Finite Group Databasebeta

← #28491884

Subgroups — #28491884

Order 15104.

352 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 75 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#21429754C211yesmaximal, characteristic
2#21425041C211yesmaximal, characteristic
3#21422608C211yesmaximal, characteristic
4#21421988C211yesmaximal, characteristic
5#21421960C211yesmaximal, characteristic
6#21421951C211yesmaximal, characteristic
7C59×#1515C211yesmaximal, characteristic
8#16837459C2211yescharacteristic
9C4×#11745664C2211yescharacteristic
10#16837336—21no—
11#16837334—21no—
12#16837299—21no—
13#16837299—21no—
14#16837289—21no—
15#16837285—21no—
16C4×C4⋊Dic59C2211yescharacteristic
17#16837248C2211yescharacteristic
18#16837161—21no—
19#16837161—21no—
20#16837139—21no—
21#16837139—21no—
22C59×#533C2211yescharacteristic
23C59×#432C2211yescharacteristic
24C59×#383C2211yescharacteristic
25C59×#328—21no—
26C59×#328—21no—
27C2×#11745664—21no—
28C2×C4⋊Dic59—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×Dic59⋊C4—21no—
34C2×Dic59⋊C4—21no—
35C2×C4×Dic59—21no—
36C2×C4×Dic59D411yescharacteristic
37C2×C4×Dic59D411yescharacteristic
38C4⋊(C59⋊C8)—21no—
39C22⋊(C59⋊C8)—21no—
40#14273638—21no—
41#14273638—21no—
42C4×C59⋊C8—21no—
43C59⋊#95—21no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95D411yescharacteristic
48C59⋊#95D411yescharacteristic
49C4⋊Q8×C59Q811yescharacteristic
50C4⋊Q8×C59Q811yescharacteristic
51#125×C59—21no—
52C22⋊Q8×C59—21no—
53C22⋊Q8×C59—21no—
54C4×Q8×C59—21no—
55C4×Q8×C59—21no—
56#117×C59—21no—
57C2×C42×C59C2311yescharacteristic
58C4⋊C8×C59—21no—
59C22⋊C8×C59—21no—
60#97×C59—21no—
61#95×C59—21no—
62#95×C59—21no—
63#95×C59D411yescharacteristic
64#95×C59D411yescharacteristic
65C2×Q8×C59—21no—
66C2×Q8×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59C2×D411yescharacteristic
70C22×C4×C59C2×D411yescharacteristic
71C22×C4×C59C2×D411yescharacteristic
72C22×Dic59—21no—
73C22×Dic59—21no—
74C22×Dic59—21no—
75C22×Dic59—21no—
76C2×C8×C59—41no—
77C4⋊C4×C59—21no—
78C4⋊C4×C59—21no—
79C4⋊C4×C59—21no—
80C4⋊C4×C59—21no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C22⋊C4×C59—41no—
84C42×C59—41no—
85C42×C59C2×Q811yescharacteristic
86C42×C59#4111yescharacteristic
87C42×C59#4111yescharacteristic
88C42×C59#4111yescharacteristic
89C4⋊Dic59—42no—
90C4⋊Dic59—42no—
91C4⋊Dic59—81no—
92Dic59⋊C4—42no—
93Dic59⋊C4—42no—
94Dic59⋊C4—42no—
95Dic59⋊C4—81no—
96C4×Dic59—42no—
97C4×Dic59—41no—
98C4×Dic59—41no—
99#11745664—22no—
100#11745664—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C23×C59#12011yescharacteristic
104Q8×C59—81no—
105Q8×C59—81no—
106C2×C4×C59—21no—
107C2×C4×C59—21no—
108C2×C4×C59—41no—
109C2×C4×C59—41no—
110C2×C4×C59—41no—
111C2×C4×C59—41no—
112C2×C4×C59—41no—
113C2×C4×C59—41no—
114C2×C4×C59—41no—
115C2×C4×C59—41no—
116C2×C4×C59—41no—
117C2×C4×C59—41no—
118C2×C4×C59C22⋊Q811yescharacteristic
119C2×C4×C59C22⋊Q811yescharacteristic
120C2×C4×C59C22⋊Q811yescharacteristic
121C2×C4×C59#12411yescharacteristic
122C2×C4×C59#12411yescharacteristic
123C2×C4×C59#12411yescharacteristic
124C2×Dic59—22no—
125C2×Dic59—22no—
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—41no—
136C8×C59—81no—
137C59⋊C8—42no—
138C59⋊C8—81no—
139#10381—591nomaximal, Sylow
140C22×C59—21no—
141C22×C59—21no—
142C22×C59#39311yescharacteristic
143C22×C59#45511yescharacteristic
144C22×C59#45611yescharacteristic
145C4×C59—21no—
146C4×C59—21no—
147C4×C59—21no—
148C4×C59—21no—
149C4×C59—21no—
150C4×C59—21no—
151C4×C59—81no—
152C4×C59—81no—
153C4×C59—81no—
154C4×C59—81no—
155Dic59—42no—
156Dic59—42no—
157Dic59—81no—
158Dic59—81no—
159#2606—591no—
160#1986—591no—
161#1515D5911yescharacteristic
162#1506—591no—
163#1300—591no—
164#1288—591no—
165#1285—591no—
166C2×C59—21no—
167C2×C59—21no—
168C2×C59#202811yescharacteristic
169C2×C59#203111yescharacteristic
170C2×C59#203111yescharacteristic
171#533C2×D5911yescharacteristic
172#432—591no—
173#432C2×D5911yescharacteristic
174C4×M16—591no—
175#398—1181no—
176#398—1181no—
177#389—1181no—
178#389—1181no—
179#387—1181no—
180#387—1181no—
181#383C2×D5911yescharacteristic
182C4×C4⋊C4—591no—
183#376—591no—
184#339—1181no—
185#339—1181no—
186#328—21no—
187#328—21no—
188#328—1181no—
189#328—1181no—
190C59#1038111yescharacteristic, complemented, Sylow
191C2×M16—1181no—
192C4⋊Q8Dic11811yescharacteristic
193C4⋊Q8Dic11811yescharacteristic
194#125—21no—
195C22⋊Q8—21no—
196C22⋊Q8—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199#117—21no—
200C2×C4⋊C4—1181no—
201C2×C4⋊C4—1181no—
202C2×C4⋊C4—1181no—
203C2×C4⋊C4—1181no—
204C2×C4⋊C4—1181no—
205C2×C4⋊C4—1181no—
206C2×C4⋊C4—1181no—
207C2×C42—591no—
208C2×C42—591no—
209C2×C42—1181no—
210C2×C42C22×D5911yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—1181no—
213C22⋊C8—21no—
214C22⋊C8—1181no—
215#97—21no—
216#97—1181no—
217#97—1181no—
218C4×C8—1181no—
219#95—21no—
220#95—21no—
221#95—591no—
222#95—591no—
223#95—1181no—
224#95—1181no—
225#95—1181no—
226#95—1181no—
227#95C22⋊D5911yescharacteristic
228#95C22⋊D5911yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—1181no—
234C22×C4—1181no—
235C22×C4—1181no—
236C22×C4—1181no—
237C22×C4D4×D5911yescharacteristic
238C22×C4D4×D5911yescharacteristic
239C22×C4C2×C22⋊D5911yescharacteristic
240M16—1182no—
241M16—2361no—
242C2×C8—41no—
243C2×C8—2361no—
244C2×C8—2361no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—4721no—
252C4⋊C4—4721no—
253C4⋊C4—2362no—
254C4⋊C4—2362no—
255C4⋊C4—2362no—
256C4⋊C4—2362no—
257C4⋊C4—2362no—
258C22⋊C4—41no—
259C42—41no—
260C42—2361no—
261C42—2361no—
262C42—2362no—
263C42C2×Dic11811yescharacteristic
264C42#1174568511yescharacteristic
265C42#1174568711yescharacteristic
266C42#1174568711yescharacteristic
267C23#1427369511yescharacteristic
268Q8—81no—
269Q8—81no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—1182no—
283C2×C4—1182no—
284C2×C4—2361no—
285C2×C4—2361no—
286C2×C4—2361no—
287C2×C4—2361no—
288C2×C4—2361no—
289C2×C4—2361no—
290C2×C4—2361no—
291C2×C4—2361no—
292C2×C4—2361no—
293C2×C4—2361no—
294C2×C4#1427370411yescharacteristic
295C2×C4#1427370411yescharacteristic
296C2×C4#1427370611yescharacteristic
297C2×C4#1427371311yescharacteristic
298C2×C4#1427371311yescharacteristic
299C2×C4#1427371411yescharacteristic
300C8—81no—
301C8—4721no—
302C8—2362no—
303C22—21no—
304C22—21no—
305C22#1683731411yescharacteristic
306C22#1683757811yescharacteristic
307C22#1683758311yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—81no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4—4721no—
319C4—4721no—
320C4—2362no—
321C4—2362no—
322C2—21no—
323C2—21no—
324C2#2142525511yescharacteristic
325C2#2142526611yescharacteristic
326C2#2142527011yescharacteristic
subgroupG/H
centerC22#16837314
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1515C2
socleC22×C59#393
prime radicalC23×C59#120
hypercenter#1515D59
hypocenterC59#10381
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1515

Complements

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

NH ≅ G/Ntype
190. C59#10381semidirect

Maximal subgroups

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

subgroupindex
#214297542
#214250412
#214226082
#214219882
#214219602
#214219512
C59×#15152
#1038159