Finite Group Databasebeta

← #28493449

Subgroups — #28493449

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#21424889C211yesmaximal, characteristic
2#21424223C211yesmaximal, characteristic, complemented
3#21424097C211yesmaximal, characteristic
4#21424093C211yesmaximal, characteristic
5#21421980C211yesmaximal, characteristic, complemented
6#21421930C211yesmaximal, characteristic, complemented
7C59×#1296C211yesmaximal, characteristic, complemented
8C2×C4×D236C2211yescharacteristic
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×#14273649—21no—
11C2×#14273647—21no—
12C2×(C2×D59)⋊C8—21no—
13C2×(C2×D59)⋊C8—21no—
14C2×C4×C59⋊C8C2211yescharacteristic
15#16837272C2211yescharacteristic
16#16837165—21no—
17#16837164—21no—
18#16837164—21no—
19#16837164—21no—
20C2×C4⋊C8×C59C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C59×#384C2211yescharacteristic
23C22×D236D411yescharacteristic
24C22×C4×D59—21no—
25C22×C59⋊C8—21no—
26C22×C59⋊C8D411yescharacteristic
27C22×C59⋊C8D411yescharacteristic
28C4×D236—21no—
29C4×D236—21no—
30C4×D236—21no—
31C4×D236—21no—
32C2×C4⋊Dic59—21no—
33C2×C4⋊Dic59—21no—
34C2×C4⋊Dic59—21no—
35C2×C4⋊Dic59D411yescharacteristic
36C2×(C2×D59)⋊C4—21no—
37C4⋊(C59⋊C8)—21no—
38C4⋊(C59⋊C8)—21no—
39#14273649—42no—
40#14273647—42no—
41(C2×D59)⋊C8—42no—
42(C2×D59)⋊C8—42no—
43C4×C59⋊C8—21no—
44C4×C59⋊C8—21no—
45C22×C8×C59—21no—
46C22×C8×C59—21no—
47C2×C4⋊C4×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C42×C59C2311yescharacteristic
51C4⋊C8×C59—21no—
52C4⋊C8×C59—21no—
53C4⋊C8×C59—21no—
54C4⋊C8×C59—21no—
55C23×D59—21no—
56C22×C4×C59—41no—
57C22×C4×C59C2×D411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59#4111yescharacteristic
60C22×Dic59—21no—
61C22×Dic59—41no—
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—41no—
75C2×C8×C59—41no—
76C2×C8×C59—41no—
77C2×C8×C59—41no—
78C2×C8×C59—41no—
79C2×C8×C59—41no—
80C4⋊C4×C59—41no—
81C4⋊C4×C59—41no—
82C4⋊C4×C59—41no—
83C4⋊C4×C59—41no—
84C4⋊C4×C59—81no—
85C42×C59#4111yescharacteristic
86C42×C59#4111yescharacteristic
87C42×C59#4111yescharacteristic
88C42×C59#4111yescharacteristic
89(C2×D59)⋊C4—41no—
90(C2×D59)⋊C4—41no—
91C4⋊Dic59—21no—
92C4⋊Dic59—21no—
93C4⋊Dic59—41no—
94C4⋊Dic59—41no—
95C4⋊Dic59—41no—
96C4⋊Dic59—41no—
97C4⋊Dic59—81no—
98C2×C59⋊C8—21no—
99C2×C59⋊C8—21no—
100C2×C59⋊C8—21no—
101C2×C59⋊C8—21no—
102C2×C59⋊C8—21no—
103C2×C59⋊C8—21no—
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#12311yescharacteristic
121C2×C4×C59#12311yescharacteristic
122C2×C4×C59#12311yescharacteristic
123C2×C4×C59#12411yescharacteristic
124C2×C4×C59#12611yescharacteristic
125C2×C4×C59#12611yescharacteristic
126C2×C4×C59C2×SD1611yescharacteristic
127C2×C4×C59#13511yescharacteristic
128C2×C4×C59#13511yescharacteristic
129C2×C4×C59#13511yescharacteristic
130C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C59#13711yescharacteristic
134C2×Dic59—41no—
135C2×Dic59—41no—
136C2×Dic59—41no—
137C2×Dic59—81no—
138C2×Dic59—81no—
139C2×Dic59—81no—
140D236—22no—
141D236—22no—
142D236—41no—
143D236—41no—
144C4×D59—81no—
145C4×D59—81no—
146C4×D59—81no—
147C4×D59—81no—
148C8×C59—81no—
149C8×C59—81no—
150C59⋊C8—41no—
151C59⋊C8—41no—
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#48111yescharacteristic
172C4×C59#48211yescharacteristic
173C4×C59#48211yescharacteristic
174C4×C59#48211yescharacteristic
175C4×C59#48311yescharacteristic
176C4×C59#48511yescharacteristic
177C4×C59#48811yescharacteristic
178C4×C59#49011yescharacteristic
179Dic59—81no—
180Dic59—161no—
181#1954—591no—
182#1834—591no—
183#1802—591no—
184#1802—591no—
185#1296—591no—
186#1296D5911yescharacteristic, complemented
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⋊C8C2×D5911yescharacteristic
199C2×C4⋊C8C2×D5911yescharacteristic
200C2×#102—1181no—
201C2×#102—1181no—
202C2×C22⋊C8—1181no—
203C2×C22⋊C8—1181no—
204C2×C4×C8—591no—
205#384—591no—
206#384C2×D5911yescharacteristic
207#340—1181no—
208#340—1181no—
209#340—1181no—
210#340—1181no—
211C59#1062511yescharacteristic, complemented, Sylow
212C22×D4—591no—
213C23×C4—1181no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—591no—
217C22×C8—591no—
218C22×C8—1181no—
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—591no—
227C2×C4⋊C4—1181no—
228C2×C4⋊C4—1181no—
229C2×C4⋊C4—1181no—
230C2×C22⋊C4—1181no—
231C2×C42C22×D5911yescharacteristic
232C4⋊C8—21no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—1181no—
237C4⋊C8—1181no—
238#102—2362no—
239#102—2362no—
240C22⋊C8—2362no—
241C22⋊C8—2362no—
242C4×C8—1181no—
243C4×C8—1181no—
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—1181no—
253C22×C4—2361no—
254C22×C4—2361no—
255C22×C4—2361no—
256C22×C4—2361no—
257C22×C4—2361no—
258C22×C4—2361no—
259C22×C4—2361no—
260C22×C4#1174568511yescharacteristic
261C22×C4D4×D5911yescharacteristic
262C22×C4D4×D5911yescharacteristic
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—1181no—
270C2×C8—1181no—
271C2×C8—1181no—
272C2×C8—1181no—
273C2×C8—1181no—
274C2×C8—1181no—
275C2×C8—2361no—
276C2×C8—2361no—
277C2×C8—2361no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—81no—
283C4⋊C4—1181no—
284C4⋊C4—1181no—
285C4⋊C4—4721no—
286C4⋊C4—2361no—
287C4⋊C4—2361no—
288C4⋊C4—2361no—
289C4⋊C4—2361no—
290C22⋊C4—2361no—
291C22⋊C4—2361no—
292C42#1174568511yescharacteristic
293C42#1174568511yescharacteristic
294C42#1174568711yescharacteristic
295C42#1174568911yescharacteristic
296C23—1182no—
297C23—2361no—
298C23—2361no—
299C23—2361no—
300C23—2361no—
301C23—2361no—
302C23—2361no—
303C23#1427370011yescharacteristic
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—4721no—
314C2×C4—4721no—
315C2×C4—4721no—
316C2×C4—4721no—
317C2×C4—4721no—
318C2×C4—4721no—
319C2×C4—4721no—
320C2×C4—2361no—
321C2×C4—2361no—
322C2×C4—2361no—
323C2×C4#1427370911yescharacteristic
324C2×C4#1427371211yescharacteristic
325C2×C4#1427371211yescharacteristic
326C2×C4#1427371311yescharacteristic
327C2×C4#1427372111yescharacteristic
328C2×C4#1427372211yescharacteristic
329C2×C4SD16×D5911yescharacteristic
330C2×C4#1427374811yescharacteristic
331C2×C4#1427375011yescharacteristic
332C2×C4#1427375011yescharacteristic
333C2×C4#1427375111yescharacteristic
334C2×C4#1427375111yescharacteristic
335C2×C4#1427375411yescharacteristic
336C2×C4#1427375611yescharacteristic
337C8—81no—
338C8—81no—
339C8—4721no—
340C8—2361no—
341C8—2361no—
342C22—4721no—
343C22—4721no—
344C22—4721no—
345C22—4721no—
346C22—2362no—
347C22—2362no—
348C22—2362no—
349C22#1683733111yescharacteristic
350C22#1683761611yescharacteristic
351C22#1683762011yescharacteristic
352C22#1683763411yescharacteristic
353C22#1683764711yescharacteristic
354C22#1683767111yescharacteristic
355C22#1683767611yescharacteristic
356C4—21no—
357C4—21no—
358C4—161no—
359C4—9441no—
360C4—4721no—
361C4#1683771911yescharacteristic
362C4#1683772811yescharacteristic
363C4#1683772911yescharacteristic
364C4#1683772911yescharacteristic
365C4#1683773411yescharacteristic
366C4#1683774211yescharacteristic
367C4#1683775811yescharacteristic
368C4#1683776511yescharacteristic
369C2—4722no—
370C2#2142350811yescharacteristic
371C2#2142351811yescharacteristic
372C2#2142362811yescharacteristic
373C2#2142364611yescharacteristic
374C2#2142551311yescharacteristic
375C2#2142553511yescharacteristic
376C2#2142554011yescharacteristic
subgroupG/H
centerC23#14273700
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socleC23×C59#121
prime radicalC22×D236D4
hypercenter#1296D59
hypocenterC59#10625
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21424223C2semidirect
5. #21421980C2semidirect
6. #21421930C2semidirect
7. C59×#1296C2semidirect
186. #1296D59semidirect
211. C59#10625semidirect

Maximal subgroups

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

subgroupindex
#214248892
#214242232
#214240972
#214240932
#214219802
#214219302
C59×#12962
#1062559