Finite Group Databasebeta

← #28484320

Subgroups — #28484320

Order 15104.

530 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×#16837459C211yesmaximal, characteristic
2#21423858C211yesmaximal, characteristic
3C2×#16837144C212yesmaximal, complemented
4#21421977C212yesmaximal, complemented
5C59×#2851C211yesmaximal, characteristic
6#16837459—24no—
7C2×C4⋊(C59⋊C8)—21no—
8C2×C22⋊(C59⋊C8)—21no—
9C2×C22⋊(C59⋊C8)—21no—
10C2×#14273638C2212yes—
11C2×#14273638C2212yes—
12#16837157—21no—
13#16837144—24no—
14C2×#125×C59C2211yescharacteristic
15C22×C42×C59C2211yescharacteristic
16C59×#389C411yescharacteristic
17C59×#389C411yescharacteristic
18C59×#387—21no—
19C59×#387—21no—
20C59×#385—21no—
21C59×#385—21no—
22C59×#382C2211yescharacteristic
23C59×#380C411yescharacteristic
24C59×#380C411yescharacteristic
25C22×C59⋊C8—22no—
26C22×C59⋊C8—22no—
27C4⋊(C59⋊C8)—24no—
28C22⋊(C59⋊C8)—24no—
29C22⋊(C59⋊C8)—24no—
30#14273638—22no—
31#14273638—22no—
32#14273638—22no—
33#14273638D414yes—
34C23×C4×C59C2×C411yescharacteristic
35C23×C4×C59D411yescharacteristic
36C23×C4×C59D411yescharacteristic
37#125×C59—22no—
38#125×C59—22no—
39C2×C4⋊C4×C59—21no—
40C2×C4⋊C4×C59—21no—
41C2×C4⋊C4×C59—21no—
42C2×C4⋊C4×C59—21no—
43C2×C4⋊C4×C59C2×C411yescharacteristic
44C2×C4⋊C4×C59C2×C411yescharacteristic
45C2×C4⋊C4×C59C2×C411yescharacteristic
46C2×C4⋊C4×C59C2×C411yescharacteristic
47C2×C22⋊C4×C59—21no—
48C2×C22⋊C4×C59—21no—
49C2×C42×C59—22no—
50C2×C42×C59—22no—
51C2×C42×C59C2×C411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C2×C42×C59C2311yescharacteristic
55#95×C59—21no—
56#95×C59—21no—
57#95×C59—21no—
58#95×C59—21no—
59#95×C59—21no—
60#95×C59—21no—
61C24×C59C22⋊C411yescharacteristic
62C22×C4×C59—22no—
63C22×C4×C59—22no—
64C22×C4×C59—22no—
65C22×C4×C59—21no—
66C22×C4×C59—22no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—21no—
72C22×C4×C59—41no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59—41no—
76C22×C4×C59C22⋊C411yescharacteristic
77C22×C4×C59C22⋊C411yescharacteristic
78C22×C4×C59C22⋊C411yescharacteristic
79C22×C4×C59C22×C411yescharacteristic
80C22×C4×C59C2×D411yescharacteristic
81C22×C4×C59C2×D411yescharacteristic
82C4⋊C4×C59—22no—
83C4⋊C4×C59—22no—
84C4⋊C4×C59—42no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—42no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—42no—
90C4⋊C4×C59—41no—
91C22⋊C4×C59—42no—
92C22⋊C4×C59—42no—
93C42×C59—22no—
94C42×C59—21no—
95C42×C59—22no—
96C42×C59—21no—
97C42×C59C2×D412yes—
98C42×C59#4112yes—
99C2×C59⋊C8—24no—
100C2×C59⋊C8—24no—
101C2×C59⋊C8—42no—
102C2×C59⋊C8—42no—
103C2×C59⋊C8—42no—
104C2×C59⋊C8—42no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59#10112yes—
112C23×C59C2×C22⋊C411yescharacteristic
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—21no—
121C2×C4×C59—21no—
122C2×C4×C59—21no—
123C2×C4×C59—21no—
124C2×C4×C59—21no—
125C2×C4×C59—21no—
126C2×C4×C59—21no—
127C2×C4×C59—44no—
128C2×C4×C59—44no—
129C2×C4×C59—42no—
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—41no—
143C2×C4×C59#10412yes—
144C2×C4×C59C4×D412yes—
145C2×C4×C59#12011yescharacteristic
146C2×C4×C59#12112yes—
147C2×C4×C59#12311yescharacteristic
148C59⋊C8—44no—
149C59⋊C8—44no—
150#9126—591nomaximal, Sylow
151C22×C59—22no—
152C22×C59—22no—
153C22×C59—22no—
154C22×C59—41no—
155C22×C59—41no—
156C22×C59—41no—
157C22×C59—41no—
158C22×C59#38611yescharacteristic
159C22×C59C2×#10111yescharacteristic
160C22×C59#41311yescharacteristic
161C22×C59C2×#10411yescharacteristic
162C22×C59#42111yescharacteristic
163C22×C59#42111yescharacteristic
164C22×C59#42111yescharacteristic
165C4×C59—22no—
166C4×C59—22no—
167C4×C59—21no—
168C4×C59—21no—
169C4×C59—22no—
170C4×C59—41no—
171C4×C59—41no—
172C4×C59—81no—
173C4×C59—81no—
174C4×C59—81no—
175C4×C59—81no—
176C2×#432—591no—
177#2851D5911yescharacteristic
178#1749—591no—
179C2×#330—592no—
180#1295—592no—
181C2×C59—42no—
182C2×C59#152911yescharacteristic
183C2×C59#153111yescharacteristic
184C2×C59#153411yescharacteristic
185C2×C59#153511yescharacteristic
186C2×C59#187111yescharacteristic
187C2×C59#189711yescharacteristic
188C2×C59#190111yescharacteristic
189C2×#125C2×D5911yescharacteristic
190C22×C42C2×D5911yescharacteristic
191#432—1184no—
192C2×C4⋊C8—1181no—
193C2×C22⋊C8—1181no—
194C2×C22⋊C8—1181no—
195C2×#97—592no—
196C2×#97—592no—
197#389Dic5911yescharacteristic
198#389Dic5911yescharacteristic
199#387—21no—
200#387—21no—
201#385—21no—
202#385—21no—
203#382C2×D5911yescharacteristic
204#380Dic5911yescharacteristic
205#380Dic5911yescharacteristic
206#336—1181no—
207#330—1184no—
208C59#912611yescharacteristic, complemented, Sylow
209C23×C4C2×Dic5911yescharacteristic
210C23×C4C22⋊D5911yescharacteristic
211C23×C4C22⋊D5911yescharacteristic
212C22×C8—1182no—
213C22×C8—1182no—
214#125—22no—
215#125—22no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4C2×Dic5911yescharacteristic
221C2×C4⋊C4C2×Dic5911yescharacteristic
222C2×C4⋊C4C2×Dic5911yescharacteristic
223C2×C4⋊C4C2×Dic5911yescharacteristic
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42C2×Dic5911yescharacteristic
229C2×C42C22⋊D5911yescharacteristic
230C2×C42C22⋊D5911yescharacteristic
231C2×C42C22×D5911yescharacteristic
232C4⋊C8—1184no—
233C22⋊C8—1184no—
234C22⋊C8—1184no—
235#97—594no—
236#97—1182no—
237#97—1182no—
238#97—1182no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245C24C22⋊Dic5911yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4C22⋊Dic5911yescharacteristic
261C22×C4C22⋊Dic5911yescharacteristic
262C22×C4C22⋊Dic5911yescharacteristic
263C22×C4C22×Dic5911yescharacteristic
264C22×C4C2×C22⋊D5911yescharacteristic
265C22×C4C2×C22⋊D5911yescharacteristic
266C2×C8—1184no—
267C2×C8—1184no—
268C2×C8—2362no—
269C2×C8—2362no—
270C2×C8—2362no—
271C2×C8—2362no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—22no—
284C42—21no—
285C42—22no—
286C42—21no—
287C42D4×D5912yes—
288C42#1174568712yes—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23#1427364612yes—
296C23C2×C22⋊Dic5911yescharacteristic
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—42no—
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—41no—
327C2×C4#1427365412yes—
328C2×C4D4×Dic5912yes—
329C2×C4#1427369511yescharacteristic
330C2×C4#1427369912yes—
331C2×C4#1427370811yescharacteristic
332C8—2364no—
333C8—2364no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22#1683728211yescharacteristic
342C22C2×#1427364611yescharacteristic
343C22#1683738611yescharacteristic
344C22C2×#1427365411yescharacteristic
345C22#1683741911yescharacteristic
346C22#1683741911yescharacteristic
347C22#1683741911yescharacteristic
348C4—22no—
349C4—22no—
350C4—21no—
351C4—21no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C4—81no—
359C2—42no—
360C2#2142270311yescharacteristic
361C2#2142271111yescharacteristic
362C2#2142272311yescharacteristic
363C2#2142272711yescharacteristic
364C2#2142439911yescharacteristic
365C2#2142454511yescharacteristic
366C2#2142456511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2851C2
socleC23×C59C2×C22⋊C4
prime radicalC24×C59C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2851D59
hypocenterC59#9126
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2851

Complements

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

NH ≅ G/Ntype
3. C2×#16837144C2semidirect
4. #21421977C2semidirect
208. C59#9126semidirect

Maximal subgroups

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

subgroupindex
C2×#168374592
#214238582
C2×#168371442
#214219772
C59×#28512
#912659