Finite Group Databasebeta

← #28600030

Subgroups — #28600030

Order 15104.

1136 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837536C211yesmaximal, characteristic
2#21426789C211yesmaximal, characteristic, complemented
3#21424971C211yesmaximal, characteristic, complemented
4#21424961C211yesmaximal, characteristic, complemented
5#21424796C211yesmaximal, characteristic, complemented
6#21424782C211yesmaximal, characteristic, complemented
7#21424720C211yesmaximal, characteristic, complemented
8#21424713C211yesmaximal, characteristic, complemented
9#21424447C211yesmaximal, characteristic, complemented
10#21424447C211yesmaximal, characteristic, complemented
11#21424418C211yesmaximal, characteristic, complemented
12#21424295C211yesmaximal, characteristic, complemented
13#21424027C211yesmaximal, characteristic, complemented
14#21423862C211yesmaximal, characteristic, complemented
15C59×#2309C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C22×#11745669C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic, complemented
20#16837536C418yescomplemented
21C2×#14273660C2211yescharacteristic, complemented
22C2×#14273658C2211yescharacteristic, complemented
23C2×#14273648C2211yescharacteristic
24C2×#14273648C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273647C2211yescharacteristic, complemented
30C2×#14273647C2211yescharacteristic, complemented
31C2×C22⋊(C59⋊C8)C2211yescharacteristic
32C2×C22⋊(C59⋊C8)C2211yescharacteristic
33C2×#14273638C2211yescharacteristic, complemented
34C2×C4×C59⋊C8C2211yescharacteristic, complemented
35#16837304C2211yescharacteristic, complemented
36#16837302—21no—
37#16837300C2211yescharacteristic, complemented
38#16837292—21no—
39#16837278—21no—
40#16837273—21no—
41#16837262C2211yescharacteristic
42C4×C4⋊Dic59C2211yescharacteristic, complemented
43#16837164C2211yescharacteristic, complemented
44#16837164C2211yescharacteristic, complemented
45#16837164C2211yescharacteristic, complemented
46#16837164C2211yescharacteristic, complemented
47#16837157C2211yescharacteristic, complemented
48#16837157C2211yescharacteristic, complemented
49C23×D4×C59C2211yescharacteristic
50C2×#117×C59C2211yescharacteristic
51C2×#117×C59C2211yescharacteristic
52C59×#390—21no—
53C59×#390—21no—
54C59×#390C2211yescharacteristic
55C59×#390C2211yescharacteristic
56C59×#390C2211yescharacteristic
57C59×#390C2211yescharacteristic
58C59×#379—21no—
59C59×#379—21no—
60C22×D236C2311yescharacteristic
61C22×C22⋊D59—21no—
62C22×C4×D59—21no—
63C2×#11745669—41no—
64C2×#11745669—41no—
65C2×#11745669—41no—
66C2×#11745669—41no—
67C2×#11745669C2×C414yes—
68C2×#11745669C2×C414yes—
69C22×C59⋊C8C2311yescharacteristic
70C22×C59⋊C8C2311yescharacteristic
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73#14273701—22no—
74#14273701C2×C414yes—
75C4×D236—41no—
76C4×D236—41no—
77C2×C4⋊Dic59C2311yescharacteristic
78C2×C4⋊Dic59C2311yescharacteristic
79C2×C4⋊Dic59C2311yescharacteristic
80C2×Dic59⋊C4—21no—
81C2×C22⋊Dic59—21no—
82C2×(C2×D59)⋊C4—21no—
83C2×(C2×D59)⋊C4—21no—
84C2×(C2×D59)⋊C4—21no—
85C2×(C2×D59)⋊C4—21no—
86C2×C4×Dic59—21no—
87#14273660—41no—
88#14273658—41no—
89#14273648—41no—
90#14273648—41no—
91#14273648—41no—
92#14273648—41no—
93#14273648C2×C414yescomplemented
94#14273648C2×C414yescomplemented
95#14273647—41no—
96#14273647—41no—
97C22⋊(C59⋊C8)—22no—
98C22⋊(C59⋊C8)C2×C414yescomplemented
99#14273638—41no—
100C4×C59⋊C8—41no—
101C59⋊#95—21no—
102C59⋊#95—21no—
103C59⋊#95—21no—
104C25×C59—21no—
105C22×D4×C59—21no—
106C22×D4×C59—22no—
107C22×D4×C59—41no—
108C22×D4×C59—41no—
109C22×D4×C59—41no—
110C22×D4×C59—41no—
111C22×D4×C59C2×C414yescomplemented
112C22×D4×C59C2311yescharacteristic
113C22×D4×C59C2311yescharacteristic
114C23×C4×C59C2311yescharacteristic
115#117×C59—41no—
116#117×C59—41no—
117#117×C59—41no—
118#117×C59—41no—
119C2×C4⋊C4×C59D411yescharacteristic
120C2×C4⋊C4×C59D411yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C4⋊C4×C59C2311yescharacteristic
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59—21no—
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59D411yescharacteristic
133C2×C22⋊C4×C59D411yescharacteristic
134C2×C42×C59—21no—
135C2×C42×C59C2311yescharacteristic
136C2×C42×C59C2311yescharacteristic
137C24×C59—21no—
138C24×C59—21no—
139C24×C59—24no—
140C24×C59—42no—
141C24×C59—42no—
142C24×C59—81no—
143C24×C59—81no—
144C24×C59—81no—
145C24×C59—81no—
146C24×C59C2×D411yescharacteristic
147C23×D59—21no—
148C2×D4×C59—24no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—21no—
152C2×D4×C59—21no—
153C2×D4×C59—21no—
154C2×D4×C59—21no—
155C2×D4×C59—21no—
156C2×D4×C59—21no—
157C2×D4×C59—21no—
158C2×D4×C59—21no—
159C2×D4×C59—44no—
160C2×D4×C59—44no—
161C2×D4×C59—42no—
162C2×D4×C59—42no—
163C2×D4×C59—44no—
164C2×D4×C59—44no—
165C2×D4×C59C22×C412yes—
166C2×D4×C59C22×C412yes—
167C22×C4×C59—21no—
168C22×C4×C59—21no—
169C22×C4×C59—21no—
170C22×C4×C59—21no—
171C22×C4×C59—21no—
172C22×C4×C59—21no—
173C22×C4×C59C22×C412yes—
174C22×C4×C59C2×D411yescharacteristic
175C22×C4×C59C2×D411yescharacteristic
176C22×C4×C59C2×D411yescharacteristic
177C22×C4×C59C2×D411yescharacteristic
178C22×C4×C59C2×D411yescharacteristic
179C22×C4×C59#4112yes—
180C22×C4×C59C2411yescharacteristic
181C2×C22⋊D59—24no—
182C2×C22⋊D59—81no—
183C2×C22⋊D59—81no—
184C22×Dic59—21no—
185C22×Dic59—21no—
186C22×Dic59—21no—
187C2×D236—21no—
188C2×D236—21no—
189C2×D236—21no—
190C2×D236—21no—
191C2×D236—21no—
192C2×D236C22×C412yes—
193C2×C4×D59—42no—
194C2×C4×D59—81no—
195C2×C4×D59—81no—
196C4⋊C4×C59—21no—
197C4⋊C4×C59—21no—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—41no—
201C4⋊C4×C59—41no—
202C22⋊C4×C59—41no—
203C22⋊C4×C59—41no—
204C22⋊C4×C59—42no—
205C22⋊C4×C59—81no—
206C22⋊C4×C59—81no—
207C22⋊C4×C59—81no—
208C22⋊C4×C59—81no—
209C22⋊C4×C59—81no—
210C22⋊C4×C59—81no—
211C22⋊C4×C59—81no—
212C22⋊C4×C59—81no—
213C42×C59—21no—
214C42×C59—21no—
215C42×C59—21no—
216C42×C59—21no—
217C42×C59—42no—
218C22⋊Dic59—81no—
219#11745669—44no—
220#11745669—44no—
221(C2×D59)⋊C4—24no—
222(C2×D59)⋊C4—42no—
223(C2×D59)⋊C4—81no—
224(C2×D59)⋊C4—81no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230C4⋊Dic59C22×C412yes—
231Dic59⋊C4—81no—
232C4×Dic59—81no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8—21no—
236C2×C59⋊C8—21no—
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⋊C8C22×C412yes—
244C2×C59⋊C8C22×C412yes—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—22no—
252C23×C59—22no—
253C23×C59—48no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59—41no—
258C23×C59—41no—
259C23×C59—41no—
260C23×C59—41no—
261C23×C59—41no—
262C23×C59—41no—
263C23×C59—41no—
264C23×C59—41no—
265C23×C59—41no—
266C23×C59—84no—
267C23×C59—84no—
268C23×C59—84no—
269C23×C59—84no—
270C23×C59—84no—
271C23×C59—84no—
272C23×C59C4×D412yes—
273C23×C59C22×D411yescharacteristic
274C22×D59—22no—
275C22×D59—41no—
276C22×D59—41no—
277C22×D59—41no—
278C22×D59—41no—
279C22×D59—41no—
280C22×D59—41no—
281D4×C59—22no—
282D4×C59—22no—
283D4×C59—22no—
284D4×C59—22no—
285D4×C59—48no—
286D4×C59—41no—
287D4×C59—41no—
288D4×C59—41no—
289D4×C59—41no—
290C2×C4×C59—21no—
291C2×C4×C59—21no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
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—21no—
303C2×C4×C59—21no—
304C2×C4×C59—21no—
305C2×C4×C59—21no—
306C2×C4×C59—21no—
307C2×C4×C59—21no—
308C2×C4×C59—41no—
309C2×C4×C59—41no—
310C2×C4×C59—41no—
311C2×C4×C59—41no—
312C2×C4×C59—41no—
313C2×C4×C59—41no—
314C2×C4×C59C4×D412yes—
315C2×C4×C59C23×C411yescharacteristic
316C2×C4×C59C2×#4111yescharacteristic
317C2×C4×C59H(5,𝔽2)11yescharacteristic
318C2×C4×C59H(5,𝔽2)11yescharacteristic
319C2×C4×C59H(5,𝔽2)11yescharacteristic
320C2×C4×C59H(5,𝔽2)11yescharacteristic
321C22⋊D59—84no—
322C2×Dic59—22no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C2×Dic59—41no—
326C2×Dic59—41no—
327C2×Dic59—41no—
328C2×Dic59—41no—
329C2×Dic59—41no—
330C2×Dic59—41no—
331D236—22no—
332D236—22no—
333D236—41no—
334D236—41no—
335C4×D59—84no—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C59⋊C8—41no—
339C59⋊C8—41no—
340#22056—591nomaximal, Sylow
341C22×C59—22no—
342C22×C59—22no—
343C22×C59—22no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59—41no—
348C22×C59—42no—
349C22×C59—42no—
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—816no—
355C22×C59—81no—
356C22×C59—81no—
357C22×C59—81no—
358C22×C59—81no—
359C22×C59—81no—
360C22×C59—81no—
361C22×C59—81no—
362C22×C59—81no—
363C22×C59C2×C4×D411yescharacteristic
364C22×C59#53411yescharacteristic
365C22×C59#53511yescharacteristic
366C22×C59#57611yescharacteristic
367C22×C59#57611yescharacteristic
368C22×C59#57611yescharacteristic
369C22×C59#57711yescharacteristic
370C2×D59—42no—
371C2×D59—42no—
372C2×D59—42no—
373C2×D59—81no—
374C2×D59—81no—
375C2×D59—81no—
376C2×D59—81no—
377C4×C59—22no—
378C4×C59—41no—
379C4×C59—41no—
380C4×C59—41no—
381C4×C59—41no—
382C4×C59—81no—
383C4×C59—81no—
384C4×C59#51811yescharacteristic
385C4×C59#51811yescharacteristic
386C4×C59#53811yescharacteristic
387C4×C59#53811yescharacteristic
388Dic59—42no—
389Dic59—81no—
390Dic59—81no—
391C2×#447—591no—
392#2324—591no—
393#2309D5911yescharacteristic, complemented
394#1972—591no—
395#1970—591no—
396#1936—591no—
397#1934—591no—
398#1926—591no—
399#1925—591no—
400#1879—591no—
401#1879—591no—
402#1875—591no—
403#1854—591no—
404#1786—591no—
405#1750—591no—
406C2×C59—42no—
407C2×C59—82no—
408C2×C59—82no—
409C2×C59#232111yescharacteristic
410C2×C59#294611yescharacteristic
411C2×C59#294811yescharacteristic
412C2×C59#319811yescharacteristic
413C2×C59#319911yescharacteristic
414C2×C59#322011yescharacteristic
415C2×C59#322411yescharacteristic
416D59—82no—
417C23×D4C2×D5911yescharacteristic
418C22×D8—591no—
419C22×D8—591no—
420C2×#121—591no—
421C2×C4×D4—591no—
422C2×#117C2×D5911yescharacteristic
423C2×#117C2×D5911yescharacteristic
424#447—598no—
425C2×#107—591no—
426C2×#106—591no—
427C2×#102—591no—
428C2×#102—591no—
429C2×#102—591no—
430C2×#102—591no—
431C2×#102—591no—
432C2×#102—591no—
433C2×#102—591no—
434C2×#102—591no—
435C2×C22⋊C8—591no—
436C2×C22⋊C8—591no—
437C2×#97—591no—
438C2×C4×C8—591no—
439#390—21no—
440#390—21no—
441#390—591no—
442#390—1181no—
443#390C2×D5911yescharacteristic
444#390C2×D5911yescharacteristic
445#390C2×D5911yescharacteristic
446#390C2×D5911yescharacteristic
447#389—591no—
448#388—1181no—
449#386—1181no—
450#385—1181no—
451#380—591no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—591no—
455#340—591no—
456#340—591no—
457#340—591no—
458#340—591no—
459#336—591no—
460#336—591no—
461C59#2205611yescharacteristic, complemented, Sylow
462C25—21no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—41no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4—41no—
469C22×D4—591no—
470C22×D4—1181no—
471C22×D4C4×D5914yescomplemented
472C22×D4C22×D5911yescharacteristic
473C22×D4C22×D5911yescharacteristic
474C23×C4—1181no—
475C23×C4C22×D5911yescharacteristic
476C2×D8—594no—
477C2×D8—594no—
478C2×D8—2361no—
479C2×D8—2361no—
480C2×D8—2361no—
481C2×D8—2361no—
482C22×C8—591no—
483C22×C8—591no—
484C22×C8—591no—
485C22×C8—591no—
486#121—594no—
487#121—1182no—
488C4×D4—2361no—
489C4×D4—2361no—
490#117—41no—
491#117—41no—
492#117—41no—
493#117—41no—
494C2×C4⋊C4—591no—
495C2×C4⋊C4—591no—
496C2×C4⋊C4—591no—
497C2×C4⋊C4—1181no—
498C2×C4⋊C4C22⋊D5911yescharacteristic
499C2×C4⋊C4C22⋊D5911yescharacteristic
500C2×C4⋊C4C22×D5911yescharacteristic
501C2×C4⋊C4C22×D5911yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1181no—
512C2×C22⋊C4—1181no—
513C2×C22⋊C4—1181no—
514C2×C22⋊C4—1181no—
515C2×C22⋊C4—1181no—
516C2×C22⋊C4C22⋊D5911yescharacteristic
517C2×C22⋊C4C22⋊D5911yescharacteristic
518C2×C42—21no—
519C2×C42—1181no—
520C2×C42C22×D5911yescharacteristic
521C2×C42C22×D5911yescharacteristic
522#107—2361no—
523#106—2361no—
524#102—594no—
525#102—594no—
526#102—2361no—
527#102—2361no—
528#102—2361no—
529#102—2361no—
530#102—2361no—
531#102—2361no—
532C22⋊C8—594no—
533C22⋊C8—1182no—
534#97—2361no—
535C4×C8—2361no—
536#95—1181no—
537#95—1181no—
538#95—1181no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—81no—
545C24—81no—
546C24—81no—
547C24—81no—
548C24—1181no—
549C24C2×C22⋊D5911yescharacteristic
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—44no—
562C2×D4—44no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—592no—
568C2×D4—1184no—
569C2×D4—1181no—
570C2×D4—1181no—
571C2×D4—1181no—
572C2×D4—1181no—
573C2×D4—1181no—
574C2×D4—4721no—
575C2×D4—4721no—
576C2×D4C2×C4×D5912yes—
577C2×D4C2×C4×D5912yes—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—1181no—
585C22×C4—1181no—
586C22×C4—1181no—
587C22×C4—4721no—
588C22×C4—4721no—
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
598D8—2364no—
599D8—2364no—
600C2×C8—592no—
601C2×C8—592no—
602C2×C8—1181no—
603C2×C8—1181no—
604C2×C8—1181no—
605C2×C8—1181no—
606C2×C8—1181no—
607C2×C8—1181no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—41no—
617C4⋊C4—41no—
618C4⋊C4—592no—
619C4⋊C4—1181no—
620C4⋊C4—1181no—
621C4⋊C4—1181no—
622C4⋊C4—1181no—
623C4⋊C4—1181no—
624C4⋊C4—4721no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C22⋊C4—81no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—81no—
636C22⋊C4—1184no—
637C22⋊C4—4721no—
638C22⋊C4—4721no—
639C22⋊C4—4721no—
640C22⋊C4—2362no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C42—4721no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23—1182no—
675C23—2361no—
676C23—2361no—
677C23—2361no—
678C23—2361no—
679C23—2361no—
680C23—2361no—
681C23C4×C22⋊D5912yes—
682C23C22×C22⋊D5911yescharacteristic
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—41no—
692D4—1182no—
693D4—1182no—
694D4—4724no—
695D4—2361no—
696D4—2361no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—1182no—
722C2×C4—4724no—
723C2×C4—2361no—
724C2×C4—2361no—
725C2×C4—2361no—
726C2×C4—2361no—
727C2×C4—2361no—
728C2×C4—2361no—
729C2×C4—2361no—
730C2×C4—2361no—
731C2×C4C4×C22⋊D5912yes—
732C2×C4C22×C4×D5911yescharacteristic
733C2×C4C2×#1174568511yescharacteristic
734C2×C4#1427377211yescharacteristic
735C2×C4#1427377211yescharacteristic
736C2×C4#1427377211yescharacteristic
737C2×C4#1427377211yescharacteristic
738C8—1182no—
739C8—1182no—
740C8—2361no—
741C8—2361no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—816no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—4721no—
765C22—4721no—
766C22—4721no—
767C22—4721no—
768C22—2362no—
769C22—2362no—
770C22—2362no—
771C22C2×C4×C22⋊D5911yescharacteristic
772C22#1683796111yescharacteristic
773C22#1683796911yescharacteristic
774C22#1683820511yescharacteristic
775C22#1683820511yescharacteristic
776C22#1683820511yescharacteristic
777C22#1683821311yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—81no—
784C4—81no—
785C4—4721no—
786C4—4721no—
787C4—2362no—
788C4#1683787511yescharacteristic
789C4#1683787511yescharacteristic
790C4#1683799011yescharacteristic
791C4#1683799011yescharacteristic
792C2—42no—
793C2—82no—
794C2—82no—
795C2—4722no—
796C2#2142675411yescharacteristic
797C2#2143292811yescharacteristic
798C2#2143294611yescharacteristic
799C2#2143494811yescharacteristic
800C2#2143495711yescharacteristic
801C2#2143514611yescharacteristic
802C2#2143519011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2309C2
socleC23×C59C22×D4
prime radicalC2×#16837536C2
cosocleC22×C4×C59C24
hypercenter#2309D59
hypocenterC59#22056
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2309

Complements

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

NH ≅ G/Ntype
2. #21426789C2semidirect
3. #21424971C2semidirect
4. #21424961C2semidirect
5. #21424796C2semidirect
6. #21424782C2semidirect
7. #21424720C2semidirect
8. #21424713C2semidirect
9. #21424447C2semidirect
10. #21424447C2semidirect
11. #21424418C2semidirect
12. #21424295C2semidirect
13. #21424027C2semidirect
14. #21423862C2semidirect
15. C59×#2309C2semidirect
19. C2×C4×D236C22semidirect
20. #16837536C4semidirect
21. C2×#14273660C22semidirect
22. C2×#14273658C22semidirect
29. C2×#14273647C22semidirect
30. C2×#14273647C22semidirect
33. C2×#14273638C22semidirect
34. C2×C4×C59⋊C8C22semidirect
35. #16837304C22semidirect
37. #16837300C22semidirect
42. C4×C4⋊Dic59C22semidirect
43. #16837164C22semidirect
44. #16837164C22semidirect
45. #16837164C22semidirect
46. #16837164C22semidirect
47. #16837157C22semidirect
48. #16837157C22semidirect
93. #14273648C2×C4semidirect
94. #14273648C2×C4semidirect
98. C22⋊(C59⋊C8)C2×C4semidirect
111. C22×D4×C59C2×C4semidirect
393. #2309D59semidirect
461. C59#22056semidirect
471. C22×D4C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375362
#214267892
#214249712
#214249612
#214247962
#214247822
#214247202
#214247132
#214244472
#214244182
#214242952
#214240272
#214238622
C59×#23092
#2205659