Finite Group Databasebeta

← #28487290

Subgroups — #28487290

Order 15104.

368 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424212C211yesmaximal, characteristic
2#21423951C211yesmaximal, characteristic
3C4×Dic59⋊C8C211yesmaximal, characteristic
4C2×#16837152C211yesmaximal, characteristic
5#21421931C211yesmaximal, characteristic
6#21421930C211yesmaximal, characteristic
7C2×C59×#335C211yesmaximal, characteristic
8C2×C4⋊(C59⋊C8)C2211yescharacteristic
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×Dic59⋊C8C411yescharacteristic
11C2×Dic59⋊C8C411yescharacteristic
12C2×#14273637—21no—
13C2×C4×C59⋊C8C2211yescharacteristic
14C42×Dic59C2211yescharacteristic
15#16837156—21no—
16#16837156—21no—
17#16837156—21no—
18#16837156C411yescharacteristic
19#16837156C411yescharacteristic
20#16837152—22no—
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4×C8×C59C2211yescharacteristic
24C59×#335—22no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8—21no—
27C22×C59⋊C8C2×C411yescharacteristic
28C22×C59⋊C8C2×C411yescharacteristic
29C2×C4×Dic59C2×C411yescharacteristic
30C2×C4×Dic59C2×C411yescharacteristic
31C2×C4×Dic59D411yescharacteristic
32C2×C4×Dic59D411yescharacteristic
33C2×C4×Dic59Q811yescharacteristic
34C2×C4×Dic59Q811yescharacteristic
35C4⋊(C59⋊C8)—21no—
36C4⋊(C59⋊C8)—21no—
37C4⋊(C59⋊C8)—21no—
38C4⋊(C59⋊C8)Q812yes—
39Dic59⋊C8—22no—
40Dic59⋊C8—22no—
41#14273637—42no—
42C4×C59⋊C8—21no—
43C4×C59⋊C8—21no—
44C22×C8×C59—21no—
45C22×C8×C59—21no—
46C22×C8×C59C2×C411yescharacteristic
47C22×C8×C59C2×C411yescharacteristic
48C2×C42×C59C2311yescharacteristic
49C4⋊C8×C59—21no—
50C4⋊C8×C59—21no—
51C4⋊C8×C59—21no—
52C4⋊C8×C59D412yes—
53C4×C8×C59—21no—
54C4×C8×C59—21no—
55C22×C4×C59C22×C411yescharacteristic
56C22×C4×C59C2×D411yescharacteristic
57C22×C4×C59C2×Q811yescharacteristic
58C22×Dic59C4⋊C411yescharacteristic
59C22×Dic59C4⋊C411yescharacteristic
60C22×Dic59C4⋊C411yescharacteristic
61C22×Dic59C4⋊C411yescharacteristic
62C2×C8×C59—21no—
63C2×C8×C59—21no—
64C2×C8×C59—21no—
65C2×C8×C59—22no—
66C2×C8×C59—21no—
67C2×C8×C59—21no—
68C2×C8×C59—41no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C2×C8×C59—41no—
72C2×C8×C59—41no—
73C2×C8×C59M1612yes—
74C42×C59C2×D411yescharacteristic
75C42×C59C2×Q811yescharacteristic
76C42×C59#4111yescharacteristic
77C42×C59#4111yescharacteristic
78C4×Dic59—21no—
79C4×Dic59—21no—
80C4×Dic59—21no—
81C4×Dic59—21no—
82C4×Dic59—21no—
83C4×Dic59—21no—
84C4×Dic59—21no—
85C4×Dic59—21no—
86C4×Dic59—22no—
87C4×Dic59—41no—
88C2×C59⋊C8—21no—
89C2×C59⋊C8—21no—
90C2×C59⋊C8—21no—
91C2×C59⋊C8—22no—
92C2×C59⋊C8—21no—
93C2×C59⋊C8—21no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C2×C59⋊C8M1612yes—
100C23×C59C2×C4⋊C411yescharacteristic
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59C4×D411yescharacteristic
104C2×C4×C59C4×Q811yescharacteristic
105C2×C4×C59#12111yescharacteristic
106C2×C4×C59C22⋊Q811yescharacteristic
107C2×C4×C59#12511yescharacteristic
108C2×C4×C59C4⋊Q811yescharacteristic
109C2×C4×C59C2×M1611yescharacteristic
110C2×C4×C59C2×M1611yescharacteristic
111C2×C4×C59#13111yescharacteristic
112C2×C4×C59#13111yescharacteristic
113C2×C4×C59#13511yescharacteristic
114C2×C4×C59#13511yescharacteristic
115C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C59#13711yescharacteristic
117C2×Dic59—21no—
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—21no—
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59—21no—
125C2×Dic59—21no—
126C2×Dic59—21no—
127C2×Dic59—21no—
128C2×Dic59#10812yes—
129C8×C59—22no—
130C8×C59—41no—
131C8×C59—42no—
132C8×C59—81no—
133C59⋊C8—22no—
134C59⋊C8—41no—
135C59⋊C8—42no—
136C59⋊C8—81no—
137#9606—591nomaximal, Sylow
138C22×C59#38911yescharacteristic
139C22×C59#42311yescharacteristic
140C22×C59#42411yescharacteristic
141C22×C59#42711yescharacteristic
142C22×C59#42811yescharacteristic
143C22×C59C2×#10811yescharacteristic
144C22×C59#43011yescharacteristic
145C4×C59—21no—
146C4×C59—21no—
147C4×C59#43511yescharacteristic
148C4×C59#43511yescharacteristic
149C4×C59#44611yescharacteristic
150C4×C59#44611yescharacteristic
151C4×C59#46311yescharacteristic
152C4×C59#46411yescharacteristic
153C4×C59#47811yescharacteristic
154C4×C59#47911yescharacteristic
155Dic59—22no—
156Dic59—41no—
157Dic59—41no—
158Dic59—41no—
159#1831—591no—
160#1767—591no—
161C4×C4⋊C8—591no—
162C2×#335D5911yescharacteristic
163C2×#334—591no—
164#1277—591no—
165#1277—591no—
166C2×C59#156811yescharacteristic
167C2×C59#156911yescharacteristic
168C2×C59#157211yescharacteristic
169C2×C59#157411yescharacteristic
170C2×C59#194011yescharacteristic
171C2×C59#194911yescharacteristic
172C2×C59#195011yescharacteristic
173C2×C4⋊C8—591no—
174C2×C4⋊C8—591no—
175C2×C4⋊C8—591no—
176C2×C4⋊C8—591no—
177C2×C4⋊C8C2×D5911yescharacteristic
178C2×C4⋊C8C2×D5911yescharacteristic
179C2×#97—1181no—
180C2×C4×C8—591no—
181C2×C4×C8C2×D5911yescharacteristic
182C43—591no—
183#336—591no—
184#336—591no—
185#336—1181no—
186#336—1181no—
187#336—1181no—
188#335—22no—
189#334—1182no—
190C59#960611yescharacteristic, complemented, Sylow
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—591no—
194C22×C8—591no—
195C22×C8—1181no—
196C22×C8—1181no—
197C22×C8C4×D5911yescharacteristic
198C22×C8C4×D5911yescharacteristic
199C2×C42—591no—
200C2×C42—591no—
201C2×C42—591no—
202C2×C42—591no—
203C2×C42—591no—
204C2×C42—591no—
205C2×C42C22×D5911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—592no—
210C4⋊C8—1182no—
211C4⋊C8—1182no—
212C4⋊C8—1181no—
213C4⋊C8—1181no—
214C4⋊C8—1181no—
215C4⋊C8C22⋊D5912yes—
216#97—2362no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—1181no—
220C4×C8—1181no—
221C22×C4—591no—
222C22×C4—591no—
223C22×C4—591no—
224C22×C4—591no—
225C22×C4C2×C4×D5911yescharacteristic
226C22×C4D4×D5911yescharacteristic
227C22×C4Q8×D5911yescharacteristic
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—22no—
232C2×C8—21no—
233C2×C8—21no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—592no—
240C2×C8—1181no—
241C2×C8—1181no—
242C2×C8—1181no—
243C2×C8—1182no—
244C2×C8—1181no—
245C2×C8—1181no—
246C2×C8—2361no—
247C2×C8—2361no—
248C2×C8—2361no—
249C2×C8—2361no—
250C2×C8—2361no—
251C2×C8#1174565912yes—
252C42—1182no—
253C42—1181no—
254C42—1181no—
255C42—1181no—
256C42—1181no—
257C42—1181no—
258C42—1181no—
259C42—1181no—
260C42—1181no—
261C42—2361no—
262C42#1174568511yescharacteristic
263C42#1174568711yescharacteristic
264C42Q8×D5911yescharacteristic
265C42C2×C22⋊D5911yescharacteristic
266C23C4⋊C4×D5911yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—592no—
270C2×C4—1181no—
271C2×C4—1181no—
272C2×C4—1181no—
273C2×C4—1181no—
274C2×C4—1181no—
275C2×C4—1181no—
276C2×C4—1181no—
277C2×C4—1181no—
278C2×C4—1181no—
279C2×C4—1181no—
280C2×C4—1181no—
281C2×C4C4×C22⋊D5911yescharacteristic
282C2×C4#1427369211yescharacteristic
283C2×C4#1427369911yescharacteristic
284C2×C4#1427370511yescharacteristic
285C2×C4#1427371711yescharacteristic
286C2×C4#1427372511yescharacteristic
287C2×C4M16×D5911yescharacteristic
288C2×C4C2×#1174565911yescharacteristic
289C2×C4#1427373311yescharacteristic
290C2×C4#1427373511yescharacteristic
291C2×C4#1427374611yescharacteristic
292C2×C4#1427375011yescharacteristic
293C2×C4#1427375111yescharacteristic
294C2×C4#1427375911yescharacteristic
295C8—22no—
296C8—41no—
297C8—42no—
298C8—81no—
299C8—1182no—
300C8—4721no—
301C8—2362no—
302C8—2361no—
303C22#1683729711yescharacteristic
304C22#1683742411yescharacteristic
305C22#1683742711yescharacteristic
306C22#1683743911yescharacteristic
307C22#1683744311yescharacteristic
308C22#108×D5911yescharacteristic
309C22#1683744911yescharacteristic
310C4—21no—
311C4—21no—
312C4—1182no—
313C4—2361no—
314C4—2361no—
315C4—2361no—
316C4#1683747111yescharacteristic
317C4#1683747311yescharacteristic
318C4#1683752911yescharacteristic
319C4#1683753111yescharacteristic
320C4#1683761511yescharacteristic
321C4#1683762611yescharacteristic
322C4#1683770511yescharacteristic
323C4#1683770811yescharacteristic
324C2#2142285811yescharacteristic
325C2#2142286211yescharacteristic
326C2#2142287511yescharacteristic
327C2#2142288611yescharacteristic
328C2#2142481611yescharacteristic
329C2#2142486111yescharacteristic
330C2#2142486811yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC2×C59×#335C2
socle, prime radicalC23×C59C2×C4⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#335D59
hypocenterC59#9606
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
190. C59#9606semidirect

Maximal subgroups

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

subgroupindex
#214242122
#214239512
C4×Dic59⋊C82
C2×#168371522
#214219312
#214219302
C2×C59×#3352
#960659