Finite Group Databasebeta

← #28609412

Subgroups — #28609412

Order 15104.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837540C211yesmaximal, characteristic
2C2×C4×#11745670C211yesmaximal, characteristic, complemented
3C2×#16837410C211yesmaximal, characteristic, complemented
4C22⋊C4×Dic118C211yesmaximal, characteristic, complemented
5#21424976C211yesmaximal, characteristic, complemented
6#21424771C211yesmaximal, characteristic, complemented
7#21424730C211yesmaximal, characteristic, complemented
8#21424535C211yesmaximal, characteristic
9#21424454C211yesmaximal, characteristic, complemented
10#21424430C211yesmaximal, characteristic, complemented
11#21424349C211yesmaximal, characteristic, complemented
12#21424295C211yesmaximal, characteristic, complemented
13#21423929C211yesmaximal, characteristic, complemented
14#21423880C211yesmaximal, characteristic, complemented
15C59×#2363C211yesmaximal, characteristic
16C23×Dic118C2211yescharacteristic
17C22×#11745670C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745664C2211yescharacteristic
20C2×C4×Dic118C2211yescharacteristic
21C2×C4×Dic118C2211yescharacteristic
22#16837540C418yescomplemented
23C4×#11745670—24no—
24C2×#14273660C2211yescharacteristic
25C2×#14273658C2211yescharacteristic
26#16837410—24no—
27C2×#14273650C2211yescharacteristic
28C2×#14273650C2211yescharacteristic
29C2×#14273650C2211yescharacteristic
30C2×#14273650C2211yescharacteristic
31C2×#14273650C2211yescharacteristic
32C2×#14273650C2211yescharacteristic
33C2×#14273648C2211yescharacteristic
34C2×#14273648C2211yescharacteristic
35C2×C22⋊(C59⋊C8)C2211yescharacteristic
36C2×#14273638C2211yescharacteristic
37C2×C4×C59⋊C8C2211yescharacteristic
38#16837308C2211yescharacteristic
39#16837308C2211yescharacteristic
40#16837306—21no—
41#16837306—21no—
42#16837262C2211yescharacteristic
43#16837260—21no—
44C22⋊C4×Dic59—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×Dic118—22no—
63C22×Dic118—22no—
64C22×Dic118—21no—
65C22×Dic118—22no—
66C22×Dic118—41no—
67C22×Dic118—41no—
68C22×Dic118C2×C414yescomplemented
69C22×Dic118C2311yescharacteristic
70C22×Dic118C2311yescharacteristic
71C23×Dic59—21no—
72C2×#11745670—22no—
73C2×#11745670—22no—
74C2×#11745670—41no—
75C2×#11745670—41no—
76C2×#11745670C2×C414yes—
77C2×#11745670C2×C414yes—
78C2×#11745664—22no—
79C2×#11745664—22no—
80C2×#11745664—41no—
81C22×C59⋊C8C2311yescharacteristic
82C22×C59⋊C8C2311yescharacteristic
83C22×C59⋊C8C2311yescharacteristic
84C22×C59⋊C8C2311yescharacteristic
85C4×Dic118—22no—
86C4×Dic118—22no—
87C4×Dic118—41no—
88C4×Dic118—41no—
89C2×C4⋊Dic59C2311yescharacteristic
90C2×C4⋊Dic59C2311yescharacteristic
91C2×Dic59⋊C4—21no—
92C2×Dic59⋊C4—21no—
93C2×C22⋊Dic59—21no—
94C2×C4×Dic59—21no—
95C2×C4×Dic59—21no—
96#14273660—41no—
97#14273658—22no—
98#14273650—22no—
99#14273650—22no—
100#14273650—22no—
101#14273650C2×C414yescomplemented
102#14273650C2×C414yescomplemented
103#14273650D414yescomplemented
104#14273648—22no—
105#14273648—41no—
106C22⋊(C59⋊C8)C2×C414yescomplemented
107#14273638—41no—
108C4×C59⋊C8—22no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95—21no—
114C22×D4×C59—21no—
115C22×D4×C59C2311yescharacteristic
116C23×C4×C59—21no—
117C23×C4×C59C2311yescharacteristic
118#121×C59—22no—
119#121×C59C2×C414yes—
120C4×D4×C59—22no—
121C4×D4×C59—41no—
122#117×C59—22no—
123#117×C59—41no—
124C2×C4⋊C4×C59—21no—
125C2×C4⋊C4×C59C2311yescharacteristic
126C2×C4⋊C4×C59C2311yescharacteristic
127C2×C4⋊C4×C59C2311yescharacteristic
128C2×C22⋊C4×C59—21no—
129C2×C22⋊C4×C59—21no—
130C2×C22⋊C4×C59—21no—
131C2×C22⋊C4×C59—21no—
132C2×C22⋊C4×C59—21no—
133C2×C22⋊C4×C59D411yescharacteristic
134C2×C22⋊C4×C59D411yescharacteristic
135C2×C42×C59—21no—
136C2×C42×C59—21no—
137C2×C42×C59C2311yescharacteristic
138C2×C42×C59C2311yescharacteristic
139#95×C59—21no—
140#95×C59—21no—
141#95×C59D411yescharacteristic
142#95×C59D411yescharacteristic
143C24×C59—21no—
144C24×C59C2×D411yescharacteristic
145C2×D4×C59—24no—
146C2×D4×C59—21no—
147C2×D4×C59—21no—
148C2×D4×C59—21no—
149C2×D4×C59—21no—
150C2×D4×C59—21no—
151C2×D4×C59—81no—
152C2×D4×C59—81no—
153C2×D4×C59C22×C412yes—
154C22×C4×C59—21no—
155C22×C4×C59—21no—
156C22×C4×C59—21no—
157C22×C4×C59—21no—
158C22×C4×C59—21no—
159C22×C4×C59—21no—
160C22×C4×C59—21no—
161C22×C4×C59—42no—
162C22×C4×C59—42no—
163C22×C4×C59—81no—
164C22×C4×C59C22×C412yes—
165C22×C4×C59C2×D411yescharacteristic
166C22×C4×C59C2×D411yescharacteristic
167C22×C4×C59C2×D411yescharacteristic
168C22×C4×C59C2×D411yescharacteristic
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59#4112yes—
171C22×C4×C59C2411yescharacteristic
172C22×Dic59—21no—
173C22×Dic59—24no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—21no—
177C22×Dic59—42no—
178C22×Dic59—42no—
179C2×Dic118—21no—
180C2×Dic118—21no—
181C2×Dic118—21no—
182C2×Dic118—21no—
183C2×Dic118—21no—
184C2×Dic118—21no—
185C2×Dic118—21no—
186C2×Dic118—28no—
187C2×Dic118—24no—
188C2×Dic118—21no—
189C2×Dic118—44no—
190C2×Dic118—44no—
191C2×Dic118—44no—
192C2×Dic118—42no—
193C2×Dic118—42no—
194C2×Dic118C22×C412yes—
195C2×Dic118C22×C412yes—
196C2×Dic118C2×D412yes—
197C2×Dic118#4112yes—
198C4⋊C4×C59—21no—
199C4⋊C4×C59—21no—
200C4⋊C4×C59—21no—
201C4⋊C4×C59—21no—
202C4⋊C4×C59—81no—
203C4⋊C4×C59C22×C412yes—
204C4⋊C4×C59C2×D412yes—
205C22⋊C4×C59—24no—
206C22⋊C4×C59—22no—
207C22⋊C4×C59—41no—
208C22⋊C4×C59—42no—
209C22⋊C4×C59—42no—
210C22⋊C4×C59—42no—
211C22⋊C4×C59—81no—
212C42×C59—21no—
213C42×C59—21no—
214C42×C59—21no—
215C42×C59—21no—
216C42×C59—42no—
217C42×C59—81no—
218C22⋊Dic59—42no—
219#11745670—28no—
220#11745670—44no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—21no—
224C4⋊Dic59—21no—
225Dic59⋊C4—42no—
226Dic59⋊C4—42no—
227C4×Dic59—42no—
228C4×Dic59—42no—
229#11745664—44no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
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⋊C8C22×C412yes—
240C2×C59⋊C8C22×C412yes—
241C2×C59⋊C8C2×D412yes—
242C23×C59—21no—
243C23×C59—21no—
244C23×C59—21no—
245C23×C59—21no—
246C23×C59—21no—
247C23×C59—21no—
248C23×C59—22no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59C4×D412yes—
256C23×C59C22×D411yescharacteristic
257D4×C59—22no—
258D4×C59—22no—
259D4×C59—41no—
260D4×C59—41no—
261D4×C59—84no—
262C2×C4×C59—21no—
263C2×C4×C59—21no—
264C2×C4×C59—21no—
265C2×C4×C59—21no—
266C2×C4×C59—22no—
267C2×C4×C59—22no—
268C2×C4×C59—22no—
269C2×C4×C59—22no—
270C2×C4×C59—22no—
271C2×C4×C59—21no—
272C2×C4×C59—22no—
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—21no—
281C2×C4×C59—41no—
282C2×C4×C59—41no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59—41no—
288C2×C4×C59—84no—
289C2×C4×C59C4×D412yes—
290C2×C4×C59#13712yes—
291C2×C4×C59C23×C411yescharacteristic
292C2×C4×C59C22×D411yescharacteristic
293C2×C4×C59C2×#4111yescharacteristic
294C2×C4×C59C2×#4111yescharacteristic
295C2×C4×C59H(5,𝔽2)11yescharacteristic
296C2×C4×C59H(5,𝔽2)11yescharacteristic
297C2×Dic59—22no—
298C2×Dic59—22no—
299C2×Dic59—22no—
300C2×Dic59—22no—
301C2×Dic59—48no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310Dic118—22no—
311Dic118—22no—
312Dic118—22no—
313Dic118—22no—
314Dic118—22no—
315Dic118—48no—
316Dic118—41no—
317Dic118—41no—
318Dic118C4×D414yes—
319C59⋊C8—22no—
320C59⋊C8—22no—
321C59⋊C8—22no—
322C59⋊C8—41no—
323#22885—591nomaximal, Sylow
324C22×C59—22no—
325C22×C59—22no—
326C22×C59—22no—
327C22×C59—41no—
328C22×C59—41no—
329C22×C59—41no—
330C22×C59—41no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—81no—
335C22×C59—81no—
336C22×C59—81no—
337C22×C59—81no—
338C22×C59C2×C4×D411yescharacteristic
339C22×C59D4211yescharacteristic
340C22×C59#54611yescharacteristic
341C22×C59C2×#13711yescharacteristic
342C22×C59#57511yescharacteristic
343C22×C59#57711yescharacteristic
344C22×C59#57711yescharacteristic
345C4×C59—22no—
346C4×C59—22no—
347C4×C59—41no—
348C4×C59—42no—
349C4×C59—42no—
350C4×C59—41no—
351C4×C59—41no—
352C4×C59—81no—
353C4×C59C2×C4×D411yescharacteristic
354C4×C59#51811yescharacteristic
355C4×C59#54611yescharacteristic
356C4×C59#55111yescharacteristic
357Dic59—24no—
358Dic59—42no—
359Dic59—81no—
360Dic59—81no—
361C2×#448—591no—
362C2×C4×SD16—591no—
363C2×#419—591no—
364#2363D5911yescharacteristic
365Q8×C22⋊C4—591no—
366#1973—591no—
367#1933—591no—
368#1927—591no—
369#1895—591no—
370#1880—591no—
371#1877—591no—
372#1863—591no—
373#1854—591no—
374#1763—591no—
375#1753—591no—
376C2×C59—42no—
377C2×C59—82no—
378C2×C59#235811yescharacteristic
379C2×C59C4×#13711yescharacteristic
380C2×C59#294911yescharacteristic
381C2×C59#326611yescharacteristic
382C2×C59#327111yescharacteristic
383C2×C59#332611yescharacteristic
384C2×C59#332911yescharacteristic
385C23×Q8—591no—
386C22×SD16—591no—
387C22×SD16—591no—
388C22×M16—591no—
389C2×#121C2×D5911yescharacteristic
390C2×C4×Q8—591no—
391C2×C4×Q8—591no—
392C2×C4×D4C2×D5911yescharacteristic
393C2×#117C2×D5911yescharacteristic
394#448—598no—
395C4×SD16—1184no—
396C2×#107—591no—
397C2×#106—591no—
398#419—1184no—
399C2×#103—591no—
400C2×#103—591no—
401C2×#103—591no—
402C2×#103—591no—
403C2×#103—591no—
404C2×#103—591no—
405C2×#102—591no—
406C2×#102—591no—
407C2×C22⋊C8—591no—
408C2×#97—591no—
409C2×C4×C8—591no—
410#391—591no—
411#391—591no—
412#391—1181no—
413#391—1181no—
414#390—21no—
415#390C2×D5911yescharacteristic
416#389C2×D5911yescharacteristic
417#388—21no—
418#386—21no—
419#380—591no—
420#380—1181no—
421C4×C4⋊C4C2×D5911yescharacteristic
422C4×C22⋊C4—21no—
423C4×C22⋊C4—1181no—
424C4×C22⋊C4C2×D5911yescharacteristic
425#340—591no—
426#340—591no—
427#340—591no—
428#340—591no—
429#336—591no—
430#336—591no—
431C59#2288511yescharacteristic, complemented, Sylow
432C22×Q8—594no—
433C22×Q8—591no—
434C22×Q8—591no—
435C22×Q8—1182no—
436C22×Q8—1182no—
437C22×Q8—1182no—
438C22×Q8—1181no—
439C22×Q8—2361no—
440C22×Q8—2361no—
441C22×D4—21no—
442C22×D4C22×D5911yescharacteristic
443C23×C4—21no—
444C23×C4—1181no—
445C23×C4C22×D5911yescharacteristic
446C2×SD16—594no—
447C2×SD16—594no—
448C2×SD16—1182no—
449C2×SD16—1182no—
450C2×SD16—2361no—
451C2×SD16—2361no—
452C2×M16—1182no—
453C2×M16—1182no—
454C2×M16—2361no—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8—591no—
458C22×C8—591no—
459#121—22no—
460#121C4×D5914yes—
461C4×Q8—1182no—
462C4×Q8—1182no—
463C4×Q8—2361no—
464C4×Q8—2361no—
465C4×D4—22no—
466C4×D4—41no—
467#117—22no—
468#117—41no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—1181no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4C22×D5911yescharacteristic
475C2×C4⋊C4C22×D5911yescharacteristic
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4C22⋊D5911yescharacteristic
484C2×C22⋊C4C22⋊D5911yescharacteristic
485C2×C42—21no—
486C2×C42—21no—
487C2×C42—1181no—
488C2×C42—1181no—
489C2×C42C22×D5911yescharacteristic
490C2×C42C22×D5911yescharacteristic
491#107—2361no—
492#106—1182no—
493#103—594no—
494#103—594no—
495#103—594no—
496#103—1182no—
497#103—1182no—
498#103—1182no—
499#102—1182no—
500#102—2361no—
501C22⋊C8—594no—
502#97—2361no—
503C4×C8—1182no—
504#95—21no—
505#95—21no—
506#95—1181no—
507#95—1181no—
508#95—1181no—
509#95—1181no—
510#95—1181no—
511#95C22⋊D5911yescharacteristic
512#95C22⋊D5911yescharacteristic
513C24—21no—
514C24C2×C22⋊D5911yescharacteristic
515C2×Q8—592no—
516C2×Q8—592no—
517C2×Q8—592no—
518C2×Q8—592no—
519C2×Q8—1188no—
520C2×Q8—1184no—
521C2×Q8—1181no—
522C2×Q8—1181no—
523C2×Q8—1181no—
524C2×Q8—1181no—
525C2×Q8—1181no—
526C2×Q8—1181no—
527C2×Q8—1181no—
528C2×Q8—1181no—
529C2×Q8—2362no—
530C2×Q8—2362no—
531C2×Q8—2364no—
532C2×Q8—2364no—
533C2×Q8—2364no—
534C2×D4—24no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—81no—
541C2×D4—81no—
542C2×D4C2×C4×D5912yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—1181no—
554C22×C4—1184no—
555C22×C4—1181no—
556C22×C4—1181no—
557C22×C4—1181no—
558C22×C4—2362no—
559C22×C4—2362no—
560C22×C4C2×C4×D5912yes—
561C22×C4#1174568512yes—
562C22×C4C2×C22⋊D5911yescharacteristic
563C22×C4C2×C22⋊D5911yescharacteristic
564C22×C4C2×C22⋊D5911yescharacteristic
565C22×C4C2×C22⋊D5911yescharacteristic
566C22×C4C2×C22⋊D5911yescharacteristic
567C22×C4C23×D5911yescharacteristic
568SD16—1188no—
569SD16—2364no—
570M16—2364no—
571C2×C8—592no—
572C2×C8—592no—
573C2×C8—592no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8—1181no—
582C2×C8—1181no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—81no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—2362no—
593C4⋊C4—2362no—
594C4⋊C4C2×C4×D5912yes—
595C4⋊C4D4×D5912yes—
596C22⋊C4—24no—
597C22⋊C4—22no—
598C22⋊C4—41no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—81no—
603C22⋊C4—2362no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—42no—
609C42—81no—
610C42—2362no—
611C42—2362no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C4×C22⋊D5912yes—
626C23C22×C22⋊D5911yescharacteristic
627Q8—594no—
628Q8—1182no—
629Q8—1182no—
630Q8—1182no—
631Q8—1182no—
632Q8—1182no—
633Q8—2368no—
634Q8—2361no—
635Q8—2361no—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—84no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4—1182no—
669C2×C4—1182no—
670C2×C4—1182no—
671C2×C4—1182no—
672C2×C4—2368no—
673C2×C4—2361no—
674C2×C4—2361no—
675C2×C4—2361no—
676C2×C4—2361no—
677C2×C4—2361no—
678C2×C4—2361no—
679C2×C4—2361no—
680C2×C4—2361no—
681C2×C4C4×C22⋊D5912yes—
682C2×C4#1427375712yes—
683C2×C4C22×C4×D5911yescharacteristic
684C2×C4C2×D4×D5911yescharacteristic
685C2×C4#41×D5911yescharacteristic
686C2×C4C2×#1174568511yescharacteristic
687C2×C4#1427377211yescharacteristic
688C2×C4#1427377311yescharacteristic
689C8—1182no—
690C8—1182no—
691C8—1182no—
692C8—2361no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22C2×C4×C22⋊D5911yescharacteristic
708C22D4×C22⋊D5911yescharacteristic
709C22#1683804011yescharacteristic
710C22C2×#1427375711yescharacteristic
711C22#1683820011yescharacteristic
712C22#1683821311yescharacteristic
713C22#1683821311yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—42no—
718C4—41no—
719C4—42no—
720C4—41no—
721C4—81no—
722C4—1184no—
723C4—4721no—
724C4—4721no—
725C4—2362no—
726C4C4×D4×D5911yescharacteristic
727C4#1683787411yescharacteristic
728C4#1683804811yescharacteristic
729C4#1683808111yescharacteristic
730C2—42no—
731C2—82no—
732C2#2142707311yescharacteristic
733C2C4×#1427375711yescharacteristic
734C2#2143295311yescharacteristic
735C2#2143560211yescharacteristic
736C2#2143567711yescharacteristic
737C2#2143634311yescharacteristic
738C2#2143638411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#2363C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
cosocleC22×C4×C59C24
hypercenter#2363D59
hypocenterC59#22885
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×C4×#11745670C2semidirect
3. C2×#16837410C2semidirect
4. C22⋊C4×Dic118C2semidirect
5. #21424976C2semidirect
6. #21424771C2semidirect
7. #21424730C2semidirect
9. #21424454C2semidirect
10. #21424430C2semidirect
11. #21424349C2semidirect
12. #21424295C2semidirect
13. #21423929C2semidirect
14. #21423880C2semidirect
22. #16837540C4semidirect
68. C22×Dic118C2×C4semidirect
101. #14273650C2×C4semidirect
102. #14273650C2×C4semidirect
103. #14273650D4semidirect
106. C22⋊(C59⋊C8)C2×C4semidirect
431. C59#22885semidirect

Maximal subgroups

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

subgroupindex
C2×#168375402
C2×C4×#117456702
C2×#168374102
C22⋊C4×Dic1182
#214249762
#214247712
#214247302
#214245352
#214244542
#214244302
#214243492
#214242952
#214239292
#214238802
C59×#23632
#2288559