Finite Group Databasebeta

← C2×#21434165 #29456760

Subgroups — C2×#21434165 #29456760

Order 15104.

2170 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837956C211yesmaximal, characteristic, complemented
2C2×C4×#11745689C211yesmaximal, characteristic
3#21434165C2116yesmaximal, direct product factor
4C2×#16837745C211yesmaximal, characteristic, complemented
5C2×#16837741C211yesmaximal, characteristic, complemented
6C2×#16837685C211yesmaximal, characteristic, complemented
7C2×#16837681C211yesmaximal, characteristic, complemented
8C2×#16837610C211yesmaximal, characteristic, complemented
9C2×#16837606C211yesmaximal, characteristic, complemented
10C2×#16837567C211yesmaximal, characteristic
11C2×#16837563C211yesmaximal, characteristic
12C2×C4×#11745672C211yesmaximal, characteristic, complemented
13C2×C4×#11745660C211yesmaximal, characteristic, complemented
14C2×C4×#11745671C211yesmaximal, characteristic, complemented
15C2×#16837453C211yesmaximal, characteristic, complemented
16C2×C4×Q16×C59C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21#16837956—24no—
22#16837956C2218yescomplemented
23C2×#14273726C2211yescharacteristic
24C2×#14273725C2211yescharacteristic
25C2×#14273717—21no—
26C2×#14273707C2211yescharacteristic
27C2×#14273705—21no—
28C2×#14273703C2211yescharacteristic
29C4×#11745689—24no—
30C4×#11745689C2218yes—
31C2×Q8×Dic59C2211yescharacteristic
32C2×C4×Dic118—21no—
33C2×C4×Dic118C2211yescharacteristic
34C2×C4×D236—21no—
35C2×C4×D236C2211yescharacteristic
36C2×#14273689—21no—
37C2×#14273689C2211yescharacteristic
38C2×#14273685—21no—
39C2×#14273685C2211yescharacteristic
40C2×#14273684—21no—
41C2×C42×D59—21no—
42C2×C42×D59C2211yescharacteristic
43#16837745C2218yescomplemented
44#16837741C2218yescomplemented
45#16837685C2218yescomplemented
46#16837681C2218yescomplemented
47#16837610C2218yescomplemented
48#16837606C2218yescomplemented
49#16837567C2218yes—
50#16837563C2218yes—
51C4×#11745672C2218yescomplemented
52C4×#11745660C2218yescomplemented
53C4×#11745671C2218yescomplemented
54#16837453C2218yescomplemented
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C4×Q16×C59C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C2×#11745689—24no—
78C2×#11745689—24no—
79C2×#11745689—22no—
80C2×#11745689C2314yes—
81C22×Dic118—21no—
82C22×Dic118C2311yescharacteristic
83C22×D236—21no—
84C22×D236C2311yescharacteristic
85C22×C4×D59—21no—
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59D411yescharacteristic
89C22×C4×D59D411yescharacteristic
90C22×C4×D59C2311yescharacteristic
91C2×#11745672—24no—
92C2×#11745672C2314yes—
93C2×#11745660—24no—
94C2×#11745660C2314yes—
95C2×#11745671—24no—
96C2×#11745671C2314yes—
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2311yescharacteristic
99#14273726—22no—
100#14273726C2314yes—
101#14273725—22no—
102#14273725C2314yes—
103#14273717—28no—
104#14273707—22no—
105#14273707C2314yes—
106#14273705—28no—
107#14273703—22no—
108#14273703C2314yes—
109Q8×Dic59—22no—
110Q8×Dic59C2314yes—
111C4×Dic118—22no—
112C4×Dic118—28no—
113C4×Dic118C2314yes—
114C4×D236—28no—
115C4×D236—22no—
116C4×D236C2314yes—
117#14273689—28no—
118#14273689—22no—
119#14273689C2314yes—
120#14273685—22no—
121#14273685—28no—
122#14273685C2314yes—
123#14273684—28no—
124C2×C4⋊Dic59—21no—
125C2×C4⋊Dic59—21no—
126C2×C4⋊Dic59C2311yescharacteristic
127C2×C4⋊Dic59C2311yescharacteristic
128C2×Dic59⋊C4—21no—
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×(C2×D59)⋊C4—21no—
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×C4×Dic59—21no—
139C2×C4×Dic59—21no—
140C2×C4×Dic59—21no—
141C2×C4×Dic59D411yescharacteristic
142C2×C4×Dic59D411yescharacteristic
143C2×C4×Dic59C2311yescharacteristic
144C42×D59—28no—
145C42×D59D414yes—
146C42×D59C2314yes—
147#14273660C2314yes—
148#14273659C2314yes—
149#14273658C2314yes—
150Dic59⋊C8C2314yes—
151Dic59⋊C8C2314yes—
152#14273652C2314yes—
153#14273651C2314yes—
154#14273651C2314yes—
155#14273650C2314yes—
156#14273649C2314yes—
157#14273647C2314yes—
158(C2×D59)⋊C8C2314yes—
159(C2×D59)⋊C8C2314yes—
160C4×C59⋊C8C2314yes—
161C22×Q8×C59C2311yescharacteristic
162C22×Q8×C59C2311yescharacteristic
163C2×Q16×C59—24no—
164C2×Q16×C59C2314yes—
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C4×Q8×C59—22no—
168C4×Q8×C59—22no—
169C4×Q8×C59C2314yes—
170C4×Q8×C59C2314yes—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C42×C59—21no—
176C2×C42×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#107×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181C4×C8×C59C2314yes—
182C23×D59—21no—
183C23×D59C2×D411yescharacteristic
184C2×Q8×C59—21no—
185C2×Q8×C59—21no—
186C2×Q8×C59—22no—
187C2×Q8×C59—22no—
188C2×Q8×C59—22no—
189C2×Q8×C59#4114yes—
190C2×Q8×C59C2412yes—
191C2×Q8×C59C2412yes—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204C22×Dic59C2×D411yescharacteristic
205#11745689—216no—
206#11745689—28no—
207#11745689—28no—
208C2×D236—28no—
209C2×D236—24no—
210C2×D236—21no—
211C2×D236—22no—
212C2×D236#4114yes—
213C2×D236C2412yes—
214C2×C4×D59—28no—
215C2×C4×D59—24no—
216C2×C4×D59—22no—
217C2×C4×D59—22no—
218C2×C4×D59—24no—
219C2×C4×D59—24no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—44no—
223C2×C4×D59—44no—
224C2×C4×D59C2×D412yes—
225C2×C4×D59C2×D414yes—
226C2×C4×D59C2×D414yes—
227C2×C4×D59C2412yes—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—21no—
231C2×Dic118—24no—
232C2×Dic118—44no—
233C2×Dic118C2412yes—
234Q16×C59—28no—
235C2×C8×C59—22no—
236C2×C8×C59—22no—
237C2×C8×C59C2412yes—
238C2×C8×C59C2412yes—
239C4⋊C4×C59—24no—
240C4⋊C4×C59—24no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59—21no—
243C4⋊C4×C59C2412yes—
244C4⋊C4×C59C2412yes—
245C42×C59—24no—
246C42×C59—24no—
247C42×C59C2×D412yes—
248C42×C59C2412yes—
249#11745672—28no—
250#11745671—28no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4—24no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—24no—
259C4⋊Dic59—24no—
260C4⋊Dic59C2412yes—
261C4⋊Dic59C2412yes—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4—24no—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270C4×Dic59C2×D414yes—
271C4×Dic59C2×D412yes—
272C4×Dic59C2×D414yes—
273C4×Dic59C2412yes—
274C2×C59⋊C8—22no—
275C2×C59⋊C8—22no—
276C2×C59⋊C8C2412yes—
277C2×C59⋊C8C2412yes—
278#11745660—28no—
279C23×C59C22×D411yescharacteristic
280C22×D59—22no—
281C22×D59—24no—
282C22×D59—22no—
283C22×D59—22no—
284C22×D59—22no—
285C22×D59—42no—
286C22×D59—42no—
287C22×D59C22×D412yes—
288Q8×C59—24no—
289Q8×C59—22no—
290Q8×C59—22no—
291Q8×C59—22no—
292Q8×C59—42no—
293Q8×C59C2×#4114yes—
294C2×C4×C59—24no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—22no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59—42no—
303C2×C4×C59#13714yes—
304C2×C4×C59C22×D412yes—
305C2×C4×C59C22×D411yescharacteristic
306C2×C4×C59C22×D412yes—
307C2×C4×C59C2×#4112yes—
308C2×C4×C59C2×#4112yes—
309C2×C4×C59C2511yescharacteristic
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59#13514yes—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322D236—216no—
323D236—24no—
324D236—22no—
325D236C2×#4114yes—
326C4×D59—216no—
327C4×D59—24no—
328C4×D59—28no—
329C4×D59—22no—
330C4×D59—22no—
331C4×D59—28no—
332C4×D59—48no—
333C4×D59—48no—
334Dic118—22no—
335Dic118—22no—
336Dic118—42no—
337Dic118—48no—
338C8×C59—22no—
339C8×C59—22no—
340C59⋊C8—22no—
341C59⋊C8—22no—
342C2×#3107—591nomaximal, Sylow
343C22×C59#52512yes—
344C22×C59C2×#13512yes—
345C22×C59C2×#13712yes—
346C22×C59C23×D411yescharacteristic
347C2×D59—22no—
348C2×D59—24no—
349C2×D59—22no—
350C2×D59—22no—
351C2×D59—44no—
352C2×D59—48no—
353C2×D59—42no—
354C2×D59—42no—
355C4×C59—24no—
356C4×C59—22no—
357C4×C59—42no—
358C4×C59—42no—
359C4×C59—42no—
360C4×C59#52512yes—
361C4×C59C2×#13714yes—
362C4×C59C22×#4111yescharacteristic
363C4×C59C22×#4111yescharacteristic
364Dic59—22no—
365Dic59—22no—
366Dic59—42no—
367Dic59—42no—
368Dic59—42no—
369Dic59C2×#13514yes—
370C2×#533—591no—
371C2×C4×#41—591no—
372#3107—5916no—
373C2×#485—591no—
374C2×#485—591no—
375C2×#475—591no—
376C2×#474—591no—
377C2×#462—591no—
378C2×#461—591no—
379C2×#452—591no—
380C2×#452—591no—
381C2×C4×Q16—591no—
382C2×C4×Q16D5911yescharacteristic, complemented
383C2×C4×SD16—591no—
384C2×C4×SD16—591no—
385C2×#431—591no—
386C2×C59#310714yescomplemented
387C2×C59C2×#52511yescharacteristic
388C2×C59C22×#13511yescharacteristic
389C2×C59C22×#13711yescharacteristic
390D59—42no—
391D59—44no—
392C22×#41—591no—
393C22×Q16—591no—
394C22×Q16C2×D5911yescharacteristic
395C22×SD16—591no—
396C22×SD16—591no—
397#533—598no—
398#533—1184no—
399C2×C4⋊Q8—591no—
400C2×C4⋊Q8—591no—
401C2×#125—1181no—
402C2×C22⋊Q8—591no—
403C2×C22⋊Q8—591no—
404C2×C22⋊Q8—1181no—
405C4×#41—598no—
406C4×#41—1184no—
407C2×C4×Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×Q8—1181no—
410C2×C4×Q8C2×D5911yescharacteristic
411C2×C4×Q8C2×D5911yescharacteristic
412C2×C4×D4—591no—
413C2×C4×D4—591no—
414C2×C4×D4—1181no—
415C2×C4×D4—1181no—
416C2×#117—591no—
417C2×#117—1181no—
418C2×#117—1181no—
419C22×C42—591no—
420C22×C42—1181no—
421#485—598no—
422#485—598no—
423#475—598no—
424#474—598no—
425#462—598no—
426#461—598no—
427#452—598no—
428#452—598no—
429C4×Q16—598no—
430C4×Q16C2×D5918yescomplemented
431C4×SD16—598no—
432C4×SD16—598no—
433#431—598no—
434C2×#107—591no—
435C2×#107C2×D5911yescharacteristic
436C2×#106—591no—
437C2×#106—591no—
438C2×C4⋊C8—591no—
439C2×C4⋊C8—591no—
440C2×#103—591no—
441C2×#103—591no—
442C2×#103—591no—
443C2×#103—591no—
444C2×#103C2×D5911yescharacteristic
445C2×#103C2×D5911yescharacteristic
446C2×#102—591no—
447C2×#102—591no—
448C2×C22⋊C8—591no—
449C2×C22⋊C8—591no—
450C2×C4×C8—591no—
451C2×C4×C8C2×D5911yescharacteristic
452C59C2×#310711yescharacteristic, complemented, Sylow
453C2×#41—594no—
454C2×#41—1182no—
455C2×#41—1184no—
456C2×#41—1184no—
457C22×Q8—591no—
458C22×Q8—1181no—
459C22×Q8C22×D5911yescharacteristic
460C22×Q8C22×D5911yescharacteristic
461C22×D4—591no—
462C22×D4—1181no—
463C23×C4—591no—
464C23×C4—591no—
465C23×C4—591no—
466C23×C4—1181no—
467C23×C4—1181no—
468C23×C4—1181no—
469C2×Q16—24no—
470C2×Q16—594no—
471C2×Q16—1184no—
472C2×Q16C22×D5914yes—
473C2×SD16—594no—
474C2×SD16—594no—
475C2×SD16—1184no—
476C2×SD16—1184no—
477C22×C8—591no—
478C22×C8—591no—
479C22×C8C22×D5911yescharacteristic
480C22×C8C22×D5911yescharacteristic
481C4⋊Q8—594no—
482C4⋊Q8—594no—
483C4⋊Q8—1182no—
484C4⋊Q8—1182no—
485#125—1188no—
486C22⋊Q8—594no—
487C22⋊Q8—594no—
488C22⋊Q8—1182no—
489C22⋊Q8—1188no—
490C22⋊Q8—1182no—
491C4×Q8—22no—
492C4×Q8—22no—
493C4×Q8—594no—
494C4×Q8—594no—
495C4×Q8—1188no—
496C4×Q8—1182no—
497C4×Q8—1182no—
498C4×Q8C22×D5914yes—
499C4×Q8C22×D5914yes—
500C4×D4—594no—
501C4×D4—594no—
502C4×D4—1188no—
503C4×D4—1182no—
504C4×D4—1188no—
505C4×D4—1182no—
506#117—594no—
507#117—1188no—
508#117—1188no—
509#117—1182no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—591no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4—1181no—
519C2×C4⋊C4—1181no—
520C2×C4⋊C4—1181no—
521C2×C4⋊C4C22×D5911yescharacteristic
522C2×C4⋊C4C22×D5911yescharacteristic
523C2×C22⋊C4—1181no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—21no—
529C2×C42—21no—
530C2×C42—591no—
531C2×C42—591no—
532C2×C42—591no—
533C2×C42—594no—
534C2×C42—594no—
535C2×C42—1188no—
536C2×C42—1181no—
537C2×C42—1181no—
538C2×C42—1181no—
539C2×C42C22×D5911yescharacteristic
540#107—594no—
541#107C22×D5914yes—
542#106—594no—
543#106—594no—
544C4⋊C8—594no—
545C4⋊C8—594no—
546#103—594no—
547#103—594no—
548#103—594no—
549#103—594no—
550#103C22×D5914yes—
551#103C22×D5914yes—
552#102—594no—
553#102—594no—
554C22⋊C8—594no—
555C22⋊C8—594no—
556C4×C8—594no—
557C4×C8C22×D5914yes—
558C24—591no—
559C24—1181no—
560#41—1188no—
561#41—11816no—
562#41—1188no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—592no—
569C2×Q8—1184no—
570C2×Q8—1181no—
571C2×Q8—1182no—
572C2×Q8—1182no—
573C2×Q8—2364no—
574C2×Q8#1174568514yes—
575C2×Q8C23×D5912yes—
576C2×Q8C23×D5912yes—
577C2×D4—594no—
578C2×D4—592no—
579C2×D4—1184no—
580C2×D4—1188no—
581C2×D4—1181no—
582C2×D4—1182no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—591no—
588C22×C4—591no—
589C22×C4—591no—
590C22×C4—594no—
591C22×C4—592no—
592C22×C4—594no—
593C22×C4—592no—
594C22×C4—1184no—
595C22×C4—1184no—
596C22×C4—1184no—
597C22×C4—1188no—
598C22×C4—1184no—
599C22×C4—1182no—
600C22×C4—1182no—
601C22×C4—1181no—
602C22×C4—1181no—
603C22×C4—1181no—
604C22×C4—1184no—
605C22×C4—2364no—
606C22×C4—2364no—
607C22×C4D4×D5911yescharacteristic
608C22×C4D4×D5911yescharacteristic
609C22×C4C23×D5911yescharacteristic
610Q16—28no—
611Q16—1188no—
612SD16—1188no—
613SD16—1188no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—592no—
617C2×C8—592no—
618C2×C8—1182no—
619C2×C8—1182no—
620C2×C8C23×D5912yes—
621C2×C8C23×D5912yes—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—592no—
627C4⋊C4—592no—
628C4⋊C4—1184no—
629C4⋊C4—1184no—
630C4⋊C4—1184no—
631C4⋊C4—1184no—
632C4⋊C4—1184no—
633C4⋊C4—1184no—
634C4⋊C4—1181no—
635C4⋊C4—1181no—
636C4⋊C4—1184no—
637C4⋊C4C23×D5912yes—
638C4⋊C4C23×D5912yes—
639C22⋊C4—1184no—
640C22⋊C4—1184no—
641C22⋊C4—1184no—
642C22⋊C4—1184no—
643C22⋊C4—1184no—
644C42—24no—
645C42—24no—
646C42—594no—
647C42—594no—
648C42—592no—
649C42—592no—
650C42—1184no—
651C42—1184no—
652C42—1184no—
653C42D4×D5912yes—
654C42C23×D5912yes—
655C23—592no—
656C23—1184no—
657C23—1182no—
658C23—1182no—
659C23—1182no—
660C23—1182no—
661C23—2362no—
662C23—2362no—
663C23C2×D4×D5911yescharacteristic
664Q8—24no—
665Q8—22no—
666Q8—22no—
667Q8—22no—
668Q8—42no—
669Q8—1182no—
670Q8—1182no—
671Q8—2368no—
672Q8—2362no—
673Q8C2×#1174568514yes—
674D4—594no—
675D4—11816no—
676D4—1184no—
677D4—1182no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—594no—
688C2×C4—592no—
689C2×C4—592no—
690C2×C4—592no—
691C2×C4—1188no—
692C2×C4—11816no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1184no—
696C2×C4—1188no—
697C2×C4—1182no—
698C2×C4—1182no—
699C2×C4—1182no—
700C2×C4—1182no—
701C2×C4—1182no—
702C2×C4—2368no—
703C2×C4—2362no—
704C2×C4—2362no—
705C2×C4—2362no—
706C2×C4—2368no—
707C2×C4#1427375914yes—
708C2×C4C2×D4×D5912yes—
709C2×C4C2×D4×D5911yescharacteristic
710C2×C4C2×D4×D5912yes—
711C2×C4#41×D5912yes—
712C2×C4C2×#1174568512yes—
713C2×C4C24×D5911yescharacteristic
714C8—22no—
715C8—22no—
716C8—1182no—
717C8—1182no—
718C22—1182no—
719C22—1182no—
720C22—1184no—
721C22—1182no—
722C22—2364no—
723C22—2368no—
724C22—2362no—
725C22—2362no—
726C22#1683791112yes—
727C22#135×D5912yes—
728C22C2×#1427375912yes—
729C22C22×D4×D5911yescharacteristic
730C4—22no—
731C4—24no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—594no—
736C4—1182no—
737C4—1182no—
738C4—2362no—
739C4—2362no—
740C4—2362no—
741C4#1683791112yes—
742C4C2×#1427375914yes—
743C4C2×#41×D5911yescharacteristic
744C4C22×#1174568511yescharacteristic
745C2—2362no—
746C2—2364no—
747C2#2143416514yesdirect product factor
748C2C2×#1683791111yescharacteristic
749C2C2×#135×D5911yescharacteristic
750C2C22×#1427375911yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×Q16×C59C2
socleC23×C59C22×D4
prime radicalC22×#11745689C22
hypercenterC2×C4×Q16D59
hypocenterC59C2×#3107
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#16837956C2semidirect
3. #21434165C2direct (N × H)
4. C2×#16837745C2semidirect
5. C2×#16837741C2semidirect
6. C2×#16837685C2semidirect
7. C2×#16837681C2semidirect
8. C2×#16837610C2semidirect
9. C2×#16837606C2semidirect
12. C2×C4×#11745672C2semidirect
13. C2×C4×#11745660C2semidirect
14. C2×C4×#11745671C2semidirect
15. C2×#16837453C2semidirect
16. C2×C4×Q16×C59C2semidirect
22. #16837956C22semidirect
43. #16837745C22semidirect
44. #16837741C22semidirect
45. #16837685C22semidirect
46. #16837681C22semidirect
47. #16837610C22semidirect
48. #16837606C22semidirect
51. C4×#11745672C22semidirect
52. C4×#11745660C22semidirect
53. C4×#11745671C22semidirect
54. #16837453C22semidirect
72. C4×Q16×C59C22semidirect
382. C2×C4×Q16D59semidirect
386. C2×C59#3107semidirect
430. C4×Q16C2×D59semidirect
452. C59C2×#3107semidirect
747. C2#21434165direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379562
C2×C4×#117456892
#214341652
C2×#168377452
C2×#168377412
C2×#168376852
C2×#168376812
C2×#168376102
C2×#168376062
C2×#168375672
C2×#168375632
C2×C4×#117456722
C2×C4×#117456602
C2×C4×#117456712
C2×#168374532
C2×C4×Q16×C592
C2×#310759