Finite Group Databasebeta

← #28492544

Subgroups — #28492544

Order 15104.

474 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837693C211yesmaximal, characteristic
2#21425057C211yesmaximal, characteristic, complemented
3#21424890C211yesmaximal, characteristic
4#21424097C211yesmaximal, characteristic
5C2×#16837150C211yesmaximal, characteristic, complemented
6#21421980C211yesmaximal, characteristic, complemented
7C2×C59×#335C211yesmaximal, characteristic, complemented
8C2×#14273727C2211yescharacteristic
9C2×C4×D236C2211yescharacteristic
10#16837693—22no—
11#16837693—22no—
12C2×#14273659—21no—
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273649—21no—
15C2×#14273649—21no—
16C2×(C2×D59)⋊C8—21no—
17C2×(C2×D59)⋊C8—21no—
18#16837272C2211yescharacteristic
19#16837165—21no—
20#16837165—21no—
21#16837165—21no—
22#16837150—22no—
23C2×C4⋊C8×C59C2211yescharacteristic
24C2×C4⋊C8×C59C2211yescharacteristic
25C2×C4×C8×C59C2211yescharacteristic
26C59×#335—22no—
27C22×Dic118—21no—
28C22×D236D411yescharacteristic
29C22×C4×D59—21no—
30C22×C59⋊C8—21no—
31#14273727—21no—
32#14273727—21no—
33#14273727—21no—
34#14273727D412yes—
35C4×D236—21no—
36C4×D236—21no—
37C4×D236—21no—
38C4×D236—21no—
39C2×C4⋊Dic59—21no—
40C2×C4⋊Dic59—21no—
41C2×C4⋊Dic59—21no—
42C2×C4⋊Dic59—21no—
43C2×C4⋊Dic59—21no—
44C2×C4⋊Dic59D411yescharacteristic
45C2×(C2×D59)⋊C4—21no—
46#14273659—24no—
47C4⋊(C59⋊C8)—21no—
48C4⋊(C59⋊C8)—21no—
49#14273649—24no—
50#14273649—42no—
51(C2×D59)⋊C8—42no—
52(C2×D59)⋊C8—42no—
53C22×C8×C59—21no—
54C22×C8×C59—21no—
55C22×C8×C59D411yescharacteristic
56C22×C8×C59D411yescharacteristic
57C2×C42×C59C2311yescharacteristic
58C4⋊C8×C59—21no—
59C4⋊C8×C59—21no—
60C4⋊C8×C59—21no—
61C4⋊C8×C59D412yes—
62C4×C8×C59—21no—
63C4×C8×C59—21no—
64C23×D59—21no—
65C22×C4×C59C2×D411yescharacteristic
66C22×C4×C59C2×D411yescharacteristic
67C22×C4×C59#4111yescharacteristic
68C22×Dic59—21no—
69C22×Dic59—41no—
70C22×Dic59—41no—
71C2×D236—21no—
72C2×D236—21no—
73C2×D236—21no—
74C2×D236—21no—
75C2×D236—21no—
76C2×D236Q1612yes—
77C2×C4×D59—41no—
78C2×C4×D59—41no—
79C2×C4×D59—41no—
80C2×C4×D59—41no—
81C2×C4×D59—41no—
82C2×C4×D59—41no—
83C2×Dic118—22no—
84C2×Dic118—41no—
85C2×Dic118—81no—
86C2×Dic118—81no—
87C2×C8×C59—21no—
88C2×C8×C59—21no—
89C2×C8×C59—22no—
90C2×C8×C59—21no—
91C2×C8×C59—21no—
92C2×C8×C59—21no—
93C2×C8×C59—41no—
94C2×C8×C59—41no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C2×C8×C59SD1612yes—
99C42×C59C2×D411yescharacteristic
100C42×C59C2×D411yescharacteristic
101C42×C59#4111yescharacteristic
102C42×C59#4111yescharacteristic
103(C2×D59)⋊C4—41no—
104(C2×D59)⋊C4—41no—
105C4⋊Dic59—22no—
106C4⋊Dic59—21no—
107C4⋊Dic59—22no—
108C4⋊Dic59—21no—
109C4⋊Dic59—41no—
110C4⋊Dic59—41no—
111C4⋊Dic59—41no—
112C4⋊Dic59—41no—
113C4⋊Dic59—41no—
114C4⋊Dic59—41no—
115C4⋊Dic59—81no—
116C2×C59⋊C8—41no—
117C2×C59⋊C8—41no—
118C2×C59⋊C8—41no—
119C23×C59#12111yescharacteristic
120C22×D59—22no—
121C22×D59—41no—
122C22×D59—41no—
123C22×D59—41no—
124C22×D59—41no—
125C22×D59—41no—
126C22×D59—41no—
127C2×C4×C59—21no—
128C2×C4×C59—21no—
129C2×C4×C59#12011yescharacteristic
130C2×C4×C59#12111yescharacteristic
131C2×C4×C59#12111yescharacteristic
132C2×C4×C59#12311yescharacteristic
133C2×C4×C59#12311yescharacteristic
134C2×C4×C59#12411yescharacteristic
135C2×C4×C59C2×SD1611yescharacteristic
136C2×C4×C59C2×Q1611yescharacteristic
137C2×C4×C59#13511yescharacteristic
138C2×C4×C59#13511yescharacteristic
139C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C59#13711yescharacteristic
142C2×C4×C59#13711yescharacteristic
143C2×Dic59—42no—
144C2×Dic59—41no—
145C2×Dic59—41no—
146C2×Dic59—41no—
147C2×Dic59—81no—
148C2×Dic59—81no—
149C2×Dic59—81no—
150C2×Dic59—81no—
151C2×Dic59—81no—
152D236—22no—
153D236—22no—
154D236—41no—
155D236—41no—
156C4×D59—81no—
157C4×D59—81no—
158C4×D59—81no—
159C4×D59—81no—
160Dic118—82no—
161Dic118—82no—
162C8×C59—22no—
163C8×C59—42no—
164C8×C59—41no—
165C8×C59—81no—
166C59⋊C8—81no—
167#10481—591nomaximal, Sylow
168C22×C59#39411yescharacteristic
169C22×C59#46111yescharacteristic
170C22×C59#46311yescharacteristic
171C22×C59#46711yescharacteristic
172C22×C59#46811yescharacteristic
173C22×C59#47111yescharacteristic
174C22×C59#47211yescharacteristic
175C2×D59—42no—
176C2×D59—42no—
177C2×D59—42no—
178C2×D59—81no—
179C2×D59—81no—
180C2×D59—81no—
181C2×D59—81no—
182C4×C59—21no—
183C4×C59—21no—
184C4×C59#44911yescharacteristic
185C4×C59#45111yescharacteristic
186C4×C59#46011yescharacteristic
187C4×C59#46411yescharacteristic
188C4×C59#46511yescharacteristic
189C4×C59#46811yescharacteristic
190C4×C59#48411yescharacteristic
191C4×C59#48511yescharacteristic
192Dic59—82no—
193Dic59—81no—
194Dic59—161no—
195C2×#476—591no—
196#1990—591no—
197#1954—591no—
198#1802—591no—
199C2×#335D5911yescharacteristic, complemented
200C2×#333—591no—
201#1296—591no—
202C2×C59#167511yescharacteristic
203C2×C59#168311yescharacteristic
204C2×C59#169111yescharacteristic
205C2×C59#169711yescharacteristic
206C2×C59#203611yescharacteristic
207C2×C59#205111yescharacteristic
208C2×C59#205511yescharacteristic
209D59—82no—
210C2×C4⋊Q8—591no—
211C2×C4×D4—591no—
212#476—1182no—
213#476—1182no—
214C2×#106—1181no—
215C2×C4⋊C8—591no—
216C2×C4⋊C8C2×D5911yescharacteristic
217C2×C4⋊C8C2×D5911yescharacteristic
218C2×#102—1181no—
219C2×#102—1181no—
220C2×C22⋊C8—1181no—
221C2×C22⋊C8—1181no—
222C2×C4×C8C2×D5911yescharacteristic
223#384—591no—
224#340—1181no—
225#340—1181no—
226#340—1181no—
227#335—22no—
228#333—1182no—
229C59#1048111yescharacteristic, complemented, Sylow
230C22×Q8—1181no—
231C22×D4—591no—
232C23×C4—1181no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—1181no—
236C22×C8D23611yescharacteristic
237C22×C8D23611yescharacteristic
238C4⋊Q8—592no—
239C4⋊Q8—1181no—
240C4⋊Q8—1181no—
241C4⋊Q8—1181no—
242C4×D4—1181no—
243C4×D4—1181no—
244C4×D4—1181no—
245C4×D4—1181no—
246C2×C4⋊C4—591no—
247C2×C4⋊C4—1181no—
248C2×C4⋊C4—1181no—
249C2×C4⋊C4—1181no—
250C2×C4⋊C4—1181no—
251C2×C4⋊C4—1181no—
252C2×C22⋊C4—1181no—
253C2×C42C22×D5911yescharacteristic
254#106—1184no—
255C4⋊C8—21no—
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—1181no—
259C4⋊C8—1181no—
260C4⋊C8C22⋊D5912yes—
261#102—1184no—
262#102—2362no—
263C22⋊C8—2362no—
264C22⋊C8—2362no—
265C4×C8—21no—
266C4×C8—21no—
267C24—1181no—
268C2×Q8—1182no—
269C2×Q8—4721no—
270C2×Q8—4721no—
271C2×Q8—2361no—
272C2×D4—592no—
273C2×D4—1181no—
274C2×D4—1181no—
275C2×D4—1181no—
276C2×D4—1181no—
277C2×D4—1181no—
278C22×C4—1181no—
279C22×C4—2361no—
280C22×C4—2361no—
281C22×C4—2361no—
282C22×C4—2361no—
283C22×C4—2361no—
284C22×C4—2361no—
285C22×C4—2361no—
286C22×C4—2361no—
287C22×C4C2×D23611yescharacteristic
288C22×C4D4×D5911yescharacteristic
289C22×C4#1174568911yescharacteristic
290C2×C8—21no—
291C2×C8—21no—
292C2×C8—22no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—2361no—
302C2×C8—2361no—
303C2×C8—2361no—
304C2×C8#1174566012yes—
305C4⋊C4—1182no—
306C4⋊C4—1181no—
307C4⋊C4—1182no—
308C4⋊C4—1181no—
309C4⋊C4—4721no—
310C4⋊C4—2361no—
311C4⋊C4—2361no—
312C4⋊C4—2361no—
313C4⋊C4—2361no—
314C4⋊C4—2361no—
315C4⋊C4—2361no—
316C22⋊C4—2361no—
317C22⋊C4—2361no—
318C42#1174568511yescharacteristic
319C42D4×D5911yescharacteristic
320C42#1174568911yescharacteristic
321C42C2×C22⋊D5911yescharacteristic
322C23—1182no—
323C23—2361no—
324C23—2361no—
325C23—2361no—
326C23—2361no—
327C23—2361no—
328C23—2361no—
329C23#1427370211yescharacteristic
330Q8—4722no—
331Q8—4722no—
332D4—1182no—
333D4—1182no—
334D4—2361no—
335D4—2361no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—4721no—
339C2×C4—4721no—
340C2×C4—4721no—
341C2×C4—4721no—
342C2×C4—4721no—
343C2×C4—4721no—
344C2×C4—4721no—
345C2×C4—4721no—
346C2×C4—4721no—
347C2×C4—2361no—
348C2×C4—2362no—
349C2×C4—2361no—
350C2×C4—2361no—
351C2×C4#1427369511yescharacteristic
352C2×C4#1427370111yescharacteristic
353C2×C4#1427370211yescharacteristic
354C2×C4#1427371211yescharacteristic
355C2×C4#1427371211yescharacteristic
356C2×C4#1427371611yescharacteristic
357C2×C4C2×#1174566011yescharacteristic
358C2×C4Q16×D5911yescharacteristic
359C2×C4#1427374611yescharacteristic
360C2×C4#1427374911yescharacteristic
361C2×C4#1427375111yescharacteristic
362C2×C4#1427375511yescharacteristic
363C2×C4#1427375911yescharacteristic
364C2×C4#1427376011yescharacteristic
365C8—22no—
366C8—41no—
367C8—42no—
368C8—81no—
369C8—4721no—
370C22—4721no—
371C22—4721no—
372C22—4721no—
373C22—4721no—
374C22—2362no—
375C22—2362no—
376C22—2362no—
377C22#1683731911yescharacteristic
378C22#1683760811yescharacteristic
379C22#1683761811yescharacteristic
380C22#1683764411yescharacteristic
381C22#1683764911yescharacteristic
382C22#1683766611yescharacteristic
383C22#1683767311yescharacteristic
384C4—21no—
385C4—21no—
386C4—9441no—
387C4—4721no—
388C4—4722no—
389C4#1683754411yescharacteristic
390C4#1683755611yescharacteristic
391C4#1683760311yescharacteristic
392C4#1683762511yescharacteristic
393C4#1683763111yescharacteristic
394C4#1683764811yescharacteristic
395C4#1683773911yescharacteristic
396C4#1683774511yescharacteristic
397C2—4722no—
398C2#2142349611yescharacteristic
399C2#2142354811yescharacteristic
400C2#2142359611yescharacteristic
401C2#2142363011yescharacteristic
402C2#2142530111yescharacteristic
403C2#2142539011yescharacteristic
404C2#2142541411yescharacteristic
subgroupG/H
centerC23#14273702
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC2×C59×#335C2
socleC23×C59#121
prime radicalC22×D236D4
hypercenterC2×#335D59
hypocenterC59#10481
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#335

Complements

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

NH ≅ G/Ntype
2. #21425057C2semidirect
5. C2×#16837150C2semidirect
6. #21421980C2semidirect
7. C2×C59×#335C2semidirect
199. C2×#335D59semidirect
229. C59#10481semidirect

Maximal subgroups

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

subgroupindex
C2×#168376932
#214250572
#214248902
#214240972
C2×#168371502
#214219802
C2×C59×#3352
#1048159