Finite Group Databasebeta

← #28493263

Subgroups — #28493263

Order 15104.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21425022C211yesmaximal, characteristic
2#21424901C211yesmaximal, characteristic
3#21424857C211yesmaximal, characteristic, complemented
4#21424812C211yesmaximal, characteristic, complemented
5C2×#16837152C211yesmaximal, characteristic, complemented
6C2×#16837145C211yesmaximal, characteristic
7C59×#1296C211yesmaximal, characteristic, complemented
8C2×#14273724C2211yescharacteristic
9C2×#14273658—21no—
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×Dic59⋊C8—21no—
12C2×#14273649—21no—
13C2×#14273649—21no—
14C2×#14273647—21no—
15C2×#14273647—21no—
16C2×C4×C59⋊C8C2211yescharacteristic
17C4×C4⋊Dic59C2211yescharacteristic
18#16837164—21no—
19#16837156—21no—
20#16837152—22no—
21#16837145—22no—
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C59×#384C2211yescharacteristic
25C22×D236—21no—
26C22×D236—21no—
27C22×D236—21no—
28C22×C59⋊C8—21no—
29C22×C59⋊C8D411yescharacteristic
30C22×C59⋊C8D411yescharacteristic
31#14273724—21no—
32#14273724—21no—
33#14273724—21no—
34#14273724Q812yes—
35C2×C4⋊Dic59D411yescharacteristic
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4×Dic59—21no—
38#14273658—42no—
39C4⋊(C59⋊C8)—21no—
40C4⋊(C59⋊C8)D412yes—
41Dic59⋊C8—42no—
42#14273649—42no—
43#14273649—42no—
44#14273647—42no—
45#14273647—42no—
46C4×C59⋊C8—21no—
47C4×C59⋊C8—21no—
48C59⋊#95—21no—
49C22×C8×C59—21no—
50C22×C8×C59—21no—
51C2×C4⋊C4×C59—21no—
52C2×C4⋊C4×C59—21no—
53C2×C4⋊C4×C59—21no—
54C2×C42×C59C2311yescharacteristic
55C4⋊C8×C59—21no—
56C4⋊C8×C59—21no—
57C4⋊C8×C59—21no—
58C4⋊C8×C59—21no—
59C23×D59—41no—
60C22×C4×C59—41no—
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59#4111yescharacteristic
64C22×Dic59—21no—
65C22×Dic59—21no—
66C2×D236—22no—
67C2×D236—22no—
68C2×D236—22no—
69C2×D236—41no—
70C2×D236—41no—
71C2×D236—41no—
72C2×D236—41no—
73C2×D236—41no—
74C2×D236—41no—
75C2×D236—41no—
76C2×D236—41no—
77C2×D236—41no—
78C2×D236—41no—
79C2×D236—41no—
80C2×D236—81no—
81C2×D236—81no—
82C2×C8×C59—41no—
83C2×C8×C59—41no—
84C2×C8×C59—41no—
85C2×C8×C59—41no—
86C2×C8×C59—41no—
87C2×C8×C59—41no—
88C4⋊C4×C59—41no—
89C4⋊C4×C59—41no—
90C4⋊C4×C59—41no—
91C4⋊C4×C59—41no—
92C4⋊C4×C59—81no—
93C42×C59C2×D411yescharacteristic
94C42×C59C2×Q811yescharacteristic
95C42×C59#4111yescharacteristic
96C42×C59#4111yescharacteristic
97C4⋊Dic59—21no—
98C4⋊Dic59—21no—
99C4⋊Dic59—21no—
100C4⋊Dic59SD1612yes—
101C4×Dic59—41no—
102C4×Dic59—41no—
103C2×C59⋊C8—21no—
104C2×C59⋊C8—21no—
105C2×C59⋊C8—21no—
106C2×C59⋊C8—22no—
107C2×C59⋊C8—21no—
108C2×C59⋊C8—21no—
109C2×C59⋊C8—41no—
110C2×C59⋊C8—41no—
111C2×C59⋊C8SD1612yes—
112C23×C59#12111yescharacteristic
113C22×D59—42no—
114C22×D59—81no—
115C22×D59—81no—
116C22×D59—81no—
117C22×D59—81no—
118C22×D59—81no—
119C22×D59—81no—
120C2×C4×C59—21no—
121C2×C4×C59—21no—
122C2×C4×C59—81no—
123C2×C4×C59—81no—
124C2×C4×C59—81no—
125C2×C4×C59#12111yescharacteristic
126C2×C4×C59#12111yescharacteristic
127C2×C4×C59C22⋊Q811yescharacteristic
128C2×C4×C59C22⋊Q811yescharacteristic
129C2×C4×C59C22⋊Q811yescharacteristic
130C2×C4×C59#12611yescharacteristic
131C2×C4×C59C2×SD1611yescharacteristic
132C2×C4×C59C2×SD1611yescharacteristic
133C2×C4×C59#13511yescharacteristic
134C2×C4×C59#13511yescharacteristic
135C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
139C2×Dic59—22no—
140C2×Dic59—41no—
141C2×Dic59—41no—
142C2×Dic59—41no—
143C2×Dic59—41no—
144C2×Dic59—41no—
145D236—42no—
146D236—42no—
147D236—42no—
148D236—42no—
149D236—82no—
150D236—82no—
151D236—81no—
152D236—81no—
153D236—81no—
154D236—81no—
155C8×C59—81no—
156C8×C59—81no—
157C59⋊C8—22no—
158C59⋊C8—42no—
159C59⋊C8—41no—
160#10595—591nomaximal, Sylow
161C22×C59#39611yescharacteristic
162C22×C59#46011yescharacteristic
163C22×C59#46311yescharacteristic
164C22×C59#46511yescharacteristic
165C22×C59#46911yescharacteristic
166C22×C59#47111yescharacteristic
167C22×C59#47211yescharacteristic
168C2×D59—82no—
169C2×D59—82no—
170C2×D59—82no—
171C2×D59—161no—
172C2×D59—161no—
173C2×D59—161no—
174C2×D59—161no—
175C4×C59—21no—
176C4×C59—21no—
177C4×C59—161no—
178C4×C59#46011yescharacteristic
179C4×C59#46311yescharacteristic
180C4×C59#46511yescharacteristic
181C4×C59#46911yescharacteristic
182C4×C59#47611yescharacteristic
183C4×C59#47611yescharacteristic
184C4×C59#47811yescharacteristic
185C4×C59#47811yescharacteristic
186Dic59—42no—
187Dic59—81no—
188#1982—591no—
189#1957—591no—
190#1948—591no—
191#1939—591no—
192C2×#334—591no—
193C2×#331—591no—
194#1296D5911yescharacteristic, complemented
195C2×C59#166611yescharacteristic
196C2×C59#167711yescharacteristic
197C2×C59#168811yescharacteristic
198C2×C59#170111yescharacteristic
199C2×C59#206311yescharacteristic
200C2×C59#206511yescharacteristic
201C2×C59#206511yescharacteristic
202D59—162no—
203C2×#127—591no—
204C2×#106—1181no—
205C2×C4⋊C8—591no—
206C2×C4⋊C8—1181no—
207C2×C4⋊C8C2×D5911yescharacteristic
208C2×C4⋊C8C2×D5911yescharacteristic
209C2×#102—1181no—
210C2×#102—1181no—
211C2×#102—1181no—
212C2×#102—1181no—
213C2×C4×C8—591no—
214#384C2×D5911yescharacteristic
215C4×C4⋊C4—591no—
216#340—1181no—
217#336—1181no—
218#334—1182no—
219#331—1182no—
220C59#1059511yescharacteristic, complemented, Sylow
221C22×D4—1181no—
222C22×D4—1181no—
223C22×D4—1181no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—591no—
227C22×C8—591no—
228C22×C8—1181no—
229#127—592no—
230#127—1181no—
231#127—1181no—
232#127—1181no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—591no—
237C2×C4⋊C4—591no—
238C2×C42—1181no—
239C2×C42C22×D5911yescharacteristic
240#106—2362no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8—592no—
246C4⋊C8—1181no—
247C4⋊C8—2362no—
248#102—2362no—
249#102—2362no—
250#102—2362no—
251#102—2362no—
252C4×C8—1181no—
253C4×C8—1181no—
254#95—1181no—
255C24—2361no—
256C2×D4—1182no—
257C2×D4—1182no—
258C2×D4—1182no—
259C2×D4—4721no—
260C2×D4—4721no—
261C2×D4—2361no—
262C2×D4—2361no—
263C2×D4—2361no—
264C2×D4—2361no—
265C2×D4—2361no—
266C2×D4—2361no—
267C2×D4—2361no—
268C2×D4—2361no—
269C2×D4—2361no—
270C2×D4—2361no—
271C2×D4—2361no—
272C22×C4—41no—
273C22×C4—1181no—
274C22×C4—1181no—
275C22×C4#1174568511yescharacteristic
276C22×C4D4×D5911yescharacteristic
277C22×C4D4×D5911yescharacteristic
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—592no—
285C2×C8—1181no—
286C2×C8—1181no—
287C2×C8—1181no—
288C2×C8—1182no—
289C2×C8—1181no—
290C2×C8—1181no—
291C2×C8—2361no—
292C2×C8—2361no—
293C4⋊C4—41no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—81no—
298C4⋊C4—592no—
299C4⋊C4—1181no—
300C4⋊C4—1181no—
301C4⋊C4—1181no—
302C42—2361no—
303C42—2361no—
304C42#1174568511yescharacteristic
305C42#1174568511yescharacteristic
306C42D4×D5911yescharacteristic
307C42Q8×D5911yescharacteristic
308C23—4721no—
309C23—4721no—
310C23—4721no—
311C23—4721no—
312C23—4721no—
313C23—4721no—
314C23—2362no—
315C23#1427370011yescharacteristic
316D4—4722no—
317D4—4722no—
318D4—4721no—
319D4—4721no—
320D4—4721no—
321D4—4721no—
322D4—2362no—
323D4—2362no—
324D4—2362no—
325D4—2362no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—1182no—
332C2×C4—2361no—
333C2×C4—2361no—
334C2×C4—2361no—
335C2×C4—2361no—
336C2×C4—2361no—
337C2×C4#1427370011yescharacteristic
338C2×C4#1427370011yescharacteristic
339C2×C4#1427370511yescharacteristic
340C2×C4#1427370511yescharacteristic
341C2×C4#1427370511yescharacteristic
342C2×C4#1427372111yescharacteristic
343C2×C4SD16×D5911yescharacteristic
344C2×C4SD16×D5911yescharacteristic
345C2×C4#1427375011yescharacteristic
346C2×C4#1427375011yescharacteristic
347C2×C4#1427375111yescharacteristic
348C2×C4#1427375111yescharacteristic
349C2×C4#1427375411yescharacteristic
350C2×C4#1427375411yescharacteristic
351C8—81no—
352C8—81no—
353C8—1182no—
354C8—2361no—
355C8—2362no—
356C22—9441no—
357C22—9441no—
358C22—9441no—
359C22—9441no—
360C22—4722no—
361C22—4722no—
362C22—4722no—
363C22#1683732611yescharacteristic
364C22#1683760111yescharacteristic
365C22#1683762011yescharacteristic
366C22#1683763411yescharacteristic
367C22#1683765411yescharacteristic
368C22#1683766811yescharacteristic
369C22#1683767111yescharacteristic
370C4—21no—
371C4—21no—
372C4—161no—
373C4—4721no—
374C4—2362no—
375C4#1683760111yescharacteristic
376C4#1683762011yescharacteristic
377C4#1683763411yescharacteristic
378C4#1683765411yescharacteristic
379C4#1683769111yescharacteristic
380C4#1683769111yescharacteristic
381C4#1683770511yescharacteristic
382C4#1683770511yescharacteristic
383C2—9442no—
384C2#2142344711yescharacteristic
385C2#2142350811yescharacteristic
386C2#2142357911yescharacteristic
387C2#2142366011yescharacteristic
388C2#2142545711yescharacteristic
389C2#2142547111yescharacteristic
390C2#2142547111yescharacteristic
subgroupG/H
centerC23#14273700
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1296C2
socleC23×C59#121
prime radicalC2×#14273724C22
hypercenter#1296D59
hypocenterC59#10595
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
3. #21424857C2semidirect
4. #21424812C2semidirect
5. C2×#16837152C2semidirect
7. C59×#1296C2semidirect
194. #1296D59semidirect
220. C59#10595semidirect

Maximal subgroups

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

subgroupindex
#214250222
#214249012
#214248572
#214248122
C2×#168371522
C2×#168371452
C59×#12962
#1059559