Finite Group Databasebeta

← #28639594

Subgroups — #28639594

Order 15104.

984 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837658C211yesmaximal, characteristic, complemented
2C2×#16837641C211yesmaximal, characteristic, complemented
3C2×#16837609C211yesmaximal, characteristic, complemented
4C2×#16837474C211yesmaximal, characteristic
5#21429005C211yesmaximal, characteristic
6#21425296C211yesmaximal, characteristic, complemented
7#21425289C211yesmaximal, characteristic, complemented
8#21425104C211yesmaximal, characteristic, complemented
9#21425104C211yesmaximal, characteristic, complemented
10#21424917C211yesmaximal, characteristic, complemented
11#21424864C211yesmaximal, characteristic, complemented
12#21424530C211yesmaximal, characteristic, complemented
13#21424520C211yesmaximal, characteristic, complemented
14#21423929C211yesmaximal, characteristic, complemented
15C59×#2542C211yesmaximal, characteristic
16C22×#11745672C2211yescharacteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745664C2211yescharacteristic
19C23×C59⋊C8C2211yescharacteristic
20C2×#14273706C2211yescharacteristic
21C2×#14273706C2211yescharacteristic
22C2×C4×Dic118C2211yescharacteristic
23#16837658—24no—
24#16837641—24no—
25#16837609—24no—
26#16837474—24no—
27C2×#14273660C2211yescharacteristic
28C2×#14273658C2211yescharacteristic
29C2×C4⋊(C59⋊C8)C2211yescharacteristic
30C2×#14273651C2211yescharacteristic
31C2×#14273651C2211yescharacteristic
32C2×#14273651C2211yescharacteristic
33C2×#14273651C2211yescharacteristic
34C2×#14273651C2211yescharacteristic
35C2×#14273651C2211yescharacteristic
36C2×#14273650C2211yescharacteristic
37C2×#14273650C2211yescharacteristic
38C2×C22⋊(C59⋊C8)C2211yescharacteristic
39C2×C22⋊(C59⋊C8)C2211yescharacteristic
40C2×#14273638C2211yescharacteristic
41#16837333—21no—
42#16837316—21no—
43#16837290—21no—
44#16837290—21no—
45#16837268C2211yescharacteristic
46#16837262C2211yescharacteristic
47#16837262C2211yescharacteristic
48#16837164C2211yescharacteristic
49#16837164C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52C2×C4⋊Q8×C59C2211yescharacteristic
53C2×C22⋊Q8×C59C2211yescharacteristic
54C2×C22⋊Q8×C59C2211yescharacteristic
55C2×C22⋊Q8×C59C2211yescharacteristic
56C2×C22⋊Q8×C59C2211yescharacteristic
57C2×C4×D4×C59C2211yescharacteristic
58C59×#399—21no—
59C59×#399—21no—
60C59×#390—21no—
61C59×#384—21no—
62C4×C4⋊C4×C59C2211yescharacteristic
63C22×Dic118C2311yescharacteristic
64C2×#11745672—22no—
65C2×#11745672—22no—
66C2×#11745672—22no—
67C2×#11745672—22no—
68C2×#11745672—41no—
69C2×#11745672—41no—
70C2×#11745664—22no—
71C2×#11745664—22no—
72C2×#11745664—41no—
73C22×C59⋊C8—22no—
74C22×C59⋊C8—22no—
75C22×C59⋊C8—41no—
76C22×C59⋊C8C2311yescharacteristic
77C22×C59⋊C8C2311yescharacteristic
78C22×C59⋊C8C2311yescharacteristic
79C22×C59⋊C8C2311yescharacteristic
80#14273706—22no—
81#14273706—22no—
82#14273706—41no—
83#14273706—41no—
84C4×Dic118—22no—
85C4×Dic118—22no—
86C2×C4⋊Dic59C2311yescharacteristic
87C2×C4⋊Dic59C2311yescharacteristic
88C2×C4⋊Dic59C2311yescharacteristic
89C2×Dic59⋊C4—21no—
90C2×Dic59⋊C4—21no—
91C2×Dic59⋊C4—21no—
92C2×C22⋊Dic59—21no—
93C2×C22⋊Dic59—21no—
94C2×C22⋊Dic59—21no—
95C2×C22⋊Dic59—21no—
96C2×C4×Dic59—21no—
97#14273660—22no—
98#14273658—22no—
99C4⋊(C59⋊C8)D414yes—
100#14273651—22no—
101#14273651—22no—
102#14273651—22no—
103#14273651—22no—
104#14273651—41no—
105#14273651—41no—
106#14273650—22no—
107#14273650D414yescomplemented
108C22⋊(C59⋊C8)—22no—
109C22⋊(C59⋊C8)—22no—
110#14273638—22no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C59⋊#95—21no—
115C22×Q8×C59C2311yescharacteristic
116C22×Q8×C59C2311yescharacteristic
117C22×D4×C59D411yescharacteristic
118C23×C4×C59C2311yescharacteristic
119C23×C4×C59C2311yescharacteristic
120C4⋊Q8×C59—22no—
121C4⋊Q8×C59—22no—
122C22⋊Q8×C59—22no—
123C22⋊Q8×C59—22no—
124C22⋊Q8×C59—22no—
125C22⋊Q8×C59—22no—
126C22⋊Q8×C59—41no—
127C22⋊Q8×C59—41no—
128C22⋊Q8×C59—41no—
129C22⋊Q8×C59—41no—
130C4×D4×C59—22no—
131C4×D4×C59—22no—
132C2×C4⋊C4×C59—21no—
133C2×C4⋊C4×C59—21no—
134C2×C4⋊C4×C59—21no—
135C2×C4⋊C4×C59—21no—
136C2×C4⋊C4×C59—21no—
137C2×C4⋊C4×C59—21no—
138C2×C4⋊C4×C59D411yescharacteristic
139C2×C4⋊C4×C59C2311yescharacteristic
140C2×C4⋊C4×C59C2311yescharacteristic
141C2×C22⋊C4×C59—21no—
142C2×C22⋊C4×C59—21no—
143C2×C22⋊C4×C59—21no—
144C2×C22⋊C4×C59—21no—
145C2×C22⋊C4×C59D411yescharacteristic
146C2×C22⋊C4×C59D411yescharacteristic
147C2×C42×C59—21no—
148C2×C42×C59C2311yescharacteristic
149#95×C59—21no—
150C24×C59C2×D411yescharacteristic
151C24×C59C2×D411yescharacteristic
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—21no—
156C2×Q8×C59—21no—
157C2×Q8×C59—21no—
158C2×Q8×C59—21no—
159C2×Q8×C59—21no—
160C2×Q8×C59—21no—
161C2×Q8×C59—21no—
162C2×Q8×C59—21no—
163C2×Q8×C59—21no—
164C2×D4×C59—22no—
165C2×D4×C59—22no—
166C2×D4×C59—41no—
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×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—21no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—21no—
182C22×C4×C59—21no—
183C22×C4×C59C2×D411yescharacteristic
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59C2×D411yescharacteristic
186C22×C4×C59C2×D411yescharacteristic
187C22×C4×C59C2411yescharacteristic
188C22×Dic59—21no—
189C22×Dic59—21no—
190C22×Dic59—21no—
191C22×Dic59—21no—
192C2×Dic118—21no—
193C2×Dic118—21no—
194C2×Dic118—21no—
195C2×Dic118—21no—
196C2×Dic118—21no—
197C2×Dic118C2×D412yes—
198C4⋊C4×C59—22no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—42no—
202C4⋊C4×C59—42no—
203C4⋊C4×C59—42no—
204C4⋊C4×C59—42no—
205C4⋊C4×C59—42no—
206C4⋊C4×C59—42no—
207C4⋊C4×C59C2×D412yes—
208C4⋊C4×C59#4112yes—
209C22⋊C4×C59—22no—
210C22⋊C4×C59—22no—
211C22⋊C4×C59—42no—
212C22⋊C4×C59—42no—
213C22⋊C4×C59—42no—
214C22⋊C4×C59—42no—
215C42×C59—42no—
216C42×C59C2×D412yes—
217C42×C59#4112yes—
218C22⋊Dic59—42no—
219C22⋊Dic59—42no—
220C22⋊Dic59—42no—
221C22⋊Dic59—42no—
222#11745672—44no—
223#11745672—44no—
224C4⋊Dic59—21no—
225C4⋊Dic59—21no—
226C4⋊Dic59—21no—
227C4⋊Dic59—21no—
228C4⋊Dic59—21no—
229C4⋊Dic59—21no—
230Dic59⋊C4—42no—
231Dic59⋊C4—42no—
232Dic59⋊C4—42no—
233C4×Dic59—42no—
234#11745664—44no—
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⋊C8—21no—
244C2×C59⋊C8—44no—
245C2×C59⋊C8C2×D412yes—
246C2×C59⋊C8C2×D412yes—
247C2×C59⋊C8C2×D412yes—
248C23×C59—21no—
249C23×C59—21no—
250C23×C59—21no—
251C23×C59—21no—
252C23×C59—21no—
253C23×C59—21no—
254C23×C59—21no—
255C23×C59—21no—
256C23×C59—21no—
257C23×C59—21no—
258C23×C59—21no—
259C23×C59—21no—
260C23×C59—21no—
261C23×C59#13712yes—
262C23×C59C22×D411yescharacteristic
263Q8×C59—41no—
264Q8×C59—41no—
265Q8×C59—41no—
266Q8×C59—41no—
267Q8×C59—41no—
268Q8×C59—41no—
269Q8×C59—41no—
270Q8×C59—41no—
271D4×C59—44no—
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
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—21no—
283C2×C4×C59—21no—
284C2×C4×C59—41no—
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—41no—
297C2×C4×C59—41no—
298C2×C4×C59—41no—
299C2×C4×C59—41no—
300C2×C4×C59—41no—
301C2×C4×C59—41no—
302C2×C4×C59#12112yes—
303C2×C4×C59#12112yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C22×D411yescharacteristic
306C2×C4×C59C2×#4111yescharacteristic
307C2×C4×C59C2×#4111yescharacteristic
308C2×C4×C59H(5,𝔽2)11yescharacteristic
309C2×C4×C59H(5,𝔽2)11yescharacteristic
310C2×Dic59—22no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—41no—
318C2×Dic59—41no—
319C2×Dic59—41no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322Dic118—22no—
323Dic118—22no—
324Dic118—41no—
325Dic118—41no—
326C59⋊C8—22no—
327C59⋊C8—22no—
328C59⋊C8—22no—
329C59⋊C8—41no—
330#25398—591nomaximal, Sylow
331C22×C59—22no—
332C22×C59—22no—
333C22×C59—22no—
334C22×C59—41no—
335C22×C59—41no—
336C22×C59—41no—
337C22×C59—41no—
338C22×C59—41no—
339C22×C59—41no—
340C22×C59—41no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59C2×#12111yescharacteristic
346C22×C59D4211yescharacteristic
347C22×C59#54611yescharacteristic
348C22×C59C2×#13711yescharacteristic
349C22×C59#57511yescharacteristic
350C22×C59#57811yescharacteristic
351C22×C59#57811yescharacteristic
352C4×C59—22no—
353C4×C59—22no—
354C4×C59—41no—
355C4×C59—41no—
356C4×C59—42no—
357C4×C59—42no—
358C4×C59—81no—
359C4×C59—81no—
360C4×C59#53211yescharacteristic
361C4×C59#54011yescharacteristic
362C4×C59D4211yescharacteristic
363C4×C59#55011yescharacteristic
364Dic59—42no—
365Dic59—81no—
366Dic59—81no—
367Dic59—81no—
368C2×#470—591no—
369C2×#467—591no—
370C2×#462—591no—
371C2×#435—591no—
372#2542D5911yescharacteristic
373#2536—591no—
374#2036—591no—
375#2035—591no—
376#2001—591no—
377#2001—591no—
378#1960—591no—
379#1949—591no—
380#1894—591no—
381#1892—591no—
382#1763—591no—
383C2×C59—42no—
384C2×C59—81no—
385C2×C59#242811yescharacteristic
386C2×C59#305611yescharacteristic
387C2×C59#305911yescharacteristic
388C2×C59#326911yescharacteristic
389C2×C59#327011yescharacteristic
390C2×C59#331211yescharacteristic
391C2×C59#331511yescharacteristic
392C22×Q16—591no—
393C22×Q16—591no—
394C22×M16—591no—
395C23×C8—591no—
396C2×C4⋊Q8C2×D5911yescharacteristic
397C2×C22⋊Q8—591no—
398C2×C22⋊Q8—591no—
399C2×C22⋊Q8C2×D5911yescharacteristic
400C2×C22⋊Q8C2×D5911yescharacteristic
401C2×C22⋊Q8C2×D5911yescharacteristic
402C2×C22⋊Q8C2×D5911yescharacteristic
403C2×C4×Q8—591no—
404C2×C4×D4C2×D5911yescharacteristic
405#470—1184no—
406#467—1184no—
407#462—1184no—
408#435—1184no—
409C2×#107—591no—
410C2×#106—591no—
411C2×C4⋊C8—591no—
412C2×#103—591no—
413C2×#103—591no—
414C2×#103—591no—
415C2×#103—591no—
416C2×#103—591no—
417C2×#103—591no—
418C2×#103—591no—
419C2×#103—591no—
420C2×C22⋊C8—591no—
421C2×C22⋊C8—591no—
422C2×#97—591no—
423#399—21no—
424#399—21no—
425#398—1181no—
426#394—1181no—
427#390—21no—
428#388—1181no—
429#388—1181no—
430#384—21no—
431#382—591no—
432#380—591no—
433#380—591no—
434C4×C4⋊C4C2×D5911yescharacteristic
435#340—591no—
436#340—591no—
437#340—591no—
438#340—591no—
439C59#2539811yescharacteristic, complemented, Sylow
440C22×Q8—591no—
441C22×Q8C22×D5911yescharacteristic
442C22×Q8C22×D5911yescharacteristic
443C22×D4C22⋊D5911yescharacteristic
444C23×C4C22×D5911yescharacteristic
445C23×C4C22×D5911yescharacteristic
446C2×Q16—1182no—
447C2×Q16—1182no—
448C2×Q16—1182no—
449C2×Q16—1182no—
450C2×Q16—2361no—
451C2×Q16—2361no—
452C2×M16—1182no—
453C2×M16—1182no—
454C2×M16—2361no—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8—591no—
458C22×C8—591no—
459C22×C8—1182no—
460C22×C8—1182no—
461C22×C8—2361no—
462C4⋊Q8—22no—
463C4⋊Q8—22no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—22no—
467C22⋊Q8—22no—
468C22⋊Q8—41no—
469C22⋊Q8—41no—
470C22⋊Q8—41no—
471C22⋊Q8—41no—
472C22⋊Q8—1182no—
473C22⋊Q8—1182no—
474C22⋊Q8—2361no—
475C22⋊Q8—2361no—
476C4×Q8—1182no—
477C4×Q8—1182no—
478C4×D4—22no—
479C4×D4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—591no—
487C2×C4⋊C4—591no—
488C2×C4⋊C4—591no—
489C2×C4⋊C4—1181no—
490C2×C4⋊C4—1181no—
491C2×C4⋊C4—1181no—
492C2×C4⋊C4C22⋊D5911yescharacteristic
493C2×C4⋊C4C22×D5911yescharacteristic
494C2×C4⋊C4C22×D5911yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—1181no—
500C2×C22⋊C4—1181no—
501C2×C22⋊C4—1181no—
502C2×C22⋊C4—1181no—
503C2×C22⋊C4C22⋊D5911yescharacteristic
504C2×C22⋊C4C22⋊D5911yescharacteristic
505C2×C42—21no—
506C2×C42—1181no—
507C2×C42C22×D5911yescharacteristic
508#107—1182no—
509#106—1182no—
510C4⋊C8—594no—
511#103—594no—
512#103—1182no—
513#103—1182no—
514#103—1182no—
515#103—1182no—
516#103—1182no—
517#103—2361no—
518#103—2361no—
519C22⋊C8—1182no—
520C22⋊C8—1182no—
521#97—1182no—
522#95—21no—
523#95—1181no—
524#95—1181no—
525#95—1181no—
526#95—1181no—
527C24C2×C22⋊D5911yescharacteristic
528C24C2×C22⋊D5911yescharacteristic
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—592no—
542C2×Q8—1181no—
543C2×Q8—1181no—
544C2×Q8—1181no—
545C2×Q8—1181no—
546C2×Q8—1181no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—41no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—1181no—
567C22×C4—1181no—
568C22×C4—1181no—
569C22×C4—1181no—
570C22×C4C2×C22⋊D5911yescharacteristic
571C22×C4C2×C22⋊D5911yescharacteristic
572C22×C4C2×C22⋊D5911yescharacteristic
573C22×C4C2×C22⋊D5911yescharacteristic
574C22×C4C23×D5911yescharacteristic
575Q16—2364no—
576Q16—2364no—
577M16—2364no—
578C2×C8—592no—
579C2×C8—592no—
580C2×C8—592no—
581C2×C8—1181no—
582C2×C8—1181no—
583C2×C8—1181no—
584C2×C8—1181no—
585C2×C8—1181no—
586C2×C8—1181no—
587C2×C8—1181no—
588C2×C8—1181no—
589C2×C8—1181no—
590C2×C8—2364no—
591C4⋊C4—22no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—1181no—
601C4⋊C4—1181no—
602C4⋊C4—1181no—
603C4⋊C4—1181no—
604C4⋊C4—1181no—
605C4⋊C4—1181no—
606C4⋊C4—2362no—
607C4⋊C4—2362no—
608C4⋊C4—2362no—
609C4⋊C4D4×D5912yes—
610C4⋊C4#1174568712yes—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—2362no—
618C22⋊C4—2362no—
619C22⋊C4—2362no—
620C22⋊C4—2362no—
621C42—42no—
622C42—2362no—
623C42D4×D5912yes—
624C42#1174568712yes—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23#1427375812yes—
639C23C22×C22⋊D5911yescharacteristic
640Q8—41no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—1182no—
649Q8—1182no—
650Q8—2361no—
651Q8—2361no—
652D4—44no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
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—1182no—
684C2×C4—2361no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4—2361no—
691C2×C4—2361no—
692C2×C4—2361no—
693C2×C4—2361no—
694C2×C4—2361no—
695C2×C4#1427369912yes—
696C2×C4#1427369912yes—
697C2×C4C2×D4×D5911yescharacteristic
698C2×C4C2×D4×D5911yescharacteristic
699C2×C4C2×#1174568711yescharacteristic
700C2×C4C2×#1174568711yescharacteristic
701C2×C4#1427377211yescharacteristic
702C2×C4#1427377211yescharacteristic
703C8—1182no—
704C8—1182no—
705C8—1182no—
706C8—2361no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22C2×#1427369911yescharacteristic
722C22D4×C22⋊D5911yescharacteristic
723C22#1683804611yescharacteristic
724C22C2×#1427375811yescharacteristic
725C22#1683820011yescharacteristic
726C22#1683821711yescharacteristic
727C22#1683821711yescharacteristic
728C4—22no—
729C4—22no—
730C4—42no—
731C4—41no—
732C4—41no—
733C4—42no—
734C4—81no—
735C4—81no—
736C4—4721no—
737C4—4721no—
738C4—4721no—
739C4—2362no—
740C4#1683795011yescharacteristic
741C4#1683800611yescharacteristic
742C4#1683803711yescharacteristic
743C4#1683807211yescharacteristic
744C2—42no—
745C2—81no—
746C2#2142768711yescharacteristic
747C2#2143372211yescharacteristic
748C2#2143374811yescharacteristic
749C2#2143564711yescharacteristic
750C2#2143566711yescharacteristic
751C2#2143614711yescharacteristic
752C2#2143619211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC59×#2542C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenter#2542D59
hypocenterC59#25398
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2542

Complements

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

NH ≅ G/Ntype
1. C2×#16837658C2semidirect
2. C2×#16837641C2semidirect
3. C2×#16837609C2semidirect
6. #21425296C2semidirect
7. #21425289C2semidirect
8. #21425104C2semidirect
9. #21425104C2semidirect
10. #21424917C2semidirect
11. #21424864C2semidirect
12. #21424530C2semidirect
13. #21424520C2semidirect
14. #21423929C2semidirect
107. #14273650D4semidirect
439. C59#25398semidirect

Maximal subgroups

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

subgroupindex
C2×#168376582
C2×#168376412
C2×#168376092
C2×#168374742
#214290052
#214252962
#214252892
#214251042
#214249172
#214248642
#214245302
#214245202
#214239292
C59×#25422
#2539859