Finite Group Databasebeta

← #28480508

Subgroups — #28480508

Order 15104.

868 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838033C211yesmaximal, characteristic
2#21424403C212yesmaximal
3C2×#16837138C212yesmaximal
4C2×#16837128C211yesmaximal, characteristic
5C59×#1441C211yesmaximal, characteristic
6#16838033—24no—
7#16838033—22no—
8#16838033C414yescomplemented
9C2×#14273726—22no—
10C2×#14273718—22no—
11C2×#14273706—21no—
12C2×#14273706C2212yes—
13C2×#14273686—21no—
14C2×#14273650—22no—
15C2×C22⋊(C59⋊C8)C2212yes—
16#16837164—22no—
17#16837138—24no—
18#16837128—22no—
19C22×C4⋊C4×C59C2211yescharacteristic
20C22×C4⋊C4×C59C2211yescharacteristic
21C2×#95×C59—21no—
22C2×#95×C59—21no—
23C2×#95×C59C2211yescharacteristic
24C22×Dic118—21no—
25C22×Dic118D412yes—
26C22×C59⋊C8—22no—
27#14273726—28no—
28#14273726—28no—
29#14273718—28no—
30#14273718—28no—
31#14273706—24no—
32#14273706—24no—
33#14273706—22no—
34#14273706—22no—
35#14273706C2×C414yes—
36#14273706D414yes—
37#14273686—24no—
38#14273686—24no—
39C2×C4⋊Dic59—21no—
40C2×C4⋊Dic59—21no—
41C2×C4⋊Dic59—21no—
42C2×C4⋊Dic59D412yes—
43C2×Dic59⋊C4—22no—
44C2×Dic59⋊C4—22no—
45C2×C22⋊Dic59—22no—
46C2×C4×Dic59—22no—
47#14273650—44no—
48C22⋊(C59⋊C8)—22no—
49C22⋊(C59⋊C8)—22no—
50C23×C4×C59—21no—
51C23×C4×C59—21no—
52C23×C4×C59D411yescharacteristic
53C23×C4×C59D411yescharacteristic
54C23×C4×C59C2311yescharacteristic
55C2×C4⋊C4×C59—22no—
56C2×C4⋊C4×C59—22no—
57C2×C4⋊C4×C59—22no—
58C2×C4⋊C4×C59—42no—
59C2×C4⋊C4×C59C2×C412yes—
60C2×C4⋊C4×C59D412yes—
61#95×C59—22no—
62#95×C59—42no—
63#95×C59—42no—
64C24×C59C2×D411yescharacteristic
65C22×C4×C59—21no—
66C22×C4×C59—21no—
67C22×C4×C59—21no—
68C22×C4×C59—21no—
69C22×C4×C59—21no—
70C22×C4×C59—21no—
71C22×C4×C59—22no—
72C22×C4×C59—22no—
73C22×C4×C59—41no—
74C22×C4×C59—41no—
75C22×C4×C59—41no—
76C22×C4×C59—41no—
77C22×C4×C59—41no—
78C22×C4×C59—41no—
79C22×C4×C59—41no—
80C22×C4×C59—41no—
81C22×C4×C59—41no—
82C22×C4×C59—41no—
83C22×C4×C59—41no—
84C22×C4×C59—41no—
85C22×C4×C59—41no—
86C22×C4×C59—41no—
87C22×C4×C59—41no—
88C22×C4×C59—41no—
89C22×C4×C59C22⋊C412yes—
90C22×C4×C59C22⋊C412yes—
91C22×C4×C59SD1612yes—
92C22×C4×C59Q1612yes—
93C22×C4×C59C22×C411yescharacteristic
94C22×C4×C59C2×D412yes—
95C22×C4×C59C2×D412yes—
96C22×C4×C59C2×D411yescharacteristic
97C22×Dic59—22no—
98C22×Dic59—22no—
99C2×Dic118—24no—
100C2×Dic118—22no—
101C2×Dic118—42no—
102C2×Dic118—42no—
103C2×Dic118—81no—
104C2×Dic118—81no—
105C2×Dic118C22⋊C414yes—
106C4⋊C4×C59—24no—
107C4⋊C4×C59—24no—
108C4⋊C4×C59—24no—
109C4⋊C4×C59—42no—
110C22⋊Dic59—24no—
111C22⋊Dic59—24no—
112C4⋊Dic59—24no—
113C4⋊Dic59—24no—
114C4⋊Dic59—24no—
115C4⋊Dic59—22no—
116C4⋊Dic59C22⋊C414yes—
117Dic59⋊C4—28no—
118Dic59⋊C4—24no—
119Dic59⋊C4—24no—
120C4×Dic59—28no—
121C2×C59⋊C8—42no—
122C2×C59⋊C8—42no—
123C2×C59⋊C8—42no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—21no—
127C23×C59—21no—
128C23×C59C2×C22⋊C411yescharacteristic
129C23×C59#12011yescharacteristic
130C23×C59#12011yescharacteristic
131C23×C59C2×SD1611yescharacteristic
132C23×C59C2×Q1611yescharacteristic
133C23×C59#13711yescharacteristic
134C23×C59#13711yescharacteristic
135C2×C4×C59—22no—
136C2×C4×C59—22no—
137C2×C4×C59—22no—
138C2×C4×C59—22no—
139C2×C4×C59—22no—
140C2×C4×C59—22no—
141C2×C4×C59—22no—
142C2×C4×C59—22no—
143C2×C4×C59—22no—
144C2×C4×C59—41no—
145C2×C4×C59—41no—
146C2×C4×C59—42no—
147C2×C4×C59—41no—
148C2×C4×C59—41no—
149C2×C4×C59—42no—
150C2×C4×C59—42no—
151C2×C4×C59—42no—
152C2×C4×C59—42no—
153C2×C4×C59—42no—
154C2×C4×C59—42no—
155C2×C4×C59—42no—
156C2×C4×C59—81no—
157C2×C4×C59—81no—
158C2×C4×C59—81no—
159C2×C4×C59—81no—
160C2×C4×C59—81no—
161C2×C4×C59—81no—
162C2×C4×C59—81no—
163C2×C4×C59—81no—
164C2×C4×C59—81no—
165C2×C4×C59#10314yescomplemented
166C2×C4×C59C2×C22⋊C412yes—
167C2×C4×C59#12012yes—
168C2×Dic59—24no—
169C2×Dic59—24no—
170C2×Dic59—42no—
171C2×Dic59—42no—
172C2×Dic59—42no—
173C2×Dic59—42no—
174Dic118—44no—
175Dic118—82no—
176Dic118—84no—
177C59⋊C8—82no—
178#8406—591nomaximal, Sylow
179C22×C59—21no—
180C22×C59—21no—
181C22×C59—21no—
182C22×C59—21no—
183C22×C59—21no—
184C22×C59—21no—
185C22×C59—21no—
186C22×C59—21no—
187C22×C59—21no—
188C22×C59—21no—
189C22×C59—21no—
190C22×C59—21no—
191C22×C59#37911yescharacteristic
192C22×C59C2×#10311yescharacteristic
193C22×C59#41911yescharacteristic
194C22×C59#44811yescharacteristic
195C22×C59#44811yescharacteristic
196C22×C59#45111yescharacteristic
197C22×C59#45111yescharacteristic
198C22×C59#45411yescharacteristic
199C22×C59#45611yescharacteristic
200C22×C59B(4,𝔽2)11yescharacteristic
201C22×C59#45811yescharacteristic
202C4×C59—24no—
203C4×C59—22no—
204C4×C59—22no—
205C4×C59—42no—
206C4×C59—82no—
207C4×C59—82no—
208Dic59—44no—
209Dic59—44no—
210C2×#544—591no—
211#1872—592no—
212C2×#328—592no—
213C2×#324—591no—
214#1441D5911yescharacteristic
215C2×C59—21no—
216C2×C59—21no—
217C2×C59—21no—
218C2×C59—21no—
219C2×C59#159911yescharacteristic
220C2×C59#160511yescharacteristic
221C2×C59#161111yescharacteristic
222C2×C59#161711yescharacteristic
223C2×C59#178711yescharacteristic
224C2×C59#179011yescharacteristic
225C2×C59#179311yescharacteristic
226#544—594no—
227#544—1184no—
228#544—1182no—
229C2×C4⋊Q8—1182no—
230C2×#125—1182no—
231C2×C22⋊Q8—592no—
232C2×C22⋊Q8—1181no—
233C2×#117—1181no—
234C22×C4⋊C4C2×D5911yescharacteristic
235C22×C4⋊C4C2×D5911yescharacteristic
236C2×#103—1182no—
237C2×C22⋊C8—592no—
238C2×#95—21no—
239C2×#95—21no—
240C2×#95C2×D5911yescharacteristic
241#340—1182no—
242#328—1184no—
243#324—1182no—
244C59#840611yescharacteristic, complemented, Sylow
245C22×Q8—592no—
246C22×Q8—1181no—
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C22⋊D5911yescharacteristic
250C23×C4C22⋊D5911yescharacteristic
251C23×C4C22×D5911yescharacteristic
252C22×C8—1182no—
253C4⋊Q8—1188no—
254C4⋊Q8—1188no—
255#125—1188no—
256#125—1188no—
257C22⋊Q8—594no—
258C22⋊Q8—594no—
259C22⋊Q8—1184no—
260C22⋊Q8—1184no—
261C22⋊Q8—1182no—
262C22⋊Q8—1182no—
263#117—1184no—
264#117—1184no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—592no—
270C2×C4⋊C4—1181no—
271C2×C4⋊C4—1181no—
272C2×C4⋊C4—1181no—
273C2×C4⋊C4—1182no—
274C2×C4⋊C4—1182no—
275C2×C4⋊C4C4×D5912yes—
276C2×C4⋊C4D23612yes—
277C2×C22⋊C4—1182no—
278C2×C42—1182no—
279#103—2364no—
280C22⋊C8—1182no—
281C22⋊C8—1182no—
282#95—22no—
283#95—42no—
284#95—42no—
285C24C2×C22⋊D5911yescharacteristic
286C2×Q8—594no—
287C2×Q8—1184no—
288C2×Q8—1182no—
289C2×Q8—4721no—
290C2×Q8—4721no—
291C2×Q8—2362no—
292C2×Q8—2362no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—1182no—
318C22×C4—1182no—
319C22×C4(C2×D59)⋊C412yes—
320C22×C4(C2×D59)⋊C412yes—
321C22×C4#1174567012yes—
322C22×C4#1174567212yes—
323C22×C4C2×C4×D5911yescharacteristic
324C22×C4C2×D23611yescharacteristic
325C22×C4D4×D5912yes—
326C22×C4D4×D5912yes—
327C2×C8—2362no—
328C2×C8—2362no—
329C2×C8—2362no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—42no—
334C4⋊C4—594no—
335C4⋊C4—1184no—
336C4⋊C4—1184no—
337C4⋊C4—1184no—
338C4⋊C4—1188no—
339C4⋊C4—1184no—
340C4⋊C4—1182no—
341C4⋊C4—1184no—
342C22⋊C4—1184no—
343C22⋊C4—1184no—
344C42—1188no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23C2×(C2×D59)⋊C411yescharacteristic
350C23#1427369511yescharacteristic
351C23#1427369511yescharacteristic
352C23C2×#1174567011yescharacteristic
353C23C2×#1174567211yescharacteristic
354C23#1427375711yescharacteristic
355C23#1427375711yescharacteristic
356Q8—4722no—
357Q8—4724no—
358Q8—2364no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—1184no—
390C2×C4—1184no—
391C2×C4—2362no—
392C2×C4—2362no—
393C2×C4—2362no—
394C2×C4—2362no—
395C2×C4#1427365014yescomplemented
396C2×C4C22⋊C4×D5912yes—
397C2×C4#1427369712yes—
398C8—4722no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22#1683725711yescharacteristic
412C22C2×#1427365011yescharacteristic
413C22#1683741011yescharacteristic
414C22#1683754011yescharacteristic
415C22#1683754011yescharacteristic
416C22#1683755711yescharacteristic
417C22#1683755711yescharacteristic
418C22#1683757411yescharacteristic
419C22#1683758411yescharacteristic
420C22#1683758811yescharacteristic
421C22#1683759111yescharacteristic
422C4—24no—
423C4—22no—
424C4—22no—
425C4—42no—
426C4—82no—
427C4—82no—
428C4—2364no—
429C4—2364no—
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2#2142303511yescharacteristic
435C2#2142306911yescharacteristic
436C2#2142310311yescharacteristic
437C2#2142313711yescharacteristic
438C2#2142403011yescharacteristic
439C2#2142404311yescharacteristic
440C2#2142405411yescharacteristic
subgroupG/H
centerC23#14273695
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC59×#1441C2
socleC23×C59#120
prime radicalC24×C59C2×D4
cosocleC23×C4×C59C23
hypercenter#1441D59
hypocenterC59#8406
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1441

Complements

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

NH ≅ G/Ntype
8. #16838033C4semidirect
165. C2×C4×C59#103semidirect
244. C59#8406semidirect
395. C2×C4#14273650semidirect

Maximal subgroups

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

subgroupindex
C2×#168380332
#214244032
C2×#168371382
C2×#168371282
C59×#14412
#840659