Finite Group Databasebeta

← #28492500

Subgroups — #28492500

Order 15104.

522 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837602C211yesmaximal, characteristic
2#21425033C211yesmaximal, characteristic, complemented
3#21424901C211yesmaximal, characteristic
4C2×#16837152C211yesmaximal, characteristic, complemented
5C2×#16837145C211yesmaximal, characteristic
6#21421979C211yesmaximal, characteristic, complemented
7C59×#1803C211yesmaximal, characteristic, complemented
8C22×#11745671—21no—
9C2×#14273724C2211yescharacteristic
10#16837602—22no—
11#16837602—22no—
12C2×C4⋊(C59⋊C8)C2211yescharacteristic
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273647—21no—
15C2×#14273647—21no—
16C2×#14273647—21no—
17C2×C4×C59⋊C8C2211yescharacteristic
18#16837157—21no—
19#16837157—21no—
20#16837152—22no—
21#16837145—22no—
22C2×C4×Q8×C59C2211yescharacteristic
23C2×C4⋊C8×C59C2211yescharacteristic
24C2×#103×C59—21no—
25C59×#384C2211yescharacteristic
26C59×#340—21no—
27C22×D236—21no—
28C22×D236—21no—
29C22×D236—21no—
30C2×#11745671—24no—
31C2×#11745671—42no—
32C2×#11745671—42no—
33C22×C59⋊C8—21no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8D411yescharacteristic
36C22×C59⋊C8D411yescharacteristic
37#14273724—21no—
38#14273724—21no—
39#14273724—21no—
40#14273724D412yes—
41C4⋊(C59⋊C8)—21no—
42C4⋊(C59⋊C8)—21no—
43C4⋊(C59⋊C8)—21no—
44C4⋊(C59⋊C8)D412yes—
45#14273647—24no—
46#14273647—42no—
47#14273647—42no—
48C4×C59⋊C8—21no—
49C4×C59⋊C8—21no—
50C22×Q8×C59D411yescharacteristic
51C22×C8×C59—21no—
52C4×Q8×C59—21no—
53C4×Q8×C59—21no—
54C4×Q8×C59—21no—
55C4×Q8×C59—21no—
56C2×C4⋊C4×C59—21no—
57C2×C4⋊C4×C59—21no—
58C2×C4⋊C4×C59—21no—
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59D411yescharacteristic
61C2×C42×C59—21no—
62C2×C42×C59C2311yescharacteristic
63C4⋊C8×C59—21no—
64C4⋊C8×C59—21no—
65#103×C59—42no—
66C23×D59—41no—
67C2×Q8×C59—21no—
68C2×Q8×C59—21no—
69C2×Q8×C59—21no—
70C2×Q8×C59—21no—
71C2×Q8×C59—21no—
72C2×Q8×C59SD1612yes—
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59—41no—
76C22×C4×C59C2×D411yescharacteristic
77C22×C4×C59C2×D411yescharacteristic
78C22×C4×C59#4111yescharacteristic
79C2×D236—22no—
80C2×D236—22no—
81C2×D236—22no—
82C2×D236—41no—
83C2×D236—41no—
84C2×D236—41no—
85C2×D236—41no—
86C2×D236—41no—
87C2×D236—41no—
88C2×D236—41no—
89C2×D236—41no—
90C2×D236—41no—
91C2×D236—41no—
92C2×D236—41no—
93C2×D236—81no—
94C2×D236—81no—
95C2×C8×C59—41no—
96C2×C8×C59—41no—
97C2×C8×C59—41no—
98C4⋊C4×C59—21no—
99C4⋊C4×C59—21no—
100C4⋊C4×C59—41no—
101C4⋊C4×C59—41no—
102C4⋊C4×C59—41no—
103C4⋊C4×C59—41no—
104C4⋊C4×C59—41no—
105C4⋊C4×C59—41no—
106C4⋊C4×C59—81no—
107C42×C59—41no—
108C42×C59—41no—
109C42×C59C2×D411yescharacteristic
110C42×C59C2×D411yescharacteristic
111C42×C59#4111yescharacteristic
112C42×C59#4111yescharacteristic
113#11745671—48no—
114C2×C59⋊C8—21no—
115C2×C59⋊C8—21no—
116C2×C59⋊C8—22no—
117C2×C59⋊C8—21no—
118C2×C59⋊C8—21no—
119C2×C59⋊C8—21no—
120C2×C59⋊C8—41no—
121C2×C59⋊C8—41no—
122C2×C59⋊C8—41no—
123C2×C59⋊C8—41no—
124C2×C59⋊C8—41no—
125C2×C59⋊C8SD1612yescomplemented
126C23×C59#12111yescharacteristic
127C22×D59—42no—
128C22×D59—81no—
129C22×D59—81no—
130C22×D59—81no—
131C22×D59—81no—
132C22×D59—81no—
133C22×D59—81no—
134Q8×C59—22no—
135Q8×C59—22no—
136Q8×C59—41no—
137Q8×C59—41no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—22no—
141C2×C4×C59—41no—
142C2×C4×C59—41no—
143C2×C4×C59—41no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—81no—
147C2×C4×C59—81no—
148C2×C4×C59—81no—
149C2×C4×C59#12011yescharacteristic
150C2×C4×C59#12111yescharacteristic
151C2×C4×C59#12111yescharacteristic
152C2×C4×C59#12311yescharacteristic
153C2×C4×C59#12311yescharacteristic
154C2×C4×C59#12411yescharacteristic
155C2×C4×C59C2×SD1611yescharacteristic
156C2×C4×C59C2×SD1611yescharacteristic
157C2×C4×C59#13511yescharacteristic
158C2×C4×C59#13511yescharacteristic
159C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C59#13711yescharacteristic
163D236—42no—
164D236—42no—
165D236—42no—
166D236—42no—
167D236—82no—
168D236—82no—
169D236—81no—
170D236—81no—
171D236—81no—
172D236—81no—
173C8×C59—81no—
174C59⋊C8—22no—
175C59⋊C8—42no—
176C59⋊C8—41no—
177C59⋊C8—81no—
178#10475—591nomaximal, Sylow
179C22×C59#39411yescharacteristic
180C22×C59#46011yescharacteristic
181C22×C59#46411yescharacteristic
182C22×C59#46511yescharacteristic
183C22×C59#46911yescharacteristic
184C22×C59#47111yescharacteristic
185C22×C59#47211yescharacteristic
186C2×D59—82no—
187C2×D59—82no—
188C2×D59—82no—
189C2×D59—161no—
190C2×D59—161no—
191C2×D59—161no—
192C2×D59—161no—
193C4×C59—21no—
194C4×C59—21no—
195C4×C59—42no—
196C4×C59—81no—
197C4×C59—161no—
198C4×C59#44911yescharacteristic
199C4×C59#45011yescharacteristic
200C4×C59#46111yescharacteristic
201C4×C59#46311yescharacteristic
202C4×C59#46511yescharacteristic
203C4×C59#46811yescharacteristic
204C4×C59#48111yescharacteristic
205C4×C59#48211yescharacteristic
206C2×#460—591no—
207#1984—591no—
208#1957—591no—
209#1803D5911yescharacteristic, complemented
210C2×#334—591no—
211C2×#331—591no—
212#1296—591no—
213C2×C59#166611yescharacteristic
214C2×C59#167811yescharacteristic
215C2×C59#168811yescharacteristic
216C2×C59#170211yescharacteristic
217C2×C59#203411yescharacteristic
218C2×C59#205111yescharacteristic
219C2×C59#205511yescharacteristic
220D59—162no—
221C22×SD16—1181no—
222C2×#127—591no—
223C2×C4×Q8C2×D5911yescharacteristic
224#460—1182no—
225#460—1182no—
226C2×C4⋊C8—591no—
227C2×C4⋊C8—591no—
228C2×C4⋊C8C2×D5911yescharacteristic
229C2×#103—21no—
230C2×#102—1181no—
231C2×#102—1181no—
232C2×#102—1181no—
233C2×C4×C8—591no—
234#384C2×D5911yescharacteristic
235#340—21no—
236#336—1181no—
237#336—1181no—
238#334—1182no—
239#331—1182no—
240C59#1047511yescharacteristic, complemented, Sylow
241C22×Q8C22⋊D5911yescharacteristic
242C22×D4—1181no—
243C22×D4—1181no—
244C22×D4—1181no—
245C2×SD16—1184no—
246C2×SD16—2362no—
247C2×SD16—2362no—
248C22×C8—21no—
249C22×C8—591no—
250C22×C8—591no—
251C22×C8—1181no—
252C22×C8—1181no—
253#127—592no—
254#127—1181no—
255#127—1181no—
256#127—1181no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4C22⋊D5911yescharacteristic
266C2×C42—21no—
267C2×C42C22×D5911yescharacteristic
268C4⋊C8—21no—
269C4⋊C8—21no—
270C4⋊C8—592no—
271C4⋊C8—1181no—
272C4⋊C8—1181no—
273C4⋊C8—1181no—
274#103—42no—
275#102—1184no—
276#102—2362no—
277#102—2362no—
278C4×C8—1181no—
279C4×C8—1181no—
280C24—2361no—
281C2×Q8—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—21no—
286C2×Q8#1174567112yes—
287C2×D4—1182no—
288C2×D4—1182no—
289C2×D4—1182no—
290C2×D4—4721no—
291C2×D4—4721no—
292C2×D4—2361no—
293C2×D4—2361no—
294C2×D4—2361no—
295C2×D4—2361no—
296C2×D4—2361no—
297C2×D4—2361no—
298C2×D4—2361no—
299C2×D4—2361no—
300C2×D4—2361no—
301C2×D4—2361no—
302C2×D4—2361no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4D4×D5911yescharacteristic
307C22×C4#1174568711yescharacteristic
308C22×C4C2×C22⋊D5911yescharacteristic
309SD16—2368no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—592no—
314C2×C8—1181no—
315C2×C8—1181no—
316C2×C8—1182no—
317C2×C8—1181no—
318C2×C8—1181no—
319C2×C8—1181no—
320C2×C8—2361no—
321C2×C8—2361no—
322C2×C8—2361no—
323C2×C8—2361no—
324C2×C8—2361no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C42—41no—
335C42—41no—
336C42#1174568511yescharacteristic
337C42#1174568511yescharacteristic
338C42D4×D5911yescharacteristic
339C42D4×D5911yescharacteristic
340C23—4721no—
341C23—4721no—
342C23—4721no—
343C23—4721no—
344C23—4721no—
345C23—4721no—
346C23—2362no—
347C23#1427369911yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—41no—
351Q8—41no—
352D4—4722no—
353D4—4722no—
354D4—4721no—
355D4—4721no—
356D4—4721no—
357D4—4721no—
358D4—2362no—
359D4—2362no—
360D4—2362no—
361D4—2362no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4#1427369511yescharacteristic
374C2×C4#1427370011yescharacteristic
375C2×C4#1427370011yescharacteristic
376C2×C4#1427370911yescharacteristic
377C2×C4#1427371011yescharacteristic
378C2×C4#1427371311yescharacteristic
379C2×C4SD16×D5911yescharacteristic
380C2×C4C2×#1174567111yescharacteristic
381C2×C4#1427374711yescharacteristic
382C2×C4#1427375011yescharacteristic
383C2×C4#1427375211yescharacteristic
384C2×C4#1427375311yescharacteristic
385C2×C4#1427375411yescharacteristic
386C2×C4#1427375911yescharacteristic
387C8—81no—
388C8—1182no—
389C8—4721no—
390C8—2361no—
391C8—2362no—
392C22—9441no—
393C22—9441no—
394C22—9441no—
395C22—9441no—
396C22—4722no—
397C22—4722no—
398C22—4722no—
399C22#1683731711yescharacteristic
400C22#1683760011yescharacteristic
401C22#1683762611yescharacteristic
402C22#1683763311yescharacteristic
403C22#1683765311yescharacteristic
404C22#1683766711yescharacteristic
405C22#1683767011yescharacteristic
406C4—21no—
407C4—21no—
408C4—42no—
409C4—81no—
410C4—161no—
411C4#1683754511yescharacteristic
412C4#1683755211yescharacteristic
413C4#1683760611yescharacteristic
414C4#1683762011yescharacteristic
415C4#1683763411yescharacteristic
416C4#1683765111yescharacteristic
417C4#1683772011yescharacteristic
418C4#1683772611yescharacteristic
419C2—9442no—
420C2#2142344611yescharacteristic
421C2#2142351411yescharacteristic
422C2#2142357811yescharacteristic
423C2#2142366611yescharacteristic
424C2#2142528511yescharacteristic
425C2#2142538611yescharacteristic
426C2#2142541011yescharacteristic
subgroupG/H
centerC23#14273699
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1803C2
socleC23×C59#121
prime radicalC2×#14273724C22
hypercenter#1803D59
hypocenterC59#10475
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
2. #21425033C2semidirect
4. C2×#16837152C2semidirect
6. #21421979C2semidirect
7. C59×#1803C2semidirect
125. C2×C59⋊C8SD16semidirect
209. #1803D59semidirect
240. C59#10475semidirect

Maximal subgroups

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

subgroupindex
C2×#168376022
#214250332
#214249012
C2×#168371522
C2×#168371452
#214219792
C59×#18032
#1047559