Finite Group Databasebeta

← #28487063

Subgroups — #28487063

Order 15104.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425047C211yesmaximal, characteristic
2#21424897C211yesmaximal, characteristic
3#21424857C211yesmaximal, characteristic
4#21423966C211yesmaximal, characteristic
5C2×#16837149C211yesmaximal, characteristic
6#21421930C211yesmaximal, characteristic
7C59×#1296C211yesmaximal, characteristic
8C2×#14273727C2211yescharacteristic
9C2×#14273658—21no—
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×#14273650—21no—
12C2×#14273650—21no—
13C2×#14273637—21no—
14C2×C4×C59⋊C8C2211yescharacteristic
15C4×C4⋊Dic59C2211yescharacteristic
16#16837165—21no—
17#16837165—21no—
18#16837164—21no—
19#16837156—21no—
20#16837149C414yescomplemented
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C59×#384C2211yescharacteristic
24C22×Dic118—21no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8D411yescharacteristic
27C22×C59⋊C8D411yescharacteristic
28#14273727—21no—
29#14273727—21no—
30#14273727—21no—
31#14273727C2×C412yes—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59D411yescharacteristic
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4×Dic59—21no—
37#14273658—42no—
38C4⋊(C59⋊C8)—21no—
39C4⋊(C59⋊C8)C2×C412yes—
40#14273650—42no—
41#14273650—42no—
42#14273637—42no—
43C4×C59⋊C8—21no—
44C4×C59⋊C8—21no—
45C59⋊#95—21no—
46C22×C8×C59—21no—
47C22×C8×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C42×C59C2311yescharacteristic
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4⋊C8×C59C2×C412yes—
56C22×C4×C59—41no—
57C22×C4×C59C2×D411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59#4111yescharacteristic
60C22×Dic59—21no—
61C22×Dic59—21no—
62C22×Dic59—41no—
63C2×Dic118—22no—
64C2×Dic118—41no—
65C2×Dic118—41no—
66C2×Dic118—41no—
67C2×Dic118—41no—
68C2×Dic118—41no—
69C2×C8×C59—22no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—81no—
80C42×C59C22×C411yescharacteristic
81C42×C59#4111yescharacteristic
82C42×C59#4111yescharacteristic
83C42×C59#4111yescharacteristic
84C4⋊Dic59—22no—
85C4⋊Dic59—22no—
86C4⋊Dic59—21no—
87C4⋊Dic59—21no—
88C4⋊Dic59—21no—
89C4⋊Dic59—21no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4×Dic59—41no—
93C4×Dic59—41no—
94C2×C59⋊C8—21no—
95C2×C59⋊C8—21no—
96C2×C59⋊C8—22no—
97C2×C59⋊C8—21no—
98C2×C59⋊C8—21no—
99C2×C59⋊C8—21no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8SD1612yes—
103C23×C59#12111yescharacteristic
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—81no—
107C2×C4×C59—81no—
108C2×C4×C59—81no—
109C2×C4×C59#11711yescharacteristic
110C2×C4×C59C4×D411yescharacteristic
111C2×C4×C59C4×D411yescharacteristic
112C2×C4×C59#12311yescharacteristic
113C2×C4×C59#12411yescharacteristic
114C2×C4×C59#12611yescharacteristic
115C2×C4×C59C2×SD1611yescharacteristic
116C2×C4×C59#13511yescharacteristic
117C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×C4×C59#13711yescharacteristic
122C2×C4×C59#13711yescharacteristic
123C2×Dic59—42no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—81no—
131C2×Dic59—81no—
132Dic118—42no—
133Dic118—42no—
134Dic118—81no—
135Dic118—81no—
136C8×C59—42no—
137C8×C59—81no—
138C59⋊C8—22no—
139C59⋊C8—42no—
140C59⋊C8—41no—
141#9570—591nomaximal, Sylow
142C22×C59#38811yescharacteristic
143C22×C59#46011yescharacteristic
144C22×C59#46311yescharacteristic
145C22×C59#46811yescharacteristic
146C22×C59#47011yescharacteristic
147C22×C59#47111yescharacteristic
148C22×C59#47311yescharacteristic
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—161no—
152C4×C59C4×SD1611yescharacteristic
153C4×C59#44011yescharacteristic
154C4×C59#44111yescharacteristic
155C4×C59#44211yescharacteristic
156C4×C59#48111yescharacteristic
157C4×C59#48211yescharacteristic
158C4×C59#48911yescharacteristic
159C4×C59#49111yescharacteristic
160Dic59—82no—
161Dic59—81no—
162Dic59—81no—
163#1988—591no—
164#1956—591no—
165#1948—591no—
166#1770—591no—
167C2×#332—591no—
168#1296D5911yescharacteristic
169#1277—591no—
170C2×C59#168611yescharacteristic
171C2×C59#169011yescharacteristic
172C2×C59#169911yescharacteristic
173C2×C59#170311yescharacteristic
174C2×C59#192611yescharacteristic
175C2×C59#193011yescharacteristic
176C2×C59#193511yescharacteristic
177C2×C4⋊Q8—591no—
178C2×#106—1181no—
179C2×C4⋊C8—591no—
180C2×C4⋊C8C2×D5911yescharacteristic
181C2×C4⋊C8C2×D5911yescharacteristic
182C2×#103—1181no—
183C2×#103—1181no—
184C2×#97—1181no—
185C2×C4×C8—591no—
186#384C2×D5911yescharacteristic
187C4×C4⋊C4—591no—
188#340—1181no—
189#340—1181no—
190#340—1181no—
191#336—1181no—
192#332—594no—
193C59#957011yescharacteristic, complemented, Sylow
194C22×Q8—1181no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—591no—
198C22×C8—591no—
199C22×C8—1181no—
200C4⋊Q8—592no—
201C4⋊Q8—1181no—
202C4⋊Q8—1181no—
203C4⋊Q8—1181no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—591no—
208C2×C4⋊C4—591no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4—1181no—
211C2×C42—1181no—
212C2×C42C22×D5911yescharacteristic
213#106—2362no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—592no—
218C4⋊C8—1181no—
219C4⋊C8C4×D5912yes—
220#103—2362no—
221#103—2362no—
222#97—2362no—
223C4×C8—1181no—
224C4×C8—1181no—
225#95—1181no—
226C2×Q8—1182no—
227C2×Q8—2361no—
228C2×Q8—2361no—
229C2×Q8—2361no—
230C2×Q8—2361no—
231C2×Q8—2361no—
232C22×C4—41no—
233C22×C4—1181no—
234C22×C4—1181no—
235C22×C4—2361no—
236C22×C4#1174568511yescharacteristic
237C22×C4D4×D5911yescharacteristic
238C22×C4D4×D5911yescharacteristic
239C2×C8—22no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—592no—
246C2×C8—1181no—
247C2×C8—1181no—
248C2×C8—1182no—
249C2×C8—1181no—
250C2×C8—1181no—
251C2×C8—1181no—
252C2×C8—2361no—
253C2×C8—2361no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—1182no—
260C4⋊C4—1182no—
261C4⋊C4—1181no—
262C4⋊C4—1181no—
263C4⋊C4—1181no—
264C4⋊C4—1181no—
265C4⋊C4—2361no—
266C4⋊C4—2361no—
267C42—2361no—
268C42—2361no—
269C42C2×C4×D5911yescharacteristic
270C42#1174568511yescharacteristic
271C42#1174568711yescharacteristic
272C42#1174568911yescharacteristic
273C23#1427370011yescharacteristic
274Q8—4721no—
275Q8—4721no—
276Q8—2362no—
277Q8—2362no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—4721no—
284C2×C4—4721no—
285C2×C4—2361no—
286C2×C4—2361no—
287C2×C4—2361no—
288C2×C4—2361no—
289C2×C4—2362no—
290C2×C4—2361no—
291C2×C4—2361no—
292C2×C4#1427368411yescharacteristic
293C2×C4(C22⋊D59)⋊C411yescharacteristic
294C2×C4#1427368911yescharacteristic
295C2×C4#1427371211yescharacteristic
296C2×C4#1427371311yescharacteristic
297C2×C4#1427372211yescharacteristic
298C2×C4SD16×D5911yescharacteristic
299C2×C4#1427375011yescharacteristic
300C2×C4#1427375111yescharacteristic
301C2×C4#1427375111yescharacteristic
302C2×C4#1427375411yescharacteristic
303C2×C4#1427375611yescharacteristic
304C2×C4#1427375611yescharacteristic
305C2×C4#1427375911yescharacteristic
306C8—42no—
307C8—81no—
308C8—1182no—
309C8—2361no—
310C8—2362no—
311C22#1683729111yescharacteristic
312C22#1683760111yescharacteristic
313C22#1683762011yescharacteristic
314C22#1683764711yescharacteristic
315C22#1683765911yescharacteristic
316C22#1683766411yescharacteristic
317C22#1683767611yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—4721no—
322C4—4721no—
323C4—4722no—
324C4#1683748711yescharacteristic
325C4#1683750111yescharacteristic
326C4#1683750811yescharacteristic
327C4#1683751111yescharacteristic
328C4#1683772211yescharacteristic
329C4#1683772911yescharacteristic
330C4#1683776011yescharacteristic
331C4#1683776911yescharacteristic
332C2#2142356711yescharacteristic
333C2#2142358911yescharacteristic
334C2#2142364611yescharacteristic
335C2#2142367411yescharacteristic
336C2#2142472111yescharacteristic
337C2#2142474911yescharacteristic
338C2#2142478411yescharacteristic
subgroupG/H
centerC23#14273700
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socle, prime radicalC23×C59#121
cosocleC2×C42×C59C23
hypercenter#1296D59
hypocenterC59#9570
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
20. #16837149C4semidirect
193. C59#9570semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214250472
#214248972
#214248572
#214239662
C2×#168371492
#214219302
C59×#12962
#957059