Finite Group Databasebeta

← #28495332

Subgroups — #28495332

Order 15104.

1630 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273654C211yesmaximal, characteristic, complemented
2C2×#16837403C211yesmaximal, characteristic, complemented
3C22×#14273644C211yesmaximal, characteristic, complemented
4C2×#16837305C211yesmaximal, characteristic, complemented
5#21423817C211yesmaximal, characteristic, complemented
6C2×#16837161C211yesmaximal, characteristic, complemented
7C2×C59×#535C211yesmaximal, characteristic
8C22×#11745664C2211yescharacteristic
9C22×#11745664C2211yescharacteristic
10C22×C4⋊Dic59C2211yescharacteristic
11C22×C22⋊Dic59—22no—
12C22×C4×Dic59C2211yescharacteristic
13C2×#14273654—22no—
14C2×#14273654—22no—
15C2×#14273654—22no—
16#16837403—22no—
17#16837403—22no—
18C2×#14273651—21no—
19C2×#14273648—21no—
20C2×#14273644—22no—
21C2×#14273644—22no—
22C2×#14273644—22no—
23#16837305—22no—
24#16837305—22no—
25#16837164—22no—
26#16837161—22no—
27C22×#41×C59C2211yescharacteristic
28C23×D4×C59C2211yescharacteristic
29C59×#535—22no—
30C59×#535—22no—
31C59×#535—22no—
32C59×#535C414yescomplemented
33C2×#127×C59—21no—
34C2×#124×C59—21no—
35C2×#121×C59—22no—
36C2×#120×C59—22no—
37C2×#117×C59C2211yescharacteristic
38C23×Dic59—21no—
39C23×Dic59—21no—
40C2×#11745664—21no—
41C2×#11745664—21no—
42C2×#11745664—21no—
43C2×#11745664—21no—
44C2×#11745664—21no—
45C2×#11745664—21no—
46C2×#11745664—21no—
47C2×#11745664—21no—
48C2×#11745664—21no—
49C2×#11745664—21no—
50C2×#11745664D412yescomplemented
51C2×#11745664D412yescomplemented
52C22×C59⋊C8—21no—
53C22×C59⋊C8—21no—
54C2×C4⋊Dic59—21no—
55C2×C4⋊Dic59—21no—
56C2×C4⋊Dic59—21no—
57C2×C4⋊Dic59—21no—
58C2×C4⋊Dic59—21no—
59C2×C4⋊Dic59D412yescomplemented
60C2×C22⋊Dic59—28no—
61C2×C22⋊Dic59—48no—
62C2×C4×Dic59—21no—
63C2×C4×Dic59—21no—
64C2×C4×Dic59—21no—
65C2×C4×Dic59—21no—
66C2×C4×Dic59—21no—
67C2×C4×Dic59D412yescomplemented
68#14273654—28no—
69#14273651—24no—
70#14273648—24no—
71#14273644—28no—
72C25×C59D412yes—
73C2×#41×C59—21no—
74C2×#41×C59—21no—
75C2×#41×C59—21no—
76C2×#41×C59—21no—
77C2×#41×C59—21no—
78C2×#41×C59—21no—
79C2×#41×C59—21no—
80C2×#41×C59—21no—
81C2×#41×C59—21no—
82C2×#41×C59—21no—
83C2×#41×C59C2×C412yes—
84C2×#41×C59D412yes—
85C22×Q8×C59D411yescharacteristic
86C22×D4×C59—21no—
87C22×D4×C59—24no—
88C22×D4×C59—21no—
89C22×D4×C59—21no—
90C22×D4×C59—21no—
91C22×D4×C59—21no—
92C22×D4×C59—21no—
93C22×D4×C59—21no—
94C22×D4×C59—21no—
95C22×D4×C59—21no—
96C22×D4×C59—21no—
97C22×D4×C59—21no—
98C22×D4×C59—21no—
99C22×D4×C59—21no—
100C22×D4×C59C2×C412yes—
101C22×D4×C59D412yes—
102C22×D4×C59D411yescharacteristic
103C23×C4×C59—21no—
104C23×C4×C59C2311yescharacteristic
105#127×C59—24no—
106#127×C59—24no—
107#124×C59—24no—
108#124×C59—24no—
109#121×C59—28no—
110#121×C59—28no—
111#120×C59—28no—
112#120×C59—28no—
113#117×C59—21no—
114#117×C59—21no—
115#117×C59C2×C412yes—
116#117×C59D412yes—
117C2×C4⋊C4×C59D412yes—
118C2×C22⋊C4×C59—24no—
119C2×C22⋊C4×C59—21no—
120C2×C42×C59—21no—
121C24×C59—22no—
122C24×C59—21no—
123C24×C59—22no—
124C24×C59—22no—
125C24×C59—22no—
126C24×C59—22no—
127C24×C59—22no—
128C24×C59—44no—
129C24×C59—44no—
130C24×C59C22⋊C414yes—
131C24×C59C2×D411yescharacteristic
132#41×C59—22no—
133#41×C59—22no—
134#41×C59—22no—
135#41×C59—22no—
136#41×C59—22no—
137#41×C59—22no—
138#41×C59—22no—
139#41×C59—22no—
140#41×C59—41no—
141#41×C59—41no—
142#41×C59—41no—
143#41×C59—41no—
144#41×C59—41no—
145#41×C59—41no—
146#41×C59—41no—
147#41×C59—41no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—21no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59C22⋊C412yescomplemented
154C2×D4×C59—22no—
155C2×D4×C59—22no—
156C2×D4×C59—216no—
157C2×D4×C59—22no—
158C2×D4×C59—22no—
159C2×D4×C59—22no—
160C2×D4×C59—22no—
161C2×D4×C59—22no—
162C2×D4×C59—22no—
163C2×D4×C59—21no—
164C2×D4×C59—22no—
165C2×D4×C59—22no—
166C2×D4×C59—21no—
167C2×D4×C59—22no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—22no—
171C2×D4×C59—22no—
172C2×D4×C59—21no—
173C2×D4×C59—22no—
174C2×D4×C59—41no—
175C2×D4×C59—41no—
176C2×D4×C59—41no—
177C2×D4×C59—41no—
178C2×D4×C59—41no—
179C2×D4×C59—41no—
180C2×D4×C59—41no—
181C2×D4×C59—41no—
182C2×D4×C59—41no—
183C2×D4×C59—41no—
184C2×D4×C59—41no—
185C2×D4×C59—41no—
186C2×D4×C59—41no—
187C2×D4×C59—41no—
188C2×D4×C59—41no—
189C2×D4×C59—41no—
190C2×D4×C59—41no—
191C2×D4×C59—41no—
192C2×D4×C59—41no—
193C2×D4×C59—41no—
194C2×D4×C59—84no—
195C2×D4×C59—84no—
196C2×D4×C59C22⋊C412yescomplemented
197C22×C4×C59—22no—
198C22×C4×C59—21no—
199C22×C4×C59—22no—
200C22×C4×C59—22no—
201C22×C4×C59—41no—
202C22×C4×C59—41no—
203C22×C4×C59—41no—
204C22×C4×C59—41no—
205C22×C4×C59C22×C411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D411yescharacteristic
208C22×C4×C59C2×D411yescharacteristic
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D411yescharacteristic
211C22×C4×C59C2×D411yescharacteristic
212C22×C4×C59C2×D411yescharacteristic
213C22×C4×C59C2×D411yescharacteristic
214C22×C4×C59C2×D411yescharacteristic
215C22×C4×C59#4111yescharacteristic
216C22×C4×C59#4111yescharacteristic
217C22×C4×C59#4111yescharacteristic
218C22×C4×C59#4111yescharacteristic
219C22×Dic59—24no—
220C22×Dic59—22no—
221C22×Dic59—22no—
222C22×Dic59—42no—
223C22×Dic59—41no—
224C22×Dic59—41no—
225C22×Dic59—44no—
226C22×Dic59—41no—
227C22×Dic59—41no—
228C4⋊C4×C59—22no—
229C4⋊C4×C59C22⋊C414yescomplemented
230C22⋊C4×C59—216no—
231C22⋊C4×C59—22no—
232C22⋊C4×C59—22no—
233C42×C59—22no—
234C42×C59—22no—
235C22⋊Dic59—416no—
236C4⋊Dic59—22no—
237C4⋊Dic59—22no—
238C4⋊Dic59—41no—
239C4⋊Dic59—41no—
240C4×Dic59—22no—
241C4×Dic59—22no—
242C4×Dic59—41no—
243C4×Dic59—41no—
244#11745664—22no—
245#11745664—22no—
246#11745664—22no—
247#11745664—22no—
248#11745664—41no—
249#11745664—41no—
250#11745664—41no—
251#11745664—41no—
252C2×C59⋊C8—22no—
253C2×C59⋊C8—22no—
254C2×C59⋊C8—41no—
255C2×C59⋊C8—41no—
256C2×C59⋊C8—41no—
257C2×C59⋊C8—41no—
258C23×C59—22no—
259C23×C59—22no—
260C23×C59—24no—
261C23×C59—22no—
262C23×C59—24no—
263C23×C59—24no—
264C23×C59—48no—
265C23×C59—44no—
266C23×C59—44no—
267C23×C59—48no—
268C23×C59—41no—
269C23×C59—42no—
270C23×C59—42no—
271C23×C59—41no—
272C23×C59—42no—
273C23×C59—42no—
274C23×C59—42no—
275C23×C59—44no—
276C23×C59—42no—
277C23×C59—44no—
278C23×C59—84no—
279C23×C59—82no—
280C23×C59—82no—
281C23×C59—84no—
282C23×C59C2×C22⋊C411yescharacteristic
283C23×C59#12011yescharacteristic
284C23×C59#12011yescharacteristic
285C23×C59#12011yescharacteristic
286C23×C59#12111yescharacteristic
287C23×C59#12111yescharacteristic
288C23×C59#12311yescharacteristic
289Q8×C59—22no—
290Q8×C59—22no—
291Q8×C59—41no—
292Q8×C59—41no—
293D4×C59—22no—
294D4×C59—22no—
295D4×C59—42no—
296D4×C59—42no—
297D4×C59—42no—
298D4×C59—42no—
299D4×C59—42no—
300D4×C59—42no—
301D4×C59—42no—
302D4×C59—42no—
303D4×C59—42no—
304D4×C59—42no—
305D4×C59—41no—
306D4×C59—42no—
307D4×C59—42no—
308D4×C59—41no—
309D4×C59—816no—
310C2×C4×C59—24no—
311C2×C4×C59—22no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59—42no—
320C2×C4×C59C2×C22⋊C411yescharacteristic
321C2×C4×C59C2×C22⋊C411yescharacteristic
322C2×C4×C59C4×D411yescharacteristic
323C2×C4×C59C4×D411yescharacteristic
324C2×C4×C59C4×D411yescharacteristic
325C2×C4×C59C4×D411yescharacteristic
326C2×C4×C59#12011yescharacteristic
327C2×C4×C59#12011yescharacteristic
328C2×C4×C59#12011yescharacteristic
329C2×C4×C59#12011yescharacteristic
330C2×C4×C59#12011yescharacteristic
331C2×C4×C59#12111yescharacteristic
332C2×C4×C59#12111yescharacteristic
333C2×C4×C59#12111yescharacteristic
334C2×C4×C59#12111yescharacteristic
335C2×C4×C59#12111yescharacteristic
336C2×C4×C59#12111yescharacteristic
337C2×C4×C59#12111yescharacteristic
338C2×C4×C59#12111yescharacteristic
339C2×C4×C59#12111yescharacteristic
340C2×C4×C59#12111yescharacteristic
341C2×C4×C59#12311yescharacteristic
342C2×C4×C59#12311yescharacteristic
343C2×C4×C59#12311yescharacteristic
344C2×C4×C59#12411yescharacteristic
345C2×C4×C59#12411yescharacteristic
346C2×C4×C59#12711yescharacteristic
347C2×C4×C59#12711yescharacteristic
348C2×Dic59—24no—
349C2×Dic59—44no—
350C2×Dic59—42no—
351C2×Dic59—44no—
352C2×Dic59—42no—
353C2×Dic59—44no—
354C2×Dic59—42no—
355C2×Dic59—82no—
356C2×Dic59—82no—
357C59⋊C8—42no—
358C59⋊C8—42no—
359#10997—591nomaximal, Sylow
360C22×C59—22no—
361C22×C59—22no—
362C22×C59—21no—
363C22×C59—21no—
364C22×C59—21no—
365C22×C59—21no—
366C22×C59—22no—
367C22×C59—22no—
368C22×C59—48no—
369C22×C59—44no—
370C22×C59—48no—
371C22×C59—42no—
372C22×C59—44no—
373C22×C59—84no—
374C22×C59—84no—
375C22×C59—84no—
376C22×C59—81no—
377C22×C59—82no—
378C22×C59—81no—
379C22×C59—82no—
380C22×C59—82no—
381C22×C59—84no—
382C22×C59#37911yescharacteristic
383C22×C59#38611yescharacteristic
384C22×C59#38611yescharacteristic
385C22×C59#39211yescharacteristic
386C22×C59#39211yescharacteristic
387C22×C59#39411yescharacteristic
388C22×C59#39411yescharacteristic
389C22×C59#45312yes—
390C22×C59#45512yes—
391C4×C59—44no—
392C4×C59—42no—
393C4×C59#38611yescharacteristic
394C4×C59#38611yescharacteristic
395C4×C59#39011yescharacteristic
396C4×C59#39011yescharacteristic
397C4×C59#39211yescharacteristic
398C4×C59#39211yescharacteristic
399C4×C59#39411yescharacteristic
400C4×C59#39411yescharacteristic
401Dic59—44no—
402Dic59—82no—
403C2×#535D5911yescharacteristic
404C22×#104—591no—
405C2×#417—591no—
406C22×#100—591no—
407C2×#390—591no—
408#1736—591no—
409C2×#339—591no—
410C2×C59—21no—
411C2×C59—21no—
412C2×C59—21no—
413C2×C59—21no—
414C2×C59—84no—
415C2×C59—82no—
416C2×C59#143811yescharacteristic
417C2×C59#179212yes—
418C2×C59#200211yescharacteristic
419C2×C59#200411yescharacteristic
420C2×C59#203712yes—
421C22×#41C2×D5911yescharacteristic
422C23×D4C2×D5911yescharacteristic
423C22×M16—591no—
424C22×M16—591no—
425#535—22no—
426#535—22no—
427#535—22no—
428#535Dic5914yescomplemented
429C2×#127—21no—
430C2×#124—21no—
431C2×#121—22no—
432C2×#120—22no—
433C2×#117C2×D5911yescharacteristic
434C22×C4⋊C4—591no—
435C22×C22⋊C4—1182no—
436C22×C42—591no—
437C2×#104—1182no—
438C2×#104—1182no—
439C2×#104—1182no—
440#417—1182no—
441#417—1182no—
442C2×#103—1181no—
443C2×#102—1181no—
444C2×#100—1182no—
445C2×#100—1182no—
446C2×#100—1182no—
447#390—1182no—
448#390—1182no—
449#340—1182no—
450#339—1182no—
451C59#1099711yescharacteristic, complemented, Sylow
452C25C22⋊D5912yes—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41C2×Dic5912yes—
464C2×#41C22⋊D5912yes—
465C22×Q8C22⋊D5911yescharacteristic
466C22×D4—21no—
467C22×D4—24no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—21no—
479C22×D4—21no—
480C22×D4C2×Dic5912yes—
481C22×D4C22⋊D5912yes—
482C22×D4C22⋊D5911yescharacteristic
483C23×C4—21no—
484C23×C4—1181no—
485C23×C4—1181no—
486C23×C4C22×D5911yescharacteristic
487C2×M16—592no—
488C2×M16—592no—
489C2×M16—1181no—
490C2×M16—1181no—
491C2×M16—1181no—
492C2×M16—1181no—
493C2×M16—1181no—
494C2×M16—1181no—
495C2×M16—1181no—
496C2×M16—1181no—
497C2×M16—1181no—
498C2×M16—1181no—
499C22×C8—1181no—
500C22×C8—1181no—
501#127—24no—
502#127—24no—
503#124—24no—
504#124—24no—
505#121—28no—
506#121—28no—
507#120—28no—
508#120—28no—
509#117—21no—
510#117—21no—
511#117C2×Dic5912yes—
512#117C22⋊D5912yes—
513C2×C4⋊C4—592no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4C22⋊D5912yes—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—1188no—
523C2×C22⋊C4—2368no—
524C2×C42—21no—
525C2×C42—592no—
526C2×C42—1181no—
527C2×C42—1181no—
528C2×C42—1181no—
529C2×C42—1181no—
530C2×C42—1181no—
531#104—1188no—
532#103—1184no—
533#102—1184no—
534#100—1188no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—44no—
543C24—44no—
544C24C22⋊Dic5914yes—
545C24C2×C22⋊D5911yescharacteristic
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8C22⋊Dic5912yescomplemented
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—216no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4—41no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—84no—
609C2×D4—84no—
610C2×D4C22⋊Dic5912yescomplemented
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—1184no—
620C22×C4—1182no—
621C22×C4—1182no—
622C22×C4—2364no—
623C22×C4—2361no—
624C22×C4—2361no—
625C22×C4—2362no—
626C22×C4—2361no—
627C22×C4—2361no—
628C22×C4D4×D5911yescharacteristic
629C22×C4D4×D5911yescharacteristic
630C22×C4D4×D5911yescharacteristic
631C22×C4D4×D5911yescharacteristic
632C22×C4#1174568711yescharacteristic
633C22×C4#1174568711yescharacteristic
634C22×C4#1174568711yescharacteristic
635C22×C4#1174568711yescharacteristic
636C22×C4C22×Dic5911yescharacteristic
637C22×C4C2×C22⋊D5911yescharacteristic
638C22×C4C2×C22⋊D5911yescharacteristic
639C22×C4C2×C22⋊D5911yescharacteristic
640C22×C4C2×C22⋊D5911yescharacteristic
641C22×C4C2×C22⋊D5911yescharacteristic
642M16—1182no—
643M16—1182no—
644M16—1182no—
645M16—1182no—
646M16—2361no—
647M16—2361no—
648M16—2361no—
649M16—2361no—
650C2×C8—1182no—
651C2×C8—1182no—
652C2×C8—2361no—
653C2×C8—2361no—
654C2×C8—2361no—
655C2×C8—2361no—
656C4⋊C4—22no—
657C4⋊C4—1182no—
658C4⋊C4—1182no—
659C4⋊C4—2361no—
660C4⋊C4—2361no—
661C4⋊C4C22⋊Dic5914yescomplemented
662C22⋊C4—216no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—23616no—
666C42—22no—
667C42—22no—
668C42—1182no—
669C42—1182no—
670C42—2361no—
671C42—2361no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—48no—
679C23—44no—
680C23—48no—
681C23—44no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—84no—
693C23—84no—
694C23—82no—
695C23—82no—
696C23C2×C22⋊Dic5911yescharacteristic
697C23#1427369511yescharacteristic
698C23#1427369611yescharacteristic
699C23#1427369611yescharacteristic
700C23#1427369911yescharacteristic
701C23#1427369911yescharacteristic
702C23#1427370811yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—42no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
719D4—41no—
720D4—42no—
721D4—42no—
722D4—41no—
723D4—816no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—1184no—
735C2×C4—4722no—
736C2×C4—4722no—
737C2×C4—2364no—
738C2×C4—2362no—
739C2×C4—2364no—
740C2×C4—2364no—
741C2×C4—2362no—
742C2×C4—2362no—
743C2×C4C2×C22⋊Dic5911yescharacteristic
744C2×C4C2×C22⋊Dic5911yescharacteristic
745C2×C4D4×Dic5911yescharacteristic
746C2×C4D4×Dic5911yescharacteristic
747C2×C4D4×Dic5911yescharacteristic
748C2×C4D4×Dic5911yescharacteristic
749C2×C4#1427369511yescharacteristic
750C2×C4#1427369511yescharacteristic
751C2×C4#1427369511yescharacteristic
752C2×C4#1427369611yescharacteristic
753C2×C4#1427369611yescharacteristic
754C2×C4#1427369811yescharacteristic
755C2×C4#1427369811yescharacteristic
756C2×C4#1427369811yescharacteristic
757C2×C4#1427369811yescharacteristic
758C2×C4#1427369911yescharacteristic
759C2×C4#1427369911yescharacteristic
760C2×C4#1427369911yescharacteristic
761C2×C4#1427369911yescharacteristic
762C2×C4#1427369911yescharacteristic
763C2×C4#1427369911yescharacteristic
764C2×C4#1427370811yescharacteristic
765C2×C4#1427370811yescharacteristic
766C2×C4#1427370811yescharacteristic
767C2×C4#1427371411yescharacteristic
768C2×C4#1427371411yescharacteristic
769C2×C4#1427372311yescharacteristic
770C2×C4#1427372311yescharacteristic
771C8—2362no—
772C8—2362no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—22no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—21no—
781C22—48no—
782C22—42no—
783C22—44no—
784C22—44no—
785C22—48no—
786C22—84no—
787C22—84no—
788C22—84no—
789C22—84no—
790C22—82no—
791C22—82no—
792C22—81no—
793C22—82no—
794C22—81no—
795C22#1683725811yescharacteristic
796C22#1683728211yescharacteristic
797C22#1683728211yescharacteristic
798C22#1683731011yescharacteristic
799C22#1683731011yescharacteristic
800C22#1683731611yescharacteristic
801C22#1683731611yescharacteristic
802C22#1683757012yes—
803C22#1683758012yes—
804C4—42no—
805C4—44no—
806C4—4722no—
807C4—2364no—
808C4#1683728211yescharacteristic
809C4#1683728211yescharacteristic
810C4#1683730511yescharacteristic
811C4#1683730511yescharacteristic
812C4#1683731011yescharacteristic
813C4#1683731011yescharacteristic
814C4#1683731611yescharacteristic
815C4#1683731611yescharacteristic
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—84no—
821C2—82no—
822C2#2142233711yescharacteristic
823C2#2142405012yes—
824C2#2142510911yescharacteristic
825C2#2142512311yescharacteristic
826C2#2142530312yes—
subgroupG/H
centerC23#14273696
commutatorC22×C4×C59C22×C4
FrattiniC23×C4C22×D59
Fitting, prime radicalC2×C59×#535C2
socleC23×C59#120
cosocleC23×C4×C59C23
hypercenterC2×#535D59
hypocenterC59#10997
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#14273654C2semidirect
2. C2×#16837403C2semidirect
3. C22×#14273644C2semidirect
4. C2×#16837305C2semidirect
5. #21423817C2semidirect
6. C2×#16837161C2semidirect
32. C59×#535C4semidirect
50. C2×#11745664D4semidirect
51. C2×#11745664D4semidirect
59. C2×C4⋊Dic59D4semidirect
67. C2×C4×Dic59D4semidirect
153. C2×Q8×C59C22⋊C4semidirect
196. C2×D4×C59C22⋊C4semidirect
229. C4⋊C4×C59C22⋊C4semidirect
428. #535Dic59semidirect
451. C59#10997semidirect
567. C2×Q8C22⋊Dic59semidirect
610. C2×D4C22⋊Dic59semidirect
661. C4⋊C4C22⋊Dic59semidirect

Maximal subgroups

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

subgroupindex
C22×#142736542
C2×#168374032
C22×#142736442
C2×#168373052
#214238172
C2×#168371612
C2×C59×#5352
#1099759