Finite Group Databasebeta

← #28645893

Subgroups — #28645893

Order 15104.

1162 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837699C211yesmaximal, characteristic, complemented
2C22×#14273647C211yesmaximal, characteristic
3C22⋊C4×D236C211yesmaximal, characteristic
4#21425620C211yesmaximal, characteristic, complemented
5#21425481C211yesmaximal, characteristic, complemented
6#21425467C211yesmaximal, characteristic, complemented
7#21425239C211yesmaximal, characteristic, complemented
8#21424356C211yesmaximal, characteristic, complemented
9#21424342C211yesmaximal, characteristic, complemented
10#21424284C211yesmaximal, characteristic, complemented
11#21424276C211yesmaximal, characteristic, complemented
12#21424119C211yesmaximal, characteristic, complemented
13#21424103C211yesmaximal, characteristic, complemented
14#21424026C211yesmaximal, characteristic
15C59×#2442C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×C4×D236C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×C22⋊C4×D59—21no—
21#16837699—24no—
22C2×#14273660C2211yescharacteristic, complemented
23C2×#14273660C2211yescharacteristic, complemented
24C2×#14273658C2211yescharacteristic, complemented
25C2×#14273658C2211yescharacteristic, complemented
26C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
27C2×C4⋊(C59⋊C8)C2211yescharacteristic, complemented
28C2×#14273647—24no—
29C2×#14273647C2211yescharacteristic
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×#14273647C2211yescharacteristic
37C2×C22⋊(C59⋊C8)C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837304C2211yescharacteristic
40#16837280—21no—
41#16837280—21no—
42#16837262C2211yescharacteristic
43#16837257—21no—
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837157C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50C2×#125×C59C2211yescharacteristic, complemented
51C22×C4⋊C4×C59C2211yescharacteristic
52C59×#400—21no—
53C59×#398—21no—
54C59×#389C2211yescharacteristic, complemented
55C59×#389C2211yescharacteristic, complemented
56C59×#385—21no—
57C59×#382C2211yescharacteristic, complemented
58C59×#380—21no—
59C59×#380C2211yescharacteristic
60C4×C22⋊C4×C59C2211yescharacteristic
61C24×D59—21no—
62C22×D236—22no—
63C22×D236—22no—
64C22×D236—21no—
65C22×D236—22no—
66C22×D236—41no—
67C22×D236—41no—
68C22×D236Q814yes—
69C22×D236C2311yescharacteristic
70C22×D236C2311yescharacteristic
71C22×C4×D59—21no—
72C22×C4×D59—21no—
73C22×C59⋊C8—22no—
74C22×C59⋊C8—22no—
75C22×C59⋊C8—41no—
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80C4×D236—22no—
81C4×D236—22no—
82C4×D236—41no—
83C4×D236—41no—
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C4⋊Dic59C2311yescharacteristic
86C2×C22⋊Dic59—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×(C2×D59)⋊C4—21no—
91C2×(C2×D59)⋊C4—21no—
92C2×(C2×D59)⋊C4—21no—
93C22⋊C4×D59—44no—
94#14273660—22no—
95#14273660—41no—
96#14273658—22no—
97#14273658—41no—
98C4⋊(C59⋊C8)—22no—
99C4⋊(C59⋊C8)—41no—
100#14273647—22no—
101#14273647—22no—
102#14273647—22no—
103#14273647—22no—
104#14273647—22no—
105#14273647—41no—
106#14273647—41no—
107#14273647D414yes—
108C22⋊(C59⋊C8)—22no—
109C59⋊#95—21no—
110C23×C4×C59—21no—
111C23×C4×C59C2311yescharacteristic
112#125×C59—22no—
113#125×C59—41no—
114C2×C4⋊C4×C59—22no—
115C2×C4⋊C4×C59—21no—
116C2×C4⋊C4×C59—21no—
117C2×C4⋊C4×C59—21no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59—21no—
120C2×C4⋊C4×C59—41no—
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C4⋊C4×C59C2311yescharacteristic
124C2×C4⋊C4×C59C2311yescharacteristic
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59D411yescharacteristic
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C42×C59C2311yescharacteristic
129C2×C42×C59C2311yescharacteristic
130#95×C59—21no—
131#95×C59—21no—
132#95×C59—21no—
133#95×C59—21no—
134#95×C59—21no—
135#95×C59D411yescharacteristic
136#95×C59D411yescharacteristic
137C24×C59C2×D411yescharacteristic
138C23×D59—21no—
139C23×D59—21no—
140C23×D59—24no—
141C23×D59—42no—
142C23×D59—42no—
143C23×D59—42no—
144C23×D59—42no—
145C23×D59—81no—
146C23×D59—81no—
147C22×C4×C59—21no—
148C22×C4×C59—21no—
149C22×C4×C59—21no—
150C22×C4×C59—21no—
151C22×C4×C59—21no—
152C22×C4×C59—21no—
153C22×C4×C59—21no—
154C22×C4×C59—21no—
155C22×C4×C59—42no—
156C22×C4×C59—42no—
157C22×C4×C59—81no—
158C22×C4×C59C2×D411yescharacteristic
159C22×C4×C59C2×D411yescharacteristic
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×Q812yes—
164C22×C4×C59#4112yes—
165C22×C4×C59C2411yescharacteristic
166C22×Dic59—21no—
167C22×Dic59—21no—
168C2×D236—21no—
169C2×D236—21no—
170C2×D236—21no—
171C2×D236—21no—
172C2×D236—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236—28no—
176C2×D236—24no—
177C2×D236—21no—
178C2×D236—44no—
179C2×D236—44no—
180C2×D236—44no—
181C2×D236—42no—
182C2×D236—42no—
183C2×D236C2×D412yes—
184C2×D236C2×Q812yes—
185C2×D236C2×Q812yes—
186C2×D236#4112yes—
187C2×C4×D59—42no—
188C2×C4×D59—42no—
189C2×C4×D59—42no—
190C2×C4×D59—42no—
191C2×C4×D59—81no—
192C2×C4×D59—81no—
193C4⋊C4×C59—21no—
194C4⋊C4×C59—21no—
195C4⋊C4×C59—21no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—42no—
201C4⋊C4×C59—42no—
202C4⋊C4×C59—42no—
203C4⋊C4×C59—81no—
204C4⋊C4×C59—81no—
205C4⋊C4×C59C2×D412yes—
206C22⋊C4×C59—22no—
207C22⋊C4×C59—22no—
208C22⋊C4×C59—42no—
209C42×C59—21no—
210C42×C59—21no—
211C42×C59—21no—
212C42×C59—21no—
213C22⋊Dic59—42no—
214(C2×D59)⋊C4—42no—
215(C2×D59)⋊C4—42no—
216(C2×D59)⋊C4—42no—
217(C2×D59)⋊C4—42no—
218(C2×D59)⋊C4—81no—
219(C2×D59)⋊C4—81no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8—21no—
227C2×C59⋊C8—21no—
228C2×C59⋊C8—21no—
229C2×C59⋊C8—21no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—44no—
236C2×C59⋊C8C2×D412yes—
237C23×C59—21no—
238C23×C59—21no—
239C23×C59—21no—
240C23×C59—21no—
241C23×C59C22⋊Q812yes—
242C23×C59#13512yes—
243C23×C59AGL(1,ℤ/8)12yes—
244C23×C59C22×D411yescharacteristic
245C22×D59—22no—
246C22×D59—22no—
247C22×D59—22no—
248C22×D59—22no—
249C22×D59—48no—
250C22×D59—41no—
251C22×D59—41no—
252C22×D59—41no—
253C22×D59—41no—
254C22×D59—41no—
255C22×D59—41no—
256C22×D59—41no—
257C22×D59—41no—
258C22×D59—41no—
259C22×D59—41no—
260C22×D59—48no—
261C22×D59—84no—
262C22×D59—84no—
263C22×D59—84no—
264C22×D59—84no—
265C22×D59—84no—
266C2×C4×C59—21no—
267C2×C4×C59—21no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—22no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—22no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—21no—
281C2×C4×C59—21no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59—41no—
290C2×C4×C59—41no—
291C2×C4×C59—41no—
292C2×C4×C59—41no—
293C2×C4×C59—41no—
294C2×C4×C59—41no—
295C2×C4×C59—41no—
296C2×C4×C59—84no—
297C2×C4×C59C22⋊Q812yes—
298C2×C4×C59C22×D411yescharacteristic
299C2×C4×C59C22×Q811yescharacteristic
300C2×C4×C59C2×#4111yescharacteristic
301C2×C4×C59C2×#4111yescharacteristic
302C2×C4×C59H(5,𝔽2)11yescharacteristic
303C2×C4×C59H(5,𝔽2)11yescharacteristic
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310D236—22no—
311D236—22no—
312D236—22no—
313D236—22no—
314D236—22no—
315D236—48no—
316D236—41no—
317D236—41no—
318D236C22⋊Q814yes—
319C4×D59—84no—
320C4×D59—84no—
321C59⋊C8—22no—
322C59⋊C8—41no—
323C59⋊C8—41no—
324C59⋊C8—41no—
325#25960—591nomaximal, Sylow
326C22×C59—22no—
327C22×C59—22no—
328C22×C59—22no—
329C22×C59—22no—
330C22×C59—22no—
331C22×C59—22no—
332C22×C59#47814yescomplemented
333C22×C59C2×C22⋊Q811yescharacteristic
334C22×C59D4211yescharacteristic
335C22×C59#54611yescharacteristic
336C22×C59C2×#13511yescharacteristic
337C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
338C22×C59#57611yescharacteristic
339C22×C59#57711yescharacteristic
340C2×D59—24no—
341C2×D59—42no—
342C2×D59—42no—
343C2×D59—42no—
344C2×D59—42no—
345C2×D59—42no—
346C2×D59—42no—
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—816no—
351C2×D59—81no—
352C2×D59—81no—
353C2×D59—81no—
354C2×D59—81no—
355C4×C59—22no—
356C4×C59—41no—
357C4×C59—42no—
358C4×C59—41no—
359C4×C59—41no—
360C4×C59—41no—
361C4×C59—81no—
362C4×C59—81no—
363C4×C59—81no—
364C4×C59C2×C22⋊Q811yescharacteristic
365C4×C59#54311yescharacteristic
366C4×C59#54611yescharacteristic
367C4×C59#55111yescharacteristic
368Dic59—81no—
369Dic59—81no—
370C2×#478—591no—
371C22×#102—591no—
372#2442D5911yescharacteristic, complemented
373D4×C22⋊C4—591no—
374#2092—591no—
375#2067—591no—
376#2065—591no—
377#2025—591no—
378#1864—591no—
379#1862—591no—
380#1852—591no—
381#1850—591no—
382#1807—591no—
383#1804—591no—
384#1786—591no—
385C2×C59—24no—
386C2×C59#243711yescharacteristic
387C2×C59C2×#47811yescharacteristic
388C2×C59#308111yescharacteristic
389C2×C59#326411yescharacteristic
390C2×C59#328211yescharacteristic
391C2×C59#329711yescharacteristic
392C2×C59#331011yescharacteristic
393D59—44no—
394D59—82no—
395C23×D4—591no—
396C23×C8—591no—
397C2×#125C2×D5911yescharacteristic, complemented
398C2×C4×D4—591no—
399C2×C4×D4—591no—
400C22×C4⋊C4C2×D5911yescharacteristic
401C22×C22⋊C4—1181no—
402#478—1184no—
403C2×#107—591no—
404C2×#107—591no—
405C2×#106—591no—
406C2×#106—591no—
407C2×C4⋊C8—591no—
408C2×C4⋊C8—591no—
409C2×#102—591no—
410C2×#102—591no—
411C2×#102—591no—
412C2×#102—591no—
413C2×#102—591no—
414C2×#102—591no—
415C2×#102—591no—
416C2×#102—591no—
417C2×#102—1184no—
418C2×C22⋊C8—591no—
419#400—21no—
420#398—21no—
421#390—591no—
422#390—591no—
423#389C2×D5911yescharacteristic, complemented
424#389C2×D5911yescharacteristic, complemented
425#386—1181no—
426#386—1181no—
427#385—21no—
428#382C2×D5911yescharacteristic, complemented
429#380—21no—
430#380—591no—
431#380C2×D5911yescharacteristic
432#379—1181no—
433C4×C22⋊C4C2×D5911yescharacteristic
434#340—591no—
435#340—591no—
436#340—591no—
437#340—591no—
438#336—591no—
439#336—591no—
440C59#2596011yescharacteristic, complemented, Sylow
441C25—1181no—
442C22×D4—594no—
443C22×D4—591no—
444C22×D4—591no—
445C22×D4—1182no—
446C22×D4—1182no—
447C22×D4—1182no—
448C22×D4—1181no—
449C22×D4—2361no—
450C22×D4—2361no—
451C23×C4—21no—
452C23×C4—1181no—
453C23×C4—1181no—
454C23×C4C22×D5911yescharacteristic
455C22×C8—591no—
456C22×C8—591no—
457C22×C8—591no—
458C22×C8—591no—
459C22×C8—1182no—
460C22×C8—1182no—
461C22×C8—2361no—
462#125—22no—
463#125—41no—
464C4×D4—1182no—
465C4×D4—1182no—
466C4×D4—2361no—
467C4×D4—2361no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—41no—
475C2×C4⋊C4—591no—
476C2×C4⋊C4—591no—
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C4⋊C4C22×D5911yescharacteristic
479C2×C4⋊C4C22×D5911yescharacteristic
480C2×C4⋊C4C22×D5911yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4—1181no—
487C2×C22⋊C4—1181no—
488C2×C22⋊C4—1181no—
489C2×C22⋊C4—2364no—
490C2×C22⋊C4C22⋊D5911yescharacteristic
491C2×C22⋊C4C22⋊D5911yescharacteristic
492C2×C42C22×D5911yescharacteristic
493C2×C42C22×D5911yescharacteristic
494#107—1182no—
495#107—2361no—
496#106—1182no—
497#106—2361no—
498C4⋊C8—1182no—
499C4⋊C8—2361no—
500#102—594no—
501#102—1182no—
502#102—1182no—
503#102—1182no—
504#102—1182no—
505#102—1182no—
506#102—2361no—
507#102—2361no—
508C22⋊C8—1182no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—1181no—
515#95C22⋊D5911yescharacteristic
516#95C22⋊D5911yescharacteristic
517C24—1181no—
518C24—1184no—
519C24—1181no—
520C24—4721no—
521C24—4721no—
522C24—2362no—
523C24—2362no—
524C24—2362no—
525C24—2362no—
526C24C2×C22⋊D5911yescharacteristic
527C2×D4—592no—
528C2×D4—592no—
529C2×D4—592no—
530C2×D4—592no—
531C2×D4—1188no—
532C2×D4—1184no—
533C2×D4—1181no—
534C2×D4—1181no—
535C2×D4—1181no—
536C2×D4—1181no—
537C2×D4—1181no—
538C2×D4—1181no—
539C2×D4—1181no—
540C2×D4—1181no—
541C2×D4—2364no—
542C2×D4—2364no—
543C2×D4—2364no—
544C2×D4—2362no—
545C2×D4—2362no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—81no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—4721no—
560C22×C4—4721no—
561C22×C4—2362no—
562C22×C4—2362no—
563C22×C4—2362no—
564C22×C4—2362no—
565C22×C4Q8×D5912yes—
566C22×C4#1174568912yes—
567C22×C4C2×C22⋊D5911yescharacteristic
568C22×C4C2×C22⋊D5911yescharacteristic
569C22×C4C2×C22⋊D5911yescharacteristic
570C22×C4C2×C22⋊D5911yescharacteristic
571C22×C4C2×C22⋊D5911yescharacteristic
572C22×C4C23×D5911yescharacteristic
573C2×C8—592no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8—2364no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—81no—
597C4⋊C4—81no—
598C4⋊C4—1181no—
599C4⋊C4—1181no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4D4×D5912yes—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—42no—
606C22⋊C4—4721no—
607C22⋊C4—4721no—
608C22⋊C4—2362no—
609C22⋊C4—2362no—
610C22⋊C4—2362no—
611C22⋊C4—2362no—
612C22⋊C4—2362no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—1182no—
622C23—1182no—
623C23—1182no—
624C23—1182no—
625C23—4724no—
626C23—4724no—
627C23—4724no—
628C23—4724no—
629C23—4724no—
630C23—2368no—
631C23—2361no—
632C23—2361no—
633C23—2361no—
634C23—2361no—
635C23—2368no—
636C23—2361no—
637C23—2361no—
638C23—2361no—
639C23—2361no—
640C23—2361no—
641C23—2361no—
642C23#1427370312yes—
643C23#1427374712yes—
644C23#1427375212yes—
645C23C22×C22⋊D5911yescharacteristic
646D4—594no—
647D4—1182no—
648D4—1182no—
649D4—1182no—
650D4—1182no—
651D4—1182no—
652D4—2368no—
653D4—2361no—
654D4—2361no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—84no—
686C2×C4—4724no—
687C2×C4—4724no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4#1427370312yes—
695C2×C4C2×D4×D5911yescharacteristic
696C2×C4C2×Q8×D5911yescharacteristic
697C2×C4#41×D5911yescharacteristic
698C2×C4C2×#1174568911yescharacteristic
699C2×C4#1427377211yescharacteristic
700C2×C4#1427377311yescharacteristic
701C8—1182no—
702C8—2361no—
703C8—2361no—
704C8—2361no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—1184no—
712C22—47216no—
713C22—4721no—
714C22—4721no—
715C22—4721no—
716C22—4721no—
717C22—2362no—
718C22—2362no—
719C22—2362no—
720C22—2362no—
721C22—2362no—
722C22—2362no—
723C22—2362no—
724C22—2362no—
725C22—2362no—
726C22#1683769914yescomplemented
727C22C2×#1427370311yescharacteristic
728C22D4×C22⋊D5911yescharacteristic
729C22#1683804011yescharacteristic
730C22C2×#1427374711yescharacteristic
731C22C2×#1427375211yescharacteristic
732C22#1683820511yescharacteristic
733C22#1683821011yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—4721no—
744C4—4721no—
745C4C22⋊Q8×D5911yescharacteristic
746C4#1683802711yescharacteristic
747C4#1683804311yescharacteristic
748C4#1683807911yescharacteristic
749C2—24no—
750C2—4722no—
751C2—2364no—
752C2#2142775911yescharacteristic
753C2C2×#1683769911yescharacteristic
754C2#2143392111yescharacteristic
755C2#2143557711yescharacteristic
756C2#2143580411yescharacteristic
757C2#2143594011yescharacteristic
758C2#2143611111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2442C2
socleC23×C59C22×D4
prime radicalC23×D236C22
hypercenter#2442D59
hypocenterC59#25960
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#16837699C2semidirect
4. #21425620C2semidirect
5. #21425481C2semidirect
6. #21425467C2semidirect
7. #21425239C2semidirect
8. #21424356C2semidirect
9. #21424342C2semidirect
10. #21424284C2semidirect
11. #21424276C2semidirect
12. #21424119C2semidirect
13. #21424103C2semidirect
15. C59×#2442C2semidirect
22. C2×#14273660C22semidirect
23. C2×#14273660C22semidirect
24. C2×#14273658C22semidirect
25. C2×#14273658C22semidirect
26. C2×C4⋊(C59⋊C8)C22semidirect
27. C2×C4⋊(C59⋊C8)C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837157C22semidirect
49. #16837157C22semidirect
50. C2×#125×C59C22semidirect
54. C59×#389C22semidirect
55. C59×#389C22semidirect
57. C59×#382C22semidirect
332. C22×C59#478semidirect
372. #2442D59semidirect
397. C2×#125C2×D59semidirect
423. #389C2×D59semidirect
424. #389C2×D59semidirect
428. #382C2×D59semidirect
440. C59#25960semidirect
726. C22#16837699semidirect

Maximal subgroups

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

subgroupindex
C2×#168376992
C22×#142736472
C22⋊C4×D2362
#214256202
#214254812
#214254672
#214252392
#214243562
#214243422
#214242842
#214242762
#214241192
#214241032
#214240262
C59×#24422
#2596059