Finite Group Databasebeta

← #28494524

Subgroups — #28494524

Order 15104.

1338 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837262C212yesmaximal
2C2×#16837169C214yesmaximal
3C2×C4×C22⋊C4×C59C211yesmaximal, characteristic
4C22×C4⋊Dic59—22no—
5C22×C22⋊Dic59C2214yes—
6#16837262—24no—
7#16837262C418yescomplemented
8C2×C59⋊#95—22no—
9#16837169—28no—
10C24×C4×C59C2211yescharacteristic
11C22×C22⋊C4×C59C2212yes—
12C22×C42×C59C412yescomplemented
13C4×C22⋊C4×C59—22no—
14C4×C22⋊C4×C59—22no—
15C2×#95×C59C412yescomplemented
16C23×Dic59—24no—
17C2×C4⋊Dic59—28no—
18C2×C4⋊Dic59—48no—
19C2×C22⋊Dic59—28no—
20C2×C22⋊Dic59—28no—
21C2×C22⋊Dic59—24no—
22C2×C22⋊Dic59C2×C418yes—
23C59⋊#95—28no—
24C25×C59C2311yescharacteristic
25C23×C4×C59—44no—
26C23×C4×C59C2×C414yes—
27C23×C4×C59C2×C411yescharacteristic
28C23×C4×C59C2×C414yes—
29C23×C4×C59C2×C411yescharacteristic
30C23×C4×C59D412yes—
31C23×C4×C59D412yes—
32C23×C4×C59D412yes—
33C23×C4×C59Q812yes—
34C2×C22⋊C4×C59—24no—
35C2×C22⋊C4×C59—24no—
36C2×C22⋊C4×C59D414yes—
37C2×C22⋊C4×C59Q814yes—
38C2×C42×C59—22no—
39C2×C42×C59—22no—
40C2×C42×C59—44no—
41#95×C59—24no—
42C24×C59—42no—
43C24×C59—42no—
44C24×C59C22×C411yescharacteristic
45C24×C59C22×C412yes—
46C24×C59C2×D412yes—
47C24×C59C2×D411yescharacteristic
48C24×C59C2×D412yes—
49C24×C59C2×Q811yescharacteristic
50C24×C59C2×Q812yes—
51C24×C59#4114yes—
52C22×C4×C59—24no—
53C22×C4×C59—28no—
54C22×C4×C59—24no—
55C22×C4×C59—24no—
56C22×C4×C59—48no—
57C22×C4×C59—44no—
58C22×C4×C59—44no—
59C22×C4×C59—42no—
60C22×C4×C59—44no—
61C22×C4×C59—44no—
62C22×C4×C59—44no—
63C22×C4×C59C4212yes—
64C22×C4×C59C4212yes—
65C22×C4×C59C22⋊C414yes—
66C22×C4×C59C22⋊C412yes—
67C22×C4×C59C22⋊C411yescharacteristic
68C22×C4×C59C22⋊C414yes—
69C22×C4×C59C22⋊C411yescharacteristic
70C22×C4×C59C4⋊C414yes—
71C22×C4×C59C4⋊C412yes—
72C22×C4×C59C4⋊C414yes—
73C22×C4×C59C4⋊C412yes—
74C22×C4×C59C4⋊C418yescomplemented
75C22×Dic59—28no—
76C22×Dic59—48no—
77C22×Dic59—48no—
78C22×Dic59—48no—
79C22⋊C4×C59—28no—
80C22⋊C4×C59—28no—
81C42×C59—44no—
82C42×C59—44no—
83C22⋊Dic59—216no—
84C22⋊Dic59—44no—
85C22⋊Dic59—44no—
86C4⋊Dic59—416no—
87C23×C59—24no—
88C23×C59—22no—
89C23×C59—24no—
90C23×C59—22no—
91C23×C59—42no—
92C23×C59—41no—
93C23×C59—41no—
94C23×C59—42no—
95C23×C59—44no—
96C23×C59—41no—
97C23×C59—44no—
98C23×C59—41no—
99C23×C59—48no—
100C23×C59C2×C4211yescharacteristic
101C23×C59C2×C22⋊C412yes—
102C23×C59C2×C22⋊C411yescharacteristic
103C23×C59C2×C4⋊C412yes—
104C23×C59C2×C4⋊C411yescharacteristic
105C23×C59C2×C4⋊C412yes—
106C23×C59#11712yes—
107C23×C59C4×D414yes—
108C23×C59C4×Q814yes—
109C23×C59#12114yes—
110C23×C59C22⋊Q814yes—
111C23×C59#12412yes—
112C23×C59#12512yes—
113C23×C59#12711yescharacteristic
114C23×C59C4⋊Q812yes—
115C23×C59C4⋊Q811yescharacteristic
116C2×C4×C59—22no—
117C2×C4×C59—24no—
118C2×C4×C59—28no—
119C2×C4×C59—24no—
120C2×C4×C59—28no—
121C2×C4×C59—24no—
122C2×C4×C59—28no—
123C2×C4×C59—42no—
124C2×C4×C59—44no—
125C2×C4×C59—44no—
126C2×C4×C59—42no—
127C2×C4×C59—48no—
128C2×C4×C59—44no—
129C2×C4×C59—44no—
130C2×C4×C59—48no—
131C2×C4×C59#9512yes—
132C2×C4×C59#9514yes—
133C2×C4×C59#9512yes—
134C2×C4×C59#9914yes—
135C2×Dic59—48no—
136C2×Dic59—48no—
137C2×Dic59—48no—
138C2×Dic59—816no—
139#10846—591nomaximal, Sylow
140C22×C59—28no—
141C22×C59—24no—
142C22×C59—24no—
143C22×C59—28no—
144C22×C59—22no—
145C22×C59—21no—
146C22×C59—22no—
147C22×C59—21no—
148C22×C59—22no—
149C22×C59—21no—
150C22×C59—22no—
151C22×C59—21no—
152C22×C59—44no—
153C22×C59—44no—
154C22×C59—42no—
155C22×C59—42no—
156C22×C59—41no—
157C22×C59—42no—
158C22×C59—41no—
159C22×C59C2×#9511yescharacteristic
160C22×C59C4×C4⋊C412yes—
161C22×C59#38012yes—
162C22×C59#38211yescharacteristic
163C22×C59#38411yescharacteristic
164C22×C59#38914yes—
165C22×C59#39012yes—
166C22×C59#39112yes—
167C22×C59C2×#9912yes—
168C22×C59#41012yes—
169C4×C59—22no—
170C4×C59—24no—
171C4×C59—48no—
172C4×C59#34214yescomplemented
173Dic59—88no—
174C2×#380—592no—
175C2×C4×C22⋊C4D5911yescharacteristic
176C2×#342—594no—
177C2×C59—22no—
178C2×C59—22no—
179C2×C59—21no—
180C2×C59—21no—
181C2×C59—24no—
182C2×C59—22no—
183C2×C59C4⋊#9511yescharacteristic
184C2×C59C2×#34211yescharacteristic
185C2×C59#174011yescharacteristic
186C2×C59#179914yes—
187C24×C4C2×D5911yescharacteristic
188C22×C4⋊C4—1182no—
189C22×C22⋊C4—594no—
190C22×C22⋊C4C2×D5912yes—
191C22×C42Dic5912yescomplemented
192#380—598no—
193#380—1184no—
194C4×C22⋊C4—22no—
195C4×C22⋊C4—22no—
196C2×#95—1182no—
197C2×#95Dic5912yescomplemented
198#342—1188no—
199C59#1084611yescharacteristic, complemented, Sylow
200C25C22×D5911yescharacteristic
201C23×C4—44no—
202C23×C4—1184no—
203C23×C4Dic11812yes—
204C23×C4C4×D5914yes—
205C23×C4D23612yes—
206C23×C4C2×Dic5911yescharacteristic
207C23×C4C2×Dic5914yes—
208C23×C4C2×Dic5911yescharacteristic
209C23×C4C22⋊D5912yes—
210C23×C4C22⋊D5912yes—
211C2×C4⋊C4—1188no—
212C2×C4⋊C4—2368no—
213C2×C22⋊C4—24no—
214C2×C22⋊C4—24no—
215C2×C22⋊C4—598no—
216C2×C22⋊C4—1188no—
217C2×C22⋊C4—1188no—
218C2×C22⋊C4—1184no—
219C2×C22⋊C4Dic11814yes—
220C2×C22⋊C4D23614yes—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—44no—
224#95—24no—
225#95—1188no—
226C24—42no—
227C24—42no—
228C24C2×Dic11811yescharacteristic
229C24C2×Dic11812yes—
230C24C2×C4×D5912yes—
231C24C2×D23611yescharacteristic
232C24C2×D23612yes—
233C24#1174568514yes—
234C24C22×Dic5911yescharacteristic
235C24C2×C22⋊D5912yes—
236C22×C4—24no—
237C22×C4—28no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—44no—
241C22×C4—48no—
242C22×C4—44no—
243C22×C4—42no—
244C22×C4—44no—
245C22×C4—44no—
246C22×C4—44no—
247C22×C4—1188no—
248C22×C4—2368no—
249C22×C4—2368no—
250C22×C4—2368no—
251C22×C4C4×Dic5912yes—
252C22×C4C4×Dic5912yes—
253C22×C4Dic59⋊C414yes—
254C22×C4Dic59⋊C414yes—
255C22×C4C4⋊Dic5912yes—
256C22×C4C4⋊Dic5912yes—
257C22×C4C4⋊Dic5918yescomplemented
258C22×C4(C2×D59)⋊C414yes—
259C22×C4(C2×D59)⋊C414yes—
260C22×C4C22⋊Dic5912yes—
261C22×C4C22⋊Dic5911yescharacteristic
262C22×C4C22⋊Dic5911yescharacteristic
263C4⋊C4—23616no—
264C22⋊C4—28no—
265C22⋊C4—28no—
266C22⋊C4—11816no—
267C22⋊C4—2364no—
268C22⋊C4—2364no—
269C42—44no—
270C42—44no—
271C23—22no—
272C23—24no—
273C23—22no—
274C23—24no—
275C23—41no—
276C23—42no—
277C23—41no—
278C23—44no—
279C23—41no—
280C23—42no—
281C23—44no—
282C23—41no—
283C23—48no—
284C23C2×C4×Dic5911yescharacteristic
285C23C2×(C2×D59)⋊C412yes—
286C23C2×C22⋊Dic5911yescharacteristic
287C23C2×Dic59⋊C412yes—
288C23C2×C4⋊Dic5911yescharacteristic
289C23C2×C4⋊Dic5912yes—
290C23#1427368612yes—
291C23C4×D23614yes—
292C23C4×Dic11814yes—
293C23#1427370114yes—
294C23#1427370614yes—
295C23#1427371512yes—
296C23#1427371912yes—
297C23#1427372411yescharacteristic
298C23#1427372712yes—
299C23#1427372711yescharacteristic
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—28no—
303C2×C4—24no—
304C2×C4—28no—
305C2×C4—24no—
306C2×C4—28no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—42no—
310C2×C4—44no—
311C2×C4—48no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—48no—
315C2×C4—47216no—
316C2×C4—2368no—
317C2×C4—2368no—
318C2×C4—2368no—
319C2×C4C59⋊#9512yes—
320C2×C4C59⋊#9514yes—
321C2×C4C59⋊#9512yes—
322C2×C4#1427364214yes—
323C22—22no—
324C22—21no—
325C22—22no—
326C22—21no—
327C22—24no—
328C22—24no—
329C22—28no—
330C22—28no—
331C22—22no—
332C22—21no—
333C22—22no—
334C22—21no—
335C22—44no—
336C22—44no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—42no—
341C22—41no—
342C22C2×C59⋊#9511yescharacteristic
343C22C4×C4⋊Dic5912yes—
344C22#1683726212yes—
345C22#1683726811yescharacteristic
346C22#1683727211yescharacteristic
347C22#1683730014yes—
348C22#1683730412yes—
349C22#1683730812yes—
350C22C2×#1427364212yes—
351C22#1683737612yes—
352C4—22no—
353C4—24no—
354C4—48no—
355C4—4728no—
356C4#1683716914yescomplemented
357C2—22no—
358C2—22no—
359C2—21no—
360C2—21no—
361C2—24no—
362C2—22no—
363C2#2142232611yescharacteristic
364C2C2×#1683716911yescharacteristic
365C2#2142382911yescharacteristic
366C2#2142408414yes—
subgroupG/H
centerC23C2×C22⋊Dic59
commutatorC23×C59C2×C42
FrattiniC25C22×D59
FittingC2×C4×C22⋊C4×C59C2
socleC23×C59C2×C22⋊C4
prime radical, cosocleC25×C59C23
hypercenterC2×C4×C22⋊C4D59
hypocenterC59#10846
LCSG ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
7. #16837262C4semidirect
12. C22×C42×C59C4semidirect
15. C2×#95×C59C4semidirect
74. C22×C4×C59C4⋊C4semidirect
172. C4×C59#342semidirect
191. C22×C42Dic59semidirect
197. C2×#95Dic59semidirect
199. C59#10846semidirect
257. C22×C4C4⋊Dic59semidirect
356. C4#16837169semidirect

Maximal subgroups

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

subgroupindex
C2×#168372622
C2×#168371692
C2×C4×C22⋊C4×C592
#1084659