Finite Group Databasebeta

← #21436266

Subgroups — #21436266

Order 7552.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838105C211yesmaximal, characteristic
2#16838067C211yesmaximal, characteristic, complemented
3#16837742C211yesmaximal, characteristic, complemented
4#16837736C211yesmaximal, characteristic, complemented
5#16837706C211yesmaximal, characteristic, complemented
6#16837651C211yesmaximal, characteristic, complemented
7#16837634C211yesmaximal, characteristic, complemented
8#16837604C211yesmaximal, characteristic, complemented
9#16837542C211yesmaximal, characteristic, complemented
10#16837542C211yesmaximal, characteristic, complemented
11#16837504C211yesmaximal, characteristic, complemented
12#16837475C211yesmaximal, characteristic, complemented
13#16837409C211yesmaximal, characteristic, complemented
14#103×D59C211yesmaximal, characteristic, complemented
15C59×#491C211yesmaximal, characteristic, complemented
16C2×Q8×D59C2211yescharacteristic
17C2×Q8×D59C2211yescharacteristic
18C2×#11745660C2211yescharacteristic
19C2×#11745671C2211yescharacteristic
20C2×#11745671C2211yescharacteristic
21C2×#11745659C2211yescharacteristic
22C2×C8×D59C2211yescharacteristic
23#14273726—21no—
24#14273722—21no—
25#14273712—21no—
26#14273705—21no—
27#14273705—21no—
28#14273703C2211yescharacteristic
29#14273703C2211yescharacteristic
30#14273702—21no—
31#14273702C2211yescharacteristic
32#14273702C2211yescharacteristic
33C4×Dic118C2211yescharacteristic
34C4×D236C2211yescharacteristic
35C4×D236C2211yescharacteristic
36#14273689—21no—
37#14273689—21no—
38#14273685C2211yescharacteristic
39C4⋊C4×D59C2211yescharacteristic
40#14273661C2211yescharacteristic
41#14273660C2211yescharacteristic
42#14273658C2211yescharacteristic
43C4⋊(C59⋊C8)C2211yescharacteristic
44#14273652C2211yescharacteristic
45#14273651C2211yescharacteristic
46#14273651C2211yescharacteristic
47#14273650C2211yescharacteristic
48#14273650C2211yescharacteristic
49#14273649C2211yescharacteristic
50(C2×D59)⋊C8C2211yescharacteristic
51(C2×D59)⋊C8C2211yescharacteristic
52C4⋊Q8×C59C2211yescharacteristic
53#125×C59C2211yescharacteristic
54#103×C59C2211yescharacteristic
55#103×C59C2211yescharacteristic
56#103×C59C2211yescharacteristic
57#103×C59C2211yescharacteristic
58#97×C59C2211yescharacteristic
59C2×Q8×C59C2311yescharacteristic
60C2×Q8×C59C2311yescharacteristic
61Q8×D59—22no—
62Q8×D59—22no—
63Q8×D59—41no—
64Q8×D59—41no—
65C2×D236—21no—
66C2×D236—21no—
67C2×D236D411yescharacteristic
68C2×D236C2311yescharacteristic
69C2×C4×D59—21no—
70C2×C4×D59—21no—
71C2×C4×D59—21no—
72C2×C4×D59—21no—
73C2×C4×D59C2311yescharacteristic
74C2×C4×D59C2311yescharacteristic
75C2×Dic118—21no—
76C2×Dic118—21no—
77C2×Dic118C2311yescharacteristic
78C2×C8×C59C2311yescharacteristic
79C2×C8×C59C2311yescharacteristic
80C4⋊C4×C59—21no—
81C4⋊C4×C59—21no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59—21no—
84C4⋊C4×C59C2311yescharacteristic
85C4⋊C4×C59C2311yescharacteristic
86C42×C59C2311yescharacteristic
87#11745671—41no—
88#11745671—41no—
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)⋊C4D411yescharacteristic
96(C2×D59)⋊C4D411yescharacteristic
97C4⋊Dic59D411yescharacteristic
98C4⋊Dic59C2311yescharacteristic
99C4⋊Dic59C2311yescharacteristic
100Dic59⋊C4—21no—
101Dic59⋊C4—21no—
102Dic59⋊C4—21no—
103Dic59⋊C4—21no—
104C4×Dic59—21no—
105C4×Dic59—21no—
106C2×C59⋊C8C2311yescharacteristic
107C2×C59⋊C8C2311yescharacteristic
108#11745660—22no—
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—21no—
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—22no—
131D236—21no—
132D236—21no—
133D236—42no—
134D236—81no—
135C4×D59—21no—
136C4×D59—21no—
137C4×D59—21no—
138C4×D59—21no—
139C4×D59—42no—
140C4×D59—42no—
141C4×D59—81no—
142C4×D59—81no—
143Dic118—21no—
144Dic118—42no—
145Dic118—42no—
146Dic118#4112yes—
147C8×C59—21no—
148C8×C59—21no—
149C59⋊C8—21no—
150C59⋊C8—21no—
151C22×C59C22×D411yescharacteristic
152C2×D59—21no—
153C2×D59—21no—
154C2×D59—21no—
155C2×D59—21no—
156C2×D59—21no—
157C2×D59—41no—
158C2×D59—41no—
159C2×D59—41no—
160C2×D59#13712yes—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—41no—
164C4×C59—41no—
165C4×C59—41no—
166C4×C59—41no—
167C4×C59C2×#4111yescharacteristic
168C4×C59H(5,𝔽2)11yescharacteristic
169Dic59—22no—
170Dic59—21no—
171Dic59—21no—
172Dic59—41no—
173Dic59—41no—
174#3320—591nomaximal, Sylow
175C2×C59#54611yescharacteristic
176C2×C59C2×#13711yescharacteristic
177C2×C59#57711yescharacteristic
178D59—22no—
179D59—41no—
180D59—81no—
181#553—591no—
182D4×Q8—591no—
183#491D5911yescharacteristic, complemented
184#485—591no—
185#484—591no—
186#479—591no—
187#468—591no—
188#465—591no—
189#461—591no—
190#448—591no—
191#448—591no—
192#440—591no—
193#435—591no—
194#419—591no—
195C2×#103—591no—
196C59#332011yescharacteristic, complemented, Sylow
197C22×Q8—591no—
198C22×Q8—591no—
199C2×SD16—591no—
200C2×SD16—591no—
201C2×SD16—591no—
202C2×M16—591no—
203C22×C8—591no—
204C4⋊Q8—1181no—
205C4⋊Q8C2×D5911yescharacteristic
206#126—1181no—
207#125C2×D5911yescharacteristic
208#123—1181no—
209C22⋊Q8—591no—
210C22⋊Q8—591no—
211C22⋊Q8—1181no—
212C22⋊Q8—1181no—
213#121—591no—
214#121—591no—
215#121—1181no—
216C4×Q8—591no—
217C4×D4—591no—
218C4×D4—591no—
219C4×D4—1181no—
220C4×D4—1181no—
221#117—591no—
222C2×C4⋊C4—591no—
223#107—591no—
224#107—591no—
225#106—591no—
226C4⋊C8—591no—
227#103—591no—
228#103—591no—
229#103—591no—
230#103—591no—
231#103—591no—
232#103C2×D5911yescharacteristic
233#103C2×D5911yescharacteristic
234#103C2×D5911yescharacteristic
235#103C2×D5911yescharacteristic
236#102—591no—
237C22⋊C8—591no—
238C22⋊C8—591no—
239#97C2×D5911yescharacteristic
240C2×Q8—591no—
241C2×Q8—1181no—
242C2×Q8—1181no—
243C2×Q8—1182no—
244C2×Q8—1182no—
245C2×Q8—2361no—
246C2×Q8—2361no—
247C2×Q8C22×D5911yescharacteristic
248C2×Q8C22×D5911yescharacteristic
249C2×D4—591no—
250C2×D4—591no—
251C2×D4—1181no—
252C2×D4—1181no—
253C22×C4—591no—
254C22×C4—591no—
255C22×C4—1181no—
256C22×C4—1181no—
257C22×C4—1181no—
258C22×C4—1181no—
259SD16—1182no—
260SD16—2361no—
261SD16—2361no—
262M16—2361no—
263C2×C8—591no—
264C2×C8—591no—
265C2×C8—2361no—
266C2×C8C22×D5911yescharacteristic
267C2×C8C22×D5911yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—591no—
273C4⋊C4—591no—
274C4⋊C4—591no—
275C4⋊C4—1181no—
276C4⋊C4—1181no—
277C4⋊C4—1181no—
278C4⋊C4—1181no—
279C4⋊C4C22×D5911yescharacteristic
280C4⋊C4C22×D5911yescharacteristic
281C22⋊C4—591no—
282C22⋊C4—591no—
283C22⋊C4—1181no—
284C22⋊C4—1181no—
285C22⋊C4—1181no—
286C22⋊C4—1181no—
287C22⋊C4—1181no—
288C22⋊C4—1181no—
289C42—1181no—
290C42—1181no—
291C42C22×D5911yescharacteristic
292C23—591no—
293C23—591no—
294C23—1181no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—592no—
300Q8—1181no—
301Q8—2362no—
302Q8—2362no—
303D4—1182no—
304D4—1181no—
305D4—1181no—
306D4—4721no—
307D4—2362no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—591no—
313C2×C4—591no—
314C2×C4—1181no—
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—2362no—
324C2×C4—2362no—
325C2×C4D4×D5911yescharacteristic
326C2×C4D4×D5911yescharacteristic
327C2×C4C23×D5911yescharacteristic
328C8—21no—
329C8—21no—
330C8—1181no—
331C8—1181no—
332C22—592no—
333C22—1181no—
334C22—1181no—
335C22—1181no—
336C22—1181no—
337C22—1181no—
338C22—2361no—
339C22—2361no—
340C22—2361no—
341C22C2×D4×D5911yescharacteristic
342C4—21no—
343C4—21no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—1181no—
349C4—1181no—
350C4—1182no—
351C4—2361no—
352C4—2361no—
353C4#41×D5911yescharacteristic
354C4#1427377311yescharacteristic
355C2—1182no—
356C2—4721no—
357C2—2361no—
358C2#1683804511yescharacteristic
359C2#137×D5911yescharacteristic
360C2#1683821111yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#491C2
socleC22×C59C22×D4
hypercenter#491D59
hypocenterC59#3320
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #16838067C2semidirect
3. #16837742C2semidirect
4. #16837736C2semidirect
5. #16837706C2semidirect
6. #16837651C2semidirect
7. #16837634C2semidirect
8. #16837604C2semidirect
9. #16837542C2semidirect
10. #16837542C2semidirect
11. #16837504C2semidirect
12. #16837475C2semidirect
13. #16837409C2semidirect
14. #103×D59C2semidirect
15. C59×#491C2semidirect
183. #491D59semidirect
196. C59#3320semidirect