Finite Group Databasebeta

← #28492038

Subgroups — #28492038

Order 15104.

620 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 113 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#21430210C211yesmaximal, characteristic
2#21424401C212yesmaximal
3C2×#16837140C212yesmaximal
4#21422360C211yesmaximal, characteristic
5C59×#1280C211yesmaximal, characteristic
6C2×#14273706C2212yes—
7C22×C4⋊Dic59C2211yescharacteristic
8C22×Dic59⋊C4—21no—
9C2×#14273652—22no—
10#16837334—22no—
11#16837323—22no—
12#16837262—21no—
13#16837262—21no—
14C2×C59⋊#95—21no—
15C2×C59⋊#95C2211yescharacteristic
16#16837165—22no—
17#16837140—24no—
18C2×C22⋊C8×C59C2212yes—
19C2×#95×C59C2211yescharacteristic
20C22×Dic118D412yes—
21C23×Dic59—21no—
22C23×Dic59—21no—
23#14273706—22no—
24#14273706—22no—
25#14273706—22no—
26#14273706—22no—
27C2×C4⋊Dic59—22no—
28C2×C4⋊Dic59—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—42no—
33C2×C4⋊Dic59D412yes—
34C2×Dic59⋊C4—22no—
35C2×Dic59⋊C4—42no—
36C2×Dic59⋊C4—42no—
37C2×Dic59⋊C4—42no—
38C2×C22⋊Dic59—22no—
39#14273652—44no—
40C59⋊#95—22no—
41C59⋊#95—22no—
42C59⋊#95—21no—
43C59⋊#95—42no—
44C59⋊#95D412yes—
45C23×C4×C59D411yescharacteristic
46C23×C4×C59D411yescharacteristic
47C23×C4×C59C2311yescharacteristic
48C22×C8×C59—22no—
49C22⋊C8×C59—22no—
50C22⋊C8×C59—22no—
51#95×C59—22no—
52C24×C59C2×D411yescharacteristic
53C22×C4×C59—21no—
54C22×C4×C59—21no—
55C22×C4×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59—41no—
58C22×C4×C59—41no—
59C22×C4×C59—41no—
60C22×C4×C59—41no—
61C22×C4×C59—41no—
62C22×C4×C59—41no—
63C22×C4×C59SD1612yes—
64C22×C4×C59Q1612yes—
65C22×C4×C59C2×D412yes—
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59#4112yes—
68C22×C4×C59#4111yescharacteristic
69C22×Dic59—22no—
70C22×Dic59—22no—
71C22×Dic59—22no—
72C22×Dic59—22no—
73C22×Dic59—22no—
74C22×Dic59—22no—
75C22×Dic59—41no—
76C22×Dic59—41no—
77C22×Dic59—41no—
78C22×Dic59—41no—
79C22×Dic59—41no—
80C22×Dic59—41no—
81C22×Dic59—41no—
82C22×Dic59—41no—
83C22×Dic59—41no—
84C22×Dic59—41no—
85C2×Dic118—22no—
86C2×Dic118—22no—
87C2×Dic118—42no—
88C2×Dic118—42no—
89C2×C8×C59—42no—
90C2×C8×C59—42no—
91C2×C8×C59—42no—
92C22⋊Dic59—42no—
93C22⋊Dic59—42no—
94C4⋊Dic59—24no—
95C4⋊Dic59—22no—
96C4⋊Dic59—22no—
97C4⋊Dic59—42no—
98C4⋊Dic59—81no—
99C4⋊Dic59—81no—
100C4⋊Dic59—81no—
101C4⋊Dic59—81no—
102Dic59⋊C4—48no—
103Dic59⋊C4—42no—
104Dic59⋊C4—42no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59#12011yescharacteristic
110C23×C59#12111yescharacteristic
111C23×C59#12411yescharacteristic
112C23×C59C2×SD1611yescharacteristic
113C23×C59C2×Q1611yescharacteristic
114C23×C59#13711yescharacteristic
115C23×C59#13711yescharacteristic
116C2×C4×C59—22no—
117C2×C4×C59—22no—
118C2×C4×C59—22no—
119C2×C4×C59—22no—
120C2×C4×C59—41no—
121C2×C4×C59—42no—
122C2×C4×C59—41no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—42no—
128C2×C4×C59—42no—
129C2×C4×C59—81no—
130C2×C4×C59—81no—
131C2×C4×C59#12112yes—
132C2×C4×C59#12312yes—
133C2×Dic59—24no—
134C2×Dic59—42no—
135C2×Dic59—42no—
136C2×Dic59—42no—
137C2×Dic59—42no—
138C2×Dic59—42no—
139C2×Dic59—42no—
140C2×Dic59—42no—
141C2×Dic59—42no—
142C2×Dic59—42no—
143C2×Dic59—42no—
144C2×Dic59—42no—
145C2×Dic59—42no—
146C2×Dic59—42no—
147C2×Dic59—42no—
148C2×Dic59—42no—
149C2×Dic59—81no—
150C2×Dic59—81no—
151C2×Dic59—81no—
152C2×Dic59—81no—
153Dic118—44no—
154Dic118—82no—
155C8×C59—82no—
156#10406—591nomaximal, Sylow
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59—21no—
163C22×C59—21no—
164C22×C59—21no—
165C22×C59—21no—
166C22×C59—21no—
167C22×C59—21no—
168C22×C59—21no—
169C22×C59#39411yescharacteristic
170C22×C59#44811yescharacteristic
171C22×C59#45111yescharacteristic
172C22×C59#45311yescharacteristic
173C22×C59#45611yescharacteristic
174C22×C59B(4,𝔽2)11yescharacteristic
175C22×C59#45811yescharacteristic
176C22×C59#46111yescharacteristic
177C22×C59#46211yescharacteristic
178C22×C59#48711yescharacteristic
179C22×C59#49111yescharacteristic
180C4×C59—22no—
181C4×C59—22no—
182C4×C59—42no—
183C4×C59—42no—
184Dic59—44no—
185Dic59—82no—
186Dic59—82no—
187Dic59—82no—
188#2659—591no—
189#1872—592no—
190C2×#328—592no—
191#1444—591no—
192#1280D5911yescharacteristic
193C2×C59—21no—
194C2×C59—21no—
195C2×C59—21no—
196C2×C59—21no—
197C2×C59#159611yescharacteristic
198C2×C59#160511yescharacteristic
199C2×C59#161111yescharacteristic
200C2×C59#161411yescharacteristic
201C2×C59#203911yescharacteristic
202C2×C59#204311yescharacteristic
203C2×C59#204411yescharacteristic
204C2×C22⋊Q8—592no—
205C22×C4⋊C4—591no—
206C22×C4⋊C4—1181no—
207C2×#103—1182no—
208C2×C22⋊C8C2×D5912yes—
209#398—1182no—
210#395—1182no—
211#380—1181no—
212#380—1181no—
213C2×#95—591no—
214C2×#95—1181no—
215C2×#95C2×D5911yescharacteristic
216#340—1182no—
217#328—1184no—
218C59#1040611yescharacteristic, complemented, Sylow
219C22×Q8—592no—
220C23×C4—1181no—
221C23×C4—1181no—
222C23×C4D23611yescharacteristic
223C23×C4D23611yescharacteristic
224C23×C4C22×D5911yescharacteristic
225C22×C8—22no—
226C22⋊Q8—1182no—
227C22⋊Q8—1182no—
228C22⋊Q8—1182no—
229C22⋊Q8—1182no—
230C2×C4⋊C4—592no—
231C2×C4⋊C4—1182no—
232C2×C4⋊C4—1181no—
233C2×C4⋊C4—1181no—
234C2×C4⋊C4—1181no—
235C2×C4⋊C4—1181no—
236C2×C4⋊C4—1182no—
237C2×C4⋊C4—2362no—
238C2×C4⋊C4—2362no—
239C2×C4⋊C4—2362no—
240C2×C4⋊C4—2362no—
241C2×C22⋊C4—1182no—
242#103—2364no—
243C22⋊C8—22no—
244C22⋊C8—22no—
245#95—22no—
246#95—592no—
247#95—1182no—
248#95—1182no—
249#95—1181no—
250#95—2362no—
251C24C2×D23611yescharacteristic
252C2×Q8—1182no—
253C2×Q8—1182no—
254C2×Q8—2362no—
255C2×Q8—2362no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—1182no—
267C22×C4—1182no—
268C22×C4—1182no—
269C22×C4—1182no—
270C22×C4—1182no—
271C22×C4—1182no—
272C22×C4—2361no—
273C22×C4—2361no—
274C22×C4—2361no—
275C22×C4—2361no—
276C22×C4—2361no—
277C22×C4—2361no—
278C22×C4—2361no—
279C22×C4—2361no—
280C22×C4—2361no—
281C22×C4—2361no—
282C22×C4#1174566012yes—
283C22×C4Dic23612yes—
284C22×C4#1174568512yes—
285C22×C4D4×D5912yes—
286C22×C4D4×D5911yescharacteristic
287C22×C4#1174568911yescharacteristic
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C4⋊C4—1184no—
292C4⋊C4—1182no—
293C4⋊C4—1182no—
294C4⋊C4—4721no—
295C4⋊C4—4721no—
296C4⋊C4—4721no—
297C4⋊C4—4721no—
298C4⋊C4—2362no—
299C4⋊C4—2368no—
300C4⋊C4—2362no—
301C4⋊C4—2362no—
302C22⋊C4—2362no—
303C22⋊C4—2362no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#1427369711yescharacteristic
309C23#1427370211yescharacteristic
310C23#1427371511yescharacteristic
311C23C2×#1174566011yescharacteristic
312C23C2×Dic23611yescharacteristic
313C23#1427376011yescharacteristic
314C23#1427376011yescharacteristic
315Q8—4722no—
316Q8—2364no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—1184no—
333C2×C4—4721no—
334C2×C4—4721no—
335C2×C4—4721no—
336C2×C4—4721no—
337C2×C4—2362no—
338C2×C4—2362no—
339C2×C4—2362no—
340C2×C4—2362no—
341C2×C4—2362no—
342C2×C4—2362no—
343C2×C4—2362no—
344C2×C4—2362no—
345C2×C4—2362no—
346C2×C4—2362no—
347C2×C4—2362no—
348C2×C4—2362no—
349C2×C4—2362no—
350C2×C4—2362no—
351C2×C4—2362no—
352C2×C4#1427370012yes—
353C2×C4#1427371212yes—
354C8—82no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#1683732011yescharacteristic
368C22#1683754311yescharacteristic
369C22#1683756011yescharacteristic
370C22#1683757211yescharacteristic
371C22#1683758711yescharacteristic
372C22#1683759011yescharacteristic
373C22#1683759311yescharacteristic
374C22#1683760811yescharacteristic
375C22#1683761311yescharacteristic
376C22#1683775311yescharacteristic
377C22#1683777111yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—4722no—
383C4—4722no—
384C4—4722no—
385C4—2364no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#2142302111yescharacteristic
391C2#2142307211yescharacteristic
392C2#2142310611yescharacteristic
393C2#2142312311yescharacteristic
394C2#2142532111yescharacteristic
395C2#2142534311yescharacteristic
396C2#2142534811yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1280C2
socleC23×C59#120
prime radicalC24×C59C2×D4
hypercenter#1280D59
hypocenterC59#10406
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
218. C59#10406semidirect

Maximal subgroups

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

subgroupindex
#214302102
#214244012
C2×#168371402
#214223602
C59×#12802
#1040659