Finite Group Databasebeta

← #28493444

Subgroups — #28493444

Order 15104.

402 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424890C211yesmaximal, characteristic
2#21424093C211yesmaximal, characteristic
3#21424093C211yesmaximal, characteristic
4#21421979C211yesmaximal, characteristic, complemented
5#21421979C211yesmaximal, characteristic, complemented
6#21421931C211yesmaximal, characteristic, complemented
7C59×#1834C211yesmaximal, characteristic, complemented
8C2×C4×D236C2211yescharacteristic
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×#14273647—21no—
13C2×#14273647—21no—
14C2×(C2×D59)⋊C8—21no—
15C2×(C2×D59)⋊C8—21no—
16#16837164—21no—
17#16837164—21no—
18C2×C4×C8×C59C2211yescharacteristic
19C59×#384C2211yescharacteristic
20C59×#384C2211yescharacteristic
21C59×#340—21no—
22C59×#340—21no—
23C22×D236D411yescharacteristic
24C22×C4×D59—21no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8—21no—
27C22×C59⋊C8—21no—
28C4×D236—21no—
29C4×D236—21no—
30C4×D236—21no—
31C4×D236—21no—
32C2×C4⋊Dic59D411yescharacteristic
33C2×(C2×D59)⋊C4—21no—
34C4⋊(C59⋊C8)—21no—
35C4⋊(C59⋊C8)—21no—
36C4⋊(C59⋊C8)—21no—
37C4⋊(C59⋊C8)—21no—
38C4⋊(C59⋊C8)—21no—
39C4⋊(C59⋊C8)—21no—
40#14273647—42no—
41#14273647—42no—
42(C2×D59)⋊C8—42no—
43(C2×D59)⋊C8—42no—
44C22×C8×C59D411yescharacteristic
45C22×C8×C59D411yescharacteristic
46C2×C4⋊C4×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C4⋊C4×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C42×C59C2311yescharacteristic
53C4×C8×C59—21no—
54C4×C8×C59—21no—
55C23×D59—21no—
56C22×C4×C59—41no—
57C22×C4×C59—41no—
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59C2×D411yescharacteristic
60C22×C4×C59#4111yescharacteristic
61C22×Dic59—21no—
62C2×D236—21no—
63C2×D236—21no—
64C2×D236—21no—
65C2×D236—21no—
66C2×D236—21no—
67C2×D236SD1612yes—
68C2×C4×D59—41no—
69C2×C4×D59—41no—
70C2×C4×D59—41no—
71C2×C4×D59—41no—
72C2×C4×D59—41no—
73C2×C4×D59—41no—
74C2×C8×C59—21no—
75C2×C8×C59—21no—
76C2×C8×C59—21no—
77C2×C8×C59—21no—
78C2×C8×C59—21no—
79C2×C8×C59—21no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—41no—
85C4⋊C4×C59—41no—
86C4⋊C4×C59—41no—
87C4⋊C4×C59—41no—
88C4⋊C4×C59—81no—
89C4⋊C4×C59—81no—
90C42×C59#4111yescharacteristic
91C42×C59#4111yescharacteristic
92C42×C59#4111yescharacteristic
93C42×C59#4111yescharacteristic
94(C2×D59)⋊C4—41no—
95(C2×D59)⋊C4—41no—
96C4⋊Dic59—21no—
97C4⋊Dic59—21no—
98C2×C59⋊C8—41no—
99C2×C59⋊C8—41no—
100C2×C59⋊C8—41no—
101C2×C59⋊C8—41no—
102C2×C59⋊C8—41no—
103C2×C59⋊C8—41no—
104C2×C59⋊C8—41no—
105C2×C59⋊C8—41no—
106C2×C59⋊C8—41no—
107C23×C59#12111yescharacteristic
108C22×D59—22no—
109C22×D59—41no—
110C22×D59—41no—
111C22×D59—41no—
112C22×D59—41no—
113C22×D59—41no—
114C22×D59—41no—
115C2×C4×C59—21no—
116C2×C4×C59—21no—
117C2×C4×C59—81no—
118C2×C4×C59—81no—
119C2×C4×C59—81no—
120C2×C4×C59—81no—
121C2×C4×C59—81no—
122C2×C4×C59—81no—
123C2×C4×C59#12311yescharacteristic
124C2×C4×C59#12311yescharacteristic
125C2×C4×C59#12311yescharacteristic
126C2×C4×C59#12411yescharacteristic
127C2×C4×C59#12611yescharacteristic
128C2×C4×C59#12611yescharacteristic
129C2×C4×C59C2×SD1611yescharacteristic
130C2×C4×C59#13511yescharacteristic
131C2×C4×C59#13511yescharacteristic
132C2×C4×C59#13511yescharacteristic
133C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C59#13711yescharacteristic
137C2×Dic59—41no—
138C2×Dic59—41no—
139C2×Dic59—41no—
140D236—22no—
141D236—22no—
142D236—41no—
143D236—41no—
144C4×D59—81no—
145C4×D59—81no—
146C4×D59—81no—
147C4×D59—81no—
148C8×C59—41no—
149C8×C59—41no—
150C59⋊C8—81no—
151C59⋊C8—81no—
152C59⋊C8—81no—
153#10625—591nomaximal, Sylow
154C22×C59#39711yescharacteristic
155C22×C59#46311yescharacteristic
156C22×C59#46311yescharacteristic
157C22×C59#46511yescharacteristic
158C22×C59#46811yescharacteristic
159C22×C59#47211yescharacteristic
160C22×C59#47311yescharacteristic
161C2×D59—42no—
162C2×D59—42no—
163C2×D59—42no—
164C2×D59—81no—
165C2×D59—81no—
166C2×D59—81no—
167C2×D59—81no—
168C4×C59—21no—
169C4×C59—21no—
170C4×C59—161no—
171C4×C59—161no—
172C4×C59#48111yescharacteristic
173C4×C59#48211yescharacteristic
174C4×C59#48211yescharacteristic
175C4×C59#48211yescharacteristic
176C4×C59#48311yescharacteristic
177C4×C59#48511yescharacteristic
178C4×C59#48811yescharacteristic
179C4×C59#49011yescharacteristic
180Dic59—81no—
181#1954—591no—
182#1834D5911yescharacteristic, complemented
183#1802—591no—
184#1802—591no—
185#1296—591no—
186#1296—591no—
187#1277—591no—
188C2×C59#167711yescharacteristic
189C2×C59#167911yescharacteristic
190C2×C59#169711yescharacteristic
191C2×C59#169911yescharacteristic
192C2×C59#207311yescharacteristic
193C2×C59#207711yescharacteristic
194C2×C59#207811yescharacteristic
195D59—82no—
196C2×C4×D4—591no—
197C2×C4⋊C8—591no—
198C2×C4⋊C8—591no—
199C2×C4⋊C8—591no—
200C2×#102—1181no—
201C2×#102—1181no—
202C2×C22⋊C8—1181no—
203C2×C22⋊C8—1181no—
204C2×C4×C8C2×D5911yescharacteristic
205#384C2×D5911yescharacteristic
206#384C2×D5911yescharacteristic
207#340—21no—
208#340—21no—
209#340—1181no—
210#340—1181no—
211C59#1062511yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C23×C4—1181no—
214C22×C8—1181no—
215C22×C8—1181no—
216C22×C8—1181no—
217C22×C8C22⋊D5911yescharacteristic
218C22×C8C22⋊D5911yescharacteristic
219C4×D4—1181no—
220C4×D4—1181no—
221C4×D4—1181no—
222C4×D4—1181no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—591no—
230C2×C22⋊C4—1181no—
231C2×C42C22×D5911yescharacteristic
232C4⋊C8—1181no—
233C4⋊C8—1181no—
234C4⋊C8—1181no—
235C4⋊C8—1181no—
236C4⋊C8—1181no—
237C4⋊C8—1181no—
238#102—2362no—
239#102—2362no—
240C22⋊C8—2362no—
241C22⋊C8—2362no—
242C4×C8—21no—
243C4×C8—21no—
244C24—1181no—
245C2×D4—592no—
246C2×D4—1181no—
247C2×D4—1181no—
248C2×D4—1181no—
249C2×D4—1181no—
250C2×D4—1181no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—1181no—
254C22×C4—2361no—
255C22×C4—2361no—
256C22×C4—2361no—
257C22×C4—2361no—
258C22×C4—2361no—
259C22×C4—2361no—
260C22×C4D4×D5911yescharacteristic
261C22×C4#1174568711yescharacteristic
262C22×C4C2×C22⋊D5911yescharacteristic
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—2361no—
270C2×C8—2361no—
271C2×C8—2361no—
272C2×C8—2361no—
273C2×C8—2361no—
274C2×C8—2361no—
275C2×C8—2361no—
276C2×C8—2361no—
277C2×C8—2361no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4—81no—
288C4⋊C4—1181no—
289C4⋊C4—1181no—
290C22⋊C4—2361no—
291C22⋊C4—2361no—
292C42#1174568511yescharacteristic
293C42#1174568511yescharacteristic
294C42#1174568911yescharacteristic
295C42#1174568911yescharacteristic
296C23—1182no—
297C23—2361no—
298C23—2361no—
299C23—2361no—
300C23—2361no—
301C23—2361no—
302C23—2361no—
303C23#1427369811yescharacteristic
304D4—1182no—
305D4—1182no—
306D4—2361no—
307D4—2361no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4—2361no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4#1427371011yescharacteristic
324C2×C4#1427371211yescharacteristic
325C2×C4#1427371211yescharacteristic
326C2×C4#1427371611yescharacteristic
327C2×C4#1427372211yescharacteristic
328C2×C4#1427372211yescharacteristic
329C2×C4SD16×D5911yescharacteristic
330C2×C4#1427374711yescharacteristic
331C2×C4#1427374711yescharacteristic
332C2×C4#1427374811yescharacteristic
333C2×C4#1427375211yescharacteristic
334C2×C4#1427375211yescharacteristic
335C2×C4#1427375411yescharacteristic
336C2×C4#1427375611yescharacteristic
337C8—41no—
338C8—41no—
339C8—4721no—
340C8—4721no—
341C8—4721no—
342C22—4721no—
343C22—4721no—
344C22—4721no—
345C22—4721no—
346C22—2362no—
347C22—2362no—
348C22—2362no—
349C22#1683732811yescharacteristic
350C22#1683761411yescharacteristic
351C22#1683761411yescharacteristic
352C22#1683762811yescharacteristic
353C22#1683764511yescharacteristic
354C22#1683766911yescharacteristic
355C22#1683767411yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—161no—
360C4—4721no—
361C4#1683772211yescharacteristic
362C4#1683772611yescharacteristic
363C4#1683772611yescharacteristic
364C4#1683772811yescharacteristic
365C4#1683773411yescharacteristic
366C4#1683774611yescharacteristic
367C4#1683775911yescharacteristic
368C4#1683776811yescharacteristic
369C2—4722no—
370C2#2142350211yescharacteristic
371C2#2142351611yescharacteristic
372C2#2142362611yescharacteristic
373C2#2142364011yescharacteristic
374C2#2142551011yescharacteristic
375C2#2142553011yescharacteristic
376C2#2142553711yescharacteristic
subgroupG/H
centerC23#14273698
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1834C2
socleC23×C59#121
prime radicalC22×D236D4
hypercenter#1834D59
hypocenterC59#10625
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1834

Complements

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

NH ≅ G/Ntype
4. #21421979C2semidirect
5. #21421979C2semidirect
6. #21421931C2semidirect
7. C59×#1834C2semidirect
182. #1834D59semidirect
211. C59#10625semidirect

Maximal subgroups

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

subgroupindex
#214248902
#214240932
#214219792
#214219312
C59×#18342
#1062559