Finite Group Databasebeta

← #21434069

Subgroups — #21434069

Order 7552.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16837981C211yesmaximal, characteristic
2#16837883C211yesmaximal, characteristic, complemented
3#16837745C211yesmaximal, characteristic, complemented
4#16837744C211yesmaximal, characteristic, complemented
5#16837739C211yesmaximal, characteristic, complemented
6#16837737C211yesmaximal, characteristic, complemented
7#16837725C211yesmaximal, characteristic, complemented
8#16837723C211yesmaximal, characteristic, complemented
9#16837714C211yesmaximal, characteristic, complemented
10#16837443C211yesmaximal, characteristic, complemented
11#107×D59C211yesmaximal, characteristic, complemented
12#16837400C211yesmaximal, characteristic, complemented
13#16837395C211yesmaximal, characteristic, complemented
14#16837367C211yesmaximal, characteristic, complemented
15C59×#480C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745687C2211yescharacteristic
18C2×#11745659C2211yescharacteristic
19C2×C8×D59C2211yescharacteristic
20#14273707C2211yescharacteristic
21#14273706C2211yescharacteristic
22#14273704—21no—
23#14273700—21no—
24#14273699—21no—
25#14273698—21no—
26#14273698C2211yescharacteristic
27#14273692—21no—
28#14273689—21no—
29C4×C22⋊D59—21no—
30C4×C22⋊D59—21no—
31#14273686C2211yescharacteristic
32#14273685C2211yescharacteristic
33#14273685C2211yescharacteristic
34C4⋊C4×D59C2211yescharacteristic
35C4⋊C4×D59C2211yescharacteristic
36C4⋊C4×D59C2211yescharacteristic
37#14273661C2211yescharacteristic
38#14273660C2211yescharacteristic
39#14273660C2211yescharacteristic
40#14273660C2211yescharacteristic
41#14273659C2211yescharacteristic
42#14273658C2211yescharacteristic
43#14273652C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273650C2211yescharacteristic
46#14273650C2211yescharacteristic
47#14273648C2211yescharacteristic
48#14273648C2211yescharacteristic
49C22⋊(C59⋊C8)C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52#121×C59C2211yescharacteristic
53C2×C4⋊C4×C59C2211yescharacteristic
54#107×C59C2211yescharacteristic
55#107×C59C2211yescharacteristic
56#102×C59C2211yescharacteristic
57#102×C59C2211yescharacteristic
58C22⋊C8×C59C2211yescharacteristic
59C2×D4×C59—21no—
60C2×D4×C59C2311yescharacteristic
61C22×C4×C59—21no—
62C22×C4×C59C2311yescharacteristic
63C2×C22⋊D59—21no—
64C2×C22⋊D59—21no—
65C2×C22⋊D59D411yescharacteristic
66C2×C22⋊D59D411yescharacteristic
67C22×Dic59—21no—
68#11745687—22no—
69#11745687—22no—
70#11745685—22no—
71#11745685—22no—
72C2×D236D411yescharacteristic
73C2×C4×D59—21no—
74C2×C4×D59—21no—
75C2×C4×D59—21no—
76C2×C4×D59C2311yescharacteristic
77C2×C4×D59C2311yescharacteristic
78C2×Dic118D411yescharacteristic
79C2×Dic118C2311yescharacteristic
80C2×C8×C59C2311yescharacteristic
81C2×C8×C59C2311yescharacteristic
82C4⋊C4×C59—21no—
83C4⋊C4×C59C2311yescharacteristic
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C22⋊C4×C59—21no—
87C22⋊Dic59—21no—
88C22⋊Dic59—21no—
89C22⋊Dic59—21no—
90(C2×D59)⋊C4—21no—
91(C2×D59)⋊C4—21no—
92(C2×D59)⋊C4—21no—
93C4⋊Dic59—21no—
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96C4⋊Dic59C2311yescharacteristic
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4—21no—
101C4×Dic59—21no—
102C4×Dic59—21no—
103C4×Dic59—21no—
104C2×C59⋊C8C2311yescharacteristic
105C2×C59⋊C8C2311yescharacteristic
106#11745659—22no—
107C8×D59—22no—
108C23×C59—21no—
109C23×C59C2×D411yescharacteristic
110C22×D59C2×D411yescharacteristic
111C22×D59C2×D411yescharacteristic
112D4×C59—21no—
113D4×C59—21no—
114D4×C59—81no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—81no—
121C2×C4×C59C2×D411yescharacteristic
122C2×C4×C59C2411yescharacteristic
123C22⋊D59—22no—
124C22⋊D59—22no—
125C22⋊D59—42no—
126C22⋊D59—81no—
127C2×Dic59—21no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—42no—
132C2×Dic59C2×D411yescharacteristic
133C2×Dic59C2×D411yescharacteristic
134D236—22no—
135C4×D59—21no—
136C4×D59—21no—
137C4×D59—81no—
138C4×D59—81no—
139C4×D59—81no—
140C4×D59#4112yes—
141C4×D59#4112yes—
142Dic118—22no—
143Dic118—21no—
144Dic118—21no—
145C8×C59—21no—
146C8×C59—21no—
147C59⋊C8—21no—
148C59⋊C8—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—41no—
153C22×C59—41no—
154C22×C59—41no—
155C22×C59C22×D411yescharacteristic
156C2×D59—21no—
157C2×D59—21no—
158C2×D59—21no—
159C2×D59—21no—
160C2×D59—21no—
161C2×D59#12312yes—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59C2×#4111yescharacteristic
167C4×C59C2×#4111yescharacteristic
168Dic59—21no—
169Dic59—41no—
170Dic59—41no—
171Dic59—41no—
172Dic59—41no—
173Dic59#12312yes—
174#3098—591nomaximal, Sylow
175C2×C59—41no—
176C2×C59—81no—
177C2×C59C2×#12311yescharacteristic
178C2×C59#57611yescharacteristic
179C2×C59#57811yescharacteristic
180D59—22no—
181D59—41no—
182#537—591no—
183#520—591no—
184#485—591no—
185#485—591no—
186#484—591no—
187#484—591no—
188#482—591no—
189#482—591no—
190#480—591no—
191#480D5911yescharacteristic, complemented
192#428—591no—
193C2×#107—591no—
194#417—591no—
195#416—591no—
196#408—591no—
197C59#309811yescharacteristic, complemented, Sylow
198C2×#41—591no—
199C2×#41—591no—
200C2×M16—591no—
201C22×C8—591no—
202C22⋊Q8—591no—
203C22⋊Q8—591no—
204C22⋊Q8—1181no—
205#121—591no—
206#121—1181no—
207#121—1181no—
208#121—1181no—
209#121C2×D5911yescharacteristic
210C4×Q8—1181no—
211C4×D4—1181no—
212C4×D4—1181no—
213C4×D4—1181no—
214#117—591no—
215#117—591no—
216#117—591no—
217C2×C4⋊C4—591no—
218C2×C4⋊C4—591no—
219C2×C4⋊C4—591no—
220C2×C4⋊C4C2×D5911yescharacteristic
221#107—591no—
222#107—591no—
223#107—591no—
224#107—591no—
225#107C2×D5911yescharacteristic
226#107C2×D5911yescharacteristic
227#106—591no—
228#106—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103—591no—
233#102—591no—
234#102—591no—
235#102C2×D5911yescharacteristic
236#102C2×D5911yescharacteristic
237C22⋊C8—591no—
238C22⋊C8—591no—
239C22⋊C8—591no—
240C22⋊C8C2×D5911yescharacteristic
241#41—1182no—
242#41—1182no—
243#41—1182no—
244#41—1182no—
245C2×Q8—591no—
246C2×Q8—591no—
247C2×D4—21no—
248C2×D4—591no—
249C2×D4—591no—
250C2×D4—591no—
251C2×D4—1181no—
252C2×D4—1181no—
253C2×D4C22×D5911yescharacteristic
254C22×C4—21no—
255C22×C4—591no—
256C22×C4—591no—
257C22×C4—1181no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4C22×D5911yescharacteristic
262M16—1182no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—1182no—
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—591no—
270C4⋊C4—591no—
271C4⋊C4—591no—
272C4⋊C4—1181no—
273C4⋊C4—1181no—
274C4⋊C4—1181no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4C22×D5911yescharacteristic
278C4⋊C4C22×D5911yescharacteristic
279C4⋊C4C22×D5911yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—1181no—
282C22⋊C4—1181no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C42—1181no—
288C42—1181no—
289C42—1181no—
290C23—21no—
291C23—591no—
292C23—591no—
293C23D4×D5911yescharacteristic
294Q8—1182no—
295Q8—1181no—
296Q8—1181no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—1182no—
301D4—1182no—
302D4—1182no—
303D4—4721no—
304D4—2362no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—591no—
312C2×C4—592no—
313C2×C4—592no—
314C2×C4—591no—
315C2×C4—1181no—
316C2×C4—1181no—
317C2×C4—1181no—
318C2×C4—1181no—
319C2×C4—1181no—
320C2×C4—1181no—
321C2×C4—4721no—
322C2×C4—4721no—
323C2×C4—4721no—
324C2×C4—2362no—
325C2×C4D4×D5911yescharacteristic
326C2×C4C23×D5911yescharacteristic
327C8—21no—
328C8—21no—
329C8—1181no—
330C8—1181no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—592no—
338C22—1181no—
339C22—1181no—
340C22—1181no—
341C22—1181no—
342C22—1181no—
343C22C2×D4×D5911yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—592no—
349C4—1181no—
350C4—2361no—
351C4—2361no—
352C4—2361no—
353C4—2361no—
354C4#41×D5911yescharacteristic
355C4#41×D5911yescharacteristic
356C2—41no—
357C2—81no—
358C2—1182no—
359C2—2361no—
360C2#123×D5911yescharacteristic
361C2#1683820311yescharacteristic
362C2#1683821811yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#480C2
socleC22×C59C22×D4
hypercenter#480D59
hypocenterC59#3098
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #16837883C2semidirect
3. #16837745C2semidirect
4. #16837744C2semidirect
5. #16837739C2semidirect
6. #16837737C2semidirect
7. #16837725C2semidirect
8. #16837723C2semidirect
9. #16837714C2semidirect
10. #16837443C2semidirect
11. #107×D59C2semidirect
12. #16837400C2semidirect
13. #16837395C2semidirect
14. #16837367C2semidirect
15. C59×#480C2semidirect
191. #480D59semidirect
197. C59#3098semidirect