Finite Group Databasebeta

← #28611384

Subgroups — #28611384

Order 15104.

1038 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837636C211yesmaximal, characteristic
2C2×#16837512C211yesmaximal, characteristic, complemented
3C2×#16837438C211yesmaximal, characteristic, complemented
4#21427132C211yesmaximal, characteristic, complemented
5#21424971C211yesmaximal, characteristic, complemented
6#21424831C211yesmaximal, characteristic, complemented
7#21424716C211yesmaximal, characteristic, complemented
8#21424713C211yesmaximal, characteristic, complemented
9#21424419C211yesmaximal, characteristic, complemented
10#21424418C211yesmaximal, characteristic, complemented
11#21424343C211yesmaximal, characteristic, complemented
12#21424342C211yesmaximal, characteristic, complemented
13#21423994C211yesmaximal, characteristic, complemented
14#21423874C211yesmaximal, characteristic, complemented
15C59×#2363C211yesmaximal, characteristic, complemented
16C22×#11745669C2211yescharacteristic
17C23×C59⋊C8C2211yescharacteristic
18C2×#14273701C2211yescharacteristic
19C2×C4×D236C2211yescharacteristic
20C2×#14273686C2211yescharacteristic
21#16837636C418yescomplemented
22#16837512—24no—
23#16837438—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273660C2211yescharacteristic
26C2×#14273660C2211yescharacteristic
27C2×#14273658C2211yescharacteristic
28C2×#14273658C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273648C2211yescharacteristic
32C2×#14273647C2211yescharacteristic
33C2×#14273647C2211yescharacteristic
34C2×#14273647C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×#14273638C2211yescharacteristic
38#16837304C2211yescharacteristic
39#16837302—21no—
40#16837300C2211yescharacteristic
41#16837291—21no—
42#16837278—21no—
43C4×C4⋊Dic59C2211yescharacteristic
44#16837249—21no—
45#16837164C2211yescharacteristic
46#16837164C2211yescharacteristic
47#16837164C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837157C2211yescharacteristic
50#16837157C2211yescharacteristic
51C2×#121×C59C2211yescharacteristic
52C2×C4×D4×C59C2211yescharacteristic
53C2×#117×C59C2211yescharacteristic
54C59×#390—21no—
55C59×#390C2211yescharacteristic
56C59×#389C2211yescharacteristic
57C59×#388—21no—
58C59×#386—21no—
59C4×C4⋊C4×C59C2211yescharacteristic
60C4×C22⋊C4×C59—21no—
61C4×C22⋊C4×C59C2211yescharacteristic
62C22×D236C2311yescharacteristic
63C22×C22⋊D59—21no—
64C22×C4×D59—21no—
65C2×#11745669—22no—
66C2×#11745669—22no—
67C2×#11745669C2×C414yes—
68C22×C59⋊C8—22no—
69C22×C59⋊C8—22no—
70C22×C59⋊C8C2×C414yescomplemented
71C22×C59⋊C8C2311yescharacteristic
72C22×C59⋊C8C2311yescharacteristic
73C22×C59⋊C8C2311yescharacteristic
74C22×C59⋊C8C2311yescharacteristic
75#14273701—22no—
76#14273701C2×C414yescomplemented
77C4×D236—22no—
78C4×D236—41no—
79#14273686—22no—
80#14273686—41no—
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×Dic59⋊C4—21no—
85C2×C22⋊Dic59—21no—
86C2×(C2×D59)⋊C4—21no—
87C2×(C2×D59)⋊C4—21no—
88C2×(C2×D59)⋊C4—21no—
89C2×(C2×D59)⋊C4—21no—
90C2×C4×Dic59—21no—
91C2×C4×Dic59—21no—
92#14273660—22no—
93#14273660—22no—
94#14273660C2×C414yescomplemented
95#14273658—22no—
96#14273658D414yescomplemented
97#14273648—22no—
98#14273648—41no—
99#14273648C2×C414yescomplemented
100#14273647—22no—
101#14273647—41no—
102#14273647C2×C414yescomplemented
103C22⋊(C59⋊C8)—22no—
104#14273638—22no—
105#14273638—22no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C22×D4×C59—21no—
109C22×D4×C59C2311yescharacteristic
110C23×C4×C59—21no—
111C23×C4×C59C2311yescharacteristic
112#121×C59—22no—
113#121×C59C2×C414yescomplemented
114C4×D4×C59—22no—
115C4×D4×C59—41no—
116#117×C59—22no—
117#117×C59—41no—
118C2×C4⋊C4×C59—21no—
119C2×C4⋊C4×C59C2311yescharacteristic
120C2×C4⋊C4×C59C2311yescharacteristic
121C2×C4⋊C4×C59C2311yescharacteristic
122C2×C22⋊C4×C59—21no—
123C2×C22⋊C4×C59—21no—
124C2×C22⋊C4×C59—21no—
125C2×C22⋊C4×C59—21no—
126C2×C22⋊C4×C59—21no—
127C2×C22⋊C4×C59D411yescharacteristic
128C2×C22⋊C4×C59D411yescharacteristic
129C2×C42×C59—21no—
130C2×C42×C59—21no—
131C2×C42×C59C2311yescharacteristic
132C2×C42×C59C2311yescharacteristic
133#95×C59—21no—
134#95×C59—21no—
135#95×C59D411yescharacteristic
136#95×C59D411yescharacteristic
137C24×C59—21no—
138C24×C59C2×D411yescharacteristic
139C23×D59—21no—
140C2×D4×C59—24no—
141C2×D4×C59—21no—
142C2×D4×C59—21no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—81no—
147C2×D4×C59—81no—
148C2×D4×C59C22×C412yes—
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—21no—
156C22×C4×C59—42no—
157C22×C4×C59—42no—
158C22×C4×C59—81no—
159C22×C4×C59C22×C412yes—
160C22×C4×C59C2×D411yescharacteristic
161C22×C4×C59C2×D411yescharacteristic
162C22×C4×C59C2×D411yescharacteristic
163C22×C4×C59C2×D411yescharacteristic
164C22×C4×C59C2×D411yescharacteristic
165C22×C4×C59#4112yes—
166C22×C4×C59C2411yescharacteristic
167C2×C22⋊D59—24no—
168C2×C22⋊D59—81no—
169C2×C22⋊D59—81no—
170C22×Dic59—21no—
171C22×Dic59—21no—
172C22×Dic59—21no—
173C2×D236—21no—
174C2×D236—21no—
175C2×D236—21no—
176C2×D236—21no—
177C2×D236—21no—
178C2×D236C22×C412yes—
179C2×C4×D59—42no—
180C2×C4×D59—42no—
181C2×C4×D59—81no—
182C4⋊C4×C59—21no—
183C4⋊C4×C59—21no—
184C4⋊C4×C59—21no—
185C4⋊C4×C59—21no—
186C4⋊C4×C59—81no—
187C4⋊C4×C59C22×C412yes—
188C4⋊C4×C59C2×D412yes—
189C22⋊C4×C59—24no—
190C22⋊C4×C59—41no—
191C22⋊C4×C59—41no—
192C22⋊C4×C59—42no—
193C22⋊C4×C59—42no—
194C22⋊C4×C59—42no—
195C22⋊C4×C59—81no—
196C42×C59—21no—
197C42×C59—21no—
198C42×C59—21no—
199C42×C59—21no—
200C42×C59—42no—
201C42×C59—81no—
202C22⋊Dic59—42no—
203#11745669—28no—
204(C2×D59)⋊C4—24no—
205(C2×D59)⋊C4—42no—
206(C2×D59)⋊C4—42no—
207(C2×D59)⋊C4—81no—
208C4⋊Dic59—21no—
209C4⋊Dic59—21no—
210C4⋊Dic59—21no—
211C4⋊Dic59—21no—
212C4⋊Dic59C22×C412yes—
213C4⋊Dic59C2×D412yes—
214Dic59⋊C4—81no—
215C4×Dic59—42no—
216C4×Dic59—81no—
217C2×C59⋊C8—21no—
218C2×C59⋊C8—21no—
219C2×C59⋊C8—28no—
220C2×C59⋊C8—21no—
221C2×C59⋊C8—21no—
222C2×C59⋊C8—21no—
223C2×C59⋊C8—21no—
224C2×C59⋊C8—21no—
225C2×C59⋊C8—21no—
226C2×C59⋊C8C22×C412yes—
227C2×C59⋊C8C22×C412yes—
228C2×C59⋊C8C2×D412yes—
229C2×C59⋊C8#4112yes—
230C23×C59—21no—
231C23×C59—21no—
232C23×C59—21no—
233C23×C59—21no—
234C23×C59—21no—
235C23×C59—21no—
236C23×C59—22no—
237C23×C59—41no—
238C23×C59—41no—
239C23×C59—41no—
240C23×C59—41no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59C4×D412yes—
244C23×C59C22×D411yescharacteristic
245C22×D59—22no—
246C22×D59—41no—
247C22×D59—41no—
248C22×D59—41no—
249C22×D59—41no—
250C22×D59—41no—
251C22×D59—41no—
252D4×C59—22no—
253D4×C59—22no—
254D4×C59—41no—
255D4×C59—41no—
256D4×C59—84no—
257C2×C4×C59—21no—
258C2×C4×C59—21no—
259C2×C4×C59—22no—
260C2×C4×C59—22no—
261C2×C4×C59—22no—
262C2×C4×C59—22no—
263C2×C4×C59—22no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—22no—
267C2×C4×C59—21no—
268C2×C4×C59—21no—
269C2×C4×C59—21no—
270C2×C4×C59—21no—
271C2×C4×C59—21no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—21no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—41no—
280C2×C4×C59—41no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—84no—
285C2×C4×C59C4×D412yes—
286C2×C4×C59C23×C411yescharacteristic
287C2×C4×C59C22×D411yescharacteristic
288C2×C4×C59C2×#4111yescharacteristic
289C2×C4×C59C2×#4111yescharacteristic
290C2×C4×C59H(5,𝔽2)11yescharacteristic
291C2×C4×C592−1+411yescharacteristic
292C22⋊D59—84no—
293C2×Dic59—22no—
294C2×Dic59—22no—
295C2×Dic59—41no—
296C2×Dic59—41no—
297C2×Dic59—41no—
298C2×Dic59—41no—
299C2×Dic59—41no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302D236—22no—
303D236—22no—
304D236—41no—
305D236—41no—
306C4×D59—84no—
307C59⋊C8—22no—
308C59⋊C8—41no—
309C59⋊C8—41no—
310C59⋊C8C4×D414yes—
311#23031—591nomaximal, Sylow
312C22×C59—22no—
313C22×C59—22no—
314C22×C59—22no—
315C22×C59—41no—
316C22×C59—41no—
317C22×C59—41no—
318C22×C59—41no—
319C22×C59—42no—
320C22×C59—42no—
321C22×C59—42no—
322C22×C59—81no—
323C22×C59—81no—
324C22×C59—81no—
325C22×C59—81no—
326C22×C59C2×C4×D411yescharacteristic
327C22×C59D4211yescharacteristic
328C22×C59#54711yescharacteristic
329C22×C59#57511yescharacteristic
330C22×C59#57511yescharacteristic
331C22×C59#57611yescharacteristic
332C22×C59#57611yescharacteristic
333C2×D59—42no—
334C2×D59—42no—
335C2×D59—42no—
336C2×D59—81no—
337C2×D59—81no—
338C2×D59—81no—
339C2×D59—81no—
340C4×C59—22no—
341C4×C59—41no—
342C4×C59—41no—
343C4×C59—42no—
344C4×C59—41no—
345C4×C59—41no—
346C4×C59—42no—
347C4×C59—81no—
348C4×C59C2×C4×D411yescharacteristic
349C4×C59#52011yescharacteristic
350C4×C59#54811yescharacteristic
351C4×C59#55311yescharacteristic
352Dic59—42no—
353Dic59—42no—
354Dic59—81no—
355C2×#466—591no—
356C2×#442—591no—
357C2×#427—591no—
358#2363—591no—
359#2363D5911yescharacteristic, complemented
360#1972—591no—
361#1943—591no—
362#1925—591no—
363#1925—591no—
364#1875—591no—
365#1875—591no—
366#1862—591no—
367#1862—591no—
368#1776—591no—
369#1752—591no—
370C2×C59—42no—
371C2×C59—82no—
372C2×C59#236111yescharacteristic
373C2×C59#294311yescharacteristic
374C2×C59#294811yescharacteristic
375C2×C59#326811yescharacteristic
376C2×C59#326811yescharacteristic
377C2×C59#334711yescharacteristic
378C2×C59#334711yescharacteristic
379D59—82no—
380C22×D8—591no—
381C23×C8—591no—
382C2×#121—591no—
383C2×#121C2×D5911yescharacteristic
384C2×C4×D4—591no—
385C2×C4×D4C2×D5911yescharacteristic
386C2×#117—591no—
387C2×#117C2×D5911yescharacteristic
388#466—598no—
389#442—1184no—
390#427—1184no—
391C2×#107—591no—
392C2×#107—591no—
393C2×#107—591no—
394C2×#106—591no—
395C2×#106—591no—
396C2×#102—591no—
397C2×#102—591no—
398C2×#102—591no—
399C2×#102—591no—
400C2×#102—591no—
401C2×#102—591no—
402C2×C22⋊C8—591no—
403C2×#97—591no—
404C2×#97—591no—
405#390—21no—
406#390—591no—
407#390—1181no—
408#390C2×D5911yescharacteristic
409#389—591no—
410#389C2×D5911yescharacteristic
411#388—21no—
412#388—1181no—
413#386—21no—
414#386—1181no—
415C4×C4⋊C4—591no—
416C4×C4⋊C4C2×D5911yescharacteristic
417C4×C22⋊C4—21no—
418C4×C22⋊C4—1181no—
419C4×C22⋊C4C2×D5911yescharacteristic
420#340—591no—
421#340—591no—
422#340—591no—
423#340—591no—
424#336—591no—
425#336—591no—
426C59#2303111yescharacteristic, complemented, Sylow
427C22×D4—21no—
428C22×D4—591no—
429C22×D4—1181no—
430C22×D4C22×D5911yescharacteristic
431C23×C4—21no—
432C23×C4—1181no—
433C23×C4C22×D5911yescharacteristic
434C2×D8—594no—
435C2×D8—1182no—
436C2×D8—1182no—
437C22×C8—591no—
438C22×C8—594no—
439C22×C8—591no—
440C22×C8—591no—
441C22×C8—591no—
442C22×C8—1182no—
443C22×C8—1182no—
444#121—22no—
445#121—594no—
446#121—1182no—
447#121C4×D5914yescomplemented
448C4×D4—22no—
449C4×D4—41no—
450C4×D4—1182no—
451C4×D4—2361no—
452#117—22no—
453#117—41no—
454#117—1182no—
455#117—2361no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—591no—
458C2×C4⋊C4—591no—
459C2×C4⋊C4—591no—
460C2×C4⋊C4—1181no—
461C2×C4⋊C4C22×D5911yescharacteristic
462C2×C4⋊C4C22×D5911yescharacteristic
463C2×C4⋊C4C22×D5911yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—1181no—
470C2×C22⋊C4—1181no—
471C2×C22⋊C4—1181no—
472C2×C22⋊C4—1181no—
473C2×C22⋊C4—1181no—
474C2×C22⋊C4C22⋊D5911yescharacteristic
475C2×C22⋊C4C22⋊D5911yescharacteristic
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—1181no—
479C2×C42—1181no—
480C2×C42C22×D5911yescharacteristic
481C2×C42C22×D5911yescharacteristic
482#107—594no—
483#107—1182no—
484#107—1182no—
485#106—594no—
486#106—1182no—
487#102—594no—
488#102—594no—
489#102—1182no—
490#102—1182no—
491#102—2361no—
492#102—2361no—
493C22⋊C8—1182no—
494#97—1182no—
495#97—1182no—
496#95—21no—
497#95—21no—
498#95—1181no—
499#95—1181no—
500#95C22⋊D5911yescharacteristic
501#95C22⋊D5911yescharacteristic
502C24—21no—
503C24—1181no—
504C24C2×C22⋊D5911yescharacteristic
505C2×D4—24no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—81no—
512C2×D4—81no—
513C2×D4—592no—
514C2×D4—1184no—
515C2×D4—1181no—
516C2×D4—1181no—
517C2×D4—1181no—
518C2×D4—1181no—
519C2×D4—1181no—
520C2×D4—4721no—
521C2×D4—4721no—
522C2×D4C2×C4×D5912yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—81no—
533C22×C4—1181no—
534C22×C4—1181no—
535C22×C4—1181no—
536C22×C4—4721no—
537C22×C4—2362no—
538C22×C4—2362no—
539C22×C4C2×C4×D5912yes—
540C22×C4#1174568512yes—
541C22×C4C2×C22⋊D5911yescharacteristic
542C22×C4C2×C22⋊D5911yescharacteristic
543C22×C4C2×C22⋊D5911yescharacteristic
544C22×C4C2×C22⋊D5911yescharacteristic
545C22×C4C2×C22⋊D5911yescharacteristic
546C22×C4C23×D5911yescharacteristic
547D8—1188no—
548C2×C8—592no—
549C2×C8—592no—
550C2×C8—592no—
551C2×C8—592no—
552C2×C8—1188no—
553C2×C8—1181no—
554C2×C8—1181no—
555C2×C8—1181no—
556C2×C8—1181no—
557C2×C8—1181no—
558C2×C8—1181no—
559C2×C8—1181no—
560C2×C8—1181no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—81no—
566C4⋊C4—592no—
567C4⋊C4—592no—
568C4⋊C4—1181no—
569C4⋊C4—1181no—
570C4⋊C4—1181no—
571C4⋊C4—1181no—
572C4⋊C4—4721no—
573C4⋊C4C2×C4×D5912yes—
574C4⋊C4D4×D5912yes—
575C22⋊C4—24no—
576C22⋊C4—41no—
577C22⋊C4—41no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—81no—
582C22⋊C4—1184no—
583C22⋊C4—4721no—
584C22⋊C4—2362no—
585C22⋊C4—2362no—
586C22⋊C4—2362no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—42no—
592C42—81no—
593C42—4721no—
594C42—2362no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—22no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—1182no—
609C23—2361no—
610C23—2361no—
611C23—2361no—
612C23—2361no—
613C23—2361no—
614C23—2361no—
615C23C4×C22⋊D5912yes—
616C23C22×C22⋊D5911yescharacteristic
617D4—22no—
618D4—22no—
619D4—41no—
620D4—41no—
621D4—84no—
622D4—1182no—
623D4—1182no—
624D4—4724no—
625D4—2361no—
626D4—2361no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—84no—
655C2×C4—1182no—
656C2×C4—1182no—
657C2×C4—4724no—
658C2×C4—2361no—
659C2×C4—2361no—
660C2×C4—2361no—
661C2×C4—2361no—
662C2×C4—2361no—
663C2×C4—2361no—
664C2×C4—2361no—
665C2×C4C4×C22⋊D5912yes—
666C2×C4C22×C4×D5911yescharacteristic
667C2×C4C2×D4×D5911yescharacteristic
668C2×C4#41×D5911yescharacteristic
669C2×C4C2×#1174568511yescharacteristic
670C2×C4#1427377211yescharacteristic
671C2×C4#1427377411yescharacteristic
672C8—594no—
673C8—1182no—
674C8—2361no—
675C8—2361no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—4721no—
691C22—4721no—
692C22—4721no—
693C22—4721no—
694C22—2362no—
695C22—2362no—
696C22—2362no—
697C22C2×C4×C22⋊D5911yescharacteristic
698C22D4×C22⋊D5911yescharacteristic
699C22#1683805111yescharacteristic
700C22#1683820011yescharacteristic
701C22#1683820011yescharacteristic
702C22#1683820511yescharacteristic
703C22#1683820511yescharacteristic
704C4—22no—
705C4—42no—
706C4—41no—
707C4—41no—
708C4—41no—
709C4—42no—
710C4—41no—
711C4—81no—
712C4—4721no—
713C4—2362no—
714C4—2362no—
715C4C4×D4×D5911yescharacteristic
716C4#1683788111yescharacteristic
717C4#1683806111yescharacteristic
718C4#1683810111yescharacteristic
719C2—42no—
720C2—82no—
721C2—4722no—
722C2#2142711311yescharacteristic
723C2#2143289411yescharacteristic
724C2#2143294611yescharacteristic
725C2#2143563211yescharacteristic
726C2#2143563711yescharacteristic
727C2#2143659011yescharacteristic
728C2#2143659611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2363C2
socleC23×C59C22×D4
prime radicalC2×#16837636C2
cosocleC22×C4×C59C24
hypercenter#2363D59
hypocenterC59#23031
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
2. C2×#16837512C2semidirect
3. C2×#16837438C2semidirect
4. #21427132C2semidirect
5. #21424971C2semidirect
6. #21424831C2semidirect
7. #21424716C2semidirect
8. #21424713C2semidirect
9. #21424419C2semidirect
10. #21424418C2semidirect
11. #21424343C2semidirect
12. #21424342C2semidirect
13. #21423994C2semidirect
14. #21423874C2semidirect
15. C59×#2363C2semidirect
21. #16837636C4semidirect
70. C22×C59⋊C8C2×C4semidirect
76. #14273701C2×C4semidirect
94. #14273660C2×C4semidirect
96. #14273658D4semidirect
99. #14273648C2×C4semidirect
102. #14273647C2×C4semidirect
113. #121×C59C2×C4semidirect
359. #2363D59semidirect
426. C59#23031semidirect
447. #121C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168376362
C2×#168375122
C2×#168374382
#214271322
#214249712
#214248312
#214247162
#214247132
#214244192
#214244182
#214243432
#214243422
#214239942
#214238742
C59×#23632
#2303159