Finite Group Databasebeta

← #28477913

Subgroups — #28477913

Order 15104.

362 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425654C211yesmaximal, characteristic
2#21425504C211yesmaximal, characteristic
3#21425504C211yesmaximal, characteristic
4#21421922C211yesmaximal, characteristic
5#21421922C211yesmaximal, characteristic
6#21421919C211yesmaximal, characteristic
7C59×#2806C211yesmaximal, characteristic
8C2×#14273651—21no—
9C2×#14273651—21no—
10#16837272C2211yescharacteristic
11#16837164—21no—
12#16837164—21no—
13#16837164—21no—
14#16837164—21no—
15#16837157C2211yescharacteristic
16#16837157C2211yescharacteristic
17#16837157C2211yescharacteristic
18C59×#398—21no—
19C59×#398—21no—
20C59×#395—21no—
21C59×#391—21no—
22C59×#391C2211yescharacteristic
23C59×#391C2211yescharacteristic
24C59×#389—21no—
25C59×#389C2211yescharacteristic
26C59×#387—21no—
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29C22×C59⋊C8—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33#14273651—42no—
34#14273651—42no—
35C22×Q8×C59D411yescharacteristic
36C22×Q8×C59D411yescharacteristic
37C2×C4⋊C4×C59—21no—
38C2×C4⋊C4×C59—21no—
39C2×C4⋊C4×C59—21no—
40C2×C4⋊C4×C59—21no—
41C2×C4⋊C4×C59—21no—
42C2×C4⋊C4×C59D411yescharacteristic
43C2×C4⋊C4×C59D411yescharacteristic
44C2×C4⋊C4×C59D411yescharacteristic
45C2×C4⋊C4×C59D411yescharacteristic
46C2×C42×C59—21no—
47C2×C42×C59C2311yescharacteristic
48#95×C59—21no—
49#95×C59—21no—
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—21no—
55#95×C59—21no—
56C2×Q8×C59—21no—
57C2×Q8×C59—21no—
58C2×Q8×C59—21no—
59C2×Q8×C59—41no—
60C2×Q8×C59—41no—
61C2×Q8×C59—41no—
62C2×Q8×C59—41no—
63C2×Q8×C59SD1612yes—
64C22×C4×C59—21no—
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×C4×C59C2×D411yescharacteristic
73C22×Dic59—41no—
74C4⋊C4×C59—21no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—81no—
81C4⋊C4×C59—81no—
82C4⋊C4×C59—81no—
83C4⋊C4×C59—81no—
84C4⋊C4×C59Q1612yes—
85C42×C59—41no—
86C42×C59—81no—
87C4⋊Dic59—42no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
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—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C23×C59#12011yescharacteristic
102Q8×C59—42no—
103Q8×C59—42no—
104Q8×C59—81no—
105Q8×C59—81no—
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—22no—
113C2×C4×C59—22no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—41no—
120C2×C4×C59—41no—
121C2×C4×C59—41no—
122C2×C4×C59—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59C2×SD1611yescharacteristic
131C2×C4×C59C2×Q1611yescharacteristic
132C2×C4×C59#13511yescharacteristic
133C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C59#13711yescharacteristic
135C2×C4×C59#13711yescharacteristic
136C2×Dic59—81no—
137C2×Dic59—81no—
138C2×Dic59—81no—
139C59⋊C8—81no—
140C59⋊C8—81no—
141C59⋊C8—81no—
142#7816—591nomaximal, Sylow
143C22×C59#44811yescharacteristic
144C22×C59#44911yescharacteristic
145C22×C59#45111yescharacteristic
146C22×C59#45411yescharacteristic
147C22×C59#45511yescharacteristic
148C22×C59#45511yescharacteristic
149C22×C59#45811yescharacteristic
150C4×C59—21no—
151C4×C59—21no—
152C4×C59—21no—
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—42no—
157C4×C59—42no—
158C4×C59—81no—
159C4×C59—81no—
160C4×C59—81no—
161C4×C59—81no—
162Dic59—161no—
163#2806D5911yescharacteristic
164#2099—591no—
165#2072—591no—
166#2072—591no—
167#1272—591no—
168#1272—591no—
169#1271—591no—
170C2×C59#160811yescharacteristic
171C2×C59#161211yescharacteristic
172C2×C59#161711yescharacteristic
173C2×C59#162611yescharacteristic
174C2×C59#164411yescharacteristic
175C2×C59#164511yescharacteristic
176C2×C59#166211yescharacteristic
177C2×#103—1181no—
178C2×#103—1181no—
179#398—21no—
180#398—21no—
181#395—21no—
182#391—21no—
183#391C2×D5911yescharacteristic
184#391C2×D5911yescharacteristic
185#389—21no—
186#389C2×D5911yescharacteristic
187#387—21no—
188#384—591no—
189#340—1181no—
190#340—1181no—
191#340—1181no—
192#340—1181no—
193#336—591no—
194#336—591no—
195#336—591no—
196C59#781611yescharacteristic, complemented, Sylow
197C22×Q8C22⋊D5911yescharacteristic
198C22×Q8C22⋊D5911yescharacteristic
199C22×C8—1181no—
200C22×C8—1181no—
201C22×C8—1181no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—1181no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4C22⋊D5911yescharacteristic
211C2×C4⋊C4C22⋊D5911yescharacteristic
212C2×C4⋊C4C22⋊D5911yescharacteristic
213C2×C4⋊C4C22⋊D5911yescharacteristic
214C2×C42—21no—
215C2×C42C22×D5911yescharacteristic
216#103—2362no—
217#103—2362no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8#1174567112yes—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—2361no—
241C22×C4C2×C22⋊D5911yescharacteristic
242C22×C4C2×C22⋊D5911yescharacteristic
243C22×C4C2×C22⋊D5911yescharacteristic
244C2×C8—2361no—
245C2×C8—2361no—
246C2×C8—2361no—
247C2×C8—2361no—
248C2×C8—2361no—
249C2×C8—2361no—
250C2×C8—2361no—
251C2×C8—2361no—
252C2×C8—2361no—
253C4⋊C4—21no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C4⋊C4—2362no—
264C4⋊C4—2361no—
265C4⋊C4—2361no—
266C4⋊C4—2361no—
267C4⋊C4—2361no—
268C4⋊C4#1174567212yes—
269C42—41no—
270C42—81no—
271C23#1427369611yescharacteristic
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—4721no—
301C2×C4—4721no—
302C2×C4—4721no—
303C2×C4C2×#1174567111yescharacteristic
304C2×C4C2×#1174567211yescharacteristic
305C2×C4#1427374711yescharacteristic
306C2×C4#1427375211yescharacteristic
307C2×C4#1427375811yescharacteristic
308C2×C4#1427375811yescharacteristic
309C8—4721no—
310C8—4721no—
311C8—4721no—
312C22#1683754111yescharacteristic
313C22#1683754711yescharacteristic
314C22#1683755811yescharacteristic
315C22#1683757511yescharacteristic
316C22#1683758011yescharacteristic
317C22#1683758011yescharacteristic
318C22#1683759211yescharacteristic
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—81no—
328C4—81no—
329C4—81no—
330C4—81no—
331C4—9441no—
332C2#2142308711yescharacteristic
333C2#2142311011yescharacteristic
334C2#2142313811yescharacteristic
335C2#2142319211yescharacteristic
336C2#2142331011yescharacteristic
337C2#2142331711yescharacteristic
338C2#2142341911yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2806C2
socle, prime radicalC23×C59#120
hypercenter#2806D59
hypocenterC59#7816
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2806

Complements

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

NH ≅ G/Ntype
196. C59#7816semidirect

Maximal subgroups

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

subgroupindex
#214256542
#214255042
#214219222
#214219192
C59×#28062
#781659