Finite Group Databasebeta

← #28484274

Subgroups — #28484274

Order 15104.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21432378C211yesmaximal, characteristic
2C2×#16837137C212yesmaximal, complemented
3#21422319C211yesmaximal, characteristic, complemented
4#21421976C212yesmaximal, complemented
5C2×C59×#407C211yesmaximal, characteristic, complemented
6C2×#14273701C411yescharacteristic, complemented
7C2×#14273701C411yescharacteristic, complemented
8C2×#14273701C2211yescharacteristic
9C2×#14273696—21no—
10C22×C22⋊Dic59—21no—
11#16837281—21no—
12#16837281—21no—
13#16837281—21no—
14#16837262C411yescharacteristic, complemented
15#16837262C411yescharacteristic, complemented
16#16837262C2211yescharacteristic
17C2×C59⋊#95—21no—
18C2×C59⋊#95C2212yes—
19#16837137—24no—
20C24×C4×C59C2211yescharacteristic
21C22×M16×C59—21no—
22C59×#407—24no—
23C2×C22⋊C8×C59—21no—
24C2×C22⋊C8×C59C2212yes—
25C22×D236C2×C411yescharacteristic
26C22×C22⋊D59—21no—
27C22×C22⋊D59—21no—
28C22×C22⋊D59—21no—
29C23×Dic59—22no—
30#14273701—22no—
31#14273701—22no—
32#14273701—42no—
33#14273701—42no—
34#14273696—44no—
35C2×C4⋊Dic59C2×C411yescharacteristic
36C2×C4⋊Dic59C2×C411yescharacteristic
37C2×C4⋊Dic59C2×C411yescharacteristic
38C2×C22⋊Dic59—24no—
39C2×C22⋊Dic59—21no—
40C2×C22⋊Dic59—21no—
41C2×C22⋊Dic59—21no—
42C2×C22⋊Dic59—42no—
43C2×C22⋊Dic59—42no—
44C2×(C2×D59)⋊C4—21no—
45C2×(C2×D59)⋊C4—21no—
46C2×(C2×D59)⋊C4—21no—
47C59⋊#95—21no—
48C59⋊#95—21no—
49C59⋊#95—21no—
50C59⋊#95—22no—
51C59⋊#95—22no—
52C59⋊#95—42no—
53C25×C59D411yescharacteristic
54C23×C4×C59—22no—
55C23×C4×C59—22no—
56C23×C4×C59—42no—
57C23×C4×C59—42no—
58C23×C4×C59C2×C411yescharacteristic
59C23×C4×C59C2×C411yescharacteristic
60C23×C4×C59D411yescharacteristic
61C23×C4×C59D411yescharacteristic
62C23×C4×C59D411yescharacteristic
63C23×C4×C59C2311yescharacteristic
64C2×M16×C59—24no—
65C2×M16×C59—42no—
66C2×M16×C59—42no—
67C22×C8×C59—22no—
68C22⋊C8×C59—24no—
69C22⋊C8×C59—22no—
70C22⋊C8×C59D414yescomplemented
71C24×C59—22no—
72C24×C59—22no—
73C24×C59—21no—
74C24×C59—21no—
75C24×C59—22no—
76C24×C59—22no—
77C24×C59—41no—
78C24×C59—41no—
79C24×C59C22⋊C411yescharacteristic
80C24×C59C22⋊C411yescharacteristic
81C24×C59C2×D411yescharacteristic
82C23×D59—21no—
83C22×C4×C59—22no—
84C22×C4×C59—22no—
85C22×C4×C59—21no—
86C22×C4×C59—21no—
87C22×C4×C59—22no—
88C22×C4×C59—22no—
89C22×C4×C59—22no—
90C22×C4×C59—22no—
91C22×C4×C59—22no—
92C22×C4×C59—22no—
93C22×C4×C59—21no—
94C22×C4×C59—21no—
95C22×C4×C59—41no—
96C22×C4×C59—41no—
97C22×C4×C59—41no—
98C22×C4×C59—41no—
99C22×C4×C59—41no—
100C22×C4×C59—41no—
101C22×C4×C59—41no—
102C22×C4×C59—48no—
103C22×C4×C59—48no—
104C22×C4×C59C22⋊C411yescharacteristic
105C22×C4×C59C22⋊C411yescharacteristic
106C22×C4×C59C22×C411yescharacteristic
107C22×C4×C59C2×D411yescharacteristic
108C22×C4×C59C2×D412yes—
109C22×C4×C59#4112yes—
110C2×C22⋊D59—42no—
111C2×C22⋊D59—42no—
112C2×C22⋊D59—42no—
113C2×C22⋊D59—42no—
114C2×C22⋊D59—42no—
115C2×C22⋊D59—42no—
116C2×C22⋊D59—42no—
117C2×C22⋊D59—42no—
118C2×C22⋊D59—41no—
119C2×C22⋊D59—41no—
120C22×Dic59—24no—
121C22×Dic59—21no—
122C22×Dic59—21no—
123C22×Dic59—21no—
124C22×Dic59—42no—
125C22×Dic59—42no—
126C22×Dic59—42no—
127C22×Dic59—42no—
128C22×Dic59—42no—
129C22×Dic59—42no—
130C2×D236—22no—
131C2×D236—41no—
132C2×D236—41no—
133M16×C59—48no—
134C2×C8×C59—24no—
135C2×C8×C59—42no—
136C2×C8×C59—42no—
137C22⋊Dic59—48no—
138C22⋊Dic59—42no—
139C22⋊Dic59—42no—
140C22⋊Dic59—42no—
141(C2×D59)⋊C4—42no—
142(C2×D59)⋊C4—42no—
143(C2×D59)⋊C4—41no—
144(C2×D59)⋊C4—41no—
145C4⋊Dic59—22no—
146C4⋊Dic59—41no—
147C4⋊Dic59—41no—
148C23×C59—21no—
149C23×C59—21no—
150C23×C59—21no—
151C23×C59—21no—
152C23×C59—24no—
153C23×C59—24no—
154C23×C59—21no—
155C23×C59—21no—
156C23×C59—21no—
157C23×C59—21no—
158C23×C59—21no—
159C23×C59—21no—
160C23×C59—21no—
161C23×C59—21no—
162C23×C59—21no—
163C23×C59—21no—
164C23×C59—21no—
165C23×C59—21no—
166C23×C59—44no—
167C23×C59—44no—
168C23×C59—44no—
169C23×C59—44no—
170C23×C59—42no—
171C23×C59—42no—
172C23×C59—42no—
173C23×C59—42no—
174C23×C59#9912yes—
175C23×C59#10412yes—
176C23×C59C2×C22⋊C411yescharacteristic
177C23×C59#12112yes—
178C23×C59AGL(1,ℤ/8)11yescharacteristic
179C23×C59AGL(1,ℤ/8)12yes—
180C23×C59#13711yescharacteristic
181C22×D59—41no—
182C22×D59—41no—
183C22×D59—41no—
184C22×D59—41no—
185C22×D59—41no—
186C22×D59—41no—
187C22×D59—41no—
188C2×C4×C59—24no—
189C2×C4×C59—24no—
190C2×C4×C59—21no—
191C2×C4×C59—21no—
192C2×C4×C59—21no—
193C2×C4×C59—21no—
194C2×C4×C59—21no—
195C2×C4×C59—21no—
196C2×C4×C59—21no—
197C2×C4×C59—21no—
198C2×C4×C59—21no—
199C2×C4×C59—42no—
200C2×C4×C59—42no—
201C2×C4×C59—44no—
202C2×C4×C59—44no—
203C2×C4×C59—44no—
204C2×C4×C59—42no—
205C2×C4×C59—42no—
206C2×C4×C59#9912yes—
207C2×C4×C59C4×D412yes—
208C2×C4×C59#12011yescharacteristic
209C2×C4×C59#12311yescharacteristic
210C22⋊D59—84no—
211C22⋊D59—84no—
212C22⋊D59—82no—
213C22⋊D59—82no—
214C2×Dic59—44no—
215C2×Dic59—44no—
216C2×Dic59—44no—
217C2×Dic59—41no—
218C2×Dic59—41no—
219C2×Dic59—41no—
220C2×Dic59—41no—
221C2×Dic59—41no—
222C2×Dic59—41no—
223C2×Dic59—41no—
224C2×Dic59—41no—
225C2×Dic59—41no—
226C2×Dic59—82no—
227C2×Dic59—82no—
228C2×Dic59—82no—
229C2×Dic59—82no—
230D236—82no—
231C8×C59—44no—
232#9117—591nomaximal, Sylow
233C22×C59—22no—
234C22×C59—22no—
235C22×C59—21no—
236C22×C59—21no—
237C22×C59—22no—
238C22×C59—22no—
239C22×C59—21no—
240C22×C59—21no—
241C22×C59—22no—
242C22×C59—22no—
243C22×C59—22no—
244C22×C59—22no—
245C22×C59—22no—
246C22×C59—22no—
247C22×C59—48no—
248C22×C59—48no—
249C22×C59—41no—
250C22×C59—41no—
251C22×C59—41no—
252C22×C59—41no—
253C22×C59—41no—
254C22×C59—41no—
255C22×C59—41no—
256C22×C59—41no—
257C22×C59#38611yescharacteristic
258C22×C59C2×#9911yescharacteristic
259C22×C59C2×#9911yescharacteristic
260C22×C59#41711yescharacteristic
261C22×C59#41811yescharacteristic
262C22×C59C2×#10411yescharacteristic
263C22×C59#42111yescharacteristic
264C22×C59#46812yes—
265C22×C59#46912yes—
266C2×D59—81no—
267C2×D59—81no—
268C2×D59—81no—
269C2×D59—81no—
270C2×D59—81no—
271C2×D59—81no—
272C2×D59—81no—
273C4×C59—21no—
274C4×C59—22no—
275C4×C59—22no—
276C4×C59—21no—
277C4×C59—41no—
278Dic59—84no—
279Dic59—81no—
280Dic59—81no—
281Dic59—81no—
282C2×#407D5911yescharacteristic, complemented
283#2847—591no—
284C2×#327—592no—
285C22⋊#95—591no—
286#1294—592no—
287C2×C59—22no—
288C2×C59—22no—
289C2×C59—42no—
290C2×C59—42no—
291C2×C59#150411yescharacteristic
292C2×C59#150711yescharacteristic
293C2×C59#151011yescharacteristic
294C2×C59#151311yescharacteristic
295C2×C59#187111yescharacteristic
296C2×C59#189511yescharacteristic
297C2×C59#189811yescharacteristic
298D59—161no—
299C24×C4C2×D5911yescharacteristic
300C22×M16—21no—
301C2×#121—591no—
302C2×#121—591no—
303C2×#121—591no—
304C2×#120—1181no—
305C22×C22⋊C4—1181no—
306#407—24no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8C2×D5912yes—
309#386—1181no—
310#386—1181no—
311#386—1181no—
312#380—591no—
313#380—591no—
314#380—591no—
315C2×#95—592no—
316C2×#95—1181no—
317#327—1184no—
318C59#911711yescharacteristic, complemented, Sylow
319C25D23611yescharacteristic
320C22×D4—591no—
321C22×D4—1181no—
322C22×D4—1181no—
323C22×D4—1181no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4—1182no—
329C23×C4C4×D5911yescharacteristic
330C23×C4C4×D5911yescharacteristic
331C23×C4D23611yescharacteristic
332C23×C4C22⋊D5911yescharacteristic
333C23×C4C22⋊D5911yescharacteristic
334C23×C4C22×D5911yescharacteristic
335C2×M16—24no—
336C2×M16—42no—
337C2×M16—42no—
338C22×C8—22no—
339#121—1182no—
340#121—1182no—
341#121—2362no—
342#121—2362no—
343#120—2364no—
344C2×C4⋊C4—591no—
345C2×C4⋊C4—591no—
346C2×C4⋊C4—591no—
347C2×C22⋊C4—1184no—
348C2×C22⋊C4—1181no—
349C2×C22⋊C4—1181no—
350C2×C22⋊C4—1181no—
351C2×C22⋊C4—1181no—
352C2×C22⋊C4—1181no—
353C2×C22⋊C4—1181no—
354C2×C22⋊C4—2362no—
355C2×C22⋊C4—2362no—
356C22⋊C8—24no—
357C22⋊C8—22no—
358C22⋊C8C22⋊D5914yescomplemented
359#95—1181no—
360#95—1181no—
361#95—1181no—
362#95—1182no—
363#95—1182no—
364#95—2362no—
365C24—22no—
366C24—22no—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—41no—
372C24—41no—
373C24—1181no—
374C24(C2×D59)⋊C411yescharacteristic
375C24(C2×D59)⋊C411yescharacteristic
376C24C2×D23611yescharacteristic
377C2×D4—1182no—
378C2×D4—2361no—
379C2×D4—2361no—
380C2×D4—2362no—
381C2×D4—2362no—
382C2×D4—2362no—
383C2×D4—2362no—
384C2×D4—2362no—
385C2×D4—2362no—
386C2×D4—2362no—
387C2×D4—2362no—
388C2×D4—2361no—
389C2×D4—2361no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—48no—
410C22×C4—48no—
411C22×C4—1184no—
412C22×C4—1181no—
413C22×C4—1181no—
414C22×C4—1181no—
415C22×C4—2362no—
416C22×C4—2362no—
417C22×C4—2362no—
418C22×C4—2362no—
419C22×C4—2362no—
420C22×C4—2362no—
421C22×C4(C2×D59)⋊C411yescharacteristic
422C22×C4(C2×D59)⋊C411yescharacteristic
423C22×C4C2×C4×D5911yescharacteristic
424C22×C4#1174568512yes—
425C22×C4C2×C22⋊D5911yescharacteristic
426C22×C4C2×C22⋊D5912yes—
427M16—48no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—1182no—
432C4⋊C4—2361no—
433C4⋊C4—2361no—
434C22⋊C4—2362no—
435C22⋊C4—2368no—
436C22⋊C4—2362no—
437C22⋊C4—2362no—
438C22⋊C4—2362no—
439C22⋊C4—2362no—
440C22⋊C4—2361no—
441C22⋊C4—2361no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—2361no—
469C23—2361no—
470C23—2361no—
471C23—2361no—
472C23—2361no—
473C23—2361no—
474C23—2361no—
475C23#1427364112yes—
476C23#1427365312yes—
477C23C2×(C2×D59)⋊C411yescharacteristic
478C23#1427370112yes—
479C23#1427375512yes—
480C23#1427375511yescharacteristic
481C23#1427376011yescharacteristic
482D4—4722no—
483D4—4724no—
484D4—4724no—
485D4—4722no—
486D4—4722no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—4722no—
506C2×C4—4722no—
507C2×C4—4722no—
508C2×C4—4722no—
509C2×C4—2364no—
510C2×C4—2364no—
511C2×C4—2364no—
512C2×C4—2361no—
513C2×C4—2361no—
514C2×C4—2361no—
515C2×C4—2361no—
516C2×C4—2361no—
517C2×C4—2361no—
518C2×C4—2361no—
519C2×C4—2361no—
520C2×C4—2361no—
521C2×C4#1427364112yes—
522C2×C4C4×C22⋊D5912yes—
523C2×C4#1427369611yescharacteristic
524C2×C4#1427371011yescharacteristic
525C8—44no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—21no—
532C22—21no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—4721no—
551C22—4721no—
552C22—4721no—
553C22—4721no—
554C22—4721no—
555C22—4721no—
556C22—4721no—
557C22#1683728111yescharacteristic
558C22C2×#1427364111yescharacteristic
559C22C2×#1427364111yescharacteristic
560C22#1683740411yescharacteristic
561C22#1683740811yescharacteristic
562C22C2×#1427365311yescharacteristic
563C22#1683741811yescharacteristic
564C22#1683764812yes—
565C22#1683765512yes—
566C4—21no—
567C4—22no—
568C4—21no—
569C4—22no—
570C4—41no—
571C4—4724no—
572C4—4721no—
573C4—4721no—
574C4—4721no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—9441no—
580C2#2142260111yescharacteristic
581C2#2142261311yescharacteristic
582C2#2142262611yescharacteristic
583C2#2142264011yescharacteristic
584C2#2142439811yescharacteristic
585C2#2142453411yescharacteristic
586C2#2142454911yescharacteristic
subgroupG/H
centerC23C2×(C2×D59)⋊C4
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
FittingC2×C59×#407C2
socleC23×C59C2×C22⋊C4
prime radical#21432378C2
cosocleC23×C4×C59C23
hypercenterC2×#407D59
hypocenterC59#9117
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16837137C2semidirect
3. #21422319C2semidirect
4. #21421976C2semidirect
5. C2×C59×#407C2semidirect
6. C2×#14273701C4semidirect
7. C2×#14273701C4semidirect
14. #16837262C4semidirect
15. #16837262C4semidirect
70. C22⋊C8×C59D4semidirect
282. C2×#407D59semidirect
318. C59#9117semidirect
358. C22⋊C8C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
#214323782
C2×#168371372
#214223192
#214219762
C2×C59×#4072
#911759