Finite Group Databasebeta

← #28477900

Subgroups — #28477900

Order 15104.

378 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 85 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#21432058C211yesmaximal, characteristic
2#21425638C211yesmaximal, characteristic
3#21425572C211yesmaximal, characteristic
4#21425506C211yesmaximal, characteristic
5#21421921C211yesmaximal, characteristic
6#21421921C211yesmaximal, characteristic
7C59×#1271C211yesmaximal, characteristic
8C2×#14273659—21no—
9C2×#14273658—21no—
10C2×#14273652—21no—
11C2×#14273652—21no—
12#16837335—21no—
13#16837334—21no—
14#16837322—21no—
15#16837308C2211yescharacteristic
16#16837308C2211yescharacteristic
17#16837306—21no—
18#16837301—21no—
19#16837288—21no—
20#16837272C2211yescharacteristic
21#16837165—21no—
22#16837164—21no—
23#16837157C2211yescharacteristic
24C59×#389C2211yescharacteristic
25C59×#336C2211yescharacteristic
26C59×#336C2211yescharacteristic
27C22×Dic118D411yescharacteristic
28C22×Dic118D411yescharacteristic
29C22×C59⋊C8—21no—
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×Dic59⋊C4—21no—
38C2×Dic59⋊C4—21no—
39C2×C4×Dic59—21no—
40#14273659—42no—
41#14273658—42no—
42#14273652—42no—
43#14273652—42no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—21no—
51C22×C8×C59—21no—
52C22×C8×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C4⋊C4×C59D411yescharacteristic
55C2×C4⋊C4×C59D411yescharacteristic
56C2×C42×C59C2311yescharacteristic
57#95×C59—21no—
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×Dic59—21no—
64C22×Dic59—21no—
65C22×Dic59—21no—
66C22×Dic59—21no—
67C22×Dic59—41no—
68C2×Dic118—21no—
69C2×Dic118—21no—
70C2×Dic118—21no—
71C2×Dic118—41no—
72C2×Dic118—41no—
73C2×Dic118—41no—
74C2×Dic118—41no—
75C2×Dic118SD1612yes—
76C2×C8×C59—22no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C2×C8×C59—41no—
80C2×C8×C59—41no—
81C2×C8×C59—41no—
82C4⋊C4×C59—21no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59SD1612yes—
87C42×C59—41no—
88C4⋊Dic59—41no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59—41no—
93C4⋊Dic59—41no—
94C4⋊Dic59—41no—
95C4⋊Dic59—41no—
96C4⋊Dic59—81no—
97C4⋊Dic59—81no—
98Dic59⋊C4—81no—
99Dic59⋊C4—81no—
100C4×Dic59—81no—
101C2×C59⋊C8—22no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C23×C59#12011yescharacteristic
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—22no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59C2×SD1611yescharacteristic
118C2×C4×C59C2×SD1611yescharacteristic
119C2×C4×C59#13511yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×C4×C59#13711yescharacteristic
122C2×C4×C59#13711yescharacteristic
123C2×Dic59—22no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C2×Dic59—41no—
129C2×Dic59—41no—
130C2×Dic59—41no—
131C2×Dic59—41no—
132C2×Dic59—41no—
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—81no—
136C2×Dic59—81no—
137C2×Dic59—81no—
138Dic118—42no—
139Dic118—42no—
140Dic118—81no—
141Dic118—81no—
142C8×C59—42no—
143C8×C59—81no—
144C59⋊C8—42no—
145#7814—591nomaximal, Sylow
146C22×C59#44811yescharacteristic
147C22×C59#44811yescharacteristic
148C22×C59#45211yescharacteristic
149C22×C59#45311yescharacteristic
150C22×C59#45511yescharacteristic
151C22×C59#45611yescharacteristic
152C22×C59#45811yescharacteristic
153C4×C59—21no—
154C4×C59—21no—
155C4×C59—21no—
156C4×C59—21no—
157C4×C59—21no—
158C4×C59—21no—
159C4×C59—42no—
160C4×C59—81no—
161Dic59—42no—
162Dic59—81no—
163Dic59—81no—
164Dic59—81no—
165Dic59—161no—
166#2806—591no—
167#2096—591no—
168#2084—591no—
169#2072—591no—
170#1272—591no—
171#1272—591no—
172#1271D5911yescharacteristic
173C2×C59#160811yescharacteristic
174C2×C59#161111yescharacteristic
175C2×C59#161811yescharacteristic
176C2×C59#162311yescharacteristic
177C2×C59#164311yescharacteristic
178C2×C59#165311yescharacteristic
179C2×C59#166111yescharacteristic
180C2×#106—1181no—
181C2×#106—1181no—
182C2×#103—1181no—
183C2×#103—1181no—
184#398—1181no—
185#398—1181no—
186#395—1181no—
187#391—591no—
188#391—591no—
189#391—1181no—
190#389—1181no—
191#389C2×D5911yescharacteristic
192#387—1181no—
193#384—591no—
194#340—1181no—
195#340—1181no—
196#336—591no—
197#336C2×D5911yescharacteristic
198#336C2×D5911yescharacteristic
199C59#781411yescharacteristic, complemented, Sylow
200C22×Q8—591no—
201C22×Q8—591no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—1181no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—591no—
207C2×C4⋊C4—591no—
208C2×C4⋊C4—1181no—
209C2×C4⋊C4—1181no—
210C2×C4⋊C4—1181no—
211C2×C4⋊C4—1181no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4—1181no—
214C2×C4⋊C4—1181no—
215C2×C4⋊C4D23611yescharacteristic
216C2×C4⋊C4D23611yescharacteristic
217C2×C42—1181no—
218C2×C42C22×D5911yescharacteristic
219#106—2362no—
220#106—2362no—
221#103—2362no—
222#103—2362no—
223#95—21no—
224#95—1181no—
225#95—1181no—
226#95—1181no—
227#95—1181no—
228#95—1181no—
229#95—1181no—
230#95—1181no—
231C2×Q8—592no—
232C2×Q8—1181no—
233C2×Q8—1181no—
234C2×Q8—1181no—
235C2×Q8—2361no—
236C2×Q8—2361no—
237C2×Q8—2361no—
238C2×Q8—2361no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—1181no—
242C22×C4—1181no—
243C22×C4—1181no—
244C22×C4—1181no—
245C22×C4—2361no—
246C22×C4C2×D23611yescharacteristic
247C22×C4D4×D5911yescharacteristic
248C22×C4D4×D5911yescharacteristic
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—1182no—
256C2×C8—2361no—
257C2×C8—2361no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—4721no—
263C4⋊C4—4721no—
264C4⋊C4—4721no—
265C4⋊C4—4721no—
266C4⋊C4—2361no—
267C4⋊C4—2361no—
268C4⋊C4—2361no—
269C4⋊C4—2361no—
270C4⋊C4—2361no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4—2361no—
274C4⋊C4#1174566012yes—
275C42—41no—
276C42—4721no—
277C23#1427369711yescharacteristic
278Q8—4721no—
279Q8—4721no—
280Q8—2362no—
281Q8—2362no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—1182no—
295C2×C4—4721no—
296C2×C4—4721no—
297C2×C4—4721no—
298C2×C4—2361no—
299C2×C4—2361no—
300C2×C4—2361no—
301C2×C4—2361no—
302C2×C4—2361no—
303C2×C4—2361no—
304C2×C4—2361no—
305C2×C4—2361no—
306C2×C4—2361no—
307C2×C4—2361no—
308C2×C4—2361no—
309C2×C4SD16×D5911yescharacteristic
310C2×C4C2×#1174566011yescharacteristic
311C2×C4#1427374611yescharacteristic
312C2×C4#1427375611yescharacteristic
313C2×C4#1427375911yescharacteristic
314C2×C4#1427376011yescharacteristic
315C8—42no—
316C8—81no—
317C8—2362no—
318C22#1683754211yescharacteristic
319C22#1683754311yescharacteristic
320C22#1683756511yescharacteristic
321C22#1683757111yescharacteristic
322C22#1683758111yescharacteristic
323C22#1683758711yescharacteristic
324C22#1683759311yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—81no—
333C4—9441no—
334C4—4721no—
335C4—4721no—
336C4—4721no—
337C4—2362no—
338C2#2142308811yescharacteristic
339C2#2142310611yescharacteristic
340C2#2142314511yescharacteristic
341C2#2142317611yescharacteristic
342C2#2142330511yescharacteristic
343C2#2142337411yescharacteristic
344C2#2142341511yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1271C2
socle, prime radicalC23×C59#120
hypercenter#1271D59
hypocenterC59#7814
LCSG ▷ C2×C42×C59 ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
199. C59#7814semidirect

Maximal subgroups

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

subgroupindex
#214320582
#214256382
#214255722
#214255062
#214219212
C59×#12712
#781459