Finite Group Databasebeta

← #28477899

Subgroups — #28477899

Order 15104.

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

normal subgroups only

This group has 378 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#21425639C211yesmaximal, characteristic
2#21425572C211yesmaximal, characteristic
3#21425504C211yesmaximal, characteristic
4#21421922C211yesmaximal, characteristic
5#21421922C211yesmaximal, characteristic
6#21421919C211yesmaximal, characteristic
7C59×#2806C211yesmaximal, characteristic
8C2×#14273658—21no—
9C2×#14273658—21no—
10C2×#14273651—21no—
11C2×#14273651—21no—
12#16837272C2211yescharacteristic
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#14273658—42no—
34#14273658—42no—
35#14273651—42no—
36#14273651—42no—
37C22×Q8×C59D411yescharacteristic
38C22×Q8×C59D411yescharacteristic
39C2×C4⋊C4×C59—21no—
40C2×C4⋊C4×C59—21no—
41C2×C4⋊C4×C59—21no—
42C2×C4⋊C4×C59—21no—
43C2×C4⋊C4×C59—21no—
44C2×C4⋊C4×C59D411yescharacteristic
45C2×C4⋊C4×C59D411yescharacteristic
46C2×C4⋊C4×C59D411yescharacteristic
47C2×C4⋊C4×C59D411yescharacteristic
48C2×C42×C59—21no—
49C2×C42×C59C2311yescharacteristic
50#95×C59—21no—
51#95×C59—21no—
52#95×C59—21no—
53#95×C59—21no—
54#95×C59—21no—
55#95×C59—21no—
56#95×C59—21no—
57#95×C59—21no—
58C2×Q8×C59—21no—
59C2×Q8×C59—21no—
60C2×Q8×C59—21no—
61C2×Q8×C59—41no—
62C2×Q8×C59—41no—
63C2×Q8×C59—41no—
64C2×Q8×C59—41no—
65C2×Q8×C59SD1612yes—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59C2×D411yescharacteristic
73C22×C4×C59C2×D411yescharacteristic
74C22×C4×C59C2×D411yescharacteristic
75C22×Dic59—41no—
76C4⋊C4×C59—21no—
77C4⋊C4×C59—41no—
78C4⋊C4×C59—41no—
79C4⋊C4×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—81no—
83C4⋊C4×C59—81no—
84C4⋊C4×C59—81no—
85C4⋊C4×C59—81no—
86C4⋊C4×C59SD1612yes—
87C42×C59—41no—
88C42×C59—81no—
89C4⋊Dic59—41no—
90C4⋊Dic59—41no—
91C4⋊Dic59—41no—
92C4⋊Dic59—41no—
93C4⋊Dic59—41no—
94C4⋊Dic59—41no—
95C2×C59⋊C8—22no—
96C2×C59⋊C8—22no—
97C2×C59⋊C8—41no—
98C2×C59⋊C8—41no—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C23×C59#12011yescharacteristic
105Q8×C59—42no—
106Q8×C59—42no—
107Q8×C59—81no—
108Q8×C59—81no—
109C2×C4×C59—21no—
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—22no—
116C2×C4×C59—22no—
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×C59—41no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59C2×SD1611yescharacteristic
134C2×C4×C59C2×SD1611yescharacteristic
135C2×C4×C59#13511yescharacteristic
136C2×C4×C59#13711yescharacteristic
137C2×C4×C59#13711yescharacteristic
138C2×C4×C59#13711yescharacteristic
139C2×Dic59—81no—
140C2×Dic59—81no—
141C2×Dic59—81no—
142C59⋊C8—42no—
143C59⋊C8—42no—
144C59⋊C8—81no—
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—42no—
161C4×C59—81no—
162C4×C59—81no—
163C4×C59—81no—
164C4×C59—81no—
165Dic59—161no—
166#2806D5911yescharacteristic
167#2096—591no—
168#2084—591no—
169#2072—591no—
170#1272—591no—
171#1272—591no—
172#1271—591no—
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—21no—
185#398—21no—
186#395—21no—
187#391—21no—
188#391C2×D5911yescharacteristic
189#391C2×D5911yescharacteristic
190#389—21no—
191#389C2×D5911yescharacteristic
192#387—21no—
193#384—591no—
194#340—1181no—
195#340—1181no—
196#336—591no—
197#336—591no—
198#336—591no—
199C59#781411yescharacteristic, complemented, Sylow
200C22×Q8C22⋊D5911yescharacteristic
201C22×Q8C22⋊D5911yescharacteristic
202C22×C8—1181no—
203C22×C8—1181no—
204C22×C8—1181no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—1181no—
211C2×C4⋊C4—1181no—
212C2×C4⋊C4—1181no—
213C2×C4⋊C4C22⋊D5911yescharacteristic
214C2×C4⋊C4C22⋊D5911yescharacteristic
215C2×C4⋊C4C22⋊D5911yescharacteristic
216C2×C4⋊C4C22⋊D5911yescharacteristic
217C2×C42—21no—
218C2×C42C22×D5911yescharacteristic
219#106—2362no—
220#106—2362no—
221#103—2362no—
222#103—2362no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8#1174567112yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—2361no—
246C22×C4C2×C22⋊D5911yescharacteristic
247C22×C4C2×C22⋊D5911yescharacteristic
248C22×C4C2×C22⋊D5911yescharacteristic
249C2×C8—1182no—
250C2×C8—1182no—
251C2×C8—2361no—
252C2×C8—2361no—
253C2×C8—2361no—
254C2×C8—2361no—
255C2×C8—2361no—
256C2×C8—2361no—
257C2×C8—2361no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—2361no—
269C4⋊C4—2361no—
270C4⋊C4—2361no—
271C4⋊C4—2361no—
272C4⋊C4—2361no—
273C4⋊C4—2361no—
274C4⋊C4#1174567112yes—
275C42—41no—
276C42—81no—
277C23#1427369611yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—22no—
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—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—4721no—
307C2×C4—4721no—
308C2×C4—4721no—
309C2×C4C2×#1174567111yescharacteristic
310C2×C4C2×#1174567111yescharacteristic
311C2×C4#1427374711yescharacteristic
312C2×C4#1427375711yescharacteristic
313C2×C4#1427375811yescharacteristic
314C2×C4#1427375811yescharacteristic
315C8—4721no—
316C8—2362no—
317C8—2362no—
318C22#1683754111yescharacteristic
319C22#1683754111yescharacteristic
320C22#1683756411yescharacteristic
321C22#1683757011yescharacteristic
322C22#1683758011yescharacteristic
323C22#1683758511yescharacteristic
324C22#1683759211yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—42no—
332C4—42no—
333C4—81no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4—9441no—
338C2#2142308711yescharacteristic
339C2#2142310411yescharacteristic
340C2#2142314411yescharacteristic
341C2#2142317411yescharacteristic
342C2#2142330311yescharacteristic
343C2#2142337311yescharacteristic
344C2#2142341311yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2806C2
socle, prime radicalC23×C59#120
hypercenter#2806D59
hypocenterC59#7814
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
199. C59#7814semidirect

Maximal subgroups

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

subgroupindex
#214256392
#214255722
#214255042
#214219222
#214219192
C59×#28062
#781459