Finite Group Databasebeta

← #28609397

Subgroups — #28609397

Order 15104.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837552C211yesmaximal, characteristic
2C2×C4×#11745671C211yesmaximal, characteristic, complemented
3C2×#16837406C211yesmaximal, characteristic
4C22⋊C4×D236C211yesmaximal, characteristic
5#21424980C211yesmaximal, characteristic, complemented
6#21424778C211yesmaximal, characteristic, complemented
7#21424723C211yesmaximal, characteristic, complemented
8#21424530C211yesmaximal, characteristic, complemented
9#21424451C211yesmaximal, characteristic, complemented
10#21424433C211yesmaximal, characteristic, complemented
11#21424342C211yesmaximal, characteristic, complemented
12#21424295C211yesmaximal, characteristic, complemented
13#21423924C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2362C211yesmaximal, characteristic, complemented
16C23×D236C2211yescharacteristic
17C22×#11745671C2211yescharacteristic
18C22×#11745671C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C2×C4×D236C2211yescharacteristic
21C2×C4×D236C2211yescharacteristic
22C2×C22⋊C4×D59—21no—
23#16837552C418yescomplemented
24C4×#11745671—24no—
25C2×#14273660C2211yescharacteristic, complemented
26C2×#14273658C2211yescharacteristic, complemented
27#16837406—24no—
28C2×#14273651C2211yescharacteristic, complemented
29C2×#14273651C2211yescharacteristic, complemented
30C2×#14273647C2211yescharacteristic
31C2×#14273647C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×#14273647C2211yescharacteristic
36C2×C22⋊(C59⋊C8)C2211yescharacteristic
37C2×#14273638C2211yescharacteristic, complemented
38C2×C4×C59⋊C8C2211yescharacteristic, complemented
39#16837304C2211yescharacteristic
40#16837304C2211yescharacteristic
41#16837280—21no—
42#16837280—21no—
43#16837262C2211yescharacteristic
44#16837257—21no—
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837164C2211yescharacteristic, complemented
48#16837164C2211yescharacteristic, complemented
49#16837157C2211yescharacteristic, complemented
50#16837157C2211yescharacteristic, complemented
51C2×C22⋊Q8×C59C2211yescharacteristic
52C2×C4×Q8×C59C2211yescharacteristic, complemented
53C2×#117×C59C2211yescharacteristic
54C59×#391C2211yescharacteristic, complemented
55C59×#389C2211yescharacteristic, complemented
56C59×#388—21no—
57C59×#388—21no—
58C59×#387—21no—
59C4×C4⋊C4×C59—21no—
60C4×C4⋊C4×C59C2211yescharacteristic, complemented
61C4×C22⋊C4×C59C2211yescharacteristic
62C24×D59—21no—
63C22×D236—22no—
64C22×D236—22no—
65C22×D236—21no—
66C22×D236—22no—
67C22×D236—41no—
68C22×D236—41no—
69C22×D236C2×C414yes—
70C22×D236C2311yescharacteristic
71C22×D236C2311yescharacteristic
72C22×C4×D59—21no—
73C22×C4×D59—21no—
74C2×#11745671—22no—
75C2×#11745671—22no—
76C2×#11745671—41no—
77C2×#11745671—41no—
78C2×#11745671C2×C414yes—
79C2×#11745671C2×C414yescomplemented
80C2×#11745664—22no—
81C2×#11745664—22no—
82C2×#11745664—41no—
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C22×C59⋊C8C2311yescharacteristic
86C22×C59⋊C8C2311yescharacteristic
87C4×D236—22no—
88C4×D236—22no—
89C4×D236—41no—
90C4×D236—41no—
91C2×C4⋊Dic59C2311yescharacteristic
92C2×C4⋊Dic59C2311yescharacteristic
93C2×C22⋊Dic59—21no—
94C2×(C2×D59)⋊C4—21no—
95C2×(C2×D59)⋊C4—21no—
96C2×(C2×D59)⋊C4—21no—
97C2×(C2×D59)⋊C4—21no—
98C2×(C2×D59)⋊C4—21no—
99C2×(C2×D59)⋊C4—21no—
100C22⋊C4×D59—44no—
101#14273660—41no—
102#14273658—22no—
103#14273651—22no—
104#14273651—41no—
105#14273647—22no—
106#14273647—22no—
107#14273647—22no—
108#14273647C2×C414yes—
109#14273647C2×C414yescomplemented
110#14273647D414yes—
111C22⋊(C59⋊C8)C2×C414yescomplemented
112#14273638—41no—
113C4×C59⋊C8—22no—
114C59⋊#95—21no—
115C22×Q8×C59C2311yescharacteristic
116C23×C4×C59C2311yescharacteristic
117C22⋊Q8×C59—22no—
118C22⋊Q8×C59C2×C414yescomplemented
119C4×Q8×C59—22no—
120C4×Q8×C59—41no—
121#117×C59—22no—
122#117×C59—41no—
123C2×C4⋊C4×C59—21no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59—21no—
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C4⋊C4×C59C2311yescharacteristic
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59D411yescharacteristic
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C42×C59—21no—
134C2×C42×C59—21no—
135C2×C42×C59—21no—
136C2×C42×C59C2311yescharacteristic
137C2×C42×C59C2311yescharacteristic
138#95×C59—21no—
139#95×C59—21no—
140#95×C59—21no—
141#95×C59—21no—
142#95×C59D411yescharacteristic
143#95×C59D411yescharacteristic
144C24×C59C2×D411yescharacteristic
145C23×D59—21no—
146C23×D59—21no—
147C23×D59—24no—
148C23×D59—42no—
149C23×D59—42no—
150C23×D59—42no—
151C23×D59—42no—
152C23×D59—81no—
153C23×D59—81no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59—21no—
157C2×Q8×C59—21no—
158C2×Q8×C59—21no—
159C2×Q8×C59C22×C412yes—
160C22×C4×C59—21no—
161C22×C4×C59—21no—
162C22×C4×C59—21no—
163C22×C4×C59—21no—
164C22×C4×C59—21no—
165C22×C4×C59—21no—
166C22×C4×C59—21no—
167C22×C4×C59—21no—
168C22×C4×C59C22×C412yes—
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2×D411yescharacteristic
172C22×C4×C59C2×D411yescharacteristic
173C22×C4×C59C2×D411yescharacteristic
174C22×C4×C59#4112yes—
175C22×C4×C59C2411yescharacteristic
176C22×Dic59—21no—
177C22×Dic59—21no—
178C2×D236—21no—
179C2×D236—21no—
180C2×D236—21no—
181C2×D236—21no—
182C2×D236—21no—
183C2×D236—21no—
184C2×D236—21no—
185C2×D236—28no—
186C2×D236—24no—
187C2×D236—21no—
188C2×D236—44no—
189C2×D236—44no—
190C2×D236—44no—
191C2×D236—42no—
192C2×D236—42no—
193C2×D236C22×C412yes—
194C2×D236C22×C412yes—
195C2×D236C2×D412yes—
196C2×D236#4112yes—
197C2×C4×D59—42no—
198C2×C4×D59—42no—
199C2×C4×D59—42no—
200C2×C4×D59—42no—
201C2×C4×D59—81no—
202C2×C4×D59—81no—
203C4⋊C4×C59—24no—
204C4⋊C4×C59—21no—
205C4⋊C4×C59—21no—
206C4⋊C4×C59—21no—
207C4⋊C4×C59—21no—
208C4⋊C4×C59—42no—
209C4⋊C4×C59—42no—
210C4⋊C4×C59C22×C412yes—
211C4⋊C4×C59C2×D412yes—
212C22⋊C4×C59—24no—
213C22⋊C4×C59—22no—
214C22⋊C4×C59—41no—
215C22⋊C4×C59—42no—
216C42×C59—21no—
217C42×C59—21no—
218C42×C59—21no—
219C42×C59—21no—
220C42×C59—42no—
221C42×C59—42no—
222C42×C59—42no—
223C22⋊Dic59—42no—
224#11745671—28no—
225#11745671—44no—
226(C2×D59)⋊C4—42no—
227(C2×D59)⋊C4—42no—
228(C2×D59)⋊C4—42no—
229(C2×D59)⋊C4—42no—
230(C2×D59)⋊C4—81no—
231(C2×D59)⋊C4—81no—
232C4⋊Dic59—21no—
233C4⋊Dic59—21no—
234C4⋊Dic59—21no—
235C4⋊Dic59—21no—
236#11745664—44no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
241C2×C59⋊C8—21no—
242C2×C59⋊C8—21no—
243C2×C59⋊C8—21no—
244C2×C59⋊C8—21no—
245C2×C59⋊C8—21no—
246C2×C59⋊C8C22×C412yes—
247C2×C59⋊C8C22×C412yes—
248C2×C59⋊C8C2×D412yes—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59C4×D412yes—
256C23×C59C22×D411yescharacteristic
257C22×D59—22no—
258C22×D59—22no—
259C22×D59—22no—
260C22×D59—22no—
261C22×D59—48no—
262C22×D59—41no—
263C22×D59—41no—
264C22×D59—41no—
265C22×D59—41no—
266C22×D59—48no—
267C22×D59—41no—
268C22×D59—41no—
269C22×D59—41no—
270C22×D59—41no—
271C22×D59—41no—
272C22×D59—41no—
273C22×D59—84no—
274C22×D59—84no—
275C22×D59—84no—
276C22×D59—84no—
277C22×D59—84no—
278Q8×C59—22no—
279Q8×C59—22no—
280Q8×C59—41no—
281Q8×C59—41no—
282C2×C4×C59—21no—
283C2×C4×C59—21no—
284C2×C4×C59—21no—
285C2×C4×C59—21no—
286C2×C4×C59—22no—
287C2×C4×C59—22no—
288C2×C4×C59—22no—
289C2×C4×C59—22no—
290C2×C4×C59—22no—
291C2×C4×C59—22no—
292C2×C4×C59—21no—
293C2×C4×C59—22no—
294C2×C4×C59—21no—
295C2×C4×C59—21no—
296C2×C4×C59—21no—
297C2×C4×C59—21no—
298C2×C4×C59—21no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—21no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—41no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59C4×D412yes—
312C2×C4×C59AGL(1,ℤ/8)12yes—
313C2×C4×C59C23×C411yescharacteristic
314C2×C4×C59C22×D411yescharacteristic
315C2×C4×C59C2×#4111yescharacteristic
316C2×C4×C59C2×#4111yescharacteristic
317C2×C4×C59H(5,𝔽2)11yescharacteristic
318C2×C4×C59H(5,𝔽2)11yescharacteristic
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325D236—22no—
326D236—22no—
327D236—22no—
328D236—22no—
329D236—22no—
330D236—48no—
331D236—41no—
332D236—41no—
333D236C4×D414yes—
334C4×D59—84no—
335C4×D59—84no—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C59⋊C8—22no—
339C59⋊C8—41no—
340#22884—591nomaximal, Sylow
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59—41no—
348C22×C59C2×C4×D411yescharacteristic
349C22×C59D4211yescharacteristic
350C22×C59#54611yescharacteristic
351C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C59#57511yescharacteristic
353C22×C59#57711yescharacteristic
354C22×C59#57711yescharacteristic
355C2×D59—24no—
356C2×D59—42no—
357C2×D59—42no—
358C2×D59—42no—
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—42no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59—816no—
366C2×D59—81no—
367C2×D59—81no—
368C2×D59—81no—
369C2×D59—81no—
370C4×C59—22no—
371C4×C59—22no—
372C4×C59—42no—
373C4×C59—42no—
374C4×C59—41no—
375C4×C59—42no—
376C4×C59—41no—
377C4×C59—41no—
378C4×C59—81no—
379C4×C59C2×C4×D411yescharacteristic
380C4×C59#51811yescharacteristic
381C4×C59#54611yescharacteristic
382C4×C59#55111yescharacteristic
383Dic59—81no—
384Dic59—81no—
385C2×#450—591no—
386C2×C4×SD16—591no—
387C2×#418—591no—
388#2362D5911yescharacteristic, complemented
389D4×C22⋊C4—591no—
390#1973—591no—
391#1934—591no—
392#1926—591no—
393#1894—591no—
394#1880—591no—
395#1877—591no—
396#1862—591no—
397#1854—591no—
398#1762—591no—
399#1753—591no—
400C2×C59—42no—
401C2×C59#235811yescharacteristic
402C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C59#294911yescharacteristic
404C2×C59#326511yescharacteristic
405C2×C59#326711yescharacteristic
406C2×C59#332311yescharacteristic
407C2×C59#332411yescharacteristic
408D59—44no—
409D59—82no—
410C23×D4—591no—
411C22×SD16—591no—
412C22×SD16—591no—
413C22×M16—591no—
414C2×C22⋊Q8C2×D5911yescharacteristic
415C2×C4×Q8C2×D5911yescharacteristic, complemented
416C2×C4×D4—591no—
417C2×C4×D4—591no—
418C2×#117C2×D5911yescharacteristic
419C22×C22⋊C4—1181no—
420#450—598no—
421C4×SD16—1184no—
422C2×#107—591no—
423C2×#106—591no—
424#418—1184no—
425C2×#103—591no—
426C2×#103—591no—
427C2×#102—591no—
428C2×#102—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×C22⋊C8—591no—
434C2×#97—591no—
435C2×C4×C8—591no—
436#391C2×D5911yescharacteristic, complemented
437#390—591no—
438#390—591no—
439#389C2×D5911yescharacteristic, complemented
440#388—21no—
441#388—21no—
442#387—21no—
443#386—1181no—
444#386—1181no—
445#380—591no—
446#379—1181no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4C2×D5911yescharacteristic, complemented
449C4×C22⋊C4C2×D5911yescharacteristic
450#340—591no—
451#340—591no—
452#340—591no—
453#340—591no—
454#336—591no—
455#336—591no—
456C59#2288411yescharacteristic, complemented, Sylow
457C25—1181no—
458C22×Q8C22×D5911yescharacteristic
459C22×D4—594no—
460C22×D4—591no—
461C22×D4—591no—
462C22×D4—1182no—
463C22×D4—1182no—
464C22×D4—1182no—
465C22×D4—1181no—
466C22×D4—2361no—
467C22×D4—2361no—
468C23×C4—1181no—
469C23×C4—1181no—
470C23×C4C22×D5911yescharacteristic
471C2×SD16—594no—
472C2×SD16—594no—
473C2×SD16—1182no—
474C2×SD16—1182no—
475C2×SD16—2361no—
476C2×SD16—2361no—
477C2×M16—1182no—
478C2×M16—1182no—
479C2×M16—2361no—
480C22×C8—591no—
481C22×C8—591no—
482C22×C8—591no—
483C22×C8—591no—
484C22⋊Q8—22no—
485C22⋊Q8C4×D5914yescomplemented
486C4×Q8—22no—
487C4×Q8—41no—
488C4×D4—1182no—
489C4×D4—1182no—
490C4×D4—2361no—
491C4×D4—2361no—
492#117—22no—
493#117—41no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—591no—
498C2×C4⋊C4—591no—
499C2×C4⋊C4C22×D5911yescharacteristic
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C4⋊C4C22×D5911yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—1181no—
505C2×C22⋊C4—1181no—
506C2×C22⋊C4—1181no—
507C2×C22⋊C4—1181no—
508C2×C22⋊C4—1181no—
509C2×C22⋊C4—1181no—
510C2×C22⋊C4—1181no—
511C2×C22⋊C4—2364no—
512C2×C22⋊C4C22⋊D5911yescharacteristic
513C2×C22⋊C4C22⋊D5911yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42C22×D5911yescharacteristic
518C2×C42C22×D5911yescharacteristic
519#107—2361no—
520#106—1182no—
521#103—1182no—
522#103—2361no—
523#102—594no—
524#102—594no—
525#102—594no—
526#102—1182no—
527#102—1182no—
528#102—1182no—
529C22⋊C8—594no—
530#97—2361no—
531C4×C8—1182no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—1181no—
537#95C22⋊D5911yescharacteristic
538#95C22⋊D5911yescharacteristic
539C24—1181no—
540C24—1184no—
541C24—1181no—
542C24—4721no—
543C24—4721no—
544C24—2362no—
545C24—2362no—
546C24—2362no—
547C24—2362no—
548C24C2×C22⋊D5911yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8C2×C4×D5912yes—
555C2×D4—592no—
556C2×D4—592no—
557C2×D4—592no—
558C2×D4—592no—
559C2×D4—1188no—
560C2×D4—1184no—
561C2×D4—1181no—
562C2×D4—1181no—
563C2×D4—1181no—
564C2×D4—1181no—
565C2×D4—1181no—
566C2×D4—1181no—
567C2×D4—1181no—
568C2×D4—1181no—
569C2×D4—2364no—
570C2×D4—2364no—
571C2×D4—2364no—
572C2×D4—2362no—
573C2×D4—2362no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—1181no—
583C22×C4—1181no—
584C22×C4—4721no—
585C22×C4—4721no—
586C22×C4—2362no—
587C22×C4—2362no—
588C22×C4—2362no—
589C22×C4—2362no—
590C22×C4C2×C4×D5912yes—
591C22×C4#1174568512yes—
592C22×C4C2×C22⋊D5911yescharacteristic
593C22×C4C2×C22⋊D5911yescharacteristic
594C22×C4C2×C22⋊D5911yescharacteristic
595C22×C4C2×C22⋊D5911yescharacteristic
596C22×C4C2×C22⋊D5911yescharacteristic
597C22×C4C23×D5911yescharacteristic
598SD16—1188no—
599SD16—2364no—
600M16—2364no—
601C2×C8—592no—
602C2×C8—592no—
603C2×C8—592no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C2×C8—1181no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—42no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4C2×C4×D5912yes—
625C4⋊C4D4×D5912yes—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—41no—
629C22⋊C4—42no—
630C22⋊C4—4721no—
631C22⋊C4—4721no—
632C22⋊C4—2362no—
633C22⋊C4—2362no—
634C22⋊C4—2362no—
635C22⋊C4—2362no—
636C22⋊C4—2362no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—42no—
642C42—42no—
643C42—42no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—1182no—
651C23—1182no—
652C23—1182no—
653C23—1182no—
654C23—4724no—
655C23—4724no—
656C23—4724no—
657C23—4724no—
658C23—4724no—
659C23—2368no—
660C23—2368no—
661C23—2361no—
662C23—2361no—
663C23—2361no—
664C23—2361no—
665C23—2361no—
666C23—2361no—
667C23—2361no—
668C23—2361no—
669C23—2361no—
670C23—2361no—
671C23C4×C22⋊D5912yes—
672C23C22×C22⋊D5911yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677D4—594no—
678D4—1182no—
679D4—1182no—
680D4—1182no—
681D4—1182no—
682D4—1182no—
683D4—2368no—
684D4—2361no—
685D4—2361no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—22no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—4724no—
716C2×C4—4724no—
717C2×C4—2361no—
718C2×C4—2361no—
719C2×C4—2361no—
720C2×C4—2361no—
721C2×C4—2361no—
722C2×C4—2361no—
723C2×C4C4×C22⋊D5912yes—
724C2×C4#1427375212yes—
725C2×C4C22×C4×D5911yescharacteristic
726C2×C4C2×D4×D5911yescharacteristic
727C2×C4#41×D5911yescharacteristic
728C2×C4C2×#1174568511yescharacteristic
729C2×C4#1427377211yescharacteristic
730C2×C4#1427377311yescharacteristic
731C8—1182no—
732C8—1182no—
733C8—1182no—
734C8—2361no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—1184no—
743C22—47216no—
744C22—4721no—
745C22—4721no—
746C22—4721no—
747C22—4721no—
748C22—2362no—
749C22—2362no—
750C22—2362no—
751C22—2362no—
752C22—2362no—
753C22—2362no—
754C22—2362no—
755C22—2362no—
756C22—2362no—
757C22C2×C4×C22⋊D5911yescharacteristic
758C22D4×C22⋊D5911yescharacteristic
759C22#1683804011yescharacteristic
760C22C2×#1427375211yescharacteristic
761C22#1683820011yescharacteristic
762C22#1683821011yescharacteristic
763C22#1683821011yescharacteristic
764C4—22no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—42no—
772C4—81no—
773C4—4721no—
774C4—4721no—
775C4C4×D4×D5911yescharacteristic
776C4#1683787411yescharacteristic
777C4#1683804811yescharacteristic
778C4#1683808111yescharacteristic
779C2—42no—
780C2—4722no—
781C2—2364no—
782C2#2142707311yescharacteristic
783C2C4×#1427375211yescharacteristic
784C2#2143295511yescharacteristic
785C2#2143559211yescharacteristic
786C2#2143562211yescharacteristic
787C2#2143630611yescharacteristic
788C2#2143632111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2362C2
socleC23×C59C22×D4
prime radicalC23×D236C22
cosocleC22×C4×C59C24
hypercenter#2362D59
hypocenterC59#22884
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11745671C2semidirect
5. #21424980C2semidirect
6. #21424778C2semidirect
7. #21424723C2semidirect
8. #21424530C2semidirect
9. #21424451C2semidirect
10. #21424433C2semidirect
11. #21424342C2semidirect
12. #21424295C2semidirect
13. #21423924C2semidirect
14. #21423880C2semidirect
15. C59×#2362C2semidirect
23. #16837552C4semidirect
25. C2×#14273660C22semidirect
26. C2×#14273658C22semidirect
28. C2×#14273651C22semidirect
29. C2×#14273651C22semidirect
37. C2×#14273638C22semidirect
38. C2×C4×C59⋊C8C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837164C22semidirect
48. #16837164C22semidirect
49. #16837157C22semidirect
50. #16837157C22semidirect
52. C2×C4×Q8×C59C22semidirect
54. C59×#391C22semidirect
55. C59×#389C22semidirect
60. C4×C4⋊C4×C59C22semidirect
79. C2×#11745671C2×C4semidirect
109. #14273647C2×C4semidirect
111. C22⋊(C59⋊C8)C2×C4semidirect
118. C22⋊Q8×C59C2×C4semidirect
388. #2362D59semidirect
415. C2×C4×Q8C2×D59semidirect
436. #391C2×D59semidirect
439. #389C2×D59semidirect
448. C4×C4⋊C4C2×D59semidirect
456. C59#22884semidirect
485. C22⋊Q8C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375522
C2×C4×#117456712
C2×#168374062
C22⋊C4×D2362
#214249802
#214247782
#214247232
#214245302
#214244512
#214244332
#214243422
#214242952
#214239242
#214238802
C59×#23622
#2288459