Finite Group Databasebeta

← #28493410

Subgroups — #28493410

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#21424093C211yesmaximal, characteristic
3#21424093C211yesmaximal, characteristic
4#21421979C211yesmaximal, characteristic, complemented
5#21421979C211yesmaximal, characteristic, complemented
6#21421931C211yesmaximal, characteristic, complemented
7C59×#1844C211yesmaximal, 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×#106×C59—21no—
19C2×#106×C59—21no—
20C2×C4×C8×C59C2211yescharacteristic
21C59×#384C2211yescharacteristic
22C59×#384C2211yescharacteristic
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
53#106×C59—42no—
54#106×C59—42no—
55C4×C8×C59—21no—
56C4×C8×C59—21no—
57C23×D59—21no—
58C22×C4×C59—41no—
59C22×C4×C59—41no—
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59#4111yescharacteristic
63C22×Dic59—21no—
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×C59D812yes—
81C2×C8×C59SD1612yes—
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—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—81no—
91C4⋊C4×C59—81no—
92C42×C59#4111yescharacteristic
93C42×C59#4111yescharacteristic
94C42×C59#4111yescharacteristic
95C42×C59#4111yescharacteristic
96(C2×D59)⋊C4—41no—
97(C2×D59)⋊C4—41no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
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—
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—81no—
120C2×C4×C59—81no—
121C2×C4×C59—81no—
122C2×C4×C59—81no—
123C2×C4×C59—81no—
124C2×C4×C59—81no—
125C2×C4×C59#12311yescharacteristic
126C2×C4×C59#12311yescharacteristic
127C2×C4×C59#12311yescharacteristic
128C2×C4×C59#12411yescharacteristic
129C2×C4×C59#12611yescharacteristic
130C2×C4×C59#12611yescharacteristic
131C2×C4×C59C2×D811yescharacteristic
132C2×C4×C59C2×SD1611yescharacteristic
133C2×C4×C59C2×SD1611yescharacteristic
134C2×C4×C59#13511yescharacteristic
135C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C59#13711yescharacteristic
138C2×C4×C59#13711yescharacteristic
139C2×Dic59—41no—
140C2×Dic59—41no—
141C2×Dic59—41no—
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—
152C59⋊C8—81no—
153C59⋊C8—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—161no—
173C4×C59—161no—
174C4×C59#48011yescharacteristic
175C4×C59#48111yescharacteristic
176C4×C59#48111yescharacteristic
177C4×C59#48211yescharacteristic
178C4×C59#48311yescharacteristic
179C4×C59#48511yescharacteristic
180C4×C59#48611yescharacteristic
181C4×C59#48911yescharacteristic
182Dic59—81no—
183#1954—591no—
184#1844D5911yescharacteristic, complemented
185#1802—591no—
186#1802—591no—
187#1296—591no—
188#1296—591no—
189#1277—591no—
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—21no—
200C2×#106—21no—
201C2×C4⋊C8—591no—
202C2×C4⋊C8—591no—
203C2×C4⋊C8—591no—
204C2×#102—1181no—
205C2×#102—1181no—
206C2×C22⋊C8—1181no—
207C2×C22⋊C8—1181no—
208C2×C4×C8C2×D5911yescharacteristic
209#384C2×D5911yescharacteristic
210#384C2×D5911yescharacteristic
211#340—1181no—
212#340—1181no—
213C59#1061911yescharacteristic, complemented, Sylow
214C22×D4—591no—
215C23×C4—1181no—
216C22×C8—1181no—
217C22×C8—1181no—
218C22×C8—1181no—
219C22×C8C22⋊D5911yescharacteristic
220C22×C8C22⋊D5911yescharacteristic
221C4×D4—1181no—
222C4×D4—1181no—
223C4×D4—1181no—
224C4×D4—1181no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—591no—
232C2×C22⋊C4—1181no—
233C2×C42C22×D5911yescharacteristic
234#106—42no—
235#106—42no—
236C4⋊C8—1181no—
237C4⋊C8—1181no—
238C4⋊C8—1181no—
239C4⋊C8—1181no—
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—41no—
256C22×C4—41no—
257C22×C4—1181no—
258C22×C4—2361no—
259C22×C4—2361no—
260C22×C4—2361no—
261C22×C4—2361no—
262C22×C4—2361no—
263C22×C4—2361no—
264C22×C4D4×D5911yescharacteristic
265C22×C4#1174568711yescharacteristic
266C22×C4C2×C22⋊D5911yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—2361no—
272C2×C8—2361no—
273C2×C8—2361no—
274C2×C8—2361no—
275C2×C8—2361no—
276C2×C8—2361no—
277C2×C8—2361no—
278C2×C8—2361no—
279C2×C8—2361no—
280C2×C8#1174566912yes—
281C2×C8#1174567112yes—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—1181no—
293C4⋊C4—1181no—
294C22⋊C4—2361no—
295C22⋊C4—2361no—
296C42#1174568511yescharacteristic
297C42#1174568511yescharacteristic
298C42#1174568911yescharacteristic
299C42#1174568911yescharacteristic
300C23—1182no—
301C23—2361no—
302C23—2361no—
303C23—2361no—
304C23—2361no—
305C23—2361no—
306C23—2361no—
307C23#1427369811yescharacteristic
308D4—1182no—
309D4—1182no—
310D4—2361no—
311D4—2361no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—4721no—
321C2×C4—4721no—
322C2×C4—4721no—
323C2×C4—4721no—
324C2×C4—2361no—
325C2×C4—2361no—
326C2×C4—2361no—
327C2×C4#1427371011yescharacteristic
328C2×C4#1427371211yescharacteristic
329C2×C4#1427371211yescharacteristic
330C2×C4#1427371611yescharacteristic
331C2×C4#1427372211yescharacteristic
332C2×C4#1427372211yescharacteristic
333C2×C4C2×#1174566911yescharacteristic
334C2×C4SD16×D5911yescharacteristic
335C2×C4C2×#1174567111yescharacteristic
336C2×C4#1427374811yescharacteristic
337C2×C4#1427375311yescharacteristic
338C2×C4#1427375411yescharacteristic
339C2×C4#1427375611yescharacteristic
340C2×C4#1427375811yescharacteristic
341C8—22no—
342C8—22no—
343C8—4721no—
344C8—4721no—
345C8—4721no—
346C22—4721no—
347C22—4721no—
348C22—4721no—
349C22—4721no—
350C22—2362no—
351C22—2362no—
352C22—2362no—
353C22#1683732811yescharacteristic
354C22#1683759411yescharacteristic
355C22#1683760411yescharacteristic
356C22#1683762811yescharacteristic
357C22#1683764511yescharacteristic
358C22#1683766211yescharacteristic
359C22#1683766211yescharacteristic
360C4—21no—
361C4—21no—
362C4—161no—
363C4—161no—
364C4—4721no—
365C4#1683771511yescharacteristic
366C4#1683772011yescharacteristic
367C4#1683772211yescharacteristic
368C4#1683772811yescharacteristic
369C4#1683773411yescharacteristic
370C4#1683774611yescharacteristic
371C4#1683775011yescharacteristic
372C4#1683776411yescharacteristic
373C2—4722no—
374C2#2142343411yescharacteristic
375C2#2142346811yescharacteristic
376C2#2142355811yescharacteristic
377C2#2142359211yescharacteristic
378C2#2142550011yescharacteristic
379C2#2142553011yescharacteristic
380C2#2142554211yescharacteristic
subgroupG/H
centerC23#14273698
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1844C2
socleC23×C59#121
prime radicalC22×D236D4
hypercenter#1844D59
hypocenterC59#10619
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1844

Complements

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

NH ≅ G/Ntype
4. #21421979C2semidirect
5. #21421979C2semidirect
6. #21421931C2semidirect
7. C59×#1844C2semidirect
184. #1844D59semidirect
213. C59#10619semidirect

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×#18442
#1061959