Finite Group Databasebeta

← #28497073

Subgroups — #28497073

Order 15104.

1118 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21426708C211yesmaximal, characteristic
2C2×#16837169C211yesmaximal, characteristic
3C2×#16837168C211yesmaximal, characteristic
4C2×#16837168C211yesmaximal, characteristic
5#21422319C211yesmaximal, characteristic
6#21422319C211yesmaximal, characteristic
7C59×C22⋊#95C211yesmaximal, characteristic
8C22×C22⋊Dic59C2211yescharacteristic
9C22×C22⋊Dic59C2211yescharacteristic
10C22×C22⋊Dic59C2211yescharacteristic
11C22×C22⋊Dic59C2211yescharacteristic
12#16837275—22no—
13#16837274—22no—
14#16837260—22no—
15C2×C59⋊#95—22no—
16C2×C59⋊#95—22no—
17#16837169—22no—
18#16837168—22no—
19#16837168C414yescomplemented
20C24×C4×C59C2211yescharacteristic
21C22×C22⋊C4×C59C2211yescharacteristic
22C22×C22⋊C4×C59C2211yescharacteristic
23C2×#95×C59—22no—
24C23×Dic59—21no—
25C23×Dic59—21no—
26C23×Dic59D412yes—
27C23×Dic59D412yes—
28C2×Dic59⋊C4—22no—
29C2×Dic59⋊C4—22no—
30C2×C22⋊Dic59—21no—
31C2×C22⋊Dic59—21no—
32C2×C22⋊Dic59—21no—
33C2×C22⋊Dic59—21no—
34C2×C22⋊Dic59—21no—
35C2×C22⋊Dic59—21no—
36C2×C22⋊Dic59—21no—
37C2×C22⋊Dic59—21no—
38C2×C22⋊Dic59—21no—
39C2×C22⋊Dic59—21no—
40C2×C22⋊Dic59—21no—
41C2×C22⋊Dic59—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—
48C2×C22⋊Dic59—21no—
49C2×C22⋊Dic59—21no—
50C2×C22⋊Dic59C2×C412yes—
51C2×C22⋊Dic59C2×C412yes—
52C2×C22⋊Dic59D412yes—
53C2×C22⋊Dic59Q812yes—
54C59⋊#95—24no—
55C59⋊#95—44no—
56C59⋊#95—44no—
57C25×C59C2311yescharacteristic
58C23×C4×C59—21no—
59C23×C4×C59—21no—
60C23×C4×C59—21no—
61C23×C4×C59—21no—
62C23×C4×C59—21no—
63C23×C4×C59—21no—
64C23×C4×C59—21no—
65C23×C4×C59—44no—
66C23×C4×C59D412yes—
67C23×C4×C59Q812yes—
68C2×C22⋊C4×C59—21no—
69C2×C22⋊C4×C59—21no—
70C2×C22⋊C4×C59—21no—
71C2×C22⋊C4×C59—21no—
72C2×C22⋊C4×C59—21no—
73C2×C22⋊C4×C59—21no—
74C2×C22⋊C4×C59—21no—
75C2×C22⋊C4×C59—21no—
76C2×C22⋊C4×C59—21no—
77C2×C22⋊C4×C59—21no—
78C2×C22⋊C4×C59—21no—
79C2×C22⋊C4×C59C2×C412yes—
80#95×C59—44no—
81C24×C59—42no—
82C24×C59—42no—
83C24×C59C22×C411yescharacteristic
84C24×C59C2×D411yescharacteristic
85C24×C59C2×D411yescharacteristic
86C24×C59C2×D411yescharacteristic
87C24×C59C2×D411yescharacteristic
88C24×C59C2×Q811yescharacteristic
89C24×C59C2×Q811yescharacteristic
90C24×C59#4111yescharacteristic
91C24×C59#4111yescharacteristic
92C24×C59#4111yescharacteristic
93C24×C59#4111yescharacteristic
94C24×C59#4111yescharacteristic
95C24×C59#4111yescharacteristic
96C24×C59#4111yescharacteristic
97C24×C59#4111yescharacteristic
98C22×C4×C59—24no—
99C22×C4×C59—24no—
100C22×C4×C59—24no—
101C22×C4×C59—22no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—22no—
105C22×C4×C59—22no—
106C22×C4×C59—22no—
107C22×C4×C59—22no—
108C22×C4×C59—44no—
109C22×C4×C59—44no—
110C22×C4×C59—44no—
111C22×C4×C59—44no—
112C22×C4×C59—42no—
113C22×C4×C59—42no—
114C22×C4×C59—42no—
115C22×C4×C59—41no—
116C22×C4×C59—41no—
117C22×C4×C59—41no—
118C22×C4×C59—41no—
119C22×C4×C59—42no—
120C22×C4×C59—42no—
121C22×C4×C59—42no—
122C22×C4×C59—42no—
123C22×C4×C59—41no—
124C22×C4×C59—41no—
125C22×Dic59—22no—
126C22×Dic59—22no—
127C22×Dic59—22no—
128C22×Dic59—22no—
129C22×Dic59—22no—
130C22×Dic59—22no—
131C22×Dic59—22no—
132C22×Dic59—42no—
133C22×Dic59—42no—
134C22×Dic59—42no—
135C22×Dic59—42no—
136C22×Dic59—42no—
137C22×Dic59—42no—
138C22×Dic59—42no—
139C22×Dic59—42no—
140C22×Dic59—41no—
141C22×Dic59—41no—
142C22×Dic59—41no—
143C22×Dic59—41no—
144C22×Dic59C4⋊C414yes—
145C22⋊C4×C59—22no—
146C22⋊C4×C59—22no—
147C22⋊C4×C59—41no—
148C22⋊C4×C59—41no—
149C22⋊C4×C59—41no—
150C22⋊C4×C59—41no—
151C22⋊C4×C59—41no—
152C22⋊C4×C59—41no—
153C22⋊Dic59—22no—
154C22⋊Dic59—22no—
155C22⋊Dic59—22no—
156C22⋊Dic59—22no—
157C22⋊Dic59—22no—
158C22⋊Dic59—22no—
159C22⋊Dic59—22no—
160C22⋊Dic59—22no—
161C22⋊Dic59—41no—
162C22⋊Dic59—41no—
163C22⋊Dic59—41no—
164C22⋊Dic59—41no—
165C22⋊Dic59—41no—
166C22⋊Dic59—41no—
167C22⋊Dic59—41no—
168C22⋊Dic59—41no—
169Dic59⋊C4—82no—
170Dic59⋊C4—82no—
171C23×C59—22no—
172C23×C59—22no—
173C23×C59—22no—
174C23×C59—22no—
175C23×C59—22no—
176C23×C59—22no—
177C23×C59—41no—
178C23×C59—41no—
179C23×C59—41no—
180C23×C59—41no—
181C23×C59—42no—
182C23×C59—42no—
183C23×C59—41no—
184C23×C59—42no—
185C23×C59—42no—
186C23×C59—41no—
187C23×C59—42no—
188C23×C59—42no—
189C23×C59—41no—
190C23×C59—41no—
191C23×C59—42no—
192C23×C59—42no—
193C23×C59C2×C4⋊C411yescharacteristic
194C23×C59#11711yescharacteristic
195C23×C59#11711yescharacteristic
196C23×C59C4×D411yescharacteristic
197C23×C59C4×D411yescharacteristic
198C23×C59C4×D411yescharacteristic
199C23×C59C4×Q811yescharacteristic
200C23×C59#12011yescharacteristic
201C23×C59#12111yescharacteristic
202C23×C59#12111yescharacteristic
203C23×C59#12111yescharacteristic
204C23×C59C22⋊Q811yescharacteristic
205C23×C59C22⋊Q811yescharacteristic
206C23×C59C22⋊Q811yescharacteristic
207C23×C59C22⋊Q811yescharacteristic
208C23×C59C22⋊Q811yescharacteristic
209C23×C59#12311yescharacteristic
210C23×C59#12311yescharacteristic
211C23×C59#12311yescharacteristic
212C23×C59#12311yescharacteristic
213C23×C59#12311yescharacteristic
214C23×C59#12411yescharacteristic
215C23×C59#12411yescharacteristic
216C23×C59#12411yescharacteristic
217C23×C59#12411yescharacteristic
218C23×C59#12511yescharacteristic
219C23×C59#12511yescharacteristic
220C23×C59#12511yescharacteristic
221C23×C59#12511yescharacteristic
222C23×C59#12511yescharacteristic
223C23×C59#12611yescharacteristic
224C23×C59#12611yescharacteristic
225C23×C59#12611yescharacteristic
226C23×C59#12611yescharacteristic
227C23×C59C4⋊Q811yescharacteristic
228C2×C4×C59—24no—
229C2×C4×C59—24no—
230C2×C4×C59—24no—
231C2×C4×C59—44no—
232C2×C4×C59—44no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—42no—
236C2×C4×C59—44no—
237C2×C4×C59—42no—
238C2×C4×C59—44no—
239C2×C4×C59—44no—
240C2×C4×C59—44no—
241C2×C4×C59—42no—
242C2×C4×C59—42no—
243C2×C4×C59—42no—
244C2×C4×C59—42no—
245C2×C4×C59—81no—
246C2×C4×C59—81no—
247C2×C4×C59—82no—
248C2×C4×C59—82no—
249C2×Dic59—24no—
250C2×Dic59—42no—
251C2×Dic59—42no—
252C2×Dic59—44no—
253C2×Dic59—44no—
254C2×Dic59—44no—
255C2×Dic59—44no—
256C2×Dic59—42no—
257C2×Dic59—42no—
258C2×Dic59—42no—
259C2×Dic59—42no—
260C2×Dic59—42no—
261C2×Dic59—82no—
262C2×Dic59—82no—
263C2×Dic59—81no—
264C2×Dic59—81no—
265C2×Dic59—81no—
266C2×Dic59—81no—
267C2×Dic59—82no—
268C2×Dic59—82no—
269#11287—591nomaximal, Sylow
270C22×C59—22no—
271C22×C59—22no—
272C22×C59—22no—
273C22×C59—22no—
274C22×C59—22no—
275C22×C59—22no—
276C22×C59—21no—
277C22×C59—21no—
278C22×C59—21no—
279C22×C59—21no—
280C22×C59—21no—
281C22×C59—21no—
282C22×C59—21no—
283C22×C59—21no—
284C22×C59—21no—
285C22×C59—21no—
286C22×C59—21no—
287C22×C59—21no—
288C22×C59—22no—
289C22×C59—22no—
290C22×C59—22no—
291C22×C59—22no—
292C22×C59—22no—
293C22×C59—22no—
294C22×C59—41no—
295C22×C59—41no—
296C22×C59—41no—
297C22×C59—41no—
298C22×C59—41no—
299C22×C59—41no—
300C22×C59—41no—
301C22×C59—41no—
302C22×C59—41no—
303C22×C59—41no—
304C22×C59—41no—
305C22×C59—41no—
306C22×C59—41no—
307C22×C59—41no—
308C22×C59—41no—
309C22×C59—41no—
310C22×C59#38211yescharacteristic
311C22×C59#38511yescharacteristic
312C22×C59#38711yescharacteristic
313C22×C59#38711yescharacteristic
314C22×C59#38811yescharacteristic
315C22×C59#38811yescharacteristic
316C22×C59#38911yescharacteristic
317C22×C59#39311yescharacteristic
318C22×C59#39411yescharacteristic
319C22×C59#39711yescharacteristic
320C22×C59#39811yescharacteristic
321C22×C59#39811yescharacteristic
322C22×C59#40011yescharacteristic
323C22×C59#40011yescharacteristic
324C22×C59#40011yescharacteristic
325C22×C59B(4,𝔽2)12yes—
326C22×C59#45812yes—
327C4×C59—44no—
328C4×C59—82no—
329C4×C59—82no—
330Dic59—44no—
331Dic59—82no—
332Dic59—82no—
333Dic59—82no—
334#2315—591no—
335C2×#342—591no—
336C2×#342—591no—
337C2×#342—591no—
338C22⋊#95—591no—
339C22⋊#95—591no—
340C22⋊#95D5911yescharacteristic
341C2×C59—21no—
342C2×C59—21no—
343C2×C59—21no—
344C2×C59—21no—
345C2×C59—21no—
346C2×C59—21no—
347C2×C59—21no—
348C2×C59—21no—
349C2×C59—21no—
350C2×C59—21no—
351C2×C59—21no—
352C2×C59—21no—
353C2×C59#144211yescharacteristic
354C2×C59#186712yes—
355C2×C59#202911yescharacteristic
356C2×C59#203011yescharacteristic
357C2×C59#204412yes—
358C24×C4C2×D5911yescharacteristic
359C22×C22⋊C4—591no—
360C22×C22⋊C4—591no—
361C22×C22⋊C4—591no—
362C22×C22⋊C4—591no—
363C22×C22⋊C4C2×D5911yescharacteristic
364C22×C22⋊C4C2×D5911yescharacteristic
365#385—1182no—
366#385—1182no—
367#380—1182no—
368C2×#95—22no—
369C2×#95—1182no—
370C2×#95—1182no—
371#342—594no—
372#342—1182no—
373#342—1182no—
374C59#1128711yescharacteristic, complemented, Sylow
375C25C22×D5911yescharacteristic
376C23×C4—21no—
377C23×C4—21no—
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C23×C4—21no—
383C23×C4—44no—
384C23×C4—592no—
385C23×C4—592no—
386C23×C4—1181no—
387C23×C4—1181no—
388C23×C4Dic11812yes—
389C23×C4C22⋊D5912yes—
390C2×C4⋊C4—1182no—
391C2×C4⋊C4—1182no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—592no—
404C2×C22⋊C4—592no—
405C2×C22⋊C4—592no—
406C2×C22⋊C4—592no—
407C2×C22⋊C4—1181no—
408C2×C22⋊C4—1181no—
409C2×C22⋊C4—1181no—
410C2×C22⋊C4—1181no—
411C2×C22⋊C4—1181no—
412C2×C22⋊C4—1181no—
413C2×C22⋊C4—1181no—
414C2×C22⋊C4—1181no—
415C2×C22⋊C4—1181no—
416C2×C22⋊C4—1181no—
417C2×C22⋊C4—1181no—
418C2×C22⋊C4—1181no—
419C2×C22⋊C4—1181no—
420C2×C22⋊C4—1181no—
421C2×C22⋊C4—1181no—
422C2×C22⋊C4—1181no—
423C2×C22⋊C4—1181no—
424C2×C22⋊C4—1181no—
425C2×C22⋊C4—1181no—
426C2×C22⋊C4—1181no—
427C2×C22⋊C4C4×D5912yes—
428#95—44no—
429#95—1184no—
430#95—2364no—
431#95—2364no—
432C24—42no—
433C24—42no—
434C24C2×Dic11811yescharacteristic
435C24C2×C4×D5911yescharacteristic
436C24#1174568511yescharacteristic
437C24#1174568511yescharacteristic
438C24#1174568511yescharacteristic
439C24#1174568511yescharacteristic
440C24D4×D5911yescharacteristic
441C24D4×D5911yescharacteristic
442C24D4×D5911yescharacteristic
443C24#1174568711yescharacteristic
444C24#1174568711yescharacteristic
445C24#1174568711yescharacteristic
446C24Q8×D5911yescharacteristic
447C24#1174568911yescharacteristic
448C24C2×C22⋊D5911yescharacteristic
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—44no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—594no—
477C22×C4—1182no—
478C22×C4—1182no—
479C22×C4—1182no—
480C22×C4—1182no—
481C22×C4—1182no—
482C22×C4—1182no—
483C22×C4—1182no—
484C22×C4—2362no—
485C22×C4—2362no—
486C22×C4—2362no—
487C22×C4—2362no—
488C22×C4—2361no—
489C22×C4—2361no—
490C22×C4—2361no—
491C22×C4—2361no—
492C22×C4—2362no—
493C22×C4—2362no—
494C22×C4—2362no—
495C22×C4—2362no—
496C4⋊C4—4722no—
497C4⋊C4—4722no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—1182no—
507C22⋊C4—1182no—
508C22⋊C4—1182no—
509C22⋊C4—1182no—
510C22⋊C4—1182no—
511C22⋊C4—1182no—
512C22⋊C4—1182no—
513C22⋊C4—1182no—
514C22⋊C4—2361no—
515C22⋊C4—2361no—
516C22⋊C4—2361no—
517C22⋊C4—2361no—
518C22⋊C4—2361no—
519C22⋊C4—2361no—
520C22⋊C4—2361no—
521C22⋊C4—2361no—
522C23—22no—
523C23—22no—
524C23—22no—
525C23—22no—
526C23—22no—
527C23—22no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—41no—
540C23—41no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23C4⋊C4×D5911yescharacteristic
545C23#1427368311yescharacteristic
546C23#1427368411yescharacteristic
547C23(C22⋊D59)⋊C411yescharacteristic
548C23C4×C22⋊D5911yescharacteristic
549C23#1427368911yescharacteristic
550C23C4×Dic11811yescharacteristic
551C23#1427369511yescharacteristic
552C23#1427369911yescharacteristic
553C23#1427370011yescharacteristic
554C23#1427370011yescharacteristic
555C23#1427370311yescharacteristic
556C23#1427370411yescharacteristic
557C23#1427370411yescharacteristic
558C23#1427370511yescharacteristic
559C23#1427370611yescharacteristic
560C23#1427370911yescharacteristic
561C23#1427370911yescharacteristic
562C23#1427371011yescharacteristic
563C23#1427371211yescharacteristic
564C23#1427371211yescharacteristic
565C23#1427371311yescharacteristic
566C23#1427371311yescharacteristic
567C23#1427371311yescharacteristic
568C23#1427371411yescharacteristic
569C23#1427371711yescharacteristic
570C23#1427371711yescharacteristic
571C23#1427371711yescharacteristic
572C23#1427371811yescharacteristic
573C23#1427371911yescharacteristic
574C23#1427372011yescharacteristic
575C23#1427372111yescharacteristic
576C23#1427372211yescharacteristic
577C23#1427372211yescharacteristic
578C23#1427372611yescharacteristic
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—44no—
588C2×C4—42no—
589C2×C4—44no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4—1184no—
601C2×C4—4721no—
602C2×C4—4721no—
603C2×C4—4721no—
604C2×C4—4721no—
605C2×C4—4722no—
606C2×C4—4722no—
607C2×C4—4722no—
608C2×C4—4722no—
609C2×C4—2364no—
610C2×C4—2364no—
611C2×C4—2364no—
612C2×C4—2362no—
613C2×C4—2362no—
614C2×C4—2362no—
615C2×C4—2362no—
616C2×C4—2362no—
617C2×C4—2362no—
618C2×C4—2362no—
619C2×C4—2364no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—22no—
641C22—22no—
642C22—22no—
643C22—22no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22#1683726611yescharacteristic
661C22#1683727311yescharacteristic
662C22#1683728511yescharacteristic
663C22#1683728611yescharacteristic
664C22#1683729111yescharacteristic
665C22#1683729611yescharacteristic
666C22#1683729911yescharacteristic
667C22#1683731411yescharacteristic
668C22#1683731711yescharacteristic
669C22#1683733111yescharacteristic
670C22#1683733511yescharacteristic
671C22#1683733611yescharacteristic
672C22#1683734011yescharacteristic
673C22#1683734311yescharacteristic
674C22#1683734411yescharacteristic
675C22#1683758812yes—
676C22#1683759112yes—
677C4—44no—
678C4—82no—
679C4—82no—
680C4—4722no—
681C4—4722no—
682C4—4722no—
683C4—2364no—
684C2—21no—
685C2—21no—
686C2—21no—
687C2—21no—
688C2—21no—
689C2—21no—
690C2—21no—
691C2—21no—
692C2—21no—
693C2—21no—
694C2—21no—
695C2—21no—
696C2#2142235411yescharacteristic
697C2#2142437512yes—
698C2#2142526011yescharacteristic
699C2#2142526311yescharacteristic
700C2#2142534512yes—
subgroupG/H
centerC23#14273695
commutatorC24×C59C22×C4
FrattiniC25C22×D59
FittingC59×C22⋊#95C2
socleC23×C59#120
prime radical, cosocleC25×C59C23
hypercenterC22⋊#95D59
hypocenterC59#11287
LCSG ▷ C24×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C25 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
19. #16837168C4semidirect
374. C59#11287semidirect

Maximal subgroups

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

subgroupindex
#214267082
C2×#168371692
C2×#168371682
#214223192
C59×C22⋊#952
#1128759