Finite Group Databasebeta

← #28487108

Subgroups — #28487108

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#21425057C211yesmaximal, characteristic
2#21425043C211yesmaximal, characteristic
3#21424855C211yesmaximal, characteristic
4#21423963C211yesmaximal, characteristic
5C2×#16837150C211yesmaximal, characteristic
6#21421980C211yesmaximal, characteristic
7C59×#1277C211yesmaximal, characteristic
8C2×#14273727C2211yescharacteristic
9C2×#14273661—21no—
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×#14273637—21no—
12#16837272C2211yescharacteristic
13C4×C4⋊Dic59C2211yescharacteristic
14#16837165—21no—
15#16837165—21no—
16#16837165—21no—
17#16837165—21no—
18#16837165—21no—
19#16837156—21no—
20#16837150C414yescomplemented
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4×C8×C59C2211yescharacteristic
24C22×Dic118—21no—
25C22×C59⋊C8—21no—
26#14273727—21no—
27#14273727—21no—
28#14273727—21no—
29#14273727C2×C412yes—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4×Dic59—21no—
38#14273661—42no—
39C4⋊(C59⋊C8)—21no—
40C4⋊(C59⋊C8)C2×C412yes—
41#14273637—42no—
42C59⋊#95—21no—
43C22×C8×C59—21no—
44C22×C8×C59—21no—
45C22×C8×C59D411yescharacteristic
46C22×C8×C59D411yescharacteristic
47C2×C42×C59C2311yescharacteristic
48C4⋊C8×C59—21no—
49C4⋊C8×C59—21no—
50C4⋊C8×C59—21no—
51C4⋊C8×C59C2×C412yes—
52C4×C8×C59—21no—
53C4×C8×C59—21no—
54C22×C4×C59C2×D411yescharacteristic
55C22×C4×C59C2×D411yescharacteristic
56C22×C4×C59#4111yescharacteristic
57C22×Dic59—21no—
58C22×Dic59—21no—
59C22×Dic59—41no—
60C22×Dic59—41no—
61C2×Dic118—22no—
62C2×Dic118—41no—
63C2×Dic118—81no—
64C2×Dic118—81no—
65C2×C8×C59—21no—
66C2×C8×C59—21no—
67C2×C8×C59—22no—
68C2×C8×C59—21no—
69C2×C8×C59—21no—
70C2×C8×C59—21no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59—41no—
74C2×C8×C59—41no—
75C2×C8×C59—41no—
76C2×C8×C59Q1612yes—
77C42×C59C22×C411yescharacteristic
78C42×C59#4111yescharacteristic
79C42×C59#4111yescharacteristic
80C42×C59#4111yescharacteristic
81C4⋊Dic59—22no—
82C4⋊Dic59—22no—
83C4⋊Dic59—21no—
84C4⋊Dic59—21no—
85C4⋊Dic59—21no—
86C4⋊Dic59—21no—
87C4⋊Dic59—41no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59—41no—
93C4⋊Dic59—81no—
94C4×Dic59—41no—
95C4×Dic59—41no—
96C2×C59⋊C8—22no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C23×C59#12111yescharacteristic
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59#11711yescharacteristic
103C2×C4×C59C4×D411yescharacteristic
104C2×C4×C59C4×D411yescharacteristic
105C2×C4×C59#12311yescharacteristic
106C2×C4×C59#12411yescharacteristic
107C2×C4×C59#12611yescharacteristic
108C2×C4×C59C2×Q1611yescharacteristic
109C2×C4×C59#13511yescharacteristic
110C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C59#13711yescharacteristic
113C2×C4×C59#13711yescharacteristic
114C2×C4×C59#13711yescharacteristic
115C2×C4×C59#13711yescharacteristic
116C2×Dic59—42no—
117C2×Dic59—41no—
118C2×Dic59—41no—
119C2×Dic59—41no—
120C2×Dic59—41no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—81no—
124C2×Dic59—81no—
125C2×Dic59—81no—
126C2×Dic59—81no—
127C2×Dic59—81no—
128Dic118—82no—
129Dic118—82no—
130C8×C59—22no—
131C8×C59—42no—
132C8×C59—41no—
133C8×C59—81no—
134C59⋊C8—42no—
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×C59C4×Q1611yescharacteristic
146C4×C59#44011yescharacteristic
147C4×C59#44011yescharacteristic
148C4×C59#44111yescharacteristic
149C4×C59#48411yescharacteristic
150C4×C59#48511yescharacteristic
151C4×C59#48911yescharacteristic
152C4×C59#49111yescharacteristic
153Dic59—82no—
154Dic59—81no—
155Dic59—81no—
156Dic59—161no—
157#1990—591no—
158#1987—591no—
159#1947—591no—
160#1770—591no—
161C2×#333—591no—
162#1296—591no—
163#1277D5911yescharacteristic
164C2×C59#169211yescharacteristic
165C2×C59#169611yescharacteristic
166C2×C59#169711yescharacteristic
167C2×C59#170311yescharacteristic
168C2×C59#192811yescharacteristic
169C2×C59#193111yescharacteristic
170C2×C59#193511yescharacteristic
171C2×C4⋊Q8—591no—
172C2×#107—1181no—
173C2×C4⋊C8—591no—
174C2×C4⋊C8C2×D5911yescharacteristic
175C2×C4⋊C8C2×D5911yescharacteristic
176C2×#97—1181no—
177C2×C4×C8C2×D5911yescharacteristic
178#384—591no—
179C4×C4⋊C4—591no—
180#340—1181no—
181#340—1181no—
182#340—1181no—
183#340—1181no—
184#340—1181no—
185#336—1181no—
186#333—594no—
187C59#957611yescharacteristic, complemented, Sylow
188C22×Q8—1181no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—1181no—
192C22×C8D23611yescharacteristic
193C22×C8D23611yescharacteristic
194C4⋊Q8—592no—
195C4⋊Q8—1181no—
196C4⋊Q8—1181no—
197C4⋊Q8—1181no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4—1181no—
201C2×C4⋊C4—1181no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4—1181no—
204C2×C4⋊C4—1181no—
205C2×C42—1181no—
206C2×C42C22×D5911yescharacteristic
207#107—2362no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—592no—
212C4⋊C8—1181no—
213C4⋊C8C4×D5912yes—
214#97—2362no—
215C4×C8—21no—
216C4×C8—21no—
217#95—1181no—
218C2×Q8—1182no—
219C2×Q8—4721no—
220C2×Q8—4721no—
221C2×Q8—2361no—
222C22×C4—1181no—
223C22×C4—1181no—
224C22×C4—2361no—
225C22×C4—2361no—
226C22×C4C2×D23611yescharacteristic
227C22×C4D4×D5911yescharacteristic
228C22×C4#1174568911yescharacteristic
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—1182no—
241C2×C8—2361no—
242C2×C8—2361no—
243C2×C8Dic23612yes—
244C4⋊C4—1182no—
245C4⋊C4—1182no—
246C4⋊C4—1181no—
247C4⋊C4—1181no—
248C4⋊C4—1181no—
249C4⋊C4—1181no—
250C4⋊C4—4721no—
251C4⋊C4—2361no—
252C4⋊C4—2361no—
253C4⋊C4—2361no—
254C4⋊C4—2361no—
255C4⋊C4—2361no—
256C4⋊C4—2361no—
257C42—2361no—
258C42—2361no—
259C42C2×C4×D5911yescharacteristic
260C42#1174568511yescharacteristic
261C42#1174568711yescharacteristic
262C42#1174568711yescharacteristic
263C23#1427370211yescharacteristic
264Q8—4722no—
265Q8—4722no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—4721no—
269C2×C4—4721no—
270C2×C4—4721no—
271C2×C4—4721no—
272C2×C4—4721no—
273C2×C4—2361no—
274C2×C4—2361no—
275C2×C4—2361no—
276C2×C4—2361no—
277C2×C4—2362no—
278C2×C4—2361no—
279C2×C4—2361no—
280C2×C4#1427368511yescharacteristic
281C2×C4(C22⋊D59)⋊C411yescharacteristic
282C2×C4C4×D23611yescharacteristic
283C2×C4#1427371111yescharacteristic
284C2×C4#1427371311yescharacteristic
285C2×C4#1427372211yescharacteristic
286C2×C4C2×Dic23611yescharacteristic
287C2×C4#1427374911yescharacteristic
288C2×C4#1427375111yescharacteristic
289C2×C4#1427375511yescharacteristic
290C2×C4#1427375611yescharacteristic
291C2×C4#1427375611yescharacteristic
292C2×C4#1427375911yescharacteristic
293C2×C4#1427376011yescharacteristic
294C8—22no—
295C8—41no—
296C8—42no—
297C8—81no—
298C8—2362no—
299C22#1683729411yescharacteristic
300C22#1683761311yescharacteristic
301C22#1683761811yescharacteristic
302C22#1683764911yescharacteristic
303C22#1683766111yescharacteristic
304C22#1683766611yescharacteristic
305C22#1683767311yescharacteristic
306C4—21no—
307C4—21no—
308C4—9441no—
309C4—4721no—
310C4—4721no—
311C4—4722no—
312C4C4×Dic23611yescharacteristic
313C4#1683749911yescharacteristic
314C4#1683750411yescharacteristic
315C4#1683750611yescharacteristic
316C4#1683773811yescharacteristic
317C4#1683774411yescharacteristic
318C4#1683776011yescharacteristic
319C4#1683776911yescharacteristic
320C2#2142360311yescharacteristic
321C2#2142362511yescharacteristic
322C2#2142363011yescharacteristic
323C2#2142367211yescharacteristic
324C2#2142473811yescharacteristic
325C2#2142475911yescharacteristic
326C2#2142478711yescharacteristic
subgroupG/H
centerC23#14273702
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1277C2
socle, prime radicalC23×C59#121
cosocleC2×C42×C59C23
hypercenter#1277D59
hypocenterC59#9576
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
20. #16837150C4semidirect
187. C59#9576semidirect

Maximal subgroups

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

subgroupindex
#214250572
#214250432
#214248552
#214239632
C2×#168371502
#214219802
C59×#12772
#957659