Finite Group Databasebeta

← #28493411

Subgroups — #28493411

Order 15104.

418 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424890C211yesmaximal, characteristic
2#21424253C211yesmaximal, characteristic, complemented
3#21424097C211yesmaximal, characteristic
4#21424097C211yesmaximal, characteristic
5#21421980C211yesmaximal, characteristic, complemented
6#21421980C211yesmaximal, characteristic, complemented
7C59×#1277C211yesmaximal, characteristic, complemented
8C2×C4×D236C2211yescharacteristic
9C2×#14273659—21no—
10C2×#14273659—21no—
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×#14273649—21no—
13C2×#14273649—21no—
14C2×(C2×D59)⋊C8—21no—
15C2×(C2×D59)⋊C8—21no—
16#16837272C2211yescharacteristic
17#16837272C2211yescharacteristic
18#16837165—21no—
19#16837165—21no—
20C2×C4⋊C8×C59C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4×C8×C59C2211yescharacteristic
23C22×D236D411yescharacteristic
24C22×C4×D59—21no—
25C22×C59⋊C8—21no—
26C4×D236—21no—
27C4×D236—21no—
28C4×D236—21no—
29C4×D236—21no—
30C2×C4⋊Dic59—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59—21no—
36C2×C4⋊Dic59D411yescharacteristic
37C2×(C2×D59)⋊C4—21no—
38#14273659—42no—
39#14273659—42no—
40C4⋊(C59⋊C8)—21no—
41C4⋊(C59⋊C8)—21no—
42#14273649—42no—
43#14273649—42no—
44(C2×D59)⋊C8—42no—
45(C2×D59)⋊C8—42no—
46C22×C8×C59—21no—
47C22×C8×C59—21no—
48C22×C8×C59D411yescharacteristic
49C22×C8×C59D411yescharacteristic
50C2×C42×C59C2311yescharacteristic
51C4⋊C8×C59—21no—
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C4×C8×C59—21no—
56C4×C8×C59—21no—
57C23×D59—21no—
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59#4111yescharacteristic
61C22×Dic59—21no—
62C22×Dic59—41no—
63C22×Dic59—41no—
64C2×D236—21no—
65C2×D236—21no—
66C2×D236—21no—
67C2×D236—21no—
68C2×D236—21no—
69C2×D236SD1612yes—
70C2×C4×D59—41no—
71C2×C4×D59—41no—
72C2×C4×D59—41no—
73C2×C4×D59—41no—
74C2×C4×D59—41no—
75C2×C4×D59—41no—
76C2×C8×C59—21no—
77C2×C8×C59—21no—
78C2×C8×C59—21no—
79C2×C8×C59—21no—
80C2×C8×C59—41no—
81C2×C8×C59—41no—
82C2×C8×C59—41no—
83C2×C8×C59—41no—
84C2×C8×C59—41no—
85C2×C8×C59—41no—
86C2×C8×C59D812yes—
87C2×C8×C59SD1612yes—
88C42×C59#4111yescharacteristic
89C42×C59#4111yescharacteristic
90C42×C59#4111yescharacteristic
91C42×C59#4111yescharacteristic
92(C2×D59)⋊C4—41no—
93(C2×D59)⋊C4—41no—
94C4⋊Dic59—21no—
95C4⋊Dic59—21no—
96C4⋊Dic59—41no—
97C4⋊Dic59—41no—
98C4⋊Dic59—41no—
99C4⋊Dic59—41no—
100C4⋊Dic59—41no—
101C4⋊Dic59—41no—
102C4⋊Dic59—41no—
103C4⋊Dic59—41no—
104C4⋊Dic59—81no—
105C4⋊Dic59—81no—
106C2×C59⋊C8—41no—
107C2×C59⋊C8—41no—
108C2×C59⋊C8—41no—
109C23×C59#12111yescharacteristic
110C22×D59—22no—
111C22×D59—41no—
112C22×D59—41no—
113C22×D59—41no—
114C22×D59—41no—
115C22×D59—41no—
116C22×D59—41no—
117C2×C4×C59—21no—
118C2×C4×C59—21no—
119C2×C4×C59#12311yescharacteristic
120C2×C4×C59#12311yescharacteristic
121C2×C4×C59#12311yescharacteristic
122C2×C4×C59#12411yescharacteristic
123C2×C4×C59#12611yescharacteristic
124C2×C4×C59#12611yescharacteristic
125C2×C4×C59C2×D811yescharacteristic
126C2×C4×C59C2×SD1611yescharacteristic
127C2×C4×C59C2×SD1611yescharacteristic
128C2×C4×C59#13511yescharacteristic
129C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C59#13711yescharacteristic
132C2×C4×C59#13711yescharacteristic
133C2×Dic59—41no—
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—81no—
137C2×Dic59—81no—
138C2×Dic59—81no—
139C2×Dic59—81no—
140C2×Dic59—81no—
141C2×Dic59—81no—
142D236—22no—
143D236—22no—
144D236—41no—
145D236—41no—
146C4×D59—81no—
147C4×D59—81no—
148C4×D59—81no—
149C4×D59—81no—
150C8×C59—22no—
151C8×C59—22no—
152C8×C59—81no—
153C8×C59—81no—
154C59⋊C8—81no—
155#10619—591nomaximal, Sylow
156C22×C59#39711yescharacteristic
157C22×C59#45911yescharacteristic
158C22×C59#46111yescharacteristic
159C22×C59#46511yescharacteristic
160C22×C59#46811yescharacteristic
161C22×C59#47111yescharacteristic
162C22×C59#47111yescharacteristic
163C2×D59—42no—
164C2×D59—42no—
165C2×D59—42no—
166C2×D59—81no—
167C2×D59—81no—
168C2×D59—81no—
169C2×D59—81no—
170C4×C59—21no—
171C4×C59—21no—
172C4×C59#48011yescharacteristic
173C4×C59#48111yescharacteristic
174C4×C59#48111yescharacteristic
175C4×C59#48211yescharacteristic
176C4×C59#48311yescharacteristic
177C4×C59#48511yescharacteristic
178C4×C59#48611yescharacteristic
179C4×C59#48911yescharacteristic
180Dic59—81no—
181Dic59—161no—
182Dic59—161no—
183#1954—591no—
184#1844—591no—
185#1802—591no—
186#1802—591no—
187#1296—591no—
188#1296—591no—
189#1277D5911yescharacteristic, complemented
190C2×C59#166511yescharacteristic
191C2×C59#167111yescharacteristic
192C2×C59#168511yescharacteristic
193C2×C59#169111yescharacteristic
194C2×C59#207111yescharacteristic
195C2×C59#207711yescharacteristic
196C2×C59#207911yescharacteristic
197D59—82no—
198C2×C4×D4—591no—
199C2×#106—1181no—
200C2×#106—1181no—
201C2×C4⋊C8—591no—
202C2×C4⋊C8C2×D5911yescharacteristic
203C2×C4⋊C8C2×D5911yescharacteristic
204C2×#102—1181no—
205C2×#102—1181no—
206C2×C22⋊C8—1181no—
207C2×C22⋊C8—1181no—
208C2×C4×C8C2×D5911yescharacteristic
209#384—591no—
210#384—591no—
211#340—1181no—
212#340—1181no—
213C59#1061911yescharacteristic, complemented, Sylow
214C22×D4—591no—
215C23×C4—1181no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—1181no—
219C22×C8D23611yescharacteristic
220C22×C8D23611yescharacteristic
221C4×D4—1181no—
222C4×D4—1181no—
223C4×D4—1181no—
224C4×D4—1181no—
225C2×C4⋊C4—591no—
226C2×C4⋊C4—1181no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4—1181no—
229C2×C4⋊C4—1181no—
230C2×C4⋊C4—1181no—
231C2×C4⋊C4—1181no—
232C2×C22⋊C4—1181no—
233C2×C42C22×D5911yescharacteristic
234#106—2362no—
235#106—2362no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—1181no—
241C4⋊C8—1181no—
242#102—2362no—
243#102—2362no—
244C22⋊C8—2362no—
245C22⋊C8—2362no—
246C4×C8—21no—
247C4×C8—21no—
248C24—1181no—
249C2×D4—592no—
250C2×D4—1181no—
251C2×D4—1181no—
252C2×D4—1181no—
253C2×D4—1181no—
254C2×D4—1181no—
255C22×C4—1181no—
256C22×C4—2361no—
257C22×C4—2361no—
258C22×C4—2361no—
259C22×C4—2361no—
260C22×C4—2361no—
261C22×C4—2361no—
262C22×C4—2361no—
263C22×C4—2361no—
264C22×C4C2×D23611yescharacteristic
265C22×C4D4×D5911yescharacteristic
266C22×C4#1174568911yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—2361no—
278C2×C8—2361no—
279C2×C8—2361no—
280C2×C8#1174566012yes—
281C2×C8D47212yes—
282C4⋊C4—1181no—
283C4⋊C4—1181no—
284C4⋊C4—4721no—
285C4⋊C4—4721no—
286C4⋊C4—2361no—
287C4⋊C4—2361no—
288C4⋊C4—2361no—
289C4⋊C4—2361no—
290C4⋊C4—2361no—
291C4⋊C4—2361no—
292C4⋊C4—2361no—
293C4⋊C4—2361no—
294C22⋊C4—2361no—
295C22⋊C4—2361no—
296C42#1174568511yescharacteristic
297C42#1174568511yescharacteristic
298C42#1174568711yescharacteristic
299C42#1174568711yescharacteristic
300C23—1182no—
301C23—2361no—
302C23—2361no—
303C23—2361no—
304C23—2361no—
305C23—2361no—
306C23—2361no—
307C23#1427370211yescharacteristic
308D4—1182no—
309D4—1182no—
310D4—2361no—
311D4—2361no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—4721no—
315C2×C4—4721no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4—4721no—
321C2×C4—4721no—
322C2×C4—4721no—
323C2×C4—4721no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4#1427370911yescharacteristic
328C2×C4#1427370911yescharacteristic
329C2×C4#1427371111yescharacteristic
330C2×C4#1427371511yescharacteristic
331C2×C4#1427372211yescharacteristic
332C2×C4#1427372211yescharacteristic
333C2×C4C2×D47211yescharacteristic
334C2×C4SD16×D5911yescharacteristic
335C2×C4C2×#1174566011yescharacteristic
336C2×C4#1427374811yescharacteristic
337C2×C4#1427375111yescharacteristic
338C2×C4#1427375511yescharacteristic
339C2×C4#1427375911yescharacteristic
340C2×C4#1427376011yescharacteristic
341C8—22no—
342C8—22no—
343C8—81no—
344C8—81no—
345C8—4721no—
346C22—4721no—
347C22—4721no—
348C22—4721no—
349C22—4721no—
350C22—2362no—
351C22—2362no—
352C22—2362no—
353C22#1683732911yescharacteristic
354C22#1683759811yescharacteristic
355C22#1683760811yescharacteristic
356C22#1683763211yescharacteristic
357C22#1683764911yescharacteristic
358C22#1683766611yescharacteristic
359C22#1683766611yescharacteristic
360C4—21no—
361C4—21no—
362C4—9441no—
363C4—9441no—
364C4—4721no—
365C4#1683771611yescharacteristic
366C4#1683771911yescharacteristic
367C4#1683772111yescharacteristic
368C4#1683772511yescharacteristic
369C4#1683773111yescharacteristic
370C4#1683774111yescharacteristic
371C4#1683774911yescharacteristic
372C4#1683776211yescharacteristic
373C2—4722no—
374C2#2142343811yescharacteristic
375C2#2142347211yescharacteristic
376C2#2142356211yescharacteristic
377C2#2142359611yescharacteristic
378C2#2142550111yescharacteristic
379C2#2142553111yescharacteristic
380C2#2142554311yescharacteristic
subgroupG/H
centerC23#14273702
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1277C2
socleC23×C59#121
prime radicalC22×D236D4
hypercenter#1277D59
hypocenterC59#10619
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #21424253C2semidirect
5. #21421980C2semidirect
6. #21421980C2semidirect
7. C59×#1277C2semidirect
189. #1277D59semidirect
213. C59#10619semidirect

Maximal subgroups

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

subgroupindex
#214248902
#214242532
#214240972
#214219802
C59×#12772
#1061959