Finite Group Databasebeta

← C2×#21434075 #29456539

Subgroups — C2×#21434075 #29456539

Order 15104.

2234 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837982C211yesmaximal, characteristic
2C2×#16837883C211yesmaximal, characteristic, complemented
3#21434075C2116yesmaximal, direct product factor
4C2×#16837736C211yesmaximal, characteristic, complemented
5C2×#16837741C211yesmaximal, characteristic, complemented
6C2×#16837740C211yesmaximal, characteristic, complemented
7C2×#16837729C211yesmaximal, characteristic, complemented
8C2×#16837727C211yesmaximal, characteristic, complemented
9C2×#16837717C211yesmaximal, characteristic, complemented
10C2×#16837715C211yesmaximal, characteristic, complemented
11C2×#16837443C211yesmaximal, characteristic, complemented
12C2×#107×D59C211yesmaximal, characteristic, complemented
13C2×#16837402C211yesmaximal, characteristic, complemented
14C2×#16837397C211yesmaximal, characteristic, complemented
15C2×#16837367C211yesmaximal, characteristic, complemented
16C2×C59×#484C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745685C2211yescharacteristic
19C22×#11745659C2211yescharacteristic
20C22×C8×D59C2211yescharacteristic
21#16837982—24no—
22#16837982C2218yes—
23C2×#14273705—21no—
24C2×#14273703C2211yescharacteristic
25C2×#14273702—21no—
26C2×#14273702C2211yescharacteristic
27C2×#14273701C2211yescharacteristic
28C2×#14273700—21no—
29C2×#14273700—21no—
30#16837883—24no—
31#16837883C2218yescomplemented
32C2×#14273692—21no—
33C2×#14273689—21no—
34C2×C4×C22⋊D59—21no—
35C2×C4×C22⋊D59—21no—
36C2×#14273686C2211yescharacteristic
37C2×#14273685C2211yescharacteristic
38C2×#14273685C2211yescharacteristic
39C2×C4⋊C4×D59C2211yescharacteristic
40C2×C4⋊C4×D59C2211yescharacteristic
41C2×C4⋊C4×D59C2211yescharacteristic
42#16837741C2218yescomplemented
43#16837740C2218yescomplemented
44#16837736C2218yescomplemented
45#16837729C2218yescomplemented
46#16837727C2218yescomplemented
47#16837717C2218yescomplemented
48#16837715C2218yescomplemented
49#16837443C2218yescomplemented
50C2×#14273661C2211yescharacteristic
51C2×#14273660C2211yescharacteristic
52C2×#14273660C2211yescharacteristic
53C2×#14273660C2211yescharacteristic
54#107×D59C2218yescomplemented
55C2×#14273659C2211yescharacteristic
56C2×#14273658C2211yescharacteristic
57#16837402C2218yescomplemented
58#16837397C2218yescomplemented
59C2×#14273651C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273649C2211yescharacteristic
63C2×#14273647C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#16837367C2218yescomplemented
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#484C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C2×#11745689—22no—
78C2×#11745689—24no—
79C2×#11745689—24no—
80C2×#11745689C2314yes—
81C2×#11745685—24no—
82C2×#11745685—24no—
83C2×#11745685D414yes—
84C2×#11745685C2314yes—
85C22×Dic118D411yescharacteristic
86C22×D236—21no—
87C22×D236—21no—
88C22×D236D411yescharacteristic
89C22×D236C2311yescharacteristic
90C22×C22⋊D59—21no—
91C22×C22⋊D59D411yescharacteristic
92C22×C22⋊D59D411yescharacteristic
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59—21no—
97C22×C4×D59C2311yescharacteristic
98C22×C4×D59C2311yescharacteristic
99C2×#11745659—24no—
100C2×#11745659C2314yes—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C2×C8×D59—24no—
104C2×C8×D59C2314yes—
105#14273705—28no—
106#14273703—22no—
107#14273703C2314yes—
108#14273702—28no—
109#14273702—22no—
110#14273702C2314yes—
111#14273701—22no—
112#14273701C2314yes—
113#14273700—28no—
114#14273700—28no—
115#14273692—28no—
116#14273689—28no—
117C4×C22⋊D59—28no—
118C4×C22⋊D59—28no—
119#14273686—22no—
120#14273686C2314yes—
121#14273685—22no—
122#14273685—22no—
123#14273685C2314yes—
124#14273685C2314yes—
125C2×C4⋊Dic59C2311yescharacteristic
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C4⋊C4×D59—22no—
133C4⋊C4×D59—22no—
134C4⋊C4×D59—22no—
135C4⋊C4×D59C2314yes—
136C4⋊C4×D59C2314yes—
137C4⋊C4×D59C2314yes—
138C2×C22⋊Dic59—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4—21no—
141C2×(C2×D59)⋊C4—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147#14273661C2314yes—
148#14273660C2314yes—
149#14273660C2314yes—
150#14273660C2314yes—
151#14273659C2314yes—
152#14273658C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273649C2314yes—
156#14273649C2314yes—
157#14273647C2314yes—
158#14273647C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160(C2×D59)⋊C8C2314yes—
161(C2×D59)⋊C8C2314yes—
162C22×Q8×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C23×C4×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22⋊Q8×C59—22no—
168C22⋊Q8×C59C2314yes—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—22no—
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C4⋊C4×C59C2314yes—
176C2×C22⋊C4×C59—21no—
177#107×C59C2314yes—
178#107×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181C22⋊C8×C59C2314yes—
182C24×C59C2×D411yescharacteristic
183C23×D59—21no—
184C23×D59C2×D411yescharacteristic
185C23×D59C2×D411yescharacteristic
186C2×Q8×C59—21no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59C2412yes—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—82no—
198C22×C4×C59C2×D411yescharacteristic
199C22×C4×C59C2×D412yes—
200C22×C4×C59C2412yes—
201C22×C4×C59C2411yescharacteristic
202C2×C22⋊D59—24no—
203C2×C22⋊D59—24no—
204C2×C22⋊D59—24no—
205C2×C22⋊D59—82no—
206C2×C22⋊D59C2×D414yes—
207C2×C22⋊D59C2×D414yes—
208C22×Dic59—21no—
209C22×Dic59—21no—
210C22×Dic59—21no—
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213#11745689—28no—
214#11745689—28no—
215#11745689—48no—
216#11745685—216no—
217#11745685—28no—
218#11745685—28no—
219C2×D236—24no—
220C2×D236—22no—
221C2×D236—22no—
222C2×D236—24no—
223C2×D236—21no—
224C2×D236—24no—
225C2×D236—44no—
226C2×D236—82no—
227C2×D236C2×D414yes—
228C2×D236C2412yes—
229C2×C4×D59—22no—
230C2×C4×D59—22no—
231C2×C4×D59—24no—
232C2×C4×D59—24no—
233C2×C4×D59—24no—
234C2×C4×D59—24no—
235C2×C4×D59—44no—
236C2×C4×D59—82no—
237C2×C4×D59—82no—
238C2×C4×D59—82no—
239C2×C4×D59C2×D412yes—
240C2×C4×D59C2×D412yes—
241C2×C4×D59#4114yes—
242C2×C4×D59#4114yes—
243C2×C4×D59C2412yes—
244C2×C4×D59C2412yes—
245C2×Dic118—24no—
246C2×Dic118C2×D414yes—
247C2×C8×C59—22no—
248C2×C8×C59—22no—
249C2×C8×C59C2412yes—
250C2×C8×C59C2412yes—
251C4⋊C4×C59—21no—
252C4⋊C4×C59—21no—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—24no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59C2412yes—
257C4⋊C4×C59C2412yes—
258C4⋊C4×C59C2412yes—
259C22⋊C4×C59—24no—
260C22⋊Dic59—24no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4—24no—
265(C2×D59)⋊C4—24no—
266C4⋊Dic59—21no—
267C4⋊Dic59—21no—
268C4⋊Dic59—21no—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271C4⋊Dic59C2412yes—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276C4×Dic59—24no—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8C2412yes—
282C2×C59⋊C8C2412yes—
283#11745659—28no—
284C8×D59—28no—
285C23×C59—22no—
286C23×C59—22no—
287C23×C59—22no—
288C23×C59C22×D412yes—
289C23×C59C22×D411yescharacteristic
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—42no—
297C22×D59—42no—
298C22×D59—42no—
299C22×D59#12314yes—
300C22×D59C22×D412yes—
301C22×D59C22×D412yes—
302Q8×C59—22no—
303Q8×C59—22no—
304Q8×C59—42no—
305C2×C4×C59—22no—
306C2×C4×C59—24no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—42no—
314C2×C4×C59—42no—
315C2×C4×C59—42no—
316C2×C4×C59—42no—
317C2×C4×C59—84no—
318C2×C4×C59C22×D412yes—
319C2×C4×C59C22×D411yescharacteristic
320C2×C4×C59C2×#4112yes—
321C2×C4×C59C2×#4112yes—
322C2×C4×C59C2511yescharacteristic
323C22⋊D59—28no—
324C22⋊D59—28no—
325C22⋊D59—84no—
326C2×Dic59—22no—
327C2×Dic59—22no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—42no—
333C2×Dic59#12314yes—
334C2×Dic59C22×D412yes—
335C2×Dic59C22×D412yes—
336D236—28no—
337D236—22no—
338D236—22no—
339D236—48no—
340D236—42no—
341D236—84no—
342C4×D59—24no—
343C4×D59—22no—
344C4×D59—22no—
345C4×D59—48no—
346C4×D59—84no—
347C4×D59—84no—
348C4×D59—84no—
349C4×D59#12318yes—
350C4×D59C2×#4114yes—
351C4×D59C2×#4114yes—
352Dic118—28no—
353C8×C59—22no—
354C8×C59—22no—
355C59⋊C8—22no—
356C59⋊C8—22no—
357C2×#3098—591nomaximal, Sylow
358C22×C59—22no—
359C22×C59—22no—
360C22×C59—22no—
361C22×C59—44no—
362C22×C59C2×#12312yes—
363C22×C59#57612yes—
364C22×C59#57812yes—
365C22×C59C23×D411yescharacteristic
366C2×D59—28no—
367C2×D59—22no—
368C2×D59—22no—
369C2×D59—22no—
370C2×D59—22no—
371C2×D59—22no—
372C2×D59—44no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—42no—
376C2×D59—84no—
377C2×D59C2×#12314yes—
378C4×C59—22no—
379C4×C59—42no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59C2×#12312yes—
384C4×C59C22×#4111yescharacteristic
385C4×C59C22×#4111yescharacteristic
386Dic59—22no—
387Dic59—42no—
388Dic59—42no—
389Dic59—42no—
390Dic59C2×#12314yes—
391C2×#537—591no—
392C2×#520—591no—
393#3098—5916no—
394C2×#484—591no—
395C2×#484D5911yescharacteristic, complemented
396C2×#485—591no—
397C2×#485—591no—
398C2×#482—591no—
399C2×#482—591no—
400C2×#480—591no—
401C2×#480—591no—
402C2×#428—591no—
403C22×#107—591no—
404C2×#417—591no—
405C2×#416—591no—
406C2×#408—591no—
407C2×C59—42no—
408C2×C59#309814yescomplemented
409C2×C59C22×#12311yescharacteristic
410C2×C59C2×#57611yescharacteristic
411C2×C59C2×#57811yescharacteristic
412D59—24no—
413D59—42no—
414D59—82no—
415C22×#41—591no—
416C22×#41—591no—
417C22×M16—591no—
418C23×C8—591no—
419#537—598no—
420#537—1184no—
421C2×C22⋊Q8—591no—
422C2×C22⋊Q8—1181no—
423C2×C22⋊Q8C2×D5911yescharacteristic
424C2×#121—591no—
425C2×#121—591no—
426C2×#121—1181no—
427C2×#121—1181no—
428C2×#121—1181no—
429#520—598no—
430#520—1184no—
431C2×C4×Q8—1181no—
432C2×C4×D4—1181no—
433C2×C4×D4—1181no—
434C2×C4×D4—1181no—
435C2×#117—591no—
436C2×#117—591no—
437C2×#117—591no—
438C22×C4⋊C4—591no—
439C22×C4⋊C4—591no—
440C22×C4⋊C4—591no—
441C22×C4⋊C4C2×D5911yescharacteristic
442#485—598no—
443#485—598no—
444#484—598no—
445#484C2×D5918yescomplemented
446#482—598no—
447#482—598no—
448#480—598no—
449#480—598no—
450#428—598no—
451C2×#107—591no—
452C2×#107—591no—
453C2×#107—591no—
454C2×#107—591no—
455C2×#107—598no—
456C2×#107C2×D5911yescharacteristic
457C2×#107C2×D5911yescharacteristic
458C2×#106—591no—
459C2×#106—591no—
460#417—598no—
461#416—598no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103C2×D5911yescharacteristic
465C2×#103C2×D5911yescharacteristic
466C2×#102—591no—
467C2×#102—591no—
468C2×#102—591no—
469C2×#102—591no—
470#408—598no—
471C2×C22⋊C8—591no—
472C2×C22⋊C8—591no—
473C2×C22⋊C8—591no—
474C2×C22⋊C8C2×D5911yescharacteristic
475C59C2×#309811yescharacteristic, complemented, Sylow
476C2×#41—594no—
477C2×#41—594no—
478C2×#41—594no—
479C2×#41—1184no—
480C2×#41—1184no—
481C2×#41—1182no—
482C2×#41—1184no—
483C2×#41—1184no—
484C22×Q8—591no—
485C22×Q8C22×D5911yescharacteristic
486C22×D4—591no—
487C22×D4—591no—
488C22×D4—591no—
489C22×D4—591no—
490C22×D4—1181no—
491C22×D4—1181no—
492C22×D4—1181no—
493C23×C4—21no—
494C23×C4—591no—
495C23×C4—591no—
496C23×C4—1181no—
497C23×C4—1181no—
498C23×C4—1181no—
499C23×C4—1181no—
500C23×C4C22×D5911yescharacteristic
501C2×M16—594no—
502C2×M16—1184no—
503C22×C8—591no—
504C22×C8—591no—
505C22×C8—594no—
506C22×C8—1184no—
507C22×C8C22×D5911yescharacteristic
508C22×C8C22×D5911yescharacteristic
509C22⋊Q8—22no—
510C22⋊Q8—594no—
511C22⋊Q8—1188no—
512C22⋊Q8—1182no—
513C22⋊Q8C22×D5914yes—
514#121—594no—
515#121—594no—
516#121—1188no—
517#121—1188no—
518#121—1182no—
519#121—1188no—
520#121—1182no—
521C4×Q8—1188no—
522C4×D4—1188no—
523C4×D4—1188no—
524C4×D4—1188no—
525#117—594no—
526#117—594no—
527#117—594no—
528#117—1182no—
529#117—1182no—
530#117—1182no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—591no—
536C2×C4⋊C4—591no—
537C2×C4⋊C4—594no—
538C2×C4⋊C4—594no—
539C2×C4⋊C4—594no—
540C2×C4⋊C4—1182no—
541C2×C4⋊C4—1182no—
542C2×C4⋊C4—1182no—
543C2×C4⋊C4—1181no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4—1181no—
547C2×C4⋊C4C22×D5911yescharacteristic
548C2×C4⋊C4C22×D5911yescharacteristic
549C2×C4⋊C4C22×D5911yescharacteristic
550C2×C4⋊C4C22×D5914yes—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C22⋊C4—1181no—
558C2×C42—1181no—
559C2×C42—1181no—
560C2×C42—1181no—
561#107—594no—
562#107—594no—
563#107—594no—
564#107—594no—
565#107C22×D5914yes—
566#107C22×D5914yes—
567#106—594no—
568#106—594no—
569#103—594no—
570#103—594no—
571#103C22×D5914yes—
572#103C22×D5914yes—
573#102—594no—
574#102—594no—
575#102—594no—
576#102—594no—
577C22⋊C8—594no—
578C22⋊C8—594no—
579C22⋊C8—594no—
580C22⋊C8C22×D5914yes—
581C24—591no—
582C24—591no—
583C24—1181no—
584C24D4×D5911yescharacteristic
585#41—11816no—
586#41—1188no—
587#41—1188no—
588#41—1188no—
589#41—1188no—
590#41—2368no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—594no—
595C2×Q8—1184no—
596C2×Q8C23×D5912yes—
597C2×D4—594no—
598C2×D4—594no—
599C2×D4—594no—
600C2×D4—592no—
601C2×D4—1184no—
602C2×D4—1184no—
603C2×D4—1184no—
604C2×D4—1184no—
605C2×D4—1184no—
606C2×D4—1184no—
607C2×D4—1181no—
608C2×D4—1182no—
609C2×D4—1182no—
610C2×D4—4722no—
611C2×D4—4722no—
612C2×D4—2364no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—24no—
620C22×C4—82no—
621C22×C4—591no—
622C22×C4—592no—
623C22×C4—594no—
624C22×C4—594no—
625C22×C4—592no—
626C22×C4—591no—
627C22×C4—592no—
628C22×C4—592no—
629C22×C4—1184no—
630C22×C4—1184no—
631C22×C4—1184no—
632C22×C4—1184no—
633C22×C4—1182no—
634C22×C4—1182no—
635C22×C4—1181no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—4722no—
639C22×C4—4722no—
640C22×C4—4722no—
641C22×C4—2364no—
642C22×C4D4×D5912yes—
643C22×C4D4×D5911yescharacteristic
644C22×C4C23×D5912yes—
645C22×C4C23×D5911yescharacteristic
646M16—1188no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—592no—
650C2×C8—592no—
651C2×C8—1188no—
652C2×C8—1182no—
653C2×C8—1182no—
654C2×C8C23×D5912yes—
655C2×C8C23×D5912yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—592no—
662C4⋊C4—592no—
663C4⋊C4—592no—
664C4⋊C4—1184no—
665C4⋊C4—1184no—
666C4⋊C4—1184no—
667C4⋊C4—1184no—
668C4⋊C4—1181no—
669C4⋊C4—1181no—
670C4⋊C4—1181no—
671C4⋊C4C23×D5912yes—
672C4⋊C4C23×D5912yes—
673C4⋊C4C23×D5912yes—
674C22⋊C4—24no—
675C22⋊C4—1184no—
676C22⋊C4—1184no—
677C22⋊C4—1184no—
678C22⋊C4—1184no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C42—1184no—
682C42—1184no—
683C42—1184no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—594no—
688C23—592no—
689C23—592no—
690C23—1182no—
691C23—1182no—
692C23—1182no—
693C23—1182no—
694C23—1182no—
695C23—1182no—
696C23—2362no—
697C23—2362no—
698C23—2362no—
699C23C2×D4×D5912yes—
700C23C2×D4×D5911yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—1188no—
705D4—1188no—
706D4—1188no—
707D4—1188no—
708D4—1182no—
709D4—1182no—
710D4—4724no—
711D4—4724no—
712D4—2368no—
713D4—2362no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—84no—
727C2×C4—594no—
728C2×C4—592no—
729C2×C4—598no—
730C2×C4—594no—
731C2×C4—594no—
732C2×C4—592no—
733C2×C4—1182no—
734C2×C4—1184no—
735C2×C4—1182no—
736C2×C4—1182no—
737C2×C4—1182no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—4724no—
741C2×C4—4724no—
742C2×C4—4724no—
743C2×C4—2368no—
744C2×C4—2362no—
745C2×C4—2362no—
746C2×C4—2362no—
747C2×C4C2×D4×D5912yes—
748C2×C4C2×D4×D5911yescharacteristic
749C2×C4#41×D5912yes—
750C2×C4#41×D5912yes—
751C2×C4C24×D5911yescharacteristic
752C8—22no—
753C8—22no—
754C8—1182no—
755C8—1182no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—44no—
760C22—594no—
761C22—1182no—
762C22—1182no—
763C22—1188no—
764C22—1182no—
765C22—1182no—
766C22—1182no—
767C22—4724no—
768C22—2362no—
769C22—2362no—
770C22—2362no—
771C22—2364no—
772C22#123×D5912yes—
773C22#1683820612yes—
774C22#1683821512yes—
775C22C22×D4×D5911yescharacteristic
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—594no—
782C4—1182no—
783C4—2362no—
784C4—2362no—
785C4—2362no—
786C4#123×D5912yes—
787C4C2×#41×D5911yescharacteristic
788C4C2×#41×D5911yescharacteristic
789C2—42no—
790C2—1184no—
791C2—4722no—
792C2—2362no—
793C2#2143407514yesdirect product factor
794C2C2×#123×D5911yescharacteristic
795C2C2×#1683820611yescharacteristic
796C2C2×#1683821511yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#484C2
socleC23×C59C22×D4
prime radicalC2×#16837982C2
hypercenterC2×#484D59
hypocenterC59C2×#3098
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
2. C2×#16837883C2semidirect
3. #21434075C2direct (N × H)
4. C2×#16837736C2semidirect
5. C2×#16837741C2semidirect
6. C2×#16837740C2semidirect
7. C2×#16837729C2semidirect
8. C2×#16837727C2semidirect
9. C2×#16837717C2semidirect
10. C2×#16837715C2semidirect
11. C2×#16837443C2semidirect
12. C2×#107×D59C2semidirect
13. C2×#16837402C2semidirect
14. C2×#16837397C2semidirect
15. C2×#16837367C2semidirect
16. C2×C59×#484C2semidirect
31. #16837883C22semidirect
42. #16837741C22semidirect
43. #16837740C22semidirect
44. #16837736C22semidirect
45. #16837729C22semidirect
46. #16837727C22semidirect
47. #16837717C22semidirect
48. #16837715C22semidirect
49. #16837443C22semidirect
54. #107×D59C22semidirect
57. #16837402C22semidirect
58. #16837397C22semidirect
65. #16837367C22semidirect
71. C59×#484C22semidirect
395. C2×#484D59semidirect
408. C2×C59#3098semidirect
445. #484C2×D59semidirect
475. C59C2×#3098semidirect
793. C2#21434075direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379822
C2×#168378832
#214340752
C2×#168377362
C2×#168377412
C2×#168377402
C2×#168377292
C2×#168377272
C2×#168377172
C2×#168377152
C2×#168374432
C2×#107×D592
C2×#168374022
C2×#168373972
C2×#168373672
C2×C59×#4842
C2×#309859