Finite Group Databasebeta

← #28487104

Subgroups — #28487104

Order 15104.

370 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425045C211yesmaximal, characteristic
2#21424852C211yesmaximal, characteristic
3#21423963C211yesmaximal, characteristic
4C2×#16837151C211yesmaximal, characteristic
5#21421979C211yesmaximal, characteristic
6#21421931C211yesmaximal, characteristic
7C59×#1990C211yesmaximal, characteristic
8C2×#14273660—21no—
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×#14273637—21no—
13C4×C4⋊Dic59C2211yescharacteristic
14#16837164—21no—
15#16837164—21no—
16#16837164—21no—
17#16837156—21no—
18#16837151C414yescomplemented
19C2×C4⋊Q8×C59C2211yescharacteristic
20C2×C4×C8×C59C2211yescharacteristic
21C59×#384C2211yescharacteristic
22C59×#340—21no—
23C59×#340—21no—
24C22×C59⋊C8—21no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8—21no—
27C2×C4⋊Dic59D411yescharacteristic
28C2×C4⋊Dic59D411yescharacteristic
29C2×C4×Dic59—21no—
30#14273660—42no—
31C4⋊(C59⋊C8)—21no—
32C4⋊(C59⋊C8)—21no—
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)—21no—
35C4⋊(C59⋊C8)C2×C412yes—
36C4⋊(C59⋊C8)C2×C412yes—
37#14273637—42no—
38C59⋊#95—21no—
39C22×Q8×C59—21no—
40C22×C8×C59D411yescharacteristic
41C22×C8×C59D411yescharacteristic
42C4⋊Q8×C59—21no—
43C4⋊Q8×C59—21no—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59C2×C412yes—
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×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—
54C2×Q8×C59—22no—
55C2×Q8×C59—41no—
56C2×Q8×C59—81no—
57C2×Q8×C59—81no—
58C22×C4×C59—41no—
59C22×C4×C59—41no—
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59#4111yescharacteristic
63C22×Dic59—21no—
64C22×Dic59—21no—
65C2×C8×C59—21no—
66C2×C8×C59—21no—
67C2×C8×C59—21no—
68C2×C8×C59—21no—
69C2×C8×C59—21no—
70C2×C8×C59Q1612yes—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—22no—
73C4⋊C4×C59—41no—
74C4⋊C4×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—21no—
85C4⋊Dic59—21no—
86C4⋊Dic59—21no—
87C4⋊Dic59—21no—
88C4×Dic59—41no—
89C4×Dic59—41no—
90C2×C59⋊C8—22no—
91C2×C59⋊C8—22no—
92C2×C59⋊C8—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C23×C59#12111yescharacteristic
100Q8×C59—82no—
101Q8×C59—82no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—42no—
105C2×C4×C59—81no—
106C2×C4×C59—81no—
107C2×C4×C59—81no—
108C2×C4×C59—81no—
109C2×C4×C59—81no—
110C2×C4×C59#11711yescharacteristic
111C2×C4×C59C4×D411yescharacteristic
112C2×C4×C59C4×D411yescharacteristic
113C2×C4×C59#12311yescharacteristic
114C2×C4×C59#12411yescharacteristic
115C2×C4×C59#12611yescharacteristic
116C2×C4×C59C2×Q1611yescharacteristic
117C2×C4×C59#13511yescharacteristic
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×C4×C59#13711yescharacteristic
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C8×C59—22no—
131C8×C59—41no—
132C59⋊C8—42no—
133C59⋊C8—42no—
134C59⋊C8—81no—
135#9576—591nomaximal, Sylow
136C22×C59#38811yescharacteristic
137C22×C59#46211yescharacteristic
138C22×C59#46311yescharacteristic
139C22×C59#46811yescharacteristic
140C22×C59#47011yescharacteristic
141C22×C59#47111yescharacteristic
142C22×C59#47211yescharacteristic
143C4×C59—21no—
144C4×C59—21no—
145C4×C59—82no—
146C4×C59—161no—
147C4×C59C4×Q1611yescharacteristic
148C4×C59#44011yescharacteristic
149C4×C59#44011yescharacteristic
150C4×C59#44111yescharacteristic
151C4×C59#48411yescharacteristic
152C4×C59#48511yescharacteristic
153C4×C59#48911yescharacteristic
154C4×C59#49111yescharacteristic
155Dic59—81no—
156Dic59—81no—
157#1990D5911yescharacteristic
158#1987—591no—
159#1947—591no—
160#1770—591no—
161C2×#333—591no—
162#1296—591no—
163#1277—591no—
164C2×C59#169211yescharacteristic
165C2×C59#169611yescharacteristic
166C2×C59#169711yescharacteristic
167C2×C59#170311yescharacteristic
168C2×C59#192811yescharacteristic
169C2×C59#193111yescharacteristic
170C2×C59#193511yescharacteristic
171C2×C4⋊Q8C2×D5911yescharacteristic
172C2×#107—1181no—
173C2×C4⋊C8—591no—
174C2×C4⋊C8—591no—
175C2×C4⋊C8—591no—
176C2×#97—1181no—
177C2×C4×C8C2×D5911yescharacteristic
178#384C2×D5911yescharacteristic
179C4×C4⋊C4—591no—
180#340—21no—
181#340—21no—
182#340—1181no—
183#340—1181no—
184#340—1181no—
185#336—1181no—
186#333—594no—
187C59#957611yescharacteristic, complemented, Sylow
188C22×Q8—21no—
189C22×C8—1181no—
190C22×C8—1181no—
191C22×C8—1181no—
192C22×C8C22⋊D5911yescharacteristic
193C22×C8C22⋊D5911yescharacteristic
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8C4×D5912yes—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—591no—
204C2×C4⋊C4—591no—
205C2×C42—1181no—
206C2×C42C22×D5911yescharacteristic
207#107—2362no—
208C4⋊C8—592no—
209C4⋊C8—592no—
210C4⋊C8—1181no—
211C4⋊C8—1181no—
212C4⋊C8—1181no—
213C4⋊C8—1181no—
214#97—2362no—
215C4×C8—21no—
216C4×C8—21no—
217#95—1181no—
218C2×Q8—22no—
219C2×Q8—41no—
220C2×Q8—81no—
221C2×Q8—81no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—1181no—
225C22×C4—1181no—
226C22×C4D4×D5911yescharacteristic
227C22×C4#1174568711yescharacteristic
228C22×C4C2×C22⋊D5911yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—1182no—
235C2×C8—1182no—
236C2×C8—2361no—
237C2×C8—2361no—
238C2×C8—2361no—
239C2×C8—2361no—
240C2×C8—2361no—
241C2×C8—2361no—
242C2×C8—2361no—
243C2×C8#1174567212yes—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—1181no—
254C4⋊C4—1181no—
255C4⋊C4—1181no—
256C4⋊C4—1181no—
257C42—2361no—
258C42—2361no—
259C42C2×C4×D5911yescharacteristic
260C42#1174568511yescharacteristic
261C42#1174568711yescharacteristic
262C42#1174568711yescharacteristic
263C23#1427369811yescharacteristic
264Q8—82no—
265Q8—82no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—2361no—
275C2×C4—2361no—
276C2×C4—2361no—
277C2×C4—2361no—
278C2×C4—2361no—
279C2×C4—2361no—
280C2×C4#1427368311yescharacteristic
281C2×C4(C22⋊D59)⋊C411yescharacteristic
282C2×C4C4×C22⋊D5911yescharacteristic
283C2×C4#1427370811yescharacteristic
284C2×C4#1427371311yescharacteristic
285C2×C4#1427372011yescharacteristic
286C2×C4C2×#1174567211yescharacteristic
287C2×C4#1427374711yescharacteristic
288C2×C4#1427375211yescharacteristic
289C2×C4#1427375411yescharacteristic
290C2×C4#1427375611yescharacteristic
291C2×C4#1427375811yescharacteristic
292C2×C4#1427375911yescharacteristic
293C2×C4#1427375911yescharacteristic
294C8—22no—
295C8—41no—
296C8—4721no—
297C8—2362no—
298C8—2362no—
299C22#1683729011yescharacteristic
300C22#1683760911yescharacteristic
301C22#1683761411yescharacteristic
302C22#1683764511yescharacteristic
303C22#1683765711yescharacteristic
304C22#1683766211yescharacteristic
305C22#1683766911yescharacteristic
306C4—21no—
307C4—21no—
308C4—82no—
309C4—161no—
310C4—4721no—
311C4—4721no—
312C4C4×#1174567211yescharacteristic
313C4#1683750011yescharacteristic
314C4#1683750511yescharacteristic
315C4#1683750611yescharacteristic
316C4#1683773511yescharacteristic
317C4#1683774011yescharacteristic
318C4#1683776311yescharacteristic
319C4#1683776911yescharacteristic
320C2#2142359911yescharacteristic
321C2#2142362111yescharacteristic
322C2#2142362611yescharacteristic
323C2#2142366811yescharacteristic
324C2#2142473411yescharacteristic
325C2#2142475511yescharacteristic
326C2#2142478311yescharacteristic
subgroupG/H
centerC23#14273698
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1990C2
socle, prime radicalC23×C59#121
cosocleC2×C42×C59C23
hypercenter#1990D59
hypocenterC59#9576
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
18. #16837151C4semidirect
187. C59#9576semidirect

Maximal subgroups

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

subgroupindex
#214250452
#214248522
#214239632
C2×#168371512
#214219792
#214219312
C59×#19902
#957659