Finite Group Databasebeta

← #21434346

Subgroups — #21434346

Order 7552.

394 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838013C211yesmaximal, characteristic, complemented
2#16837874C211yesmaximal, characteristic
3#16837742C211yesmaximal, characteristic, complemented
4#16837741C211yesmaximal, characteristic, complemented
5#16837703C211yesmaximal, characteristic, complemented
6#16837702C211yesmaximal, characteristic, complemented
7#16837604C211yesmaximal, characteristic, complemented
8#16837551C211yesmaximal, characteristic
9#16837551C211yesmaximal, characteristic
10#16837505C211yesmaximal, characteristic, complemented
11#16837503C211yesmaximal, characteristic, complemented
12SD16×Dic59C211yesmaximal, characteristic, complemented
13#16837487C211yesmaximal, characteristic, complemented
14#16837462C211yesmaximal, characteristic, complemented
15C59×#461C211yesmaximal, characteristic, complemented
16C2×D4×D59C2211yescharacteristic
17C2×#11745671C2211yescharacteristic
18C2×#11745671C2211yescharacteristic
19#14273722—21no—
20#14273722—21no—
21#14273719C2211yescharacteristic, complemented
22#14273717—21no—
23#14273717—21no—
24#14273703C2211yescharacteristic
25#14273703C2211yescharacteristic
26Q8×Dic59C2211yescharacteristic, complemented
27Q8×Dic59C2211yescharacteristic, complemented
28C4×D236C2211yescharacteristic
29D4×Dic59C2211yescharacteristic
30#14273689C2211yescharacteristic
31C4×C22⋊D59—21no—
32(C22⋊D59)⋊C4—21no—
33#14273685C2211yescharacteristic
34#14273684C2211yescharacteristic
35C2×(C2×D59)⋊C4—21no—
36C22⋊C4×D59—21no—
37#14273661C2211yescharacteristic, complemented
38#14273660C2211yescharacteristic, complemented
39#14273659C2211yescharacteristic, complemented
40#14273658C2211yescharacteristic, complemented
41C4⋊(C59⋊C8)C2211yescharacteristic, complemented
42#14273651C2211yescharacteristic, complemented
43#14273651C2211yescharacteristic, complemented
44#14273649C2211yescharacteristic
45#14273649C2211yescharacteristic
46#14273648C2211yescharacteristic
47#14273648C2211yescharacteristic
48(C2×D59)⋊C8C2211yescharacteristic
49(C2×D59)⋊C8C2211yescharacteristic
50#14273637C2211yescharacteristic, complemented
51C8×Dic59C2211yescharacteristic, complemented
52C2×SD16×C59C2211yescharacteristic
53C2×SD16×C59C2211yescharacteristic
54C4⋊Q8×C59C2211yescharacteristic, complemented
55C4×D4×C59C2211yescharacteristic
56C4⋊C8×C59C2211yescharacteristic, complemented
57#103×C59C2211yescharacteristic, complemented
58#103×C59C2211yescharacteristic, complemented
59C23×D59—21no—
60C2×Q8×C59C2311yescharacteristic
61C2×Q8×C59C2311yescharacteristic
62C2×D4×C59C2311yescharacteristic
63C22×C4×C59—21no—
64C2×C22⋊D59—21no—
65C22×Dic59—21no—
66D4×D59—22no—
67D4×D59—22no—
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59C2311yescharacteristic
72SD16×C59—22no—
73SD16×C59—22no—
74C2×C8×C59C2311yescharacteristic
75C2×C8×C59C2311yescharacteristic
76C4⋊C4×C59—21no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59C2311yescharacteristic
79C22⋊C4×C59—21no—
80C42×C59C2311yescharacteristic
81C22⋊Dic59—21no—
82#11745671—22no—
83#11745671—22no—
84(C2×D59)⋊C4—21no—
85(C2×D59)⋊C4—21no—
86(C2×D59)⋊C4—21no—
87(C2×D59)⋊C4—21no—
88(C2×D59)⋊C4—21no—
89(C2×D59)⋊C4D411yescharacteristic
90(C2×D59)⋊C4D411yescharacteristic
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59C2311yescharacteristic
94C4⋊Dic59C2311yescharacteristic
95C4⋊Dic59C2311yescharacteristic
96Dic59⋊C4—21no—
97Dic59⋊C4—21no—
98Dic59⋊C4—21no—
99Dic59⋊C4—21no—
100Dic59⋊C4D411yescharacteristic
101Dic59⋊C4D411yescharacteristic
102C4×Dic59—21no—
103C4×Dic59—21no—
104C4×Dic59—21no—
105C4×Dic59C2311yescharacteristic
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108C23×C59—21no—
109C22×D59—21no—
110C22×D59—24no—
111C22×D59—81no—
112C22×D59—81no—
113C22×D59C2×D411yescharacteristic
114Q8×C59—21no—
115Q8×C59—21no—
116Q8×C59—21no—
117Q8×C59—21no—
118D4×C59—21no—
119D4×C59#4112yes—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—81no—
124C2×C4×C59C2×D411yescharacteristic
125C2×C4×C59C2×D411yescharacteristic
126C2×C4×C59C2411yescharacteristic
127C22⋊D59—24no—
128C2×Dic59—21no—
129C2×Dic59—21no—
130C2×Dic59—21no—
131C2×Dic59—81no—
132C2×Dic59C2×D411yescharacteristic
133C2×Dic59C2×D411yescharacteristic
134C2×Dic59C2×D411yescharacteristic
135D236—21no—
136D236#4112yes—
137C4×D59—21no—
138C4×D59—21no—
139C4×D59—81no—
140C4×D59—81no—
141C8×C59—21no—
142C8×C59—21no—
143C59⋊C8—21no—
144C59⋊C8—21no—
145C22×C59—22no—
146C22×C59—41no—
147C22×C59—41no—
148C22×C59C22×D411yescharacteristic
149C2×D59—21no—
150C2×D59—22no—
151C2×D59—21no—
152C2×D59—21no—
153C2×D59—41no—
154C2×D59—41no—
155C2×D59—84no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—41no—
159C4×C59—41no—
160C4×C59—41no—
161C4×C59C2×#4111yescharacteristic
162C4×C59C2×#4111yescharacteristic
163Dic59—21no—
164Dic59—21no—
165Dic59—21no—
166Dic59—41no—
167Dic59—41no—
168Dic59—41no—
169#3123—591nomaximal, Sylow
170C2×C59—42no—
171C2×C59#52511yescharacteristic
172C2×C59#57711yescharacteristic
173C2×C59#57711yescharacteristic
174D59—41no—
175D59—42no—
176#541—591no—
177#518—591no—
178#485—591no—
179#485—591no—
180#478—591no—
181#478—591no—
182#461—591no—
183#461D5911yescharacteristic, complemented
184#450—591no—
185#450—591no—
186#440—591no—
187#440—591no—
188C4×SD16—591no—
189C4×SD16—591no—
190#433—591no—
191C59#312311yescharacteristic, complemented, Sylow
192C22×D4—591no—
193C2×SD16—591no—
194C2×SD16—591no—
195C2×SD16C2×D5911yescharacteristic
196C2×SD16C2×D5911yescharacteristic
197C4⋊Q8C2×D5911yescharacteristic, complemented
198#126—1181no—
199#126—1181no—
200#125—591no—
201#125—1181no—
202#125—1181no—
203C22⋊Q8—591no—
204C22⋊Q8—591no—
205C4×Q8—591no—
206C4×Q8—591no—
207C4×D4—591no—
208C4×D4—591no—
209C4×D4—591no—
210C4×D4—1181no—
211C4×D4—1181no—
212C4×D4C2×D5911yescharacteristic
213#117—591no—
214#117—591no—
215C2×C22⋊C4—1181no—
216C2×C22⋊C4—1181no—
217#107—591no—
218#107—591no—
219#106—591no—
220#106—591no—
221C4⋊C8—591no—
222C4⋊C8C2×D5911yescharacteristic, complemented
223#103—591no—
224#103—591no—
225#103C2×D5911yescharacteristic, complemented
226#103C2×D5911yescharacteristic, complemented
227#102—591no—
228#102—591no—
229#102—591no—
230#102—591no—
231C22⋊C8—591no—
232C22⋊C8—591no—
233#97—591no—
234C4×C8—591no—
235C24—1181no—
236C2×Q8C22×D5911yescharacteristic
237C2×Q8C22×D5911yescharacteristic
238C2×D4—591no—
239C2×D4—1181no—
240C2×D4—1182no—
241C2×D4—1182no—
242C2×D4C22×D5911yescharacteristic
243C22×C4—21no—
244C22×C4—591no—
245C22×C4—1181no—
246C22×C4—1181no—
247C22×C4—1181no—
248SD16—22no—
249SD16—22no—
250SD16—1182no—
251SD16—1182no—
252C2×C8—591no—
253C2×C8—591no—
254C2×C8C22×D5911yescharacteristic
255C2×C8C22×D5911yescharacteristic
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—591no—
259C4⋊C4—591no—
260C4⋊C4—591no—
261C4⋊C4—591no—
262C4⋊C4—591no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4—1181no—
266C4⋊C4—1181no—
267C4⋊C4—1181no—
268C4⋊C4—1181no—
269C4⋊C4C22×D5911yescharacteristic
270C22⋊C4—21no—
271C22⋊C4—591no—
272C22⋊C4—591no—
273C22⋊C4—1181no—
274C22⋊C4—1181no—
275C22⋊C4—1181no—
276C22⋊C4—1181no—
277C22⋊C4—1181no—
278C22⋊C4—1181no—
279C42—591no—
280C42—1181no—
281C42—1181no—
282C42—1181no—
283C42C22×D5911yescharacteristic
284C23—21no—
285C23—591no—
286C23—1184no—
287C23—1181no—
288C23—4721no—
289C23—4721no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294D4—21no—
295D4—592no—
296D4—1184no—
297D4—1181no—
298D4#1174568712yes—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—81no—
303C2×C4—591no—
304C2×C4—591no—
305C2×C4—591no—
306C2×C4—1181no—
307C2×C4—1181no—
308C2×C4—1181no—
309C2×C4—1181no—
310C2×C4—1181no—
311C2×C4—4721no—
312C2×C4—4721no—
313C2×C4—4721no—
314C2×C4D4×D5911yescharacteristic
315C2×C4D4×D5911yescharacteristic
316C2×C4C23×D5911yescharacteristic
317C8—21no—
318C8—21no—
319C8—1181no—
320C8—1181no—
321C22—22no—
322C22—41no—
323C22—41no—
324C22—1181no—
325C22—1182no—
326C22—1181no—
327C22—1181no—
328C22—4724no—
329C22—2361no—
330C22—2361no—
331C22C2×D4×D5911yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1181no—
338C4—1181no—
339C4—1181no—
340C4—2361no—
341C4—2361no—
342C4—2361no—
343C4#41×D5911yescharacteristic
344C4C2×#1174568711yescharacteristic
345C2—42no—
346C2—2361no—
347C2—2362no—
348C2#1683791211yescharacteristic
349C2#1683820811yescharacteristic
350C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#461C2
socleC22×C59C22×D4
hypercenter#461D59
hypocenterC59#3123
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16838013C2semidirect
3. #16837742C2semidirect
4. #16837741C2semidirect
5. #16837703C2semidirect
6. #16837702C2semidirect
7. #16837604C2semidirect
10. #16837505C2semidirect
11. #16837503C2semidirect
12. SD16×Dic59C2semidirect
13. #16837487C2semidirect
14. #16837462C2semidirect
15. C59×#461C2semidirect
21. #14273719C22semidirect
26. Q8×Dic59C22semidirect
27. Q8×Dic59C22semidirect
37. #14273661C22semidirect
38. #14273660C22semidirect
39. #14273659C22semidirect
40. #14273658C22semidirect
41. C4⋊(C59⋊C8)C22semidirect
42. #14273651C22semidirect
43. #14273651C22semidirect
50. #14273637C22semidirect
51. C8×Dic59C22semidirect
54. C4⋊Q8×C59C22semidirect
56. C4⋊C8×C59C22semidirect
57. #103×C59C22semidirect
58. #103×C59C22semidirect
183. #461D59semidirect
191. C59#3123semidirect
197. C4⋊Q8C2×D59semidirect
222. C4⋊C8C2×D59semidirect
225. #103C2×D59semidirect
226. #103C2×D59semidirect