Finite Group Databasebeta

← #28478117

Subgroups — #28478117

Order 15104.

552 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432729C211yesmaximal, characteristic
2C2×#16837455C211yesmaximal, characteristic
3#21421927C214yesmaximal, complemented
4C2×C59×#432C211yesmaximal, characteristic
5#16837459—21no—
6#16837459—21no—
7#16837455—21no—
8#16837455—21no—
9#16837455C412yes—
10#16837455C412yes—
11#16837455C2212yes—
12#16837455C2212yes—
13#16837426—21no—
14C2×C4⋊(C59⋊C8)—21no—
15#16837366—21no—
16C2×C22⋊(C59⋊C8)—21no—
17C4×#11745664C412yes—
18C2×C4×C59⋊C8C412yes—
19C22×C42×C59C2211yescharacteristic
20C59×#432—21no—
21C59×#432—21no—
22C59×#432—21no—
23C59×#432—21no—
24C2×C4⋊C8×C59C412yes—
25C2×C22⋊C8×C59C412yes—
26C2×#97×C59C2212yes—
27C2×#11745664—22no—
28C22×C59⋊C8—22no—
29C4⋊(C59⋊C8)—22no—
30C4⋊(C59⋊C8)—22no—
31C4⋊(C59⋊C8)—22no—
32C4⋊(C59⋊C8)—22no—
33C22⋊(C59⋊C8)—22no—
34C22⋊(C59⋊C8)—22no—
35C22⋊(C59⋊C8)—22no—
36C22⋊(C59⋊C8)—22no—
37#14273638—22no—
38C4×C59⋊C8—22no—
39C4×C59⋊C8C2×C414yes—
40C4×C59⋊C8C2×C414yes—
41C23×C4×C59C2×C411yescharacteristic
42C23×C4×C59D411yescharacteristic
43C23×C4×C59Q811yescharacteristic
44C22×C8×C59C2×C414yes—
45C2×C42×C59C2×C411yescharacteristic
46C2×C42×C59C2×C411yescharacteristic
47C2×C42×C59C2×C411yescharacteristic
48C2×C42×C59C2×C411yescharacteristic
49C2×C42×C59C2×C411yescharacteristic
50C2×C42×C59D411yescharacteristic
51C2×C42×C59D411yescharacteristic
52C2×C42×C59D411yescharacteristic
53C2×C42×C59D411yescharacteristic
54C2×C42×C59D411yescharacteristic
55C2×C42×C59Q811yescharacteristic
56C2×C42×C59C2311yescharacteristic
57C4⋊C8×C59—22no—
58C4⋊C8×C59—22no—
59C22⋊C8×C59—22no—
60C22⋊C8×C59—22no—
61#97×C59—22no—
62#97×C59—22no—
63C24×C59C4⋊C411yescharacteristic
64C22×C4×C59—24no—
65C22×C4×C59—42no—
66C22×C4×C59—42no—
67C22×C4×C59C4211yescharacteristic
68C22×C4×C59C4211yescharacteristic
69C22×C4×C59C22⋊C411yescharacteristic
70C22×C4×C59C22⋊C411yescharacteristic
71C22×C4×C59C22⋊C411yescharacteristic
72C22×C4×C59C22⋊C411yescharacteristic
73C22×C4×C59C22⋊C411yescharacteristic
74C22×C4×C59C22⋊C411yescharacteristic
75C22×C4×C59C4⋊C411yescharacteristic
76C22×C4×C59C4⋊C411yescharacteristic
77C22×C4×C59C4⋊C411yescharacteristic
78C22×C4×C59C4⋊C411yescharacteristic
79C22×C4×C59C4⋊C411yescharacteristic
80C22×C4×C59C4⋊C411yescharacteristic
81C22×C4×C59C4⋊C411yescharacteristic
82C22×C4×C59C22×C411yescharacteristic
83C22×C4×C59C2×D411yescharacteristic
84C22×C4×C59C2×Q811yescharacteristic
85C2×C8×C59—24no—
86C2×C8×C59—28no—
87C42×C59C4211yescharacteristic
88C42×C59C4211yescharacteristic
89C42×C59C22⋊C411yescharacteristic
90C42×C59C22⋊C411yescharacteristic
91C42×C59C22⋊C411yescharacteristic
92C42×C59C22⋊C411yescharacteristic
93C42×C59C22⋊C411yescharacteristic
94C42×C59C22⋊C411yescharacteristic
95C42×C59C4⋊C411yescharacteristic
96C42×C59C4⋊C411yescharacteristic
97C42×C59C4⋊C411yescharacteristic
98C42×C59C4⋊C411yescharacteristic
99C42×C59C22×C411yescharacteristic
100C42×C59C22×C411yescharacteristic
101C42×C59C2×D411yescharacteristic
102C42×C59C2×D411yescharacteristic
103#11745664—44no—
104C2×C59⋊C8—24no—
105C2×C59⋊C8—24no—
106C2×C59⋊C8—44no—
107C23×C59—22no—
108C23×C59—22no—
109C23×C59—41no—
110C23×C59#9511yescharacteristic
111C23×C59#9511yescharacteristic
112C23×C59C2×C4⋊C411yescharacteristic
113C2×C4×C59—22no—
114C2×C4×C59—22no—
115C2×C4×C59—22no—
116C2×C4×C59—22no—
117C2×C4×C59—22no—
118C2×C4×C59—22no—
119C2×C4×C59—22no—
120C2×C4×C59—22no—
121C2×C4×C59—22no—
122C2×C4×C59—22no—
123C2×C4×C59—41no—
124C2×C4×C59—41no—
125C2×C4×C59—41no—
126C2×C4×C59—41no—
127C2×C4×C59—41no—
128C2×C4×C59—41no—
129C2×C4×C59—41no—
130C2×C4×C59#9511yescharacteristic
131C2×C4×C59#9511yescharacteristic
132C2×C4×C59#9511yescharacteristic
133C2×C4×C59#9511yescharacteristic
134C2×C4×C59#9511yescharacteristic
135C2×C4×C59#9511yescharacteristic
136C2×C4×C59C2×C4211yescharacteristic
137C2×C4×C59C2×C22⋊C411yescharacteristic
138C2×C4×C59C2×C22⋊C411yescharacteristic
139C2×C4×C59C2×C22⋊C411yescharacteristic
140C2×C4×C59C2×C4⋊C411yescharacteristic
141C2×C4×C59C2×C4⋊C411yescharacteristic
142C2×C4×C59#13114yes—
143C8×C59—44no—
144C59⋊C8—44no—
145C59⋊C8—44no—
146#7863—591nomaximal, Sylow
147C22×C59—21no—
148C22×C59—21no—
149C22×C59—21no—
150C22×C59—21no—
151C22×C59—21no—
152C22×C59—21no—
153C22×C59—21no—
154C22×C59—44no—
155C22×C59H(3,ℤ/4)12yes—
156C22×C59C2×#9511yescharacteristic
157C22×C59#42412yes—
158C4×C59—21no—
159C4×C59—21no—
160C4×C59—21no—
161C4×C59—21no—
162C4×C59—21no—
163C4×C59—21no—
164C4×C59—21no—
165C4×C59—21no—
166C4×C59—21no—
167C4×C59#33812yes—
168C4×C59#40512yes—
169C4×C59#40812yes—
170#2920—591no—
171C2×#432D5911yescharacteristic
172C2×#431—591no—
173#1275—594no—
174C2×C59—22no—
175C2×C59—22no—
176C2×C59—41no—
177C2×C59#172911yescharacteristic
178C2×C59C2×H(3,ℤ/4)11yescharacteristic
179C2×C59C2×#33811yescharacteristic
180C22×C42C2×D5911yescharacteristic
181#432—21no—
182#432—21no—
183#432—21no—
184#432—21no—
185#432—1181no—
186#432—1181no—
187#431—592no—
188#431—592no—
189#431—592no—
190#431—592no—
191#431—1181no—
192#431—1181no—
193#423—1181no—
194C2×C4⋊C8—1181no—
195C2×C4⋊C8Dic5912yes—
196#407—1181no—
197C2×C22⋊C8—1181no—
198C2×C22⋊C8Dic5912yes—
199C4×M16—592no—
200C2×#97C2×D5912yes—
201C2×C4×C8—592no—
202C59#786311yescharacteristic, complemented, Sylow
203C23×C4Dic11811yescharacteristic
204C23×C4D23611yescharacteristic
205C23×C4C2×Dic5911yescharacteristic
206C2×M16—1182no—
207C22×C8—1182no—
208C22×C8C2×Dic5914yes—
209C2×C42Dic11811yescharacteristic
210C2×C42C4×D5911yescharacteristic
211C2×C42C4×D5911yescharacteristic
212C2×C42C4×D5911yescharacteristic
213C2×C42C4×D5911yescharacteristic
214C2×C42D23611yescharacteristic
215C2×C42C2×Dic5911yescharacteristic
216C2×C42C22⋊D5911yescharacteristic
217C2×C42C22⋊D5911yescharacteristic
218C2×C42C22⋊D5911yescharacteristic
219C2×C42C22⋊D5911yescharacteristic
220C2×C42C22×D5911yescharacteristic
221C4⋊C8—22no—
222C4⋊C8—22no—
223C4⋊C8—1182no—
224C4⋊C8—1182no—
225C4⋊C8—1182no—
226C4⋊C8—1182no—
227C22⋊C8—22no—
228C22⋊C8—22no—
229C22⋊C8—1182no—
230C22⋊C8—1182no—
231C22⋊C8—1182no—
232C22⋊C8—1182no—
233#97—22no—
234#97—22no—
235#97—1182no—
236C4×C8—594no—
237C4×C8—594no—
238C4×C8—1182no—
239C24C4⋊Dic5911yescharacteristic
240C22×C4—24no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4C4×Dic5911yescharacteristic
244C22×C4C4×Dic5911yescharacteristic
245C22×C4Dic59⋊C411yescharacteristic
246C22×C4Dic59⋊C411yescharacteristic
247C22×C4Dic59⋊C411yescharacteristic
248C22×C4Dic59⋊C411yescharacteristic
249C22×C4C4⋊Dic5911yescharacteristic
250C22×C4C4⋊Dic5911yescharacteristic
251C22×C4C4⋊Dic5911yescharacteristic
252C22×C4(C2×D59)⋊C411yescharacteristic
253C22×C4(C2×D59)⋊C411yescharacteristic
254C22×C4(C2×D59)⋊C411yescharacteristic
255C22×C4(C2×D59)⋊C411yescharacteristic
256C22×C4C22⋊Dic5911yescharacteristic
257C22×C4C22⋊Dic5911yescharacteristic
258C22×C4C2×Dic11811yescharacteristic
259C22×C4C2×D23611yescharacteristic
260C22×C4C22×Dic5911yescharacteristic
261M16—2364no—
262C2×C8—24no—
263C2×C8—28no—
264C2×C8—1184no—
265C2×C8—1184no—
266C2×C8—2364no—
267C42C4×Dic5911yescharacteristic
268C42C4×Dic5911yescharacteristic
269C42Dic59⋊C411yescharacteristic
270C42Dic59⋊C411yescharacteristic
271C42Dic59⋊C411yescharacteristic
272C42Dic59⋊C411yescharacteristic
273C42(C2×D59)⋊C411yescharacteristic
274C42(C2×D59)⋊C411yescharacteristic
275C42(C2×D59)⋊C411yescharacteristic
276C42(C2×D59)⋊C411yescharacteristic
277C42C22⋊Dic5911yescharacteristic
278C42C22⋊Dic5911yescharacteristic
279C42C2×C4×D5911yescharacteristic
280C42C2×C4×D5911yescharacteristic
281C42C2×C22⋊D5911yescharacteristic
282C42C2×C22⋊D5911yescharacteristic
283C23—22no—
284C23—22no—
285C23—41no—
286C23C59⋊#9511yescharacteristic
287C23C59⋊#9511yescharacteristic
288C23C2×C4⋊Dic5911yescharacteristic
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4C59⋊#9511yescharacteristic
307C2×C4C59⋊#9511yescharacteristic
308C2×C4C59⋊#9511yescharacteristic
309C2×C4C59⋊#9511yescharacteristic
310C2×C4C59⋊#9511yescharacteristic
311C2×C4C59⋊#9511yescharacteristic
312C2×C4C2×C4×Dic5911yescharacteristic
313C2×C4C2×(C2×D59)⋊C411yescharacteristic
314C2×C4C2×(C2×D59)⋊C411yescharacteristic
315C2×C4C2×C22⋊Dic5911yescharacteristic
316C2×C4C2×Dic59⋊C411yescharacteristic
317C2×C4C2×Dic59⋊C411yescharacteristic
318C2×C4#1427373414yes—
319C8—44no—
320C8—2364no—
321C8—2364no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—44no—
330C22#1683715912yes—
331C22C2×C59⋊#9511yescharacteristic
332C22#1683742912yes—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4C59⋊#33812yes—
343C4#1683735812yes—
344C4#1683736912yes—
345C2—22no—
346C2—22no—
347C2—41no—
348C2#2142379311yescharacteristic
349C2C2×#1683715911yescharacteristic
350C2C2×C59⋊#33811yescharacteristic
subgroupG/H
centerC2×C4C2×C4×Dic59
commutatorC2×C4×C59C2×C42
FrattiniC2×C42C22×D59
FittingC2×C59×#432C2
socleC22×C59C2×#95
prime radicalC24×C59C4⋊C4
cosocleC2×C42×C59C23
hypercenterC2×#432D59
hypocenterC59#7863
LCSG ▷ C2×C4×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #21421927C2semidirect
202. C59#7863semidirect

Maximal subgroups

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

subgroupindex
#214327292
C2×#168374552
#214219272
C2×C59×#4322
#786359