Finite Group Databasebeta

← #28609415

Subgroups — #28609415

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×SD16×Dic59C211yesmaximal, characteristic, complemented
2C2×#16837411C211yesmaximal, characteristic, complemented
3#21427138C211yesmaximal, characteristic
4Q8×C22⋊Dic59C211yesmaximal, characteristic, complemented
5#21424979C211yesmaximal, characteristic, complemented
6#21424774C211yesmaximal, characteristic, complemented
7#21424732C211yesmaximal, characteristic, complemented
8#21424535C211yesmaximal, characteristic
9#21424453C211yesmaximal, characteristic, complemented
10#21424432C211yesmaximal, characteristic, complemented
11#21424352C211yesmaximal, characteristic, complemented
12#21424297C211yesmaximal, characteristic, complemented
13#21423928C211yesmaximal, characteristic, complemented
14#21423882C211yesmaximal, characteristic, complemented
15C2×C59×#448C211yesmaximal, characteristic
16C22×#11745664C2211yescharacteristic
17C2×Q8×Dic59C2211yescharacteristic
18C2×Q8×Dic59C2211yescharacteristic
19C2×D4×Dic59C2211yescharacteristic
20C2×#14273686C2211yescharacteristic
21SD16×Dic59—24no—
22C2×#14273661C2211yescharacteristic
23C2×#14273659C2211yescharacteristic
24#16837411—24no—
25C2×#14273651C2211yescharacteristic
26C2×#14273651C2211yescharacteristic
27C2×#14273651C2211yescharacteristic
28C2×#14273651C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273637C2211yescharacteristic
32C2×C8×Dic59C2211yescharacteristic
33#16837309—21no—
34#16837309—21no—
35#16837309C2211yescharacteristic
36#16837309C2211yescharacteristic
37#16837305—21no—
38#16837305C2211yescharacteristic
39#16837301C2211yescharacteristic
40#16837295—21no—
41#16837282—21no—
42#16837262—21no—
43#16837262C2211yescharacteristic
44C4⋊C4×Dic59C2211yescharacteristic
45C22⋊C4×Dic59—21no—
46C4×C22⋊Dic59—21no—
47C4×C22⋊Dic59C2211yescharacteristic
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54C23×Q8×C59C2211yescharacteristic
55C22×SD16×C59C2211yescharacteristic
56C22×SD16×C59C2211yescharacteristic
57C2×#121×C59C2211yescharacteristic
58C59×#448C418yescomplemented
59C2×#103×C59C2211yescharacteristic
60C2×#103×C59C2211yescharacteristic
61C2×C22⋊C8×C59C2211yescharacteristic
62C23×Dic59—21no—
63C2×#11745664—22no—
64C2×#11745664—22no—
65C2×#11745664—41no—
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68Q8×Dic59—22no—
69Q8×Dic59—22no—
70Q8×Dic59—41no—
71Q8×Dic59—41no—
72D4×Dic59—22no—
73D4×Dic59—41no—
74#14273686—22no—
75#14273686—41no—
76C2×C4⋊Dic59—21no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59C2311yescharacteristic
80C2×C4⋊Dic59C2311yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C22⋊Dic59—21no—
84C2×C22⋊Dic59—21no—
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59D411yescharacteristic
89C2×C22⋊Dic59D411yescharacteristic
90C2×C4×Dic59—21no—
91C2×C4×Dic59—21no—
92C2×C4×Dic59—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59C2311yescharacteristic
95C2×C4×Dic59C2311yescharacteristic
96#14273661—41no—
97#14273659—22no—
98#14273651—22no—
99#14273651—22no—
100#14273651—22no—
101#14273651D414yescomplemented
102#14273648—22no—
103#14273648—41no—
104#14273637—41no—
105C8×Dic59—22no—
106C59⋊#95—21no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95—21no—
113C59⋊#95D411yescharacteristic
114C59⋊#95D411yescharacteristic
115C22×Q8×C59—21no—
116C22×Q8×C59—22no—
117C22×Q8×C59—22no—
118C22×Q8×C59—22no—
119C22×Q8×C59—41no—
120C22×Q8×C59—41no—
121C22×Q8×C59C2×C414yescomplemented
122C22×Q8×C59C2311yescharacteristic
123C22×Q8×C59C2311yescharacteristic
124C22×D4×C59—21no—
125C22×D4×C59C2311yescharacteristic
126C23×C4×C59—21no—
127C23×C4×C59C2311yescharacteristic
128C2×SD16×C59—22no—
129C2×SD16×C59—22no—
130C2×SD16×C59—41no—
131C2×SD16×C59—41no—
132C2×SD16×C59C2×C414yes—
133C2×SD16×C59C2×C414yes—
134C22×C8×C59C2311yescharacteristic
135C22×C8×C59C2311yescharacteristic
136#121×C59—22no—
137#121×C59C2×C414yes—
138C2×C4⋊C4×C59C2311yescharacteristic
139C2×C22⋊C4×C59—21no—
140#103×C59C2×C414yescomplemented
141#103×C59C2×C414yescomplemented
142C22⋊C8×C59C2×C414yescomplemented
143C24×C59—21no—
144C24×C59C2×D411yescharacteristic
145C2×Q8×C59—24no—
146C2×Q8×C59—21no—
147C2×Q8×C59—21no—
148C2×Q8×C59—21no—
149C2×Q8×C59—21no—
150C2×Q8×C59—28no—
151C2×Q8×C59—21no—
152C2×Q8×C59—21no—
153C2×Q8×C59—21no—
154C2×Q8×C59—21no—
155C2×Q8×C59—42no—
156C2×Q8×C59—42no—
157C2×Q8×C59—44no—
158C2×Q8×C59—44no—
159C2×Q8×C59—44no—
160C2×Q8×C59C22×C412yes—
161C2×Q8×C59C22×C412yes—
162C2×Q8×C59C2×D412yes—
163C2×Q8×C59#4112yes—
164C2×D4×C59—24no—
165C2×D4×C59—21no—
166C2×D4×C59—21no—
167C2×D4×C59—21no—
168C2×D4×C59—21no—
169C2×D4×C59—21no—
170C2×D4×C59—81no—
171C2×D4×C59—81no—
172C2×D4×C59C22×C412yes—
173C22×C4×C59—21no—
174C22×C4×C59—21no—
175C22×C4×C59—21no—
176C22×C4×C59—21no—
177C22×C4×C59—21no—
178C22×C4×C59—24no—
179C22×C4×C59—21no—
180C22×C4×C59—21no—
181C22×C4×C59—42no—
182C22×C4×C59—42no—
183C22×C4×C59C22×C412yes—
184C22×C4×C59C2×D411yescharacteristic
185C22×C4×C59#4112yes—
186C22×C4×C59C2411yescharacteristic
187C22×Dic59—21no—
188C22×Dic59—21no—
189C22×Dic59—21no—
190C22×Dic59—21no—
191C22×Dic59—42no—
192C22×Dic59—42no—
193C22×Dic59—81no—
194C22×Dic59C2×D411yescharacteristic
195C22×Dic59C2×D411yescharacteristic
196C22×Dic59C2×D411yescharacteristic
197C22×Dic59C2×D411yescharacteristic
198SD16×C59—28no—
199SD16×C59—44no—
200C2×C8×C59—21no—
201C2×C8×C59—21no—
202C2×C8×C59—21no—
203C2×C8×C59—21no—
204C2×C8×C59C22×C412yes—
205C2×C8×C59C22×C412yes—
206C4⋊C4×C59—21no—
207C4⋊C4×C59C22×C412yes—
208C22⋊C4×C59—24no—
209C22⋊Dic59—22no—
210C22⋊Dic59—41no—
211C22⋊Dic59—42no—
212C22⋊Dic59—42no—
213C22⋊Dic59—42no—
214C22⋊Dic59—42no—
215C22⋊Dic59—81no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—21no—
222C4⋊Dic59—21no—
223C4⋊Dic59—42no—
224C4⋊Dic59—42no—
225C4⋊Dic59—81no—
226C4⋊Dic59C2×D412yes—
227C4×Dic59—21no—
228C4×Dic59—21no—
229C4×Dic59—21no—
230C4×Dic59—21no—
231C4×Dic59—42no—
232C4×Dic59—42no—
233C4×Dic59—42no—
234C4×Dic59—81no—
235#11745664—44no—
236C2×C59⋊C8—21no—
237C2×C59⋊C8—21no—
238C2×C59⋊C8—21no—
239C2×C59⋊C8—21no—
240C2×C59⋊C8—21no—
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
257Q8×C59—22no—
258Q8×C59—22no—
259Q8×C59—22no—
260Q8×C59—22no—
261Q8×C59—22no—
262Q8×C59—48no—
263Q8×C59—41no—
264Q8×C59—41no—
265Q8×C59C4×D414yes—
266D4×C59—22no—
267D4×C59—22no—
268D4×C59—41no—
269D4×C59—41no—
270D4×C59—84no—
271C2×C4×C59—22no—
272C2×C4×C59—21no—
273C2×C4×C59—22no—
274C2×C4×C59—22no—
275C2×C4×C59—21no—
276C2×C4×C59—22no—
277C2×C4×C59—22no—
278C2×C4×C59—22no—
279C2×C4×C59—22no—
280C2×C4×C59—22no—
281C2×C4×C59—22no—
282C2×C4×C59—48no—
283C2×C4×C59—41no—
284C2×C4×C59—41no—
285C2×C4×C59—41no—
286C2×C4×C59—41no—
287C2×C4×C59C4×D412yes—
288C2×C4×C59C23×C411yescharacteristic
289C2×C4×C59C22×D411yescharacteristic
290C2×C4×C59C2×#4111yescharacteristic
291C2×C4×C59C2×#4111yescharacteristic
292C2×C4×C59H(5,𝔽2)11yescharacteristic
293C2×C4×C59H(5,𝔽2)11yescharacteristic
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—22no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—21no—
301C2×Dic59—21no—
302C2×Dic59—21no—
303C2×Dic59—21no—
304C2×Dic59—21no—
305C2×Dic59—21no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—41no—
312C2×Dic59—41no—
313C2×Dic59—41no—
314C2×Dic59—41no—
315C2×Dic59—41no—
316C2×Dic59—41no—
317C2×Dic59—84no—
318C2×Dic59#13712yes—
319C8×C59—22no—
320C8×C59—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—24no—
347C4×C59—42no—
348C4×C59—42no—
349C4×C59C2×C4×D411yescharacteristic
350C4×C59#51811yescharacteristic
351C4×C59#54611yescharacteristic
352C4×C59#55111yescharacteristic
353Dic59—22no—
354Dic59—41no—
355Dic59—42no—
356Dic59—41no—
357Dic59—41no—
358Dic59—81no—
359Dic59—81no—
360Dic59—81no—
361C2×#448D5911yescharacteristic
362C2×C4×SD16—591no—
363C2×#419—591no—
364#2363—591no—
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×Q8C2×D5911yescharacteristic
386C22×SD16C2×D5911yescharacteristic
387C22×SD16C2×D5911yescharacteristic
388C22×M16—591no—
389C2×#121C2×D5911yescharacteristic
390C2×C4×Q8—591no—
391C2×C4×Q8—591no—
392C2×C4×D4—591no—
393C2×#117—591no—
394#448Dic5918yescomplemented
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×#103C2×D5911yescharacteristic
404C2×#103C2×D5911yescharacteristic
405C2×#102—591no—
406C2×#102—591no—
407C2×C22⋊C8C2×D5911yescharacteristic
408C2×#97—591no—
409C2×C4×C8—591no—
410#391—591no—
411#391—591no—
412#391—1181no—
413#391—1181no—
414#390—591no—
415#390—1181no—
416#389—591no—
417#388—1181no—
418#386—1181no—
419#380—591no—
420#380—1181no—
421C4×C4⋊C4—591no—
422C4×C22⋊C4—591no—
423C4×C22⋊C4—1181no—
424C4×C22⋊C4—1181no—
425#340—591no—
426#340—591no—
427#340—591no—
428#340—591no—
429#336—591no—
430#336—591no—
431C59#2288511yescharacteristic, complemented, Sylow
432C22×Q8—21no—
433C22×Q8—22no—
434C22×Q8—22no—
435C22×Q8—22no—
436C22×Q8—41no—
437C22×Q8—41no—
438C22×Q8C2×Dic5914yescomplemented
439C22×Q8C22×D5911yescharacteristic
440C22×Q8C22×D5911yescharacteristic
441C22×D4—21no—
442C22×D4C22×D5911yescharacteristic
443C23×C4—21no—
444C23×C4—1181no—
445C23×C4C22×D5911yescharacteristic
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C2×SD16C2×Dic5914yes—
451C2×SD16C2×Dic5914yes—
452C2×M16—1182no—
453C2×M16—1182no—
454C2×M16—2361no—
455C22×C8—591no—
456C22×C8—591no—
457C22×C8C22×D5911yescharacteristic
458C22×C8C22×D5911yescharacteristic
459#121—22no—
460#121C2×Dic5914yes—
461C4×Q8—1182no—
462C4×Q8—1182no—
463C4×Q8—2361no—
464C4×Q8—2361no—
465C4×D4—1182no—
466C4×D4—2361no—
467#117—1182no—
468#117—2361no—
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—1181no—
474C2×C4⋊C4—1181no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4C22×D5911yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—591no—
479C2×C22⋊C4—591no—
480C2×C22⋊C4—1181no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C42—591no—
486C2×C42—591no—
487C2×C42—1181no—
488C2×C42—1181no—
489C2×C42—1181no—
490C2×C42—1181no—
491#107—2361no—
492#106—1182no—
493#103—594no—
494#103—1182no—
495#103—1182no—
496#103—1182no—
497#103C2×Dic5914yescomplemented
498#103C2×Dic5914yescomplemented
499#102—1182no—
500#102—2361no—
501C22⋊C8C2×Dic5914yescomplemented
502#97—2361no—
503C4×C8—1182no—
504#95—591no—
505#95—591no—
506#95—1181no—
507#95—1181no—
508#95—1181no—
509#95—1181no—
510#95—1181no—
511#95—1181no—
512#95—1181no—
513C24—21no—
514C24D4×D5911yescharacteristic
515C2×Q8—24no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—28no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—42no—
526C2×Q8—42no—
527C2×Q8—44no—
528C2×Q8—44no—
529C2×Q8—44no—
530C2×Q8D4×D5912yes—
531C2×Q8#1174568712yes—
532C2×Q8C22×Dic5912yes—
533C2×Q8C22×Dic5912yes—
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×D4C22×Dic5912yes—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—591no—
554C22×C4—591no—
555C22×C4—591no—
556C22×C4—591no—
557C22×C4—1181no—
558C22×C4—1181no—
559C22×C4—1181no—
560C22×C4—1181no—
561C22×C4—4721no—
562C22×C4—2362no—
563C22×C4—2362no—
564C22×C4D4×D5911yescharacteristic
565C22×C4#1174568712yes—
566C22×C4C22×Dic5912yes—
567C22×C4C23×D5911yescharacteristic
568SD16—28no—
569SD16—44no—
570M16—2364no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—592no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8—1181no—
579C2×C8—1181no—
580C2×C8—1181no—
581C2×C8C22×Dic5912yes—
582C2×C8C22×Dic5912yes—
583C4⋊C4—21no—
584C4⋊C4—592no—
585C4⋊C4—1181no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—1181no—
591C4⋊C4—1181no—
592C4⋊C4—4721no—
593C4⋊C4—2362no—
594C4⋊C4—2362no—
595C4⋊C4C22×Dic5912yes—
596C22⋊C4—24no—
597C22⋊C4—1182no—
598C22⋊C4—4721no—
599C22⋊C4—2361no—
600C22⋊C4—2362no—
601C22⋊C4—2362no—
602C22⋊C4—2362no—
603C22⋊C4—2362no—
604C42—1181no—
605C42—1181no—
606C42—1181no—
607C42—1181no—
608C42—4721no—
609C42—2362no—
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—
625C23D4×Dic5912yes—
626C23C2×D4×D5911yescharacteristic
627Q8—22no—
628Q8—22no—
629Q8—22no—
630Q8—22no—
631Q8—22no—
632Q8—48no—
633Q8—41no—
634Q8—41no—
635Q8D4×Dic5914yes—
636D4—22no—
637D4—22no—
638D4—41no—
639D4—41no—
640D4—84no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—592no—
658C2×C4—1181no—
659C2×C4—1181no—
660C2×C4—1181no—
661C2×C4—1181no—
662C2×C4—1181no—
663C2×C4—1181no—
664C2×C4—1181no—
665C2×C4—1181no—
666C2×C4—1181no—
667C2×C4—1182no—
668C2×C4—1181no—
669C2×C4—1181no—
670C2×C4—4724no—
671C2×C4—2361no—
672C2×C4—2361no—
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×C4—2361no—
682C2×C4D4×Dic5912yes—
683C2×C4C23×Dic5911yescharacteristic
684C2×C4C2×D4×D5911yescharacteristic
685C2×C4C2×#1174568711yescharacteristic
686C2×C4C2×#1174568711yescharacteristic
687C2×C4#1427377211yescharacteristic
688C2×C4#1427377211yescharacteristic
689C8—22no—
690C8—22no—
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×D4×Dic5911yescharacteristic
708C22#1683803411yescharacteristic
709C22#1683803911yescharacteristic
710C22#137×D5911yescharacteristic
711C22#1683820111yescharacteristic
712C22#1683820811yescharacteristic
713C22#1683820811yescharacteristic
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—1182no—
719C4—4721no—
720C4—4721no—
721C4—4721no—
722C4—2361no—
723C4—2361no—
724C4—2362no—
725C4—2361no—
726C4C2×D4×Dic5911yescharacteristic
727C4#1683787711yescharacteristic
728C4#1683803911yescharacteristic
729C4#1683808311yescharacteristic
730C2—42no—
731C2—82no—
732C2#2142708011yescharacteristic
733C2#137×Dic5911yescharacteristic
734C2#2143295611yescharacteristic
735C2#2143560911yescharacteristic
736C2#2143568411yescharacteristic
737C2#2143635311yescharacteristic
738C2#2143638311yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#448C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
cosocleC22×C4×C59C24
hypercenterC2×#448D59
hypocenterC59#22885
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic59C2semidirect
2. C2×#16837411C2semidirect
4. Q8×C22⋊Dic59C2semidirect
5. #21424979C2semidirect
6. #21424774C2semidirect
7. #21424732C2semidirect
9. #21424453C2semidirect
10. #21424432C2semidirect
11. #21424352C2semidirect
12. #21424297C2semidirect
13. #21423928C2semidirect
14. #21423882C2semidirect
58. C59×#448C4semidirect
101. #14273651D4semidirect
121. C22×Q8×C59C2×C4semidirect
140. #103×C59C2×C4semidirect
141. #103×C59C2×C4semidirect
142. C22⋊C8×C59C2×C4semidirect
394. #448Dic59semidirect
431. C59#22885semidirect
438. C22×Q8C2×Dic59semidirect
497. #103C2×Dic59semidirect
498. #103C2×Dic59semidirect
501. C22⋊C8C2×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic592
C2×#168374112
#214271382
Q8×C22⋊Dic592
#214249792
#214247742
#214247322
#214245352
#214244532
#214244322
#214243522
#214242972
#214239282
#214238822
C2×C59×#4482
#2288559