Finite Group Databasebeta

← #28477823

Subgroups — #28477823

Order 15104.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#21432087C211yesmaximal, characteristic
2#21425653C211yesmaximal, characteristic
3#21425568C211yesmaximal, characteristic
4#21421920C211yesmaximal, characteristic
5#21421919C211yesmaximal, characteristic
6#21421918C211yesmaximal, characteristic
7C59×#2084C211yesmaximal, characteristic
8C2×#14273660—21no—
9#16837342—21no—
10#16837341—21no—
11#16837340—21no—
12#16837300C2211yescharacteristic
13#16837300C2211yescharacteristic
14#16837289—21no—
15#16837288—21no—
16#16837283—21no—
17#16837164—21no—
18#16837164—21no—
19#16837164—21no—
20#16837157C2211yescharacteristic
21#16837157C2211yescharacteristic
22C2×#106×C59—21no—
23C59×#389C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C59×#340—21no—
26C59×#336C2211yescharacteristic
27C22×C59⋊C8—21no—
28C22×C59⋊C8—21no—
29C2×C4⋊Dic59D411yescharacteristic
30C2×C4⋊Dic59D411yescharacteristic
31C2×C4⋊Dic59D411yescharacteristic
32C2×C4⋊Dic59D411yescharacteristic
33C2×Dic59⋊C4—21no—
34C2×Dic59⋊C4—21no—
35C2×C4×Dic59—21no—
36#14273660—42no—
37C59⋊#95—21no—
38C59⋊#95—21no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C59⋊#95—21no—
42C59⋊#95—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C22×C8×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59D411yescharacteristic
52C2×C4⋊C4×C59D411yescharacteristic
53C2×C42×C59C2311yescharacteristic
54#106×C59—42no—
55#95×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59—21no—
58C22×C4×C59—41no—
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×Dic59—21no—
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66C2×C8×C59—22no—
67C2×C8×C59—41no—
68C2×C8×C59—41no—
69C4⋊C4×C59—21no—
70C4⋊C4×C59—21no—
71C4⋊C4×C59—41no—
72C4⋊C4×C59—42no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C4⋊C4×C59—41no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C42×C59—41no—
80C4⋊Dic59—21no—
81C4⋊Dic59—21no—
82C4⋊Dic59—21no—
83C4⋊Dic59—21no—
84C4⋊Dic59—41no—
85C4⋊Dic59—41no—
86Dic59⋊C4—41no—
87Dic59⋊C4—41no—
88Dic59⋊C4—41no—
89Dic59⋊C4—41no—
90C4×Dic59—81no—
91C2×C59⋊C8—22no—
92C2×C59⋊C8—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C23×C59#12011yescharacteristic
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—21no—
103C2×C4×C59—21no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—81no—
111C2×C4×C59—81no—
112C2×C4×C59—81no—
113C2×C4×C59#13511yescharacteristic
114C2×C4×C59#13511yescharacteristic
115C2×C4×C59#13511yescharacteristic
116C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C59#13711yescharacteristic
119C2×Dic59—41no—
120C2×Dic59—41no—
121C2×Dic59—41no—
122C2×Dic59—41no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C8×C59—42no—
132C59⋊C8—42no—
133C59⋊C8—81no—
134#7803—591nomaximal, Sylow
135C22×C59#44911yescharacteristic
136C22×C59#44911yescharacteristic
137C22×C59#45211yescharacteristic
138C22×C59#45411yescharacteristic
139C22×C59#45611yescharacteristic
140C22×C59#45611yescharacteristic
141C22×C59#45811yescharacteristic
142C4×C59—21no—
143C4×C59—21no—
144C4×C59—21no—
145C4×C59—21no—
146C4×C59—21no—
147C4×C59—21no—
148C4×C59—81no—
149C4×C59—81no—
150C4×C59—161no—
151Dic59—81no—
152Dic59—81no—
153Dic59—81no—
154Dic59—81no—
155#2810—591no—
156#2099—591no—
157#2084D5911yescharacteristic
158#2083—591no—
159#1271—591no—
160#1271—591no—
161#1271—591no—
162C2×C59#160911yescharacteristic
163C2×C59#160911yescharacteristic
164C2×C59#161511yescharacteristic
165C2×C59#162811yescharacteristic
166C2×C59#165011yescharacteristic
167C2×C59#165211yescharacteristic
168C2×C59#166311yescharacteristic
169C2×#107—1181no—
170C2×#106—21no—
171#400—1181no—
172#400—1181no—
173#400—1181no—
174#389—591no—
175#389—591no—
176#389C2×D5911yescharacteristic
177#387—1181no—
178#387—1181no—
179#387—1181no—
180#384C2×D5911yescharacteristic
181#340—21no—
182#340—1181no—
183#340—1181no—
184#340—1181no—
185#336—591no—
186#336—591no—
187#336C2×D5911yescharacteristic
188C59#780311yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—1181no—
191C22×C8—1181no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—591no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4—591no—
199C2×C4⋊C4—591no—
200C2×C4⋊C4—1181no—
201C2×C4⋊C4—1181no—
202C2×C4⋊C4C22⋊D5911yescharacteristic
203C2×C4⋊C4C22⋊D5911yescharacteristic
204C2×C42—1181no—
205C2×C42C22×D5911yescharacteristic
206#107—2362no—
207#106—42no—
208#95—21no—
209#95—1181no—
210#95—1181no—
211#95—1181no—
212#95—1181no—
213#95—1181no—
214#95—1181no—
215#95—1181no—
216#95—1181no—
217#95—1181no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—41no—
221C22×C4—1181no—
222C22×C4—1181no—
223C22×C4—1181no—
224C22×C4—1181no—
225C22×C4D4×D5911yescharacteristic
226C22×C4D4×D5911yescharacteristic
227C22×C4C2×C22⋊D5911yescharacteristic
228C2×C8—22no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—1182no—
232C2×C8—2361no—
233C2×C8—2361no—
234C2×C8—2361no—
235C2×C8—2361no—
236C2×C8—2361no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—1181no—
248C4⋊C4—1181no—
249C4⋊C4—1181no—
250C4⋊C4—1181no—
251C4⋊C4—2361no—
252C4⋊C4—2361no—
253C4⋊C4—2361no—
254C4⋊C4—2361no—
255C4⋊C4—2361no—
256C4⋊C4—2361no—
257C42—41no—
258C42—4721no—
259C23#1427369511yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—2361no—
276C2×C4—2361no—
277C2×C4—2361no—
278C2×C4—2361no—
279C2×C4—2361no—
280C2×C4—2361no—
281C2×C4—2361no—
282C2×C4—2361no—
283C2×C4—2361no—
284C2×C4—2361no—
285C2×C4—2361no—
286C2×C4—2361no—
287C2×C4#1427374711yescharacteristic
288C2×C4#1427374811yescharacteristic
289C2×C4#1427374811yescharacteristic
290C2×C4#1427375311yescharacteristic
291C2×C4#1427375411yescharacteristic
292C2×C4#1427375611yescharacteristic
293C8—42no—
294C8—4721no—
295C8—2362no—
296C22#1683754511yescharacteristic
297C22#1683754611yescharacteristic
298C22#1683756111yescharacteristic
299C22#1683757311yescharacteristic
300C22#1683758311yescharacteristic
301C22#1683758411yescharacteristic
302C22#1683759111yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—161no—
312C4—4721no—
313C4—4721no—
314C4—4721no—
315C4—4721no—
316C2#2142309111yescharacteristic
317C2#2142309211yescharacteristic
318C2#2142312411yescharacteristic
319C2#2142320511yescharacteristic
320C2#2142335011yescharacteristic
321C2#2142336311yescharacteristic
322C2#2142342311yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2084C2
socle, prime radicalC23×C59#120
hypercenter#2084D59
hypocenterC59#7803
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2084

Complements

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

NH ≅ G/Ntype
188. C59#7803semidirect

Maximal subgroups

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

subgroupindex
#214320872
#214256532
#214255682
#214219202
#214219192
#214219182
C59×#20842
#780359