Finite Group Databasebeta

← #28483669

Subgroups — #28483669

Order 15104.

560 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 111 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#21433125C211yesmaximal, characteristic
2#21424195C212yesmaximal, complemented
3C4×#14273642C211yesmaximal, characteristic
4#21421982C212yesmaximal, complemented
5C59×#2395C211yesmaximal, characteristic
6#16837474—24no—
7#16837459—21no—
8C2×#14273642—21no—
9#16837366C2212yes—
10C2×C22⋊(C59⋊C8)—21no—
11C4×C22⋊Dic59C2212yes—
12#16837169—21no—
13#16837161—24no—
14C2×C4×D4×C59C2211yescharacteristic
15C2×#117×C59C2211yescharacteristic
16C59×#400C411yescharacteristic, complemented
17C59×#399C411yescharacteristic, complemented
18C59×#398C411yescharacteristic, complemented
19C59×#397—21no—
20C59×#397C411yescharacteristic, complemented
21C59×#394—21no—
22C4×C4⋊C4×C59—21no—
23C4×C22⋊C4×C59—21no—
24C4×C22⋊C4×C59C2211yescharacteristic
25C2×#11745664D414yes—
26C22×C59⋊C8—22no—
27C2×C22⋊Dic59—22no—
28C2×C4×Dic59—22no—
29C4⋊(C59⋊C8)—22no—
30#14273642—24no—
31C22⋊(C59⋊C8)—22no—
32C22⋊(C59⋊C8)—22no—
33C22⋊(C59⋊C8)—22no—
34#14273638—22no—
35C59⋊#95—22no—
36C22×D4×C59D411yescharacteristic
37C23×C4×C59D411yescharacteristic
38C23×C4×C59C2311yescharacteristic
39C4×D4×C59—22no—
40C4×D4×C59—22no—
41#117×C59—22no—
42#117×C59—22no—
43C2×C4⋊C4×C59—21no—
44C2×C4⋊C4×C59—21no—
45C2×C4⋊C4×C59C2×C411yescharacteristic
46C2×C4⋊C4×C59C2×C411yescharacteristic
47C2×C4⋊C4×C59C2×C411yescharacteristic
48C2×C22⋊C4×C59—21no—
49C2×C22⋊C4×C59—21no—
50C2×C22⋊C4×C59—21no—
51C2×C22⋊C4×C59—21no—
52C2×C22⋊C4×C59C2×C411yescharacteristic
53C2×C22⋊C4×C59D411yescharacteristic
54C2×C42×C59—21no—
55C2×C42×C59—21no—
56C2×C42×C59D411yescharacteristic
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59—21no—
61#95×C59C2×C411yescharacteristic
62#95×C59C2×C411yescharacteristic
63C24×C59C22⋊C411yescharacteristic
64C24×C59C2×D411yescharacteristic
65C2×D4×C59—22no—
66C2×D4×C59—22no—
67C2×D4×C59—41no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—21no—
73C22×C4×C59—21no—
74C22×C4×C59—42no—
75C22×C4×C59—42no—
76C22×C4×C59C22⋊C411yescharacteristic
77C22×C4×C59C22⋊C411yescharacteristic
78C22×C4×C59C22⋊C411yescharacteristic
79C22×C4×C59C22×C411yescharacteristic
80C22×C4×C59C2×D412yes—
81C22×C4×C59C2×D411yescharacteristic
82C22×C4×C59#4112yes—
83C22×Dic59—42no—
84C4⋊C4×C59—22no—
85C4⋊C4×C59—22no—
86C4⋊C4×C59—22no—
87C4⋊C4×C59—42no—
88C4⋊C4×C59—42no—
89C22⋊C4×C59—22no—
90C22⋊C4×C59—22no—
91C22⋊C4×C59—42no—
92C22⋊C4×C59—42no—
93C22⋊C4×C59—42no—
94C22⋊C4×C59—42no—
95C42×C59—21no—
96C42×C59—21no—
97C42×C59—42no—
98C42×C59—41no—
99C42×C59—41no—
100C22⋊Dic59—24no—
101C22⋊Dic59—42no—
102C4×Dic59—44no—
103#11745664—44no—
104C2×C59⋊C8—24no—
105C2×C59⋊C8—82no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—41no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59#10412yes—
115C23×C59C2×C22⋊C411yescharacteristic
116C23×C59#12112yes—
117D4×C59—44no—
118C2×C4×C59—24no—
119C2×C4×C59—22no—
120C2×C4×C59—22no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—41no—
127C2×C4×C59—42no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59—42no—
131C2×C4×C59—41no—
132C2×C4×C59—41no—
133C2×C4×C59—41no—
134C2×C4×C59—41no—
135C2×C4×C59—41no—
136C2×C4×C59—41no—
137C2×C4×C59—41no—
138C2×C4×C59—41no—
139C2×C4×C59—41no—
140C2×C4×C59—41no—
141C2×C4×C59—41no—
142C2×C4×C59—81no—
143C2×C4×C59C4×D412yes—
144C2×C4×C59#12011yescharacteristic
145C2×C4×C59#12311yescharacteristic
146C2×Dic59—44no—
147C2×Dic59—82no—
148C2×Dic59—82no—
149C59⋊C8—44no—
150#9011—591nomaximal, Sylow
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—22no—
154C22×C59—22no—
155C22×C59—22no—
156C22×C59—22no—
157C22×C59—42no—
158C22×C59—41no—
159C22×C59—41no—
160C22×C59—81no—
161C22×C59—81no—
162C22×C59—81no—
163C22×C59#38611yescharacteristic
164C22×C59C2×#10411yescharacteristic
165C22×C59#42111yescharacteristic
166C4×C59—21no—
167C4×C59—22no—
168C4×C59—42no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—81no—
173C4×C59—81no—
174C4×C59—81no—
175C4×C59#45812yes—
176Dic59—84no—
177#2973—591no—
178#2395D5911yescharacteristic
179#1826—592no—
180C4×#99—591no—
181#1297—592no—
182C2×C59—21no—
183C2×C59—21no—
184C2×C59—42no—
185C2×C59—42no—
186C2×C59#187111yescharacteristic
187C2×C59#188411yescharacteristic
188C2×C59#189011yescharacteristic
189C2×C4×D4C2×D5911yescharacteristic
190C2×#117C2×D5911yescharacteristic
191#435—1184no—
192#432—1181no—
193C2×#99—1181no—
194#407—592no—
195C2×C22⋊C8—1181no—
196#400Dic5911yescharacteristic, complemented
197#399Dic5911yescharacteristic, complemented
198#398Dic5911yescharacteristic, complemented
199#397—21no—
200#397Dic5911yescharacteristic, complemented
201#394—21no—
202C4×C4⋊C4—21no—
203C4×C22⋊C4—21no—
204C4×C22⋊C4—592no—
205C4×C22⋊C4C2×D5911yescharacteristic
206#342—1181no—
207#339—1184no—
208C59#901111yescharacteristic, complemented, Sylow
209C22×D4C22⋊D5911yescharacteristic
210C23×C4C22⋊D5911yescharacteristic
211C23×C4C22×D5911yescharacteristic
212C2×M16—594no—
213C22×C8—1182no—
214C4×D4—22no—
215C4×D4—22no—
216#117—22no—
217#117—22no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×Dic5911yescharacteristic
221C2×C4⋊C4C2×Dic5911yescharacteristic
222C2×C4⋊C4C2×Dic5911yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—1182no—
228C2×C22⋊C4C2×Dic5911yescharacteristic
229C2×C22⋊C4C22⋊D5911yescharacteristic
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—1182no—
233C2×C42C22⋊D5911yescharacteristic
234C4⋊C8—1182no—
235#99—1184no—
236C22⋊C8—1182no—
237C22⋊C8—1182no—
238C22⋊C8—1182no—
239#97—1182no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—1182no—
245#95C2×Dic5911yescharacteristic
246#95C2×Dic5911yescharacteristic
247C24C22⋊Dic5911yescharacteristic
248C24C2×C22⋊D5911yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—2362no—
261C22×C4C22⋊Dic5911yescharacteristic
262C22×C4C22⋊Dic5911yescharacteristic
263C22×C4C22⋊Dic5911yescharacteristic
264C22×C4D4×D5912yes—
265C22×C4#1174568712yes—
266C22×C4C22×Dic5911yescharacteristic
267C22×C4C2×C22⋊D5911yescharacteristic
268M16—2364no—
269C2×C8—1184no—
270C2×C8—4722no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—42no—
282C22⋊C4—1184no—
283C22⋊C4—2362no—
284C42—21no—
285C42—21no—
286C42—42no—
287C42—41no—
288C42—41no—
289C42—2364no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23#1427365412yes—
299C23C2×C22⋊Dic5911yescharacteristic
300C23#1427369912yes—
301D4—44no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—22no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—4722no—
328C2×C4—4722no—
329C2×C4—2364no—
330C2×C4D4×Dic5912yes—
331C2×C4#1427369511yescharacteristic
332C2×C4#1427370811yescharacteristic
333C8—2364no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—42no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1683728211yescharacteristic
347C22C2×#1427365411yescharacteristic
348C22#1683741911yescharacteristic
349C4—21no—
350C4—22no—
351C4—42no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—4724no—
359C4#1683759112yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—42no—
364C2#2142439911yescharacteristic
365C2#2142448011yescharacteristic
366C2#2142451011yescharacteristic
subgroupG/H
centerC2×C4#14273695
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#2395C2
socleC22×C59#386
prime radicalC22×D4×C59D4
cosocleC23×C4×C59C23
hypercenter#2395D59
hypocenterC59#9011
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2395

Complements

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

NH ≅ G/Ntype
2. #21424195C2semidirect
4. #21421982C2semidirect
16. C59×#400C4semidirect
17. C59×#399C4semidirect
18. C59×#398C4semidirect
20. C59×#397C4semidirect
196. #400Dic59semidirect
197. #399Dic59semidirect
198. #398Dic59semidirect
200. #397Dic59semidirect
208. C59#9011semidirect

Maximal subgroups

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

subgroupindex
#214331252
#214241952
C4×#142736422
#214219822
C59×#23952
#901159