Finite Group Databasebeta

← #28611096

Subgroups — #28611096

Order 15104.

1122 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837514C211yesmaximal, characteristic, complemented
2C2×D8×Dic59C211yesmaximal, characteristic, complemented
3#21427161C211yesmaximal, characteristic, complemented
4#21427006C211yesmaximal, characteristic, complemented
5#21424921C211yesmaximal, characteristic, complemented
6#21424866C211yesmaximal, characteristic, complemented
7#21424795C211yesmaximal, characteristic, complemented
8#21424781C211yesmaximal, characteristic, complemented
9#21424446C211yesmaximal, characteristic, complemented
10#21424446C211yesmaximal, characteristic, complemented
11#21424359C211yesmaximal, characteristic, complemented
12#21424345C211yesmaximal, characteristic, complemented
13#21423973C211yesmaximal, characteristic, complemented
14#21423921C211yesmaximal, characteristic, complemented
15C2×C59×#459C211yesmaximal, characteristic
16C2×D4×Dic59—21no—
17C2×D4×Dic59C2211yescharacteristic
18C2×D4×Dic59C2211yescharacteristic
19C2×D4×Dic59C2211yescharacteristic
20C2×D4×Dic59C2211yescharacteristic
21#16837514—24no—
22D8×Dic59—24no—
23C2×#14273661C2211yescharacteristic
24C2×#14273659C2211yescharacteristic
25C2×#14273648C2211yescharacteristic
26C2×#14273648C2211yescharacteristic
27C2×#14273648C2211yescharacteristic
28C2×#14273648C2211yescharacteristic
29C2×#14273648C2211yescharacteristic
30C2×#14273648C2211yescharacteristic
31C2×#14273638C2211yescharacteristic
32C2×#14273637C2211yescharacteristic
33C2×C8×Dic59C2211yescharacteristic
34#16837305—21no—
35#16837305C2211yescharacteristic
36#16837305C2211yescharacteristic
37#16837301C2211yescharacteristic
38#16837301C2211yescharacteristic
39#16837282—21no—
40#16837282—21no—
41#16837277—21no—
42#16837277—21no—
43#16837268C2211yescharacteristic
44#16837262—21no—
45C4×C4⋊Dic59C2211yescharacteristic
46C4×C4⋊Dic59C2211yescharacteristic
47C2×C59⋊#95—21no—
48#16837165C2211yescharacteristic
49#16837165C2211yescharacteristic
50#16837164C2211yescharacteristic
51#16837164C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54C22×D8×C59C2211yescharacteristic
55C22×D8×C59C2211yescharacteristic
56C2×#127×C59C2211yescharacteristic
57C2×C4×D4×C59C2211yescharacteristic
58C59×#459C418yescomplemented
59C2×C4⋊C8×C59C2211yescharacteristic
60C2×#102×C59C2211yescharacteristic
61C2×#102×C59C2211yescharacteristic
62C23×Dic59—21no—
63C23×Dic59—21no—
64C23×Dic59—21no—
65C23×Dic59—21no—
66C22×C59⋊C8C2311yescharacteristic
67C22×C59⋊C8C2311yescharacteristic
68D4×Dic59—22no—
69D4×Dic59—22no—
70D4×Dic59—22no—
71D4×Dic59—22no—
72D4×Dic59—41no—
73D4×Dic59—41no—
74D4×Dic59—41no—
75D4×Dic59—41no—
76D4×Dic59—44no—
77C2×C4⋊Dic59—21no—
78C2×C4⋊Dic59—21no—
79C2×C4⋊Dic59D411yescharacteristic
80C2×C4⋊Dic59D411yescharacteristic
81C2×C4⋊Dic59C2311yescharacteristic
82C2×C4⋊Dic59C2311yescharacteristic
83C2×C4⋊Dic59C2311yescharacteristic
84C2×C4⋊Dic59C2311yescharacteristic
85C2×C22⋊Dic59—21no—
86C2×C22⋊Dic59—21no—
87C2×C22⋊Dic59—21no—
88C2×C22⋊Dic59—21no—
89C2×C22⋊Dic59—21no—
90C2×C22⋊Dic59—21no—
91C2×C22⋊Dic59—21no—
92C2×C22⋊Dic59—21no—
93C2×C4×Dic59—21no—
94C2×C4×Dic59C2311yescharacteristic
95C2×C4×Dic59C2311yescharacteristic
96#14273661—22no—
97#14273659—22no—
98#14273648—22no—
99#14273648—22no—
100#14273648—22no—
101#14273648—41no—
102#14273648—41no—
103#14273648D414yescomplemented
104#14273638—22no—
105#14273637—22no—
106C8×Dic59—22no—
107C59⋊#95—21no—
108C59⋊#95—21no—
109C59⋊#95—21no—
110C59⋊#95—21no—
111C59⋊#95—21no—
112C59⋊#95D411yescharacteristic
113C59⋊#95D411yescharacteristic
114C22×D4×C59—21no—
115C22×D4×C59—21no—
116C22×D4×C59C2311yescharacteristic
117C22×D4×C59C2311yescharacteristic
118C22×D4×C59C2311yescharacteristic
119C23×C4×C59—21no—
120C2×D8×C59—22no—
121C2×D8×C59—22no—
122C2×D8×C59—22no—
123C2×D8×C59—22no—
124C2×D8×C59C2×C414yescomplemented
125C2×D8×C59C2×C414yescomplemented
126C22×C8×C59C2311yescharacteristic
127C22×C8×C59C2311yescharacteristic
128#127×C59—22no—
129#127×C59C2×C414yescomplemented
130C4×D4×C59—22no—
131C4×D4×C59C2×C414yescomplemented
132C2×C4⋊C4×C59C2311yescharacteristic
133C2×C22⋊C4×C59—21no—
134C2×C42×C59C2311yescharacteristic
135C4⋊C8×C59C2×C414yescomplemented
136#102×C59C2×C414yescomplemented
137#102×C59C2×C414yescomplemented
138C24×C59—21no—
139C24×C59—21no—
140C24×C59—21no—
141C2×D4×C59—24no—
142C2×D4×C59—24no—
143C2×D4×C59—21no—
144C2×D4×C59—21no—
145C2×D4×C59—21no—
146C2×D4×C59—21no—
147C2×D4×C59—21no—
148C2×D4×C59—21no—
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—42no—
157C2×D4×C59—42no—
158C2×D4×C59—81no—
159C2×D4×C59—81no—
160C2×D4×C59C22×C412yes—
161C2×D4×C59C22×C412yes—
162C2×D4×C59C22×C412yes—
163C2×D4×C59C2×D412yes—
164C2×D4×C59#4112yes—
165C22×C4×C59—21no—
166C22×C4×C59—24no—
167C22×C4×C59—81no—
168C22×C4×C59—81no—
169C22×C4×C59C2×D411yescharacteristic
170C22×C4×C59C2×D411yescharacteristic
171C22×C4×C59C2411yescharacteristic
172C22×Dic59—21no—
173C22×Dic59—21no—
174C22×Dic59—21no—
175C22×Dic59—21no—
176C22×Dic59—42no—
177C22×Dic59—42no—
178C22×Dic59—42no—
179C22×Dic59—42no—
180C22×Dic59—42no—
181C22×Dic59—42no—
182C22×Dic59—42no—
183C22×Dic59—42no—
184C22×Dic59—81no—
185C22×Dic59—81no—
186C22×Dic59—81no—
187C22×Dic59—81no—
188C22×Dic59C2×D411yescharacteristic
189C22×Dic59C2×D411yescharacteristic
190C22×Dic59C2×D411yescharacteristic
191C22×Dic59C2×D411yescharacteristic
192D8×C59—28no—
193D8×C59—28no—
194C2×C8×C59—21no—
195C2×C8×C59—21no—
196C2×C8×C59—21no—
197C2×C8×C59—21no—
198C2×C8×C59C22×C412yes—
199C2×C8×C59C22×C412yes—
200C4⋊C4×C59—21no—
201C4⋊C4×C59C22×C412yes—
202C22⋊C4×C59—24no—
203C42×C59C22×C412yes—
204C42×C59#4112yes—
205C22⋊Dic59—42no—
206C22⋊Dic59—42no—
207C22⋊Dic59—42no—
208C22⋊Dic59—42no—
209C22⋊Dic59—42no—
210C22⋊Dic59—42no—
211C22⋊Dic59—81no—
212C22⋊Dic59—81no—
213C4⋊Dic59—21no—
214C4⋊Dic59—22no—
215C4⋊Dic59—21no—
216C4⋊Dic59—21no—
217C4⋊Dic59—21no—
218C4⋊Dic59—21no—
219C4⋊Dic59—21no—
220C4⋊Dic59—21no—
221C4⋊Dic59—41no—
222C4⋊Dic59—81no—
223C4⋊Dic59—81no—
224C4⋊Dic59C2×D412yes—
225C4×Dic59—21no—
226C4×Dic59—21no—
227C4×Dic59—21no—
228C4×Dic59—21no—
229C4×Dic59—42no—
230C2×C59⋊C8—21no—
231C2×C59⋊C8—21no—
232C2×C59⋊C8—21no—
233C2×C59⋊C8—21no—
234C2×C59⋊C8—21no—
235C2×C59⋊C8C2×D412yes—
236C23×C59—22no—
237C23×C59—22no—
238C23×C59—22no—
239C23×C59—22no—
240C23×C59—22no—
241C23×C59—41no—
242C23×C59—41no—
243C23×C59—41no—
244C23×C59—41no—
245C23×C59—41no—
246C23×C59—41no—
247C23×C59—41no—
248C23×C59—41no—
249C23×C59—41no—
250C23×C59—41no—
251C23×C59—41no—
252C23×C59—41no—
253C23×C59—41no—
254C23×C59—41no—
255C23×C59—41no—
256C23×C59—41no—
257C23×C59C22×D411yescharacteristic
258D4×C59—22no—
259D4×C59—22no—
260D4×C59—22no—
261D4×C59—22no—
262D4×C59—22no—
263D4×C59—22no—
264D4×C59—22no—
265D4×C59—48no—
266D4×C59—41no—
267D4×C59—41no—
268D4×C59—41no—
269D4×C59—41no—
270D4×C59—84no—
271D4×C59C4×D414yescomplemented
272C2×C4×C59—21no—
273C2×C4×C59—21no—
274C2×C4×C59—21no—
275C2×C4×C59—21no—
276C2×C4×C59—22no—
277C2×C4×C59—41no—
278C2×C4×C59—41no—
279C2×C4×C59—84no—
280C2×C4×C59C4×D412yes—
281C2×C4×C59C4×D412yes—
282C2×C4×C59C23×C411yescharacteristic
283C2×C4×C59C22×D411yescharacteristic
284C2×C4×C59C2×#4111yescharacteristic
285C2×C4×C59C2×#4111yescharacteristic
286C2×C4×C59H(5,𝔽2)11yescharacteristic
287C2×C4×C592−1+411yescharacteristic
288C2×Dic59—21no—
289C2×Dic59—21no—
290C2×Dic59—21no—
291C2×Dic59—21no—
292C2×Dic59—21no—
293C2×Dic59—22no—
294C2×Dic59—21no—
295C2×Dic59—21no—
296C2×Dic59—21no—
297C2×Dic59—21no—
298C2×Dic59—21no—
299C2×Dic59—21no—
300C2×Dic59—41no—
301C2×Dic59—41no—
302C2×Dic59—41no—
303C2×Dic59—41no—
304C2×Dic59—41no—
305C2×Dic59—41no—
306C2×Dic59—41no—
307C2×Dic59—41no—
308C2×Dic59—41no—
309C2×Dic59—41no—
310C2×Dic59—41no—
311C2×Dic59—84no—
312C2×Dic59—84no—
313C2×Dic59—84no—
314C2×Dic59—84no—
315C2×Dic59AGL(1,ℤ/8)12yes—
316C8×C59—22no—
317C8×C59—22no—
318C59⋊C8—22no—
319C59⋊C8—41no—
320#23008—591nomaximal, Sylow
321C22×C59—24no—
322C22×C59—42no—
323C22×C59—42no—
324C22×C59—42no—
325C22×C59—42no—
326C22×C59—42no—
327C22×C59—42no—
328C22×C59—42no—
329C22×C59—42no—
330C22×C59—42no—
331C22×C59—42no—
332C22×C59—42no—
333C22×C59—42no—
334C22×C59—81no—
335C22×C59—81no—
336C22×C59—81no—
337C22×C59—81no—
338C22×C59—81no—
339C22×C59—81no—
340C22×C59—81no—
341C22×C59—81no—
342C22×C59C2×C4×D411yescharacteristic
343C22×C59D4211yescharacteristic
344C22×C59#54811yescharacteristic
345C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
346C22×C59#57511yescharacteristic
347C22×C59#57611yescharacteristic
348C22×C59#57611yescharacteristic
349C4×C59—22no—
350C4×C59—22no—
351C4×C59—42no—
352C4×C59C2×C4×D411yescharacteristic
353C4×C59#52011yescharacteristic
354C4×C59#54711yescharacteristic
355C4×C59#55311yescharacteristic
356Dic59—22no—
357Dic59—41no—
358Dic59—42no—
359Dic59—41no—
360Dic59—41no—
361Dic59—81no—
362Dic59—81no—
363Dic59—81no—
364C2×#459D5911yescharacteristic
365C2×#442—591no—
366C2×C4×D8—591no—
367#2366—591no—
368#2349—591no—
369#1961—591no—
370#1949—591no—
371#1936—591no—
372#1934—591no—
373#1879—591no—
374#1879—591no—
375#1864—591no—
376#1862—591no—
377#1771—591no—
378#1762—591no—
379C2×C59—44no—
380C2×C59—82no—
381C2×C59—82no—
382C2×C59#236111yescharacteristic
383C2×C59C4×AGL(1,ℤ/8)11yescharacteristic
384C2×C59#294811yescharacteristic
385C2×C59#326411yescharacteristic
386C2×C59#326811yescharacteristic
387C2×C59#336611yescharacteristic
388C2×C59#337011yescharacteristic
389C22×D8C2×D5911yescharacteristic
390C22×D8C2×D5911yescharacteristic
391C2×#127C2×D5911yescharacteristic
392C2×C4×D4—591no—
393C2×C4×D4—591no—
394C2×C4×D4—591no—
395C2×C4×D4—591no—
396C2×C4×D4—1181no—
397C2×C4×D4C2×D5911yescharacteristic
398#459Dic5918yescomplemented
399#442—1184no—
400C4×D8—1184no—
401C2×#107—591no—
402C2×#106—591no—
403C2×C4⋊C8C2×D5911yescharacteristic
404C2×#102—591no—
405C2×#102—591no—
406C2×#102—591no—
407C2×#102—591no—
408C2×#102—591no—
409C2×#102—591no—
410C2×#102C2×D5911yescharacteristic
411C2×#102C2×D5911yescharacteristic
412C2×#97—591no—
413C2×#97—591no—
414C2×C4×C8—591no—
415#390—591no—
416#390—591no—
417#390—1181no—
418#389—591no—
419#389—591no—
420#386—1181no—
421#386—1181no—
422#385—1181no—
423#385—1181no—
424#382—591no—
425#380—1181no—
426C4×C4⋊C4—591no—
427C4×C4⋊C4—591no—
428C2×#95—1181no—
429#340—591no—
430#340—591no—
431#340—591no—
432#340—591no—
433#336—591no—
434#336—591no—
435C59#2300811yescharacteristic, complemented, Sylow
436C22×D4—21no—
437C22×D4—21no—
438C22×D4C22×D5911yescharacteristic
439C22×D4C22×D5911yescharacteristic
440C22×D4C22×D5911yescharacteristic
441C23×C4—21no—
442C23×C4—1181no—
443C23×C4—1181no—
444C23×C4—1181no—
445C23×C4—1181no—
446C2×D8—22no—
447C2×D8—22no—
448C2×D8—22no—
449C2×D8—22no—
450C2×D8C2×Dic5914yescomplemented
451C2×D8C2×Dic5914yescomplemented
452C22×C8—591no—
453C22×C8—591no—
454C22×C8C22×D5911yescharacteristic
455C22×C8C22×D5911yescharacteristic
456#127—22no—
457#127C2×Dic5914yescomplemented
458C4×D4—22no—
459C4×D4—1182no—
460C4×D4—1182no—
461C4×D4—1182no—
462C4×D4—1182no—
463C4×D4—2361no—
464C4×D4—2361no—
465C4×D4—2361no—
466C4×D4—2361no—
467C4×D4—2364no—
468C4×D4C2×Dic5914yescomplemented
469C2×C4⋊C4—591no—
470C2×C4⋊C4—591no—
471C2×C4⋊C4—591no—
472C2×C4⋊C4—591no—
473C2×C4⋊C4—591no—
474C2×C4⋊C4—591no—
475C2×C4⋊C4—1181no—
476C2×C4⋊C4—1181no—
477C2×C4⋊C4C22×D5911yescharacteristic
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1181no—
480C2×C22⋊C4—1181no—
481C2×C22⋊C4—1181no—
482C2×C22⋊C4—1181no—
483C2×C22⋊C4—1181no—
484C2×C22⋊C4—1181no—
485C2×C22⋊C4—1181no—
486C2×C22⋊C4—1181no—
487C2×C42—591no—
488C2×C42—591no—
489C2×C42—1181no—
490C2×C42C22×D5911yescharacteristic
491#107—1182no—
492#106—1182no—
493C4⋊C8C2×Dic5914yescomplemented
494#102—594no—
495#102—1182no—
496#102—1182no—
497#102—1182no—
498#102—2361no—
499#102—2361no—
500#102C2×Dic5914yescomplemented
501#102C2×Dic5914yescomplemented
502#97—1182no—
503#97—1182no—
504C4×C8—1182no—
505#95—591no—
506#95—591no—
507#95—1181no—
508#95—1181no—
509#95—1181no—
510#95—1181no—
511#95—1181no—
512C24—21no—
513C24—21no—
514C24—21no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—21no—
527C2×D4—21no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—81no—
533C2×D4—81no—
534C2×D4D4×D5912yes—
535C2×D4#1174568712yes—
536C2×D4C22×Dic5912yes—
537C2×D4C22×Dic5912yes—
538C2×D4C22×Dic5912yes—
539C22×C4—21no—
540C22×C4—24no—
541C22×C4—81no—
542C22×C4—81no—
543C22×C4—591no—
544C22×C4—591no—
545C22×C4—591no—
546C22×C4—591no—
547C22×C4—1181no—
548C22×C4—1181no—
549C22×C4—1181no—
550C22×C4—1181no—
551C22×C4—4721no—
552C22×C4—4721no—
553C22×C4—4721no—
554C22×C4—4721no—
555C22×C4—2362no—
556C22×C4—2362no—
557C22×C4—2362no—
558C22×C4—2362no—
559C22×C4—2362no—
560C22×C4—2362no—
561C22×C4—2362no—
562C22×C4—2362no—
563C22×C4D4×D5911yescharacteristic
564C22×C4D4×D5911yescharacteristic
565C22×C4C23×D5911yescharacteristic
566D8—28no—
567D8—28no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—592no—
573C2×C8—1181no—
574C2×C8—1181no—
575C2×C8—1181no—
576C2×C8—1181no—
577C2×C8—1181no—
578C2×C8C22×Dic5912yes—
579C2×C8C22×Dic5912yes—
580C4⋊C4—21no—
581C4⋊C4—592no—
582C4⋊C4—1182no—
583C4⋊C4—1181no—
584C4⋊C4—1181no—
585C4⋊C4—1181no—
586C4⋊C4—1181no—
587C4⋊C4—1181no—
588C4⋊C4—1181no—
589C4⋊C4—1181no—
590C4⋊C4—4721no—
591C4⋊C4—4721no—
592C4⋊C4—2361no—
593C4⋊C4C22×Dic5912yes—
594C22⋊C4—24no—
595C22⋊C4—4721no—
596C22⋊C4—4721no—
597C22⋊C4—2362no—
598C22⋊C4—2362no—
599C22⋊C4—2362no—
600C22⋊C4—2362no—
601C22⋊C4—2362no—
602C22⋊C4—2362no—
603C42—1181no—
604C42—1181no—
605C42—1181no—
606C42—1181no—
607C42—2362no—
608C42#1174568712yes—
609C42C22×Dic5912yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23C2×D4×D5911yescharacteristic
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—22no—
637D4—22no—
638D4—22no—
639D4—48no—
640D4—41no—
641D4—41no—
642D4—41no—
643D4—41no—
644D4—84no—
645D4D4×Dic5914yescomplemented
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—84no—
654C2×C4—592no—
655C2×C4—1181no—
656C2×C4—1181no—
657C2×C4—1181no—
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—1182no—
667C2×C4—4724no—
668C2×C4—4724no—
669C2×C4—4724no—
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×C4D4×Dic5912yes—
684C2×C4C23×Dic5911yescharacteristic
685C2×C4C2×D4×D5911yescharacteristic
686C2×C4C2×#1174568711yescharacteristic
687C2×C4C2×#1174568711yescharacteristic
688C2×C4#1427377311yescharacteristic
689C2×C4#1427377411yescharacteristic
690C8—22no—
691C8—22no—
692C8—1182no—
693C8—2361no—
694C22—24no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22C2×D4×Dic5911yescharacteristic
716C22#1683803611yescharacteristic
717C22#1683805811yescharacteristic
718C22AGL(1,ℤ/8)×D5911yescharacteristic
719C22#1683819811yescharacteristic
720C22#1683820311yescharacteristic
721C22#1683820311yescharacteristic
722C4—22no—
723C4—22no—
724C4—42no—
725C4—1182no—
726C4—4721no—
727C4—4721no—
728C4—4721no—
729C4—2361no—
730C4—2362no—
731C4—2361no—
732C4—2361no—
733C4C2×D4×Dic5911yescharacteristic
734C4#1683788511yescharacteristic
735C4#1683805211yescharacteristic
736C4#1683810411yescharacteristic
737C2—44no—
738C2—82no—
739C2—82no—
740C2#2142711611yescharacteristic
741C2AGL(1,ℤ/8)×Dic5911yescharacteristic
742C2#2143294811yescharacteristic
743C2#2143557111yescharacteristic
744C2#2143564211yescharacteristic
745C2#2143679811yescharacteristic
746C2#2143684211yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC2×C59×#459C2
socleC23×C59C22×D4
cosocleC22×C4×C59C24
hypercenterC2×#459D59
hypocenterC59#23008
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16837514C2semidirect
2. C2×D8×Dic59C2semidirect
3. #21427161C2semidirect
4. #21427006C2semidirect
5. #21424921C2semidirect
6. #21424866C2semidirect
7. #21424795C2semidirect
8. #21424781C2semidirect
9. #21424446C2semidirect
10. #21424446C2semidirect
11. #21424359C2semidirect
12. #21424345C2semidirect
13. #21423973C2semidirect
14. #21423921C2semidirect
58. C59×#459C4semidirect
103. #14273648D4semidirect
124. C2×D8×C59C2×C4semidirect
125. C2×D8×C59C2×C4semidirect
129. #127×C59C2×C4semidirect
131. C4×D4×C59C2×C4semidirect
135. C4⋊C8×C59C2×C4semidirect
136. #102×C59C2×C4semidirect
137. #102×C59C2×C4semidirect
271. D4×C59C4×D4semidirect
398. #459Dic59semidirect
435. C59#23008semidirect
450. C2×D8C2×Dic59semidirect
451. C2×D8C2×Dic59semidirect
457. #127C2×Dic59semidirect
468. C4×D4C2×Dic59semidirect
493. C4⋊C8C2×Dic59semidirect
500. #102C2×Dic59semidirect
501. #102C2×Dic59semidirect
645. D4D4×Dic59semidirect

Maximal subgroups

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

subgroupindex
C2×#168375142
C2×D8×Dic592
#214271612
#214270062
#214249212
#214248662
#214247952
#214247812
#214244462
#214243592
#214243452
#214239732
#214239212
C2×C59×#4592
#2300859