Finite Group Databasebeta

← #28487293

Subgroups — #28487293

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#21424213C211yesmaximal, characteristic
2C4×C4⋊(C59⋊C8)C211yesmaximal, characteristic
3C2×#16837154C211yesmaximal, characteristic
4C2×#16837152C211yesmaximal, characteristic
5#21421930C211yesmaximal, characteristic
6#21421930C211yesmaximal, characteristic
7C59×#1767C211yesmaximal, characteristic
8C2×C4⋊(C59⋊C8)C411yescharacteristic
9C2×C4⋊(C59⋊C8)C411yescharacteristic
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×C4×C59⋊C8C2211yescharacteristic
13C2×C4×C59⋊C8C2211yescharacteristic
14#16837157—21no—
15#16837157—21no—
16#16837157C411yescharacteristic
17#16837157C411yescharacteristic
18#16837154—22no—
19#16837152—22no—
20C2×C4⋊C8×C59C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×#97×C59—21no—
23C43×C59C2211yescharacteristic
24C59×#336—21no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8—21no—
27C22×C59⋊C8C2×C411yescharacteristic
28C22×C59⋊C8C2×C411yescharacteristic
29C22×C59⋊C8C2×C411yescharacteristic
30C22×C59⋊C8C2×C411yescharacteristic
31C4⋊(C59⋊C8)—22no—
32C4⋊(C59⋊C8)—22no—
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)—21no—
35C4⋊(C59⋊C8)—21no—
36C4⋊(C59⋊C8)—21no—
37C4×C59⋊C8—21no—
38C4×C59⋊C8—21no—
39C4×C59⋊C8—21no—
40C4×C59⋊C8—21no—
41C22×C8×C59—21no—
42C22×C8×C59—21no—
43C2×C42×C59C2×C411yescharacteristic
44C2×C42×C59C2×C411yescharacteristic
45C2×C42×C59D411yescharacteristic
46C2×C42×C59D411yescharacteristic
47C2×C42×C59Q811yescharacteristic
48C2×C42×C59Q811yescharacteristic
49C2×C42×C59C2311yescharacteristic
50C4⋊C8×C59—21no—
51C4⋊C8×C59—21no—
52C4⋊C8×C59D412yes—
53C4⋊C8×C59Q812yes—
54#97×C59—42no—
55C22×C4×C59C4⋊C411yescharacteristic
56C22×C4×C59C4⋊C411yescharacteristic
57C22×C4×C59C4⋊C411yescharacteristic
58C22×C4×C59C4⋊C411yescharacteristic
59C22×C4×C59C22×C411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×Q811yescharacteristic
62C2×C8×C59—22no—
63C2×C8×C59—22no—
64C2×C8×C59—41no—
65C2×C8×C59—41no—
66C2×C8×C59—41no—
67C2×C8×C59—41no—
68C42×C59—22no—
69C42×C59—21no—
70C42×C59—21no—
71C42×C59—21no—
72C42×C59—21no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59—41no—
78C42×C59C2×D411yescharacteristic
79C42×C59C2×Q811yescharacteristic
80C42×C59#4111yescharacteristic
81C42×C59#4111yescharacteristic
82C2×C59⋊C8—21no—
83C2×C59⋊C8—21no—
84C2×C59⋊C8—21no—
85C2×C59⋊C8—21no—
86C2×C59⋊C8—21no—
87C2×C59⋊C8—21no—
88C2×C59⋊C8—21no—
89C2×C59⋊C8—21no—
90C2×C59⋊C8—21no—
91C2×C59⋊C8—21no—
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⋊C8M1612yes—
99C2×C59⋊C8M1612yes—
100C23×C59C2×C4⋊C411yescharacteristic
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—21no—
105C2×C4×C59—21no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—21no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59#10812yes—
115C2×C4×C59C4×D411yescharacteristic
116C2×C4×C59C4×Q811yescharacteristic
117C2×C4×C59#12111yescharacteristic
118C2×C4×C59C22⋊Q811yescharacteristic
119C2×C4×C59#12511yescharacteristic
120C2×C4×C59C4⋊Q811yescharacteristic
121C2×C4×C59C2×M1611yescharacteristic
122C2×C4×C59C2×M1611yescharacteristic
123C2×C4×C59#13111yescharacteristic
124C2×C4×C59#13111yescharacteristic
125C2×C4×C59#13511yescharacteristic
126C2×C4×C59#13511yescharacteristic
127C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C59#13711yescharacteristic
129C8×C59—42no—
130C8×C59—42no—
131C59⋊C8—22no—
132C59⋊C8—22no—
133C59⋊C8—41no—
134C59⋊C8—41no—
135C59⋊C8—81no—
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—22no—
146C4×C59—21no—
147C4×C59—21no—
148C4×C59—41no—
149C4×C59—41no—
150C4×C59—41no—
151C4×C59#43511yescharacteristic
152C4×C59#43511yescharacteristic
153C4×C59#44611yescharacteristic
154C4×C59#44611yescharacteristic
155C4×C59#46311yescharacteristic
156C4×C59#46411yescharacteristic
157C4×C59#47811yescharacteristic
158C4×C59#47911yescharacteristic
159#1831—591no—
160#1767D5911yescharacteristic
161C4×C4⋊C8—591no—
162C2×#335—591no—
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—21no—
180C2×C4×C8—591no—
181C2×C4×C8—591no—
182C43C2×D5911yescharacteristic
183#336—21no—
184#336—591no—
185#336—591no—
186#336—1181no—
187#336—1181no—
188#335—1182no—
189#334—1182no—
190C59#960611yescharacteristic, complemented, Sylow
191C22×C8—21no—
192C22×C8—21no—
193C22×C8—591no—
194C22×C8—591no—
195C22×C8—591no—
196C22×C8—591no—
197C22×C8—1181no—
198C22×C8—1181no—
199C2×C42Dic11811yescharacteristic
200C2×C42Dic11811yescharacteristic
201C2×C42C4×D5911yescharacteristic
202C2×C42C4×D5911yescharacteristic
203C2×C42C22⋊D5911yescharacteristic
204C2×C42C22⋊D5911yescharacteristic
205C2×C42C22×D5911yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—1182no—
209C4⋊C8—1182no—
210C4⋊C8—1181no—
211C4⋊C8—1181no—
212C4⋊C8—1181no—
213C4⋊C8—1181no—
214C4⋊C8Dic11812yes—
215C4⋊C8D23612yes—
216#97—42no—
217C4×C8—1181no—
218C4×C8—1181no—
219C4×C8—1181no—
220C4×C8—1181no—
221C22×C4Dic59⋊C411yescharacteristic
222C22×C4Dic59⋊C411yescharacteristic
223C22×C4Dic59⋊C411yescharacteristic
224C22×C4Dic59⋊C411yescharacteristic
225C22×C4C2×Dic11811yescharacteristic
226C22×C4C2×C4×D5911yescharacteristic
227C22×C4C2×C22⋊D5911yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—592no—
235C2×C8—592no—
236C2×C8—1181no—
237C2×C8—1181no—
238C2×C8—1181no—
239C2×C8—1181no—
240C2×C8—1181no—
241C2×C8—1181no—
242C2×C8—1181no—
243C2×C8—1181no—
244C2×C8—1181no—
245C2×C8—1181no—
246C2×C8—2361no—
247C2×C8—2361no—
248C2×C8—2361no—
249C2×C8—2361no—
250C2×C8—2361no—
251C2×C8—2361no—
252C42—22no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—41no—
262C42C2×Dic11811yescharacteristic
263C42C2×D23611yescharacteristic
264C42#1174568511yescharacteristic
265C42#1174568511yescharacteristic
266C23C2×Dic59⋊C411yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4#1427366212yes—
281C2×C4C4×D23611yescharacteristic
282C2×C4C4×Dic11811yescharacteristic
283C2×C4#1427370111yescharacteristic
284C2×C4#1427370611yescharacteristic
285C2×C4#1427371911yescharacteristic
286C2×C4#1427372711yescharacteristic
287C2×C4M16×D5911yescharacteristic
288C2×C4M16×D5911yescharacteristic
289C2×C4#1427373511yescharacteristic
290C2×C4#1427373511yescharacteristic
291C2×C4#1427374711yescharacteristic
292C2×C4#1427374711yescharacteristic
293C2×C4#1427375311yescharacteristic
294C2×C4#1427375811yescharacteristic
295C8—42no—
296C8—42no—
297C8—1182no—
298C8—1182no—
299C8—4721no—
300C8—4721no—
301C8—2361no—
302C8—2361no—
303C22#1683730011yescharacteristic
304C22#1683742511yescharacteristic
305C22#1683743011yescharacteristic
306C22#1683743811yescharacteristic
307C22#1683744211yescharacteristic
308C22C2×#1427366211yescharacteristic
309C22#1683745011yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4#1683747511yescharacteristic
317C4#1683747511yescharacteristic
318C4#1683753011yescharacteristic
319C4#1683753011yescharacteristic
320C4#1683761711yescharacteristic
321C4#1683762411yescharacteristic
322C4#1683770211yescharacteristic
323C4#1683770911yescharacteristic
324C2#2142285711yescharacteristic
325C2#2142286111yescharacteristic
326C2#2142287711yescharacteristic
327C2#2142288711yescharacteristic
328C2#2142481911yescharacteristic
329C2#2142486411yescharacteristic
330C2#2142487111yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1767C2
socle, prime radicalC23×C59C2×C4⋊C4
cosocleC2×C42×C59C23
hypercenter#1767D59
hypocenterC59#9606
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C43 ◁ #1767

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
#214242132
C4×C4⋊(C59⋊C8)2
C2×#168371542
C2×#168371522
#214219302
C59×#17672
#960659