Finite Group Databasebeta

← #28483671

Subgroups — #28483671

Order 15104.

558 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 103 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#21433137C211yesmaximal, characteristic
2#21427355C211yesmaximal, characteristic
3#21424196C212yesmaximal, complemented
4#21421982C212yesmaximal, complemented
5C4×#99×C59C211yesmaximal, characteristic
6C2×#14273686C2211yescharacteristic
7#16837480—24no—
8#16837455—21no—
9#16837366—21no—
10#16837366C2212yes—
11#16837341C411yescharacteristic, complemented
12#16837338C411yescharacteristic, complemented
13#16837332C411yescharacteristic, complemented
14#16837330—21no—
15#16837327C411yescharacteristic, complemented
16#16837316—21no—
17C4×Dic59⋊C4—21no—
18C4×C22⋊Dic59—21no—
19C4×C22⋊Dic59C2211yescharacteristic
20#16837162—24no—
21C2×C4×D4×C59C2211yescharacteristic
22C2×#99×C59—21no—
23C4×C22⋊C4×C59C2212yes—
24C59×#342—21no—
25C2×#11745664—22no—
26C2×#11745664D414yes—
27#14273686—22no—
28#14273686—22no—
29C2×C4⋊Dic59C2×C411yescharacteristic
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×Dic59⋊C4—21no—
32C2×Dic59⋊C4—21no—
33C2×C22⋊Dic59—21no—
34C2×C22⋊Dic59—21no—
35C2×C22⋊Dic59—21no—
36C2×C22⋊Dic59—21no—
37C2×C4×Dic59—21no—
38C2×C4×Dic59—21no—
39C4⋊(C59⋊C8)—22no—
40C22⋊(C59⋊C8)—22no—
41C22⋊(C59⋊C8)—22no—
42C22⋊(C59⋊C8)—22no—
43C4×C59⋊C8—22no—
44C59⋊#95—21no—
45C59⋊#95—21no—
46C59⋊#95—21no—
47C59⋊#95—21no—
48C59⋊#95C2×C411yescharacteristic
49C59⋊#95C2×C411yescharacteristic
50C22×D4×C59D411yescharacteristic
51C23×C4×C59D411yescharacteristic
52C23×C4×C59C2311yescharacteristic
53C4×D4×C59—22no—
54C4×D4×C59—22no—
55C2×C4⋊C4×C59C2×C411yescharacteristic
56C2×C22⋊C4×C59—22no—
57C2×C22⋊C4×C59C2×C411yescharacteristic
58C2×C22⋊C4×C59D411yescharacteristic
59C2×C42×C59—22no—
60C2×C42×C59D411yescharacteristic
61#99×C59—24no—
62#95×C59—22no—
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—42no—
71C22×C4×C59—42no—
72C22×C4×C59—42no—
73C22×C4×C59C22⋊C411yescharacteristic
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C22⋊C411yescharacteristic
76C22×C4×C59C22×C411yescharacteristic
77C22×C4×C59C2×D412yes—
78C22×C4×C59C2×D411yescharacteristic
79C22×C4×C59#4112yes—
80C22×Dic59—21no—
81C22×Dic59—21no—
82C22×Dic59—21no—
83C22×Dic59—21no—
84C4⋊C4×C59—22no—
85C22⋊C4×C59—22no—
86C22⋊C4×C59—22no—
87C22⋊C4×C59—24no—
88C22⋊C4×C59—42no—
89C42×C59—21no—
90C42×C59—21no—
91C42×C59—44no—
92C22⋊Dic59—42no—
93C22⋊Dic59—42no—
94C22⋊Dic59—42no—
95C22⋊Dic59—42no—
96C4⋊Dic59—22no—
97C4⋊Dic59—22no—
98Dic59⋊C4—42no—
99Dic59⋊C4—42no—
100C4×Dic59—42no—
101C4×Dic59—41no—
102C4×Dic59—41no—
103#11745664—44no—
104#11745664—82no—
105C2×C59⋊C8—24no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59—41no—
112C23×C59—41no—
113C23×C59—41no—
114C23×C59—41no—
115C23×C59C2×C22⋊C411yescharacteristic
116C23×C59#12112yes—
117D4×C59—44no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—24no—
121C2×C4×C59—22no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—41no—
125C2×C4×C59—42no—
126C2×C4×C59—42no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—44no—
130C2×C4×C59—81no—
131C2×C4×C59—82no—
132C2×C4×C59—82no—
133C2×C4×C59#10412yes—
134C2×C4×C59C4×D412yes—
135C2×C4×C59#12011yescharacteristic
136C2×C4×C59#12311yescharacteristic
137C2×Dic59—22no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—41no—
148C2×Dic59—41no—
149C59⋊C8—44no—
150#9012—591nomaximal, Sylow
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—22no—
154C22×C59—22no—
155C22×C59—22no—
156C22×C59—42no—
157C22×C59—41no—
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—22no—
167C4×C59—21no—
168C4×C59—22no—
169C4×C59—41no—
170C4×C59—41no—
171C4×C59—84no—
172C4×C59#45812yes—
173Dic59—42no—
174Dic59—81no—
175Dic59—81no—
176Dic59—81no—
177#2975—591no—
178#2395—591no—
179#1826—592no—
180C4×#99D5911yescharacteristic
181#1297—592no—
182C2×C59—21no—
183C2×C59—21no—
184C2×C59—42no—
185C2×C59—81no—
186C2×C59#187111yescharacteristic
187C2×C59#188411yescharacteristic
188C2×C59#189011yescharacteristic
189C2×C4×D4C2×D5911yescharacteristic
190C2×#117—591no—
191#436—1184no—
192#431—1181no—
193C2×#99—21no—
194#407—592no—
195#407—1181no—
196#400—591no—
197#399—591no—
198#398—591no—
199#397—591no—
200#397—1181no—
201#394—1181no—
202C4×C4⋊C4—1181no—
203C4×C22⋊C4—591no—
204C4×C22⋊C4—1181no—
205C4×C22⋊C4C2×D5912yes—
206#342—21no—
207#339—1184no—
208C59#901211yescharacteristic, complemented, Sylow
209C22×D4C22⋊D5911yescharacteristic
210C23×C4D23611yescharacteristic
211C23×C4C22×D5911yescharacteristic
212C2×M16—594no—
213C2×M16—1182no—
214C4×D4—22no—
215C4×D4—22no—
216#117—1182no—
217#117—1182no—
218C2×C4⋊C4—591no—
219C2×C4⋊C4—591no—
220C2×C4⋊C4—1181no—
221C2×C4⋊C4—1181no—
222C2×C4⋊C4C4×D5911yescharacteristic
223C2×C22⋊C4—22no—
224C2×C22⋊C4—1181no—
225C2×C22⋊C4—1181no—
226C2×C22⋊C4—1181no—
227C2×C22⋊C4—1181no—
228C2×C22⋊C4C4×D5911yescharacteristic
229C2×C22⋊C4C22⋊D5911yescharacteristic
230C2×C42—22no—
231C2×C42—1181no—
232C2×C42—1181no—
233C2×C42D23611yescharacteristic
234C4⋊C8—1182no—
235#99—24no—
236C22⋊C8—1182no—
237C22⋊C8—1182no—
238C22⋊C8—1182no—
239C4×C8—1182no—
240#95—22no—
241#95—591no—
242#95—591no—
243#95—1181no—
244#95—1181no—
245#95—1181no—
246#95—1181no—
247C24(C2×D59)⋊C411yescharacteristic
248C24C2×C22⋊D5911yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4—1181no—
258C22×C4—1181no—
259C22×C4—1181no—
260C22×C4—1181no—
261C22×C4(C2×D59)⋊C411yescharacteristic
262C22×C4(C2×D59)⋊C411yescharacteristic
263C22×C4(C2×D59)⋊C411yescharacteristic
264C22×C4C2×C4×D5911yescharacteristic
265C22×C4C2×D23611yescharacteristic
266C22×C4D4×D5912yes—
267C22×C4#1174568712yes—
268M16—4722no—
269M16—2364no—
270C2×C8—1184no—
271C4⋊C4—22no—
272C4⋊C4—1182no—
273C4⋊C4—1182no—
274C4⋊C4—2362no—
275C4⋊C4—2362no—
276C22⋊C4—22no—
277C22⋊C4—22no—
278C22⋊C4—24no—
279C22⋊C4—42no—
280C22⋊C4—2362no—
281C22⋊C4—2362no—
282C22⋊C4—2362no—
283C22⋊C4—2362no—
284C42—21no—
285C42—21no—
286C42—44no—
287C42—2362no—
288C42—2361no—
289C42—2361no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×(C2×D59)⋊C411yescharacteristic
300C23#1427369912yes—
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—81no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—1182no—
318C2×C4—2361no—
319C2×C4—2361no—
320C2×C4—2361no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4—2361no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4—2361no—
328C2×C4—2361no—
329C2×C4#1427365512yes—
330C2×C4(C22⋊D59)⋊C412yes—
331C2×C4#1427369711yescharacteristic
332C2×C4#1427371111yescharacteristic
333C8—2364no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#1683727911yescharacteristic
347C22C2×#1427365511yescharacteristic
348C22#1683742011yescharacteristic
349C4—22no—
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—84no—
355C4—4721no—
356C4—4721no—
357C4—4721no—
358C4—2362no—
359C4#1683759312yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#2142439611yescharacteristic
365C2#2142447711yescharacteristic
366C2#2142450711yescharacteristic
subgroupG/H
centerC2×C4#14273697
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC4×#99×C59C2
socleC22×C59#386
prime radicalC22×D4×C59D4
cosocleC23×C4×C59C23
hypercenterC4×#99D59
hypocenterC59#9012
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #21424196C2semidirect
4. #21421982C2semidirect
11. #16837341C4semidirect
12. #16837338C4semidirect
13. #16837332C4semidirect
15. #16837327C4semidirect
208. C59#9012semidirect

Maximal subgroups

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

subgroupindex
#214331372
#214273552
#214241962
#214219822
C4×#99×C592
#901259