharacteristic
373C4#1427377211yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—81no—
378C2#1683796111yescharacteristic
379C2#1683821311yescharacteristic
380C2#1683821711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#537C2
socleC22×C59C22×D4
hypercenter#537D59
hypocenterC59#3201
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #16837973C2semidirect
2. #16837740C2semidirect
3. #16837737C2semidirect
4. #16837732C2semidirect
5. #16837723C2semidirect
6. #16837658C2semidirect
7. #16837646C2semidirect
8. #16837641C2semidirect
9. #16837629C2semidirect
10. #16837564C2semidirect
11. #16837564C2semidirect
12. #16837557C2semidirect
13. #16837540C2semidirect
14. #16837369C2semidirect
206. C59#3201semidirect