Finite Group Databasebeta

← #28491985

Subgroups — #28491985

Order 15104.

694 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#21429901C211yesmaximal, characteristic
2#21424403C211yesmaximal, characteristic, complemented
3#21424289C211yesmaximal, characteristic, complemented
4C2×#16837138C211yesmaximal, characteristic, complemented
5C2×#16837126C211yesmaximal, characteristic
6#21421975C211yesmaximal, characteristic, complemented
7C59×#1439C211yesmaximal, characteristic
8C2×#14273706C2211yescharacteristic
9C2×#14273658—21no—
10C2×#14273650—21no—
11C2×C22⋊(C59⋊C8)C2211yescharacteristic
12C2×C22⋊(C59⋊C8)C2211yescharacteristic
13#16837338—21no—
14#16837325—21no—
15#16837325—21no—
16#16837314—21no—
17#16837275—21no—
18#16837262C2211yescharacteristic
19#16837258—21no—
20#16837164—21no—
21#16837164—21no—
22#16837138—22no—
23#16837126—22no—
24C22×C4⋊C4×C59C2211yescharacteristic
25C22×C22⋊C4×C59—21no—
26C22×C22⋊C4×C59C2211yescharacteristic
27C2×#95×C59—21no—
28C2×#95×C59C2211yescharacteristic
29C22×Dic118D411yescharacteristic
30C22×C59⋊C8—21no—
31C22×C59⋊C8—21no—
32#14273706—21no—
33#14273706—21no—
34#14273706—21no—
35#14273706—21no—
36C2×C4⋊Dic59D411yescharacteristic
37C2×C4⋊Dic59D411yescharacteristic
38C2×C4⋊Dic59D411yescharacteristic
39C2×Dic59⋊C4—21no—
40C2×Dic59⋊C4—21no—
41C2×Dic59⋊C4—21no—
42C2×C22⋊Dic59—21no—
43C2×C22⋊Dic59—21no—
44C2×C22⋊Dic59—21no—
45C2×C22⋊Dic59—21no—
46C2×C22⋊Dic59—21no—
47C2×C22⋊Dic59—21no—
48#14273658—42no—
49#14273650—42no—
50C22⋊(C59⋊C8)—21no—
51C22⋊(C59⋊C8)—21no—
52C22⋊(C59⋊C8)—21no—
53C22⋊(C59⋊C8)D412yes—
54C59⋊#95—21no—
55C59⋊#95—21no—
56C59⋊#95—21no—
57C25×C59D411yescharacteristic
58C23×C4×C59—21no—
59C23×C4×C59—21no—
60C23×C4×C59D411yescharacteristic
61C23×C4×C59C2311yescharacteristic
62C2×C4⋊C4×C59—21no—
63C2×C4⋊C4×C59—21no—
64C2×C4⋊C4×C59—42no—
65C2×C22⋊C4×C59—21no—
66C2×C22⋊C4×C59—21no—
67C2×C22⋊C4×C59—21no—
68C2×C22⋊C4×C59—21no—
69C2×C22⋊C4×C59—21no—
70C2×C22⋊C4×C59—21no—
71C2×C22⋊C4×C59—42no—
72C2×C22⋊C4×C59—42no—
73C2×C22⋊C4×C59—42no—
74#95×C59—21no—
75#95×C59—21no—
76#95×C59—42no—
77C24×C59—21no—
78C24×C59—21no—
79C24×C59—21no—
80C24×C59—21no—
81C24×C59—21no—
82C24×C59—21no—
83C24×C59—41no—
84C24×C59—41no—
85C24×C59—41no—
86C24×C59—41no—
87C24×C59SD1612yes—
88C24×C59C2×D411yescharacteristic
89C22×C4×C59—22no—
90C22×C4×C59—22no—
91C22×C4×C59—21no—
92C22×C4×C59—21no—
93C22×C4×C59—21no—
94C22×C4×C59—41no—
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—41no—
103C22×C4×C59—41no—
104C22×C4×C59—41no—
105C22×C4×C59—41no—
106C22×C4×C59—41no—
107C22×C4×C59—41no—
108C22×C4×C59—41no—
109C22×C4×C59—41no—
110C22×C4×C59C2×D411yescharacteristic
111C22×C4×C59C2×D411yescharacteristic
112C22×C4×C59C2×D411yescharacteristic
113C22×C4×C59#4111yescharacteristic
114C22×C4×C59#4111yescharacteristic
115C22×C4×C59#4111yescharacteristic
116C22×Dic59—21no—
117C22×Dic59—21no—
118C22×Dic59—21no—
119C22×Dic59—21no—
120C2×Dic118—21no—
121C2×Dic118—21no—
122C2×Dic118—41no—
123C2×Dic118—41no—
124C4⋊C4×C59—22no—
125C4⋊C4×C59—22no—
126C4⋊C4×C59—41no—
127C4⋊C4×C59—41no—
128C22⋊C4×C59—48no—
129C22⋊C4×C59—41no—
130C22⋊C4×C59—41no—
131C22⋊C4×C59—41no—
132C22⋊C4×C59—41no—
133C22⋊Dic59—41no—
134C22⋊Dic59—41no—
135C22⋊Dic59—41no—
136C22⋊Dic59—41no—
137C22⋊Dic59—81no—
138C22⋊Dic59—81no—
139C22⋊Dic59—81no—
140C22⋊Dic59—81no—
141C4⋊Dic59—21no—
142C4⋊Dic59—21no—
143C4⋊Dic59—41no—
144C4⋊Dic59—41no—
145Dic59⋊C4—41no—
146Dic59⋊C4—41no—
147Dic59⋊C4—81no—
148Dic59⋊C4—81no—
149C2×C59⋊C8—22no—
150C2×C59⋊C8—41no—
151C2×C59⋊C8—41no—
152C2×C59⋊C8—41no—
153C2×C59⋊C8—41no—
154C2×C59⋊C8—41no—
155C23×C59—21no—
156C23×C59—21no—
157C23×C59—21no—
158C23×C59—21no—
159C23×C59—22no—
160C23×C59—22no—
161C23×C59—22no—
162C23×C59—42no—
163C23×C59—42no—
164C23×C59—42no—
165C23×C59—42no—
166C23×C59—42no—
167C23×C59—42no—
168C23×C59—41no—
169C23×C59—41no—
170C23×C59—41no—
171C23×C59—41no—
172C23×C59—41no—
173C23×C59—41no—
174C23×C59—41no—
175C23×C59—41no—
176C23×C59—81no—
177C23×C59—81no—
178C23×C59—81no—
179C23×C59—81no—
180C23×C59—81no—
181C23×C59—81no—
182C23×C59#12011yescharacteristic
183C23×C59#12111yescharacteristic
184C23×C59#12311yescharacteristic
185C23×C59C2×SD1611yescharacteristic
186C23×C59#13511yescharacteristic
187C23×C59#13711yescharacteristic
188C23×C59#13711yescharacteristic
189C2×C4×C59—21no—
190C2×C4×C59—21no—
191C2×C4×C59—21no—
192C2×C4×C59—21no—
193C2×C4×C59—41no—
194C2×C4×C59—41no—
195C2×C4×C59—41no—
196C2×C4×C59—41no—
197C2×C4×C59—42no—
198C2×C4×C59—42no—
199C2×C4×C59—42no—
200C2×C4×C59—42no—
201C2×C4×C59—42no—
202C2×C4×C59—42no—
203C2×C4×C59—41no—
204C2×C4×C59—41no—
205C2×C4×C59—41no—
206C2×C4×C59—42no—
207C2×C4×C59—81no—
208C2×C4×C59—81no—
209C2×C4×C59—81no—
210C2×C4×C59—81no—
211C2×C4×C59—81no—
212C2×C4×C59—81no—
213C2×C4×C59—81no—
214C2×C4×C59—81no—
215C2×C4×C59—81no—
216C2×C4×C59#12111yescharacteristic
217C2×C4×C59#12111yescharacteristic
218C2×C4×C59#12311yescharacteristic
219C2×C4×C59#12411yescharacteristic
220C2×Dic59—41no—
221C2×Dic59—41no—
222C2×Dic59—41no—
223C2×Dic59—41no—
224C2×Dic59—41no—
225C2×Dic59—41no—
226C2×Dic59—41no—
227C2×Dic59—41no—
228C2×Dic59—41no—
229C2×Dic59—41no—
230C2×Dic59—41no—
231C2×Dic59—41no—
232Dic118—42no—
233Dic118—81no—
234C59⋊C8—42no—
235C59⋊C8—81no—
236#10398—591nomaximal, Sylow
237C22×C59—21no—
238C22×C59—21no—
239C22×C59—21no—
240C22×C59—21no—
241C22×C59—21no—
242C22×C59—21no—
243C22×C59—21no—
244C22×C59—21no—
245C22×C59—21no—
246C22×C59—21no—
247C22×C59—21no—
248C22×C59—21no—
249C22×C59—44no—
250C22×C59—42no—
251C22×C59—42no—
252C22×C59—42no—
253C22×C59—82no—
254C22×C59—82no—
255C22×C59—82no—
256C22×C59—81no—
257C22×C59—81no—
258C22×C59—81no—
259C22×C59—81no—
260C22×C59#39411yescharacteristic
261C22×C59#44811yescharacteristic
262C22×C59#45211yescharacteristic
263C22×C59#45311yescharacteristic
264C22×C59#45511yescharacteristic
265C22×C59B(4,𝔽2)11yescharacteristic
266C22×C59#45811yescharacteristic
267C22×C59#46511yescharacteristic
268C22×C59#47011yescharacteristic
269C22×C59#48311yescharacteristic
270C22×C59#48511yescharacteristic
271C4×C59—21no—
272C4×C59—21no—
273C4×C59—21no—
274C4×C59—21no—
275C4×C59—82no—
276C4×C59—82no—
277C4×C59—81no—
278Dic59—81no—
279Dic59—81no—
280Dic59—81no—
281Dic59—81no—
282#2626—591no—
283#1872—591no—
284#1853—591no—
285C2×#328—591no—
286C2×#323—591no—
287#1439D5911yescharacteristic
288#1294—591no—
289C2×C59—21no—
290C2×C59—21no—
291C2×C59—21no—
292C2×C59—21no—
293C2×C59—82no—
294C2×C59#159611yescharacteristic
295C2×C59#160611yescharacteristic
296C2×C59#160811yescharacteristic
297C2×C59#161811yescharacteristic
298C2×C59#203511yescharacteristic
299C2×C59#203711yescharacteristic
300C2×C59#204411yescharacteristic
301C2×C22⋊Q8—591no—
302C22×C4⋊C4C2×D5911yescharacteristic
303C22×C22⋊C4—21no—
304C22×C22⋊C4C2×D5911yescharacteristic
305C2×#106—1181no—
306C2×#103—1181no—
307C2×C22⋊C8—591no—
308C2×C22⋊C8—591no—
309#399—1181no—
310#396—1181no—
311#396—1181no—
312#393—1181no—
313#385—1181no—
314#380—591no—
315#379—1181no—
316C2×#95—21no—
317C2×#95C2×D5911yescharacteristic
318#340—1181no—
319#340—1181no—
320#328—1182no—
321#323—1182no—
322C59#1039811yescharacteristic, complemented, Sylow
323C25C22⋊D5911yescharacteristic
324C22×Q8—591no—
325C23×C4—21no—
326C23×C4—21no—
327C23×C4C22⋊D5911yescharacteristic
328C23×C4C22×D5911yescharacteristic
329C22×C8—1181no—
330C22×C8—1181no—
331C22⋊Q8—1181no—
332C22⋊Q8—1181no—
333C22⋊Q8—1181no—
334C22⋊Q8—1181no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—591no—
339C2×C4⋊C4—591no—
340C2×C4⋊C4—591no—
341C2×C4⋊C4—1181no—
342C2×C4⋊C4—1181no—
343C2×C4⋊C4—1181no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—1181no—
354C2×C22⋊C4—1181no—
355C2×C22⋊C4—1181no—
356C2×C22⋊C4—1181no—
357C2×C22⋊C4—1181no—
358C2×C22⋊C4—1181no—
359#106—2362no—
360#103—2362no—
361C22⋊C8—592no—
362C22⋊C8—1181no—
363C22⋊C8—1181no—
364C22⋊C8—1181no—
365#95—21no—
366#95—21no—
367#95—42no—
368#95—1181no—
369#95—1181no—
370#95—1181no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—21no—
376C24—21no—
377C24—41no—
378C24—41no—
379C24—41no—
380C24—41no—
381C24#1174567012yes—
382C24C2×C22⋊D5911yescharacteristic
383C2×Q8—1181no—
384C2×Q8—1181no—
385C2×Q8—2361no—
386C2×Q8—2361no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—41no—
402C22×C4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—1181no—
409C22×C4—1181no—
410C22×C4—1181no—
411C22×C4—1181no—
412C22×C4#1174568511yescharacteristic
413C22×C4#1174568511yescharacteristic
414C22×C4D4×D5911yescharacteristic
415C22×C4D4×D5911yescharacteristic
416C22×C4D4×D5911yescharacteristic
417C22×C4#1174568711yescharacteristic
418C2×C8—1182no—
419C2×C8—2361no—
420C2×C8—2361no—
421C2×C8—2361no—
422C2×C8—2361no—
423C2×C8—2361no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—1181no—
429C4⋊C4—1181no—
430C4⋊C4—4721no—
431C4⋊C4—4721no—
432C4⋊C4—2361no—
433C4⋊C4—2361no—
434C4⋊C4—2361no—
435C4⋊C4—2361no—
436C22⋊C4—48no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—4721no—
442C22⋊C4—4721no—
443C22⋊C4—4721no—
444C22⋊C4—4721no—
445C22⋊C4—2361no—
446C22⋊C4—2361no—
447C22⋊C4—2361no—
448C22⋊C4—2361no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—22no—
454C23—22no—
455C23—22no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—41no—
470C23—81no—
471C23—81no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23#1427369511yescharacteristic
477C23#1427369911yescharacteristic
478C23#1427371011yescharacteristic
479C23C2×#1174567011yescharacteristic
480C23#1427374711yescharacteristic
481C23#1427375711yescharacteristic
482C23#1427375811yescharacteristic
483Q8—4721no—
484Q8—2362no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
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—2361no—
522C2×C4—2361no—
523C2×C4—2361no—
524C2×C4#1427370011yescharacteristic
525C2×C4#1427370011yescharacteristic
526C2×C4#1427370911yescharacteristic
527C2×C4#1427371311yescharacteristic
528C8—4721no—
529C8—2362no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—82no—
547C22—82no—
548C22—82no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#1683731711yescharacteristic
554C22#1683754011yescharacteristic
555C22#1683756211yescharacteristic
556C22#1683756911yescharacteristic
557C22#1683757911yescharacteristic
558C22#1683758811yescharacteristic
559C22#1683759111yescharacteristic
560C22#1683762911yescharacteristic
561C22#1683765811yescharacteristic
562C22#1683773211yescharacteristic
563C22#1683774311yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—82no—
569C4—81no—
570C4—82no—
571C4—4721no—
572C4—4721no—
573C4—4721no—
574C4—4721no—
575C2—21no—
576C2—21no—
577C2—21no—
578C2—21no—
579C2—82no—
580C2#2142301811yescharacteristic
581C2#2142307411yescharacteristic
582C2#2142308611yescharacteristic
583C2#2142314211yescharacteristic
584C2#2142529211yescharacteristic
585C2#2142530611yescharacteristic
586C2#2142534511yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC23×C4×C59C23
FrattiniC23×C4C22×D59
FittingC59×#1439C2
socleC23×C59#120
prime radicalC25×C59D4
hypercenter#1439D59
hypocenterC59#10398
LCSG ▷ C23×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. #21424403C2semidirect
3. #21424289C2semidirect
4. C2×#16837138C2semidirect
6. #21421975C2semidirect
322. C59#10398semidirect

Maximal subgroups

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

subgroupindex
#214299012
#214244032
#214242892
C2×#168371382
C2×#168371262
#214219752
C59×#14392
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