Finite Group Databasebeta

← #28586488

Subgroups — #28586488

Order 15104.

1598 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×#16837884C211yesmaximal, characteristic
2C2×#16837402C211yesmaximal, characteristic
3C2×#16837397C211yesmaximal, characteristic
4C2×#16837356C211yesmaximal, characteristic, complemented
5#21426450C211yesmaximal, characteristic, complemented
6#21423928C211yesmaximal, characteristic, complemented
7#21423926C211yesmaximal, characteristic, complemented
8#21423924C211yesmaximal, characteristic, complemented
9#21423920C211yesmaximal, characteristic, complemented
10#103×Dic59C211yesmaximal, characteristic, complemented
11C4×#14273649C211yesmaximal, characteristic, complemented
12#21423910C211yesmaximal, characteristic, complemented
13#21423814C211yesmaximal, characteristic, complemented
14#340×D59C211yesmaximal, characteristic, complemented
15C4×#103×C59C211yesmaximal, characteristic, complemented
16C22×#11745689C2211yescharacteristic
17C22×#11745659C2211yescharacteristic
18C22×C8×D59C2211yescharacteristic
19#16837884—24no—
20#16837884C418yescomplemented
21C2×Q8×Dic59C2211yescharacteristic
22C2×C4×D236—21no—
23C2×C4×D236C2211yescharacteristic
24C2×#14273689—21no—
25C2×#14273689C2211yescharacteristic
26C2×#14273685C2211yescharacteristic
27C2×#14273684—21no—
28C2×#14273684C2211yescharacteristic
29C2×C4⋊C4×D59—21no—
30C2×C4⋊C4×D59C2211yescharacteristic
31C2×C4⋊C4×D59C2211yescharacteristic
32#16837402C418yescomplemented
33#16837397C418yescomplemented
34C2×#14273651C2211yescharacteristic
35C2×#14273651C2211yescharacteristic
36C2×#14273649C2211yescharacteristic
37C2×#14273649C2211yescharacteristic
38C2×#14273647C2211yescharacteristic
39C2×#14273647C2211yescharacteristic
40#16837356—24no—
41C2×#14273638C2211yescharacteristic
42C2×#14273637C2211yescharacteristic
43C2×C8×Dic59C2211yescharacteristic
44C4⋊C4×Dic59C2211yescharacteristic
45C4⋊C4×Dic59C2211yescharacteristic
46C4×Dic59⋊C4—21no—
47C4×C4⋊Dic59C2211yescharacteristic
48#16837253—21no—
49C4×(C2×D59)⋊C4—21no—
50#16837249—21no—
51#16837165C2211yescharacteristic
52#16837165C2211yescharacteristic
53#16837164C2211yescharacteristic
54#16837164C2211yescharacteristic
55#16837164C2211yescharacteristic
56#16837164C2211yescharacteristic
57C2×C4×Q8×C59C2211yescharacteristic
58C2×#103×C59C2211yescharacteristic
59C2×#103×C59C2211yescharacteristic
60C2×C4×C8×C59C2211yescharacteristic
61C4×C4⋊C4×C59C2211yescharacteristic
62C59×#340C2211yescharacteristic
63C59×#340C2211yescharacteristic
64C2×#11745689—22no—
65C2×#11745689—22no—
66C2×#11745689—22no—
67C2×#11745689C2×C414yes—
68C2×#11745689C2×C414yes—
69C2×#11745689C2×C414yes—
70C22×D236—21no—
71C22×D236C2311yescharacteristic
72C22×C4×D59—21no—
73C22×C4×D59—21no—
74C22×C4×D59—21no—
75C22×C4×D59—21no—
76C22×C4×D59—21no—
77C22×C4×D59C2311yescharacteristic
78C2×#11745659—22no—
79C2×#11745659—22no—
80C2×#11745659C2×C414yescomplemented
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C2×C8×D59—22no—
84C2×C8×D59—22no—
85C2×C8×D59C2×C414yescomplemented
86Q8×Dic59—22no—
87Q8×Dic59C2×C414yescomplemented
88C4×D236—22no—
89C4×D236—28no—
90C4×D236C2×C414yescomplemented
91#14273689—28no—
92#14273689—22no—
93#14273689C2×C414yescomplemented
94#14273685—22no—
95#14273685C2×C414yescomplemented
96#14273684—28no—
97#14273684C2×C414yes—
98#14273684D414yes—
99C2×C4⋊Dic59—21no—
100C2×C4⋊Dic59C2311yescharacteristic
101C2×C4⋊Dic59C2311yescharacteristic
102C2×C4⋊Dic59C2311yescharacteristic
103C2×Dic59⋊C4—21no—
104C2×Dic59⋊C4—21no—
105C2×Dic59⋊C4D411yescharacteristic
106C2×Dic59⋊C4D411yescharacteristic
107C4⋊C4×D59—22no—
108C4⋊C4×D59—22no—
109C4⋊C4×D59—28no—
110C4⋊C4×D59C2×C414yes—
111C4⋊C4×D59C2×C414yescomplemented
112C2×(C2×D59)⋊C4—21no—
113C2×(C2×D59)⋊C4—21no—
114C2×(C2×D59)⋊C4—21no—
115C2×(C2×D59)⋊C4D411yescharacteristic
116C2×(C2×D59)⋊C4D411yescharacteristic
117C2×C4×Dic59—21no—
118C2×C4×Dic59—21no—
119C2×C4×Dic59—21no—
120C2×C4×Dic59—21no—
121C2×C4×Dic59—21no—
122C2×C4×Dic59C2311yescharacteristic
123#14273651C2×C414yescomplemented
124#14273651C2×C414yescomplemented
125#14273649C2×C414yescomplemented
126#14273649C2×C414yescomplemented
127#14273647C2×C414yescomplemented
128#14273647C2×C414yescomplemented
129#14273638—22no—
130#14273637—22no—
131C8×Dic59—22no—
132C59⋊#95—21no—
133C59⋊#95—21no—
134C59⋊#95—21no—
135C22×Q8×C59C2311yescharacteristic
136C22×C8×C59C2311yescharacteristic
137C22×C8×C59C2311yescharacteristic
138C4×Q8×C59—22no—
139C4×Q8×C59C2×C414yescomplemented
140C2×C4⋊C4×C59—21no—
141C2×C4⋊C4×C59C2311yescharacteristic
142C2×C4⋊C4×C59C2311yescharacteristic
143C2×C4⋊C4×C59C2311yescharacteristic
144C2×C42×C59—21no—
145C2×C42×C59—21no—
146C2×C42×C59C2311yescharacteristic
147#103×C59C2×C414yescomplemented
148#103×C59C2×C414yescomplemented
149C4×C8×C59—22no—
150#95×C59—21no—
151C23×D59—21no—
152C23×D59C2×D411yescharacteristic
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59C22×C412yes—
157C2×Q8×C59C22×C412yes—
158C2×Q8×C59C22×C412yes—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59C2411yescharacteristic
166C22×Dic59—21no—
167C22×Dic59—21no—
168C22×Dic59—21no—
169C22×Dic59C2×D411yescharacteristic
170C22×Dic59C2×D411yescharacteristic
171C22×Dic59C2×D411yescharacteristic
172#11745689—28no—
173#11745689—28no—
174#11745689—28no—
175#11745689C42116yescomplemented
176C2×D236—24no—
177C2×D236—24no—
178C2×D236—24no—
179C2×D236—21no—
180C2×D236—21no—
181C2×D236—21no—
182C2×D236C22×C412yes—
183C2×D236C22×C412yes—
184C2×D236C22×C412yes—
185C2×C4×D59—24no—
186C2×C4×D59—24no—
187C2×C4×D59—24no—
188C2×C4×D59—24no—
189C2×C4×D59—24no—
190C2×C4×D59—24no—
191C2×C4×D59—24no—
192C2×C4×D59—81no—
193C2×C4×D59—81no—
194C2×C4×D59—81no—
195C2×C4×D59—81no—
196C2×C4×D59—81no—
197C2×C4×D59—81no—
198C2×C4×D59—81no—
199C2×C4×D59—81no—
200C2×C4×D59C22×C412yes—
201C2×C4×D59C22×C412yes—
202C2×C4×D59C22×C412yes—
203C2×C4×D59C2×D412yes—
204C2×C4×D59#4112yes—
205C2×C4×D59#4112yes—
206C2×C8×C59—21no—
207C2×C8×C59—21no—
208C2×C8×C59—21no—
209C2×C8×C59—21no—
210C2×C8×C59C22×C412yes—
211C2×C8×C59C22×C412yes—
212C4⋊C4×C59—24no—
213C4⋊C4×C59—21no—
214C4⋊C4×C59—21no—
215C4⋊C4×C59—21no—
216C4⋊C4×C59C22×C412yes—
217C4⋊C4×C59C22×C412yes—
218C4⋊C4×C59C22×C412yes—
219C42×C59—24no—
220C42×C59—81no—
221C42×C59C22×C412yes—
222C42×C59C2×D412yes—
223(C2×D59)⋊C4—24no—
224(C2×D59)⋊C4—24no—
225(C2×D59)⋊C4—24no—
226(C2×D59)⋊C4C22⋊C414yes—
227(C2×D59)⋊C4C22⋊C414yes—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230C4⋊Dic59—21no—
231C4⋊Dic59—24no—
232C4⋊Dic59C22×C412yes—
233C4⋊Dic59C22×C412yes—
234C4⋊Dic59C22×C412yes—
235Dic59⋊C4—24no—
236Dic59⋊C4—24no—
237Dic59⋊C4C22⋊C414yes—
238Dic59⋊C4C22⋊C414yes—
239C4×Dic59—24no—
240C4×Dic59—24no—
241C4×Dic59—81no—
242C4×Dic59—81no—
243C4×Dic59—81no—
244C4×Dic59C22×C412yes—
245C4×Dic59C2×D412yes—
246C2×C59⋊C8—21no—
247C2×C59⋊C8—21no—
248C2×C59⋊C8—21no—
249C2×C59⋊C8—21no—
250C2×C59⋊C8C22×C412yes—
251C2×C59⋊C8C22×C412yes—
252#11745659—28no—
253C8×D59—28no—
254C23×C59C22×D411yescharacteristic
255C22×D59—21no—
256C22×D59—21no—
257C22×D59—21no—
258C22×D59—21no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—22no—
262C22×D59—41no—
263C22×D59—41no—
264C22×D59—41no—
265C22×D59—41no—
266C22×D59C2×C22⋊C412yes—
267C22×D59C4×D412yes—
268C22×D59C4×D412yes—
269Q8×C59—22no—
270Q8×C59—22no—
271Q8×C59—22no—
272Q8×C59C2×C4214yes—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—22no—
276C2×C4×C59—21no—
277C2×C4×C59—21no—
278C2×C4×C59—21no—
279C2×C4×C59—21no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—22no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—41no—
289C2×C4×C59C2×C22⋊C412yes—
290C2×C4×C59C2×C22⋊C412yes—
291C2×C4×C59C23×C411yescharacteristic
292C2×C4×C59C23×C411yescharacteristic
293C2×C4×C59C23×C411yescharacteristic
294C2×C4×C59C22×D411yescharacteristic
295C2×C4×C59C2×#4111yescharacteristic
296C2×C4×C59C2×#4111yescharacteristic
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—22no—
302C2×Dic59—22no—
303C2×Dic59—22no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59C2×C22⋊C412yes—
311C2×Dic59C2×C22⋊C412yes—
312C2×Dic59C2×C22⋊C412yes—
313C2×Dic59C4×D412yes—
314C2×Dic59C4×D412yes—
315D236—216no—
316D236—22no—
317D236—22no—
318D236—22no—
319D236C2×C4214yes—
320C4×D59—216no—
321C4×D59—84no—
322C4×D59—84no—
323C4×D59—84no—
324C4×D59—84no—
325C4×D59C2×C4214yes—
326C4×D59#11714yes—
327C4×D59C4×D414yes—
328C4×D59C4×D414yes—
329C8×C59—22no—
330C8×C59—22no—
331C59⋊C8—22no—
332C59⋊C8—22no—
333#20415—591nomaximal, Sylow
334C22×C59C22×C22⋊C411yescharacteristic
335C22×C59C2×C4×D411yescharacteristic
336C22×C59C2×C4×D411yescharacteristic
337C22×C59#57611yescharacteristic
338C22×C59#57711yescharacteristic
339C22×C59#57711yescharacteristic
340C22×C59#57811yescharacteristic
341C2×D59—22no—
342C2×D59—22no—
343C2×D59—22no—
344C2×D59—22no—
345C2×D59—22no—
346C2×D59—22no—
347C2×D59—24no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—42no—
351C2×D59—42no—
352C2×D59—42no—
353C2×D59—42no—
354C2×D59C4×C22⋊C414yes—
355C4×C59—22no—
356C4×C59—22no—
357C4×C59—24no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59—42no—
361C4×C59C22×C4211yescharacteristic
362C4×C59C2×#11711yescharacteristic
363C4×C59C2×C4×D411yescharacteristic
364C4×C59C2×C4×D411yescharacteristic
365Dic59—22no—
366Dic59—22no—
367Dic59—42no—
368Dic59—42no—
369Dic59—42no—
370Dic59C4×C22⋊C414yes—
371C2×#520—591no—
372C2×#417—591no—
373C2×#416—591no—
374C2×#405—591no—
375#2274—591no—
376#1763—591no—
377#1763—591no—
378#1762—591no—
379#1762—591no—
380C4×#103—591no—
381C4×#103D5911yescharacteristic, complemented
382C4×#102—591no—
383C4×#102—591no—
384#1736—591no—
385C2×#340—591no—
386C2×C59C2×C4×C22⋊C411yescharacteristic
387C2×C59#289711yescharacteristic
388C2×C59#289811yescharacteristic
389C2×C59#294611yescharacteristic
390C2×C59#294711yescharacteristic
391C2×C59#295111yescharacteristic
392C2×C59#295211yescharacteristic
393D59—24no—
394D59—44no—
395C22×#41—591no—
396C22×M16—591no—
397C23×C8—591no—
398#520—598no—
399#520—1184no—
400C2×C4×Q8—591no—
401C2×C4×Q8C2×D5911yescharacteristic
402C2×C4×D4—591no—
403C2×C4×D4—591no—
404C2×C4×D4—1181no—
405C2×C4×D4—1181no—
406C2×#117—591no—
407C2×#117—591no—
408C2×#117—1181no—
409C22×C4⋊C4—591no—
410C22×C4⋊C4—591no—
411C22×C4⋊C4—1181no—
412#417—598no—
413#416—598no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#103C2×D5911yescharacteristic
417C2×#103C2×D5911yescharacteristic
418C2×#102—591no—
419C2×#102—591no—
420C2×#102—591no—
421C2×#102—591no—
422#405—1184no—
423C2×#97—591no—
424C2×#97—591no—
425C2×C4×C8—591no—
426C2×C4×C8C2×D5911yescharacteristic
427C4×C4⋊C4—591no—
428C4×C4⋊C4—591no—
429C4×C4⋊C4—591no—
430C4×C4⋊C4—1181no—
431C4×C4⋊C4—1181no—
432C4×C4⋊C4C2×D5911yescharacteristic
433C4×C22⋊C4—1181no—
434C4×C22⋊C4—1181no—
435#340—591no—
436#340—591no—
437#340—591no—
438#340—591no—
439#340—591no—
440#340—591no—
441#340C2×D5911yescharacteristic
442#340C2×D5911yescharacteristic
443C59#2041511yescharacteristic, complemented, Sylow
444C2×#41—594no—
445C2×#41—594no—
446C2×#41—594no—
447C2×#41—1182no—
448C2×#41—1182no—
449C2×#41—1182no—
450C22×Q8C22×D5911yescharacteristic
451C22×D4—591no—
452C22×D4—1181no—
453C23×C4—591no—
454C23×C4—1181no—
455C23×C4—1181no—
456C23×C4—1181no—
457C23×C4—1181no—
458C23×C4—1181no—
459C2×M16—594no—
460C2×M16—1182no—
461C2×M16—1182no—
462C22×C8—591no—
463C22×C8—591no—
464C22×C8—594no—
465C22×C8—1182no—
466C22×C8—1182no—
467C22×C8C22×D5911yescharacteristic
468C22×C8C22×D5911yescharacteristic
469C4×Q8—22no—
470C4×Q8—594no—
471C4×Q8—1182no—
472C4×Q8C4×D5914yescomplemented
473C4×D4—594no—
474C4×D4—594no—
475C4×D4—1188no—
476C4×D4—1182no—
477C4×D4—1188no—
478C4×D4—1182no—
479#117—594no—
480#117—594no—
481#117—594no—
482#117—1188no—
483#117—1182no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—591no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—591no—
490C2×C4⋊C4—594no—
491C2×C4⋊C4—594no—
492C2×C4⋊C4—1188no—
493C2×C4⋊C4—1182no—
494C2×C4⋊C4—1182no—
495C2×C4⋊C4—1181no—
496C2×C4⋊C4—1181no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4C22×D5911yescharacteristic
499C2×C4⋊C4C22×D5911yescharacteristic
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C22⋊C4—591no—
502C2×C22⋊C4—591no—
503C2×C22⋊C4—1181no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—591no—
509C2×C42—1181no—
510C2×C42—1181no—
511C2×C42—1181no—
512C2×C42—1181no—
513C2×C42—1181no—
514C2×C42C22×D5911yescharacteristic
515#103—594no—
516#103—594no—
517#103C4×D5914yescomplemented
518#103C4×D5914yescomplemented
519#102—594no—
520#102—594no—
521#102—594no—
522#102—594no—
523#97—1182no—
524#97—1182no—
525C4×C8—22no—
526C4×C8—1182no—
527#95—21no—
528#95—1181no—
529#95—1181no—
530#95—1181no—
531C24—591no—
532C24—1181no—
533#41—5916no—
534#41—1188no—
535#41—1188no—
536#41—1188no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×C4×D5912yes—
541C2×Q8C2×C4×D5912yes—
542C2×Q8C2×C4×D5912yes—
543C2×D4—592no—
544C2×D4—592no—
545C2×D4—592no—
546C2×D4—1184no—
547C2×D4—1184no—
548C2×D4—1184no—
549C2×D4—1181no—
550C2×D4—1181no—
551C2×D4—1181no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—591no—
557C22×C4—592no—
558C22×C4—592no—
559C22×C4—592no—
560C22×C4—592no—
561C22×C4—592no—
562C22×C4—592no—
563C22×C4—591no—
564C22×C4—591no—
565C22×C4—1184no—
566C22×C4—1184no—
567C22×C4—1184no—
568C22×C4—1184no—
569C22×C4—1184no—
570C22×C4—1184no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4—1181no—
574C22×C4—1184no—
575C22×C4—4721no—
576C22×C4—4721no—
577C22×C4—4721no—
578C22×C4—4721no—
579C22×C4—4721no—
580C22×C4—4721no—
581C22×C4—4721no—
582C22×C4—4721no—
583C22×C4D4×D5911yescharacteristic
584C22×C4D4×D5911yescharacteristic
585C22×C4C23×D5911yescharacteristic
586M16—1188no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—592no—
592C2×C8—592no—
593C2×C8—1188no—
594C2×C8—1181no—
595C2×C8—1181no—
596C2×C8—1181no—
597C2×C8—1181no—
598C2×C8C2×C4×D5912yes—
599C2×C8C2×C4×D5912yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—594no—
605C4⋊C4—594no—
606C4⋊C4—592no—
607C4⋊C4—592no—
608C4⋊C4—592no—
609C4⋊C4—1184no—
610C4⋊C4—1184no—
611C4⋊C4—1184no—
612C4⋊C4—1181no—
613C4⋊C4—1181no—
614C4⋊C4—1181no—
615C4⋊C4C2×C4×D5912yes—
616C4⋊C4C2×C4×D5912yes—
617C4⋊C4C2×C4×D5912yes—
618C22⋊C4—594no—
619C22⋊C4—594no—
620C22⋊C4—1184no—
621C22⋊C4—1184no—
622C22⋊C4—1184no—
623C42—24no—
624C42—81no—
625C42—592no—
626C42—592no—
627C42—1184no—
628C42—1184no—
629C42—4721no—
630C42—4721no—
631C42—4721no—
632C42C2×C4×D5912yes—
633C42D4×D5912yes—
634C23—592no—
635C23—592no—
636C23—592no—
637C23—1181no—
638C23—1181no—
639C23—1181no—
640C23—1181no—
641C23—1182no—
642C23—1182no—
643C23—1182no—
644C23—2361no—
645C23—2361no—
646C23—2361no—
647C23—2361no—
648C23C2×D4×D5911yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8C42×D5914yes—
653D4—594no—
654D4—11816no—
655D4—1182no—
656D4—1182no—
657D4—1182no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—592no—
675C2×C4—592no—
676C2×C4—592no—
677C2×C4—594no—
678C2×C4—594no—
679C2×C4—594no—
680C2×C4—594no—
681C2×C4—592no—
682C2×C4—592no—
683C2×C4—11816no—
684C2×C4—1181no—
685C2×C4—1181no—
686C2×C4—1181no—
687C2×C4—1181no—
688C2×C4—1182no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—4724no—
692C2×C4—4724no—
693C2×C4—4724no—
694C2×C4—4724no—
695C2×C4—2361no—
696C2×C4—2361no—
697C2×C4—2361no—
698C2×C4—2361no—
699C2×C4—2361no—
700C2×C4—2361no—
701C2×C4C22⋊C4×D5912yes—
702C2×C4C22⋊C4×D5912yes—
703C2×C4C22×C4×D5911yescharacteristic
704C2×C4C22×C4×D5911yescharacteristic
705C2×C4C22×C4×D5911yescharacteristic
706C2×C4C2×D4×D5911yescharacteristic
707C2×C4#41×D5911yescharacteristic
708C2×C4#41×D5911yescharacteristic
709C8—22no—
710C8—22no—
711C8—1182no—
712C8—1182no—
713C22—594no—
714C22—1182no—
715C22—1182no—
716C22—1182no—
717C22—1182no—
718C22—1182no—
719C22—1182no—
720C22—1184no—
721C22—2362no—
722C22—2362no—
723C22—2362no—
724C22—2362no—
725C22—2362no—
726C22—2362no—
727C22C2×C22⋊C4×D5911yescharacteristic
728C22C4×D4×D5911yescharacteristic
729C22C4×D4×D5911yescharacteristic
730C22#1683820411yescharacteristic
731C22#1683820811yescharacteristic
732C22#1683820911yescharacteristic
733C22#1683821511yescharacteristic
734C4—22no—
735C4—22no—
736C4—24no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—594no—
741C4—1182no—
742C4—1182no—
743C4—2362no—
744C4—2362no—
745C4—2362no—
746C4C2×C42×D5911yescharacteristic
747C4#117×D5911yescharacteristic
748C4C4×D4×D5911yescharacteristic
749C4C4×D4×D5911yescharacteristic
750C2—1184no—
751C2—2364no—
752C2C4×C22⋊C4×D5911yescharacteristic
753C2#2143261811yescharacteristic
754C2#2143262411yescharacteristic
755C2#2143292311yescharacteristic
756C2#2143293411yescharacteristic
757C2#2143297111yescharacteristic
758C2#2143297411yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC4×#103×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745689C22
cosocleC22×C4×C59C24
hypercenterC4×#103D59
hypocenterC59#20415
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
4. C2×#16837356C2semidirect
5. #21426450C2semidirect
6. #21423928C2semidirect
7. #21423926C2semidirect
8. #21423924C2semidirect
9. #21423920C2semidirect
10. #103×Dic59C2semidirect
11. C4×#14273649C2semidirect
12. #21423910C2semidirect
13. #21423814C2semidirect
14. #340×D59C2semidirect
15. C4×#103×C59C2semidirect
20. #16837884C4semidirect
32. #16837402C4semidirect
33. #16837397C4semidirect
80. C2×#11745659C2×C4semidirect
85. C2×C8×D59C2×C4semidirect
87. Q8×Dic59C2×C4semidirect
90. C4×D236C2×C4semidirect
93. #14273689C2×C4semidirect
95. #14273685C2×C4semidirect
111. C4⋊C4×D59C2×C4semidirect
123. #14273651C2×C4semidirect
124. #14273651C2×C4semidirect
125. #14273649C2×C4semidirect
126. #14273649C2×C4semidirect
127. #14273647C2×C4semidirect
128. #14273647C2×C4semidirect
139. C4×Q8×C59C2×C4semidirect
147. #103×C59C2×C4semidirect
148. #103×C59C2×C4semidirect
175. #11745689C42semidirect
381. C4×#103D59semidirect
443. C59#20415semidirect
472. C4×Q8C4×D59semidirect
517. #103C4×D59semidirect
518. #103C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168378842
C2×#168374022
C2×#168373972
C2×#168373562
#214264502
#214239282
#214239262
#214239242
#214239202
#103×Dic592
C4×#142736492
#214239102
#214238142
#340×D592
C4×#103×C592
#2041559