Finite Group Databasebeta

← #28483693

Subgroups — #28483693

Order 15104.

836 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C2×#16837314C211yesmaximal, characteristic
2#21424030C212yesmaximal, complemented
3C2×#16837126C211yesmaximal, characteristic
4#21421974C212yesmaximal, complemented
5C59×#2312C211yesmaximal, characteristic
6C23×Dic118C2211yescharacteristic
7C22×C22⋊Dic59—21no—
8C2×#14273650—24no—
9C2×C22⋊(C59⋊C8)C2212yes—
10#16837314—22no—
11#16837314C414yescomplemented
12C2×C59⋊#95—21no—
13C2×C59⋊#95C2211yescharacteristic
14#16837126—22no—
15C22×C22⋊C4×C59C2211yescharacteristic
16C59×#388—24no—
17C59×#380C2212yes—
18C59×#379—21no—
19C4×C22⋊C4×C59—21no—
20C22×Dic118—22no—
21C22×Dic118—22no—
22C22×Dic118—21no—
23C22×Dic118—44no—
24C22×Dic118C2×C412yes—
25C23×Dic59—21no—
26C23×Dic59—21no—
27C22×C59⋊C8—22no—
28C2×C22⋊Dic59—24no—
29C2×C22⋊Dic59—44no—
30#14273650—48no—
31C22⋊(C59⋊C8)—22no—
32C22⋊(C59⋊C8)—22no—
33C59⋊#95—24no—
34C59⋊#95—21no—
35C59⋊#95C2×C412yes—
36C25×C59D411yescharacteristic
37C23×C4×C59D411yescharacteristic
38C23×C4×C59C2311yescharacteristic
39C2×C4⋊C4×C59D414yes—
40C2×C22⋊C4×C59—22no—
41C2×C22⋊C4×C59—22no—
42C2×C22⋊C4×C59—22no—
43C2×C22⋊C4×C59—22no—
44C2×C22⋊C4×C59—22no—
45C2×C22⋊C4×C59C2×C412yes—
46C2×C22⋊C4×C59D412yes—
47C2×C42×C59—22no—
48#95×C59—22no—
49#95×C59—22no—
50C24×C59—21no—
51C24×C59—22no—
52C24×C59—21no—
53C24×C59—22no—
54C24×C59—42no—
55C24×C59—42no—
56C24×C59C22⋊C412yes—
57C24×C59C2×D411yescharacteristic
58C22×C4×C59—21no—
59C22×C4×C59—21no—
60C22×C4×C59—24no—
61C22×C4×C59—42no—
62C22×C4×C59—42no—
63C22×C4×C59C22⋊C412yes—
64C22×C4×C59C22×C411yescharacteristic
65C22×C4×C59C2×D412yes—
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59#4112yes—
68C22×Dic59—24no—
69C22×Dic59—22no—
70C22×Dic59—22no—
71C22×Dic59—42no—
72C22×Dic59—41no—
73C22×Dic59—41no—
74C22×Dic59—42no—
75C22×Dic59—42no—
76C22×Dic59—42no—
77C2×Dic118—28no—
78C2×Dic118—24no—
79C2×Dic118—44no—
80C2×Dic118—48no—
81C2×Dic118—44no—
82C2×Dic118—44no—
83C2×Dic118—42no—
84C4⋊C4×C59—44no—
85C22⋊C4×C59—24no—
86C22⋊C4×C59—24no—
87C22⋊C4×C59—42no—
88C22⋊C4×C59—42no—
89C22⋊C4×C59—82no—
90C22⋊C4×C59—82no—
91C42×C59—82no—
92C22⋊Dic59—48no—
93C2×C59⋊C8—44no—
94C2×C59⋊C8—42no—
95C23×C59—22no—
96C23×C59—22no—
97C23×C59—22no—
98C23×C59—22no—
99C23×C59—22no—
100C23×C59—42no—
101C23×C59—42no—
102C23×C59—48no—
103C23×C59—42no—
104C23×C59—42no—
105C23×C59—42no—
106C23×C59—42no—
107C23×C59—81no—
108C23×C59—81no—
109C23×C59—84no—
110C23×C59C2×C22⋊C411yescharacteristic
111C23×C59#12011yescharacteristic
112C23×C59#12311yescharacteristic
113C23×C59#13512yes—
114C23×C59#13712yes—
115C2×C4×C59—24no—
116C2×C4×C59—22no—
117C2×C4×C59—41no—
118C2×C4×C59—41no—
119C2×C4×C59—42no—
120C2×C4×C59—42no—
121C2×C4×C59—42no—
122C2×C4×C59—44no—
123C2×C4×C59—44no—
124C2×C4×C59—44no—
125C2×C4×C59—81no—
126C2×C4×C59C4×D412yes—
127C2×C4×C59#12112yes—
128C2×Dic59—24no—
129C2×Dic59—42no—
130C2×Dic59—44no—
131C2×Dic59—42no—
132C2×Dic59—44no—
133C2×Dic59—42no—
134C2×Dic59—42no—
135C2×Dic59—42no—
136C2×Dic59—84no—
137Dic118—28no—
138Dic118—48no—
139Dic118—44no—
140C59⋊C8—82no—
141#9016—591nomaximal, Sylow
142C22×C59—24no—
143C22×C59—24no—
144C22×C59—21no—
145C22×C59—21no—
146C22×C59—21no—
147C22×C59—21no—
148C22×C59—44no—
149C22×C59—42no—
150C22×C59—42no—
151C22×C59—42no—
152C22×C59—82no—
153C22×C59—84no—
154C22×C59—84no—
155C22×C59#38611yescharacteristic
156C22×C59#41611yescharacteristic
157C22×C59#41911yescharacteristic
158C22×C59#45212yes—
159C22×C59#45512yes—
160C22×C59B(4,𝔽2)12yes—
161C22×C59#48512yes—
162C4×C59—22no—
163C4×C59—22no—
164C4×C59—42no—
165C4×C59—84no—
166Dic59—44no—
167Dic59—82no—
168C2×#393—591no—
169#2312D5911yescharacteristic
170#1787—592no—
171C2×#323—591no—
172#1294—592no—
173C2×C59—21no—
174C2×C59—21no—
175C2×C59—22no—
176C2×C59—82no—
177C2×C59#160614yes—
178C2×C59#187311yescharacteristic
179C2×C59#188511yescharacteristic
180C2×C59#188911yescharacteristic
181C23×Q8—591no—
182C22×C22⋊C4—1181no—
183C22×C22⋊C4C2×D5911yescharacteristic
184C2×#103—1184no—
185C2×C22⋊C8—592no—
186#393—594no—
187#393—1182no—
188#388—24no—
189#380C2×D5912yes—
190#379—21no—
191C4×C22⋊C4—21no—
192C2×#95—591no—
193C2×#95—1181no—
194#323—1182no—
195C59#901611yescharacteristic, complemented, Sylow
196C25C22⋊D5911yescharacteristic
197C22×Q8—592no—
198C22×Q8—1181no—
199C22×Q8—1182no—
200C22×Q8—1182no—
201C22×Q8—2364no—
202C23×C4—1181no—
203C23×C4—1181no—
204C23×C4C22⋊D5911yescharacteristic
205C23×C4C22×D5911yescharacteristic
206C22×C8—1182no—
207C2×C4⋊C4C22⋊D5914yes—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—1184no—
214C2×C22⋊C4—2364no—
215C2×C22⋊C4C4×D5912yes—
216C2×C22⋊C4D23612yes—
217C2×C42—22no—
218#103—2368no—
219C22⋊C8—1182no—
220C22⋊C8—1182no—
221#95—22no—
222#95—22no—
223#95—592no—
224#95—1184no—
225#95—1181no—
226C24—21no—
227C24—22no—
228C24—21no—
229C24—22no—
230C24—42no—
231C24—42no—
232C24(C2×D59)⋊C412yes—
233C24C2×C22⋊D5911yescharacteristic
234C2×Q8—1188no—
235C2×Q8—1184no—
236C2×Q8—2364no—
237C2×Q8—2364no—
238C2×Q8—2364no—
239C2×Q8—2368no—
240C2×Q8—2362no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—1184no—
247C22×C4—1182no—
248C22×C4—1182no—
249C22×C4—2362no—
250C22×C4—2362no—
251C22×C4—2362no—
252C22×C4—2362no—
253C22×C4—2361no—
254C22×C4—2361no—
255C22×C4(C2×D59)⋊C412yes—
256C22×C4C2×C4×D5911yescharacteristic
257C22×C4C2×D23611yescharacteristic
258C22×C4#1174568512yes—
259C22×C4C2×C22⋊D5912yes—
260C2×C8—2364no—
261C2×C8—2362no—
262C4⋊C4—44no—
263C22⋊C4—24no—
264C22⋊C4—24no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—82no—
268C22⋊C4—82no—
269C22⋊C4—2368no—
270C42—82no—
271C23—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—42no—
277C23—42no—
278C23—48no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—81no—
284C23—81no—
285C23—84no—
286C23C2×(C2×D59)⋊C411yescharacteristic
287C23#1427369611yescharacteristic
288C23#1427371011yescharacteristic
289C23#1427374712yes—
290C23#1427375712yes—
291Q8—1188no—
292Q8—2368no—
293Q8—2364no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—81no—
305C2×C4—1184no—
306C2×C4—4724no—
307C2×C4—2362no—
308C2×C4—2362no—
309C2×C4—2362no—
310C2×C4—2362no—
311C2×C4—2364no—
312C2×C4—2362no—
313C2×C4—2364no—
314C2×C4C4×C22⋊D5912yes—
315C2×C4#1427370112yes—
316C8—4722no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—24no—
322C22—24no—
323C22—44no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—82no—
328C22—84no—
329C22—84no—
330C22#1683728111yescharacteristic
331C22#1683739611yescharacteristic
332C22#1683741011yescharacteristic
333C22#1683756412yes—
334C22#1683758012yes—
335C22#1683758912yes—
336C22#1683774312yes—
337C4—22no—
338C4—22no—
339C4—42no—
340C4—84no—
341C4—4722no—
342C4—2364no—
343C2—21no—
344C2—21no—
345C2—22no—
346C2—82no—
347C2#2142307614yes—
348C2#2142440811yescharacteristic
349C2#2142448411yescharacteristic
350C2#2142450411yescharacteristic
subgroupG/H
centerC23#14273696
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#2312C2
socleC23×C59#120
prime radicalC25×C59D4
cosocleC23×C4×C59C23
hypercenter#2312D59
hypocenterC59#9016
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2312

Complements

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

NH ≅ G/Ntype
2. #21424030C2semidirect
4. #21421974C2semidirect
11. #16837314C4semidirect
195. C59#9016semidirect

Maximal subgroups

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

subgroupindex
C2×#168373142
#214240302
C2×#168371262
#214219742
C59×#23122
#901659