Finite Group Databasebeta

← #28487666

Subgroups — #28487666

Order 15104.

686 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432448C211yesmaximal, characteristic
2C4×C22⋊(C59⋊C8)C211yesmaximal, characteristic
3C2×#16837138C214yesmaximal
4C59×C4⋊#95C211yesmaximal, characteristic
5C2×#14273727C411yescharacteristic, complemented
6C2×#14273706C2212yes—
7C2×C22⋊(C59⋊C8)C2212yes—
8C2×C4×C59⋊C8—21no—
9#16837308C412yescomplemented
10#16837300—21no—
11#16837300—21no—
12#16837272C411yescharacteristic, complemented
13#16837262—21no—
14#16837262—21no—
15#16837157—21no—
16#16837138—28no—
17C22×C4⋊C4×C59—21no—
18C22×C42×C59C2211yescharacteristic
19C2×#95×C59—21no—
20C2×#95×C59C2212yes—
21C22×Dic118C2×C412yes—
22C22×C59⋊C8—22no—
23#14273727—42no—
24#14273706—24no—
25#14273706—24no—
26C2×C4⋊Dic59—21no—
27C2×C4⋊Dic59—21no—
28C2×C4⋊Dic59—21no—
29C2×C4⋊Dic59—21no—
30C2×C4⋊Dic59C2×C412yes—
31C2×Dic59⋊C4—22no—
32C2×C22⋊Dic59—22no—
33C22⋊(C59⋊C8)—22no—
34C22⋊(C59⋊C8)D414yes—
35C4×C59⋊C8—42no—
36C59⋊#95—22no—
37C59⋊#95—22no—
38C23×C4×C59—22no—
39C23×C4×C59D411yescharacteristic
40C23×C4×C59D411yescharacteristic
41C23×C4×C59C2311yescharacteristic
42C2×C4⋊C4×C59—24no—
43C2×C4⋊C4×C59—42no—
44C2×C4⋊C4×C59—42no—
45C2×C42×C59—42no—
46C2×C42×C59C2×C411yescharacteristic
47C2×C42×C59C2×C411yescharacteristic
48C2×C42×C59D411yescharacteristic
49C2×C42×C59D411yescharacteristic
50#95×C59—24no—
51#95×C59—42no—
52C24×C59C2×D411yescharacteristic
53C22×C4×C59—22no—
54C22×C4×C59—22no—
55C22×C4×C59—24no—
56C22×C4×C59—41no—
57C22×C4×C59—41no—
58C22×C4×C59—41no—
59C22×C4×C59—41no—
60C22×C4×C59—42no—
61C22×C4×C59—42no—
62C22×C4×C59—42no—
63C22×C4×C59—42no—
64C22×C4×C59—42no—
65C22×C4×C59—42no—
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C22⋊C411yescharacteristic
69C22×C4×C59C22⋊C411yescharacteristic
70C22×C4×C59SD1612yes—
71C22×C4×C59SD1612yes—
72C22×C4×C59Q1612yes—
73C22×C4×C59Q1612yes—
74C22×C4×C59C22×C411yescharacteristic
75C22×C4×C59C2×D411yescharacteristic
76C22×C4×C59C2×D412yes—
77C22×C4×C59#4112yes—
78C22×Dic59—22no—
79C22×Dic59—22no—
80C2×Dic118—24no—
81C2×Dic118—42no—
82C2×Dic118—42no—
83C4⋊C4×C59—48no—
84C42×C59—22no—
85C42×C59—22no—
86C42×C59—41no—
87C42×C59—41no—
88C22⋊Dic59—42no—
89C22⋊Dic59—42no—
90C4⋊Dic59—24no—
91C4⋊Dic59—42no—
92C4⋊Dic59—42no—
93C4⋊Dic59—42no—
94C4⋊Dic59—42no—
95Dic59⋊C4—44no—
96C2×C59⋊C8—24no—
97C2×C59⋊C8—42no—
98C2×C59⋊C8—42no—
99C23×C59—21no—
100C23×C59—21no—
101C23×C59—21no—
102C23×C59—21no—
103C23×C59C2×C22⋊C411yescharacteristic
104C23×C59#12411yescharacteristic
105C23×C59#12711yescharacteristic
106C23×C59C2×SD1611yescharacteristic
107C23×C59C2×SD1611yescharacteristic
108C23×C59C2×Q1611yescharacteristic
109C23×C59C2×Q1611yescharacteristic
110C2×C4×C59—21no—
111C2×C4×C59—21no—
112C2×C4×C59—21no—
113C2×C4×C59—21no—
114C2×C4×C59—21no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59—21no—
120C2×C4×C59—24no—
121C2×C4×C59—24no—
122C2×C4×C59—42no—
123C2×C4×C59—42no—
124C2×C4×C59—42no—
125C2×C4×C59—42no—
126C2×C4×C59—44no—
127C2×C4×C59—44no—
128C2×C4×C59—44no—
129C2×C4×C59—82no—
130C2×C4×C59—82no—
131C2×C4×C59—82no—
132C2×C4×C59—82no—
133C2×C4×C59#9912yes—
134C2×C4×C59#10312yes—
135C2×C4×C59#10312yes—
136C2×C4×C59#10312yes—
137C2×C4×C59#10312yes—
138C2×C4×C59#10412yes—
139C2×C4×C59C4×D412yes—
140C2×C4×C59#12112yes—
141C2×Dic59—42no—
142C2×Dic59—42no—
143C2×Dic59—42no—
144C2×Dic59—42no—
145C2×Dic59—42no—
146C2×Dic59—42no—
147Dic118—84no—
148C59⋊C8—44no—
149#9679—591nomaximal, Sylow
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—21no—
155C22×C59—21no—
156C22×C59—21no—
157C22×C59—21no—
158C22×C59—21no—
159C22×C59—21no—
160C22×C59—21no—
161C22×C59—21no—
162C22×C59#39011yescharacteristic
163C22×C59C2×#9911yescharacteristic
164C22×C59#41011yescharacteristic
165C22×C59C2×#10311yescharacteristic
166C22×C59C2×#10311yescharacteristic
167C22×C59C2×#10411yescharacteristic
168C22×C59#42111yescharacteristic
169C22×C59#48711yescharacteristic
170C22×C59#48711yescharacteristic
171C22×C59#49211yescharacteristic
172C22×C59#49411yescharacteristic
173C4×C59—22no—
174C4×C59—22no—
175C4×C59—22no—
176C4×C59—22no—
177C4×C59—22no—
178C4×C59—84no—
179C4×C59#32814yescomplemented
180Dic59—82no—
181Dic59—82no—
182#2857—591no—
183C4×C22⋊C8—591no—
184C2×#328—594no—
185C4⋊#95D5911yescharacteristic
186C2×C59—21no—
187C2×C59—21no—
188C2×C59—21no—
189C2×C59—21no—
190C2×C59C2×#32811yescharacteristic
191C2×C59#150311yescharacteristic
192C2×C59#151811yescharacteristic
193C2×C59#152011yescharacteristic
194C2×C59#195611yescharacteristic
195C2×C59#196411yescharacteristic
196C2×C59#198011yescharacteristic
197C2×C4⋊Q8—591no—
198C2×C22⋊Q8—592no—
199C22×C4⋊C4—21no—
200C22×C42C2×D5911yescharacteristic
201C2×C22⋊C8—592no—
202C2×C4×C8—1181no—
203#391—592no—
204#389—1181no—
205#389—1181no—
206#384—591no—
207#380—1181no—
208#380—1181no—
209C2×#95—21no—
210C2×#95C2×D5912yes—
211#336—1181no—
212#328—1188no—
213C59#967911yescharacteristic, complemented, Sylow
214C22×Q8—592no—
215C23×C4—22no—
216C23×C4C22⋊D5911yescharacteristic
217C23×C4C22⋊D5911yescharacteristic
218C23×C4C22×D5911yescharacteristic
219C22×C8—1182no—
220C4⋊Q8—2362no—
221C22⋊Q8—1184no—
222C22⋊Q8—1184no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—42no—
225C2×C4⋊C4—42no—
226C2×C4⋊C4—592no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4—1181no—
229C2×C4⋊C4—1181no—
230C2×C4⋊C4—1181no—
231C2×C4⋊C4—1182no—
232C2×C22⋊C4—1182no—
233C2×C42—42no—
234C2×C42C4×D5911yescharacteristic
235C2×C42C4×D5911yescharacteristic
236C2×C42D23611yescharacteristic
237C2×C42D23611yescharacteristic
238C22⋊C8—594no—
239C22⋊C8—1182no—
240C4×C8—2362no—
241#95—24no—
242#95—42no—
243#95—1182no—
244#95—1182no—
245C24C2×C22⋊D5911yescharacteristic
246C2×Q8—1184no—
247C2×Q8—2362no—
248C2×Q8—2362no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—42no—
257C22×C4—42no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—1182no—
263C22×C4—1182no—
264C22×C4(C2×D59)⋊C411yescharacteristic
265C22×C4(C2×D59)⋊C411yescharacteristic
266C22×C4(C2×D59)⋊C411yescharacteristic
267C22×C4(C2×D59)⋊C411yescharacteristic
268C22×C4#1174567012yes—
269C22×C4#1174567012yes—
270C22×C4#1174567212yes—
271C22×C4#1174567212yes—
272C22×C4C2×C4×D5911yescharacteristic
273C22×C4C2×D23611yescharacteristic
274C22×C4D4×D5912yes—
275C22×C4#1174568912yes—
276C2×C8—1184no—
277C2×C8—2362no—
278C2×C8—2362no—
279C4⋊C4—48no—
280C4⋊C4—1184no—
281C4⋊C4—2362no—
282C4⋊C4—2362no—
283C4⋊C4—2362no—
284C4⋊C4—2362no—
285C4⋊C4—2364no—
286C22⋊C4—2362no—
287C22⋊C4—2362no—
288C42—22no—
289C42—22no—
290C42—41no—
291C42—41no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23C2×(C2×D59)⋊C411yescharacteristic
297C23#1427371611yescharacteristic
298C23#1427372311yescharacteristic
299C23C2×#1174567011yescharacteristic
300C23C2×#1174567011yescharacteristic
301C23C2×#1174567211yescharacteristic
302C23C2×#1174567211yescharacteristic
303Q8—4724no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—82no—
324C2×C4—82no—
325C2×C4—82no—
326C2×C4—82no—
327C2×C4—2362no—
328C2×C4—2362no—
329C2×C4—2362no—
330C2×C4—2362no—
331C2×C4—2362no—
332C2×C4—2362no—
333C2×C4#1427364112yes—
334C2×C4#1427365012yes—
335C2×C4#1427365012yes—
336C2×C4#1427365012yes—
337C2×C4#1427365012yes—
338C2×C4#1427365512yes—
339C2×C4#1427368912yes—
340C2×C4#1427370212yes—
341C8—2364no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22#1683730311yescharacteristic
355C22C2×#1427364111yescharacteristic
356C22#1683737511yescharacteristic
357C22C2×#1427365011yescharacteristic
358C22C2×#1427365011yescharacteristic
359C22C2×#1427365511yescharacteristic
360C22#1683742011yescharacteristic
361C22#1683775411yescharacteristic
362C22#1683775411yescharacteristic
363C22#1683777411yescharacteristic
364C22#1683778111yescharacteristic
365C4—22no—
366C4—22no—
367C4—22no—
368C4—22no—
369C4—22no—
370C4—84no—
371C4—4722no—
372C4—4722no—
373C4#1683713814yescomplemented
374C2—21no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2C2×#1683713811yescharacteristic
379C2#2142259411yescharacteristic
380C2#2142265911yescharacteristic
381C2#2142266711yescharacteristic
382C2#2142489711yescharacteristic
383C2#2142493111yescharacteristic
384C2#2142501411yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×C4⋊#95C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenterC4⋊#95D59
hypocenterC59#9679
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
5. C2×#14273727C4semidirect
9. #16837308C4semidirect
12. #16837272C4semidirect
179. C4×C59#328semidirect
213. C59#9679semidirect
373. C4#16837138semidirect

Maximal subgroups

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

subgroupindex
#214324482
C4×C22⋊(C59⋊C8)2
C2×#168371382
C59×C4⋊#952
#967959