Finite Group Databasebeta

← C2×#21434115 #29456705

Subgroups — C2×#21434115 #29456705

Order 15104.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837938C211yesmaximal, characteristic, complemented
2C2×#41×Dic59C211yesmaximal, characteristic, complemented
3#21434115C2116yesmaximal, direct product factor
4C2×#16837740C211yesmaximal, characteristic, complemented
5C2×#16837727C211yesmaximal, characteristic, complemented
6C2×#16837707C211yesmaximal, characteristic, complemented
7C2×#16837700C211yesmaximal, characteristic, complemented
8C2×#16837626C211yesmaximal, characteristic, complemented
9C2×#16837619C211yesmaximal, characteristic, complemented
10C2×#16837547C211yesmaximal, characteristic
11C2×Q16×Dic59C211yesmaximal, characteristic, complemented
12C2×SD16×Dic59C211yesmaximal, characteristic, complemented
13C2×#16837487C211yesmaximal, characteristic, complemented
14C2×#16837482C211yesmaximal, characteristic, complemented
15C2×#16837452C211yesmaximal, characteristic, complemented
16C2×C59×#452C211yesmaximal, characteristic, complemented
17C22×#11745671C2211yescharacteristic
18C22×#11745669C2211yescharacteristic
19#16837938—24no—
20#16837938C2218yescomplemented
21C2×#14273722—21no—
22C2×#14273718C2211yescharacteristic
23C2×#14273716C2211yescharacteristic
24C2×#14273711—21no—
25C2×#14273701C2211yescharacteristic
26#41×Dic59—24no—
27#41×Dic59C2218yescomplemented
28C2×Q8×Dic59C2211yescharacteristic
29C2×Q8×Dic59C2211yescharacteristic
30C2×Q8×Dic59C2211yescharacteristic
31C2×D4×Dic59—21no—
32C2×D4×Dic59—21no—
33C2×D4×Dic59C2211yescharacteristic
34C2×D4×Dic59C2211yescharacteristic
35C2×#14273689C2211yescharacteristic
36C2×(C22⋊D59)⋊C4—21no—
37C2×#14273686—21no—
38C2×#14273686C2211yescharacteristic
39C2×#14273685—21no—
40C22×C4×Dic59—21no—
41C22×C4×Dic59C2211yescharacteristic
42#16837740C2218yescomplemented
43#16837727C2218yescomplemented
44#16837707C2218yescomplemented
45#16837700C2218yescomplemented
46#16837626C2218yescomplemented
47#16837619C2218yescomplemented
48#16837547C2218yes—
49Q16×Dic59C2218yescomplemented
50SD16×Dic59C2218yescomplemented
51#16837487C2218yescomplemented
52#16837482C2218yescomplemented
53#16837452C2218yescomplemented
54C2×#14273661C2211yescharacteristic
55C2×#14273660C2211yescharacteristic
56C2×#14273659C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273649C2211yescharacteristic
64C2×#14273649C2211yescharacteristic
65C2×#14273648C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×C8×Dic59C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×#41×C59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C22×SD16×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C59×#452C2218yescomplemented
74C2×#103×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×D236C2311yescharacteristic
78C22×C22⋊D59—21no—
79C23×Dic59—21no—
80C23×Dic59—21no—
81C23×Dic59D411yescharacteristic
82C23×Dic59D411yescharacteristic
83C22×C4×D59—21no—
84C2×#11745671—24no—
85C2×#11745671C2314yes—
86C2×#11745669—24no—
87C2×#11745669C2314yes—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90#14273722—28no—
91#14273718—22no—
92#14273718C2314yes—
93#14273716—22no—
94#14273716C2314yes—
95#14273711—28no—
96#14273701—22no—
97#14273701C2314yes—
98Q8×Dic59—22no—
99Q8×Dic59—22no—
100Q8×Dic59—22no—
101Q8×Dic59C2314yes—
102Q8×Dic59C2314yes—
103Q8×Dic59C2314yes—
104D4×Dic59—28no—
105D4×Dic59—28no—
106D4×Dic59—22no—
107D4×Dic59—22no—
108D4×Dic59C2314yes—
109D4×Dic59C2314yes—
110#14273689—22no—
111#14273689C2314yes—
112(C22⋊D59)⋊C4—28no—
113#14273686—22no—
114#14273686—28no—
115#14273686C2314yes—
116#14273685—28no—
117C2×C4⋊Dic59—21no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59—21no—
121C2×C4⋊Dic59C2311yescharacteristic
122C2×C4⋊Dic59C2311yescharacteristic
123C2×C4⋊Dic59C2311yescharacteristic
124C2×Dic59⋊C4—21no—
125C2×C22⋊Dic59—21no—
126C2×C22⋊Dic59—21no—
127C2×C22⋊Dic59—21no—
128C2×(C2×D59)⋊C4—21no—
129C2×(C2×D59)⋊C4—21no—
130C2×(C2×D59)⋊C4—21no—
131C2×(C2×D59)⋊C4—21no—
132C2×C4×Dic59—21no—
133C2×C4×Dic59—21no—
134C2×C4×Dic59—21no—
135C2×C4×Dic59—21no—
136C2×C4×Dic59—28no—
137C2×C4×Dic59D411yescharacteristic
138C2×C4×Dic59D414yes—
139C2×C4×Dic59D411yescharacteristic
140C2×C4×Dic59C2311yescharacteristic
141C2×C4×Dic59C2314yes—
142C2×C4×Dic59C2311yescharacteristic
143#14273661C2314yes—
144#14273660C2314yes—
145#14273659C2314yes—
146#14273658C2314yes—
147Dic59⋊C8C2314yes—
148Dic59⋊C8C2314yes—
149#14273651C2314yes—
150#14273651C2314yes—
151#14273651C2314yes—
152#14273649C2314yes—
153#14273649C2314yes—
154#14273648C2314yes—
155C22⋊(C59⋊C8)C2314yes—
156C8×Dic59C2314yes—
157C8×Dic59C2314yes—
158C2×#41×C59—24no—
159C2×#41×C59—24no—
160C2×#41×C59—22no—
161C2×#41×C59C2314yes—
162C22×Q8×C59C2311yescharacteristic
163C22×Q8×C59C2311yescharacteristic
164C22×D4×C59—21no—
165C22×D4×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C23×C4×C59C2311yescharacteristic
168C2×Q16×C59—24no—
169C2×Q16×C59C2314yes—
170C2×SD16×C59—24no—
171C2×SD16×C59C2314yes—
172C22×C8×C59C2311yescharacteristic
173C22×C8×C59C2311yescharacteristic
174C22⋊Q8×C59—22no—
175C22⋊Q8×C59C2314yes—
176C2×C4⋊C4×C59—21no—
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C22⋊C4×C59—21no—
179#103×C59C2314yes—
180#102×C59C2314yes—
181C22⋊C8×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C23×D59—21no—
185#41×C59—216no—
186#41×C59—28no—
187#41×C59—28no—
188C2×Q8×C59—21no—
189C2×Q8×C59—21no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59—22no—
193C2×Q8×C59#4114yes—
194C2×Q8×C59C2412yes—
195C2×Q8×C59C2412yes—
196C2×D4×C59—28no—
197C2×D4×C59—24no—
198C2×D4×C59—21no—
199C2×D4×C59—22no—
200C2×D4×C59#4114yes—
201C2×D4×C59C2412yes—
202C22×C4×C59—28no—
203C22×C4×C59—21no—
204C22×C4×C59—24no—
205C22×C4×C59—22no—
206C22×C4×C59—22no—
207C22×C4×C59—21no—
208C22×C4×C59—21no—
209C22×C4×C59C2×D411yescharacteristic
210C22×C4×C59C2×D412yes—
211C22×C4×C59C2412yes—
212C22×C4×C59C2411yescharacteristic
213C2×C22⋊D59—24no—
214C2×C22⋊D59—44no—
215C22×Dic59—24no—
216C22×Dic59—21no—
217C22×Dic59—21no—
218C22×Dic59—21no—
219C22×Dic59—24no—
220C22×Dic59—24no—
221C22×Dic59—42no—
222C22×Dic59—44no—
223C22×Dic59—44no—
224C22×Dic59C2×D411yescharacteristic
225C22×Dic59C2×D411yescharacteristic
226C22×Dic59C2×D411yescharacteristic
227C22×Dic59C2×D414yes—
228C22×Dic59C2×D414yes—
229C22×Dic59C2×D411yescharacteristic
230C2×D236—22no—
231C2×D236—22no—
232C2×D236—21no—
233C2×D236C2412yes—
234C2×C4×D59—24no—
235C2×C4×D59—44no—
236Q16×C59—28no—
237SD16×C59—28no—
238C2×C8×C59—22no—
239C2×C8×C59—22no—
240C2×C8×C59C2412yes—
241C2×C8×C59C2412yes—
242C4⋊C4×C59—24no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59C2412yes—
245C22⋊C4×C59—24no—
246C22⋊Dic59—24no—
247C22⋊Dic59—24no—
248C22⋊Dic59—24no—
249#11745671—28no—
250#11745669—28no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4—24no—
254(C2×D59)⋊C4—24no—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—21no—
258C4⋊Dic59—24no—
259C4⋊Dic59—24no—
260C4⋊Dic59—24no—
261C4⋊Dic59—24no—
262C4⋊Dic59C2412yes—
263C4⋊Dic59C2412yes—
264C4⋊Dic59C2412yes—
265Dic59⋊C4—24no—
266C4×Dic59—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270C4×Dic59C2×D414yes—
271C4×Dic59C2×D414yes—
272C4×Dic59C2×D412yes—
273C4×Dic59C2×D412yes—
274C4×Dic59C2412yes—
275C4×Dic59C2412yes—
276C2×C59⋊C8—22no—
277C2×C59⋊C8—22no—
278C2×C59⋊C8C2412yes—
279C2×C59⋊C8C2412yes—
280C23×C59—22no—
281C23×C59—24no—
282C23×C59—22no—
283C23×C59—22no—
284C23×C59—22no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59C22×D412yes—
288C23×C59C22×D411yescharacteristic
289C22×D59—22no—
290C22×D59—42no—
291C22×D59—42no—
292C22×D59—42no—
293Q8×C59—24no—
294Q8×C59—22no—
295Q8×C59—22no—
296Q8×C59—22no—
297Q8×C59—42no—
298Q8×C59C2×#4114yes—
299D4×C59—216no—
300D4×C59—24no—
301D4×C59—22no—
302D4×C59C2×#4114yes—
303C2×C4×C59—216no—
304C2×C4×C59—22no—
305C2×C4×C59—24no—
306C2×C4×C59—22no—
307C2×C4×C59—24no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—42no—
313C2×C4×C59—42no—
314C2×C4×C59C22×D412yes—
315C2×C4×C59C22×D411yescharacteristic
316C2×C4×C59C2×#4112yes—
317C2×C4×C59C2×#4112yes—
318C2×C4×C59C2511yescharacteristic
319C22⋊D59—48no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—28no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—44no—
328C2×Dic59—48no—
329C2×Dic59—42no—
330C2×Dic59—42no—
331C2×Dic59—42no—
332C2×Dic59—48no—
333C2×Dic59#13514yes—
334C2×Dic59C22×D412yes—
335C2×Dic59C22×D412yes—
336C2×Dic59C22×D412yes—
337C2×Dic59C22×D412yes—
338D236—22no—
339D236—22no—
340D236—42no—
341C4×D59—48no—
342C8×C59—22no—
343C8×C59—22no—
344C59⋊C8—22no—
345C59⋊C8—22no—
346C2×#3102—591nomaximal, Sylow
347C22×C59—22no—
348C22×C59—24no—
349C22×C59—22no—
350C22×C59—22no—
351C22×C59—44no—
352C22×C59—48no—
353C22×C59—42no—
354C22×C59—42no—
355C22×C59#52512yes—
356C22×C59C2×#13512yes—
357C22×C59#57512yes—
358C22×C59C23×D411yescharacteristic
359C2×D59—42no—
360C2×D59—42no—
361C2×D59—42no—
362C2×D59—84no—
363C4×C59—22no—
364C4×C59—24no—
365C4×C59—42no—
366C4×C59—42no—
367C4×C59#52512yes—
368C4×C59C22×#4111yescharacteristic
369C4×C59C22×#4111yescharacteristic
370Dic59—22no—
371Dic59—22no—
372Dic59—22no—
373Dic59—42no—
374Dic59—42no—
375Dic59—42no—
376Dic59C2×#13514yes—
377C2×#529—591no—
378C2×C4×#41—591no—
379#3102—5916no—
380C2×#485—591no—
381C2×#482—591no—
382C2×#479—591no—
383C2×#478—591no—
384C2×#464—591no—
385C2×#463—591no—
386C2×#452D5911yescharacteristic, complemented
387C2×#449—591no—
388C2×C4×Q16—591no—
389C2×C4×SD16—591no—
390C2×C4×SD16—591no—
391C2×C4×D8—591no—
392C2×#431—591no—
393C2×C59—42no—
394C2×C59—44no—
395C2×C59#310214yescomplemented
396C2×C59C2×#52511yescharacteristic
397C2×C59C22×#13511yescharacteristic
398C2×C59C2×#57511yescharacteristic
399D59—82no—
400C22×#41C2×D5911yescharacteristic
401C22×Q16C2×D5911yescharacteristic
402C22×SD16—591no—
403C22×SD16C2×D5911yescharacteristic
404C22×D8—591no—
405#529—598no—
406#529—1184no—
407C2×#126—1181no—
408C2×#125—591no—
409C2×#124—591no—
410C2×#123—1181no—
411C2×C22⋊Q8C2×D5911yescharacteristic
412C2×#121—591no—
413C4×#41—598no—
414C4×#41—1184no—
415C2×C4×Q8—591no—
416C2×C4×Q8—591no—
417C2×C4×Q8—591no—
418C2×C4×D4—591no—
419C2×C4×D4—591no—
420C2×C4×D4—591no—
421C2×C4×D4—1181no—
422C2×C4×D4—1181no—
423C2×C4×D4—1181no—
424C2×#117—591no—
425C2×#117—1181no—
426C2×#117—1181no—
427C22×C42—591no—
428C22×C42—1181no—
429#485—598no—
430#482—598no—
431#479—598no—
432#478—598no—
433#464—598no—
434#463—598no—
435#452C2×D5918yescomplemented
436#449—598no—
437C4×Q16—598no—
438C4×SD16—598no—
439C4×SD16—598no—
440C4×D8—598no—
441#431—598no—
442C2×#107—591no—
443C2×#107—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8—591no—
447C2×C4⋊C8—591no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103C2×D5911yescharacteristic
452C2×#102—591no—
453C2×#102—591no—
454C2×#102—591no—
455C2×#102C2×D5911yescharacteristic
456C2×C22⋊C8—591no—
457C2×C22⋊C8C2×D5911yescharacteristic
458C2×C4×C8—591no—
459C2×C4×C8—591no—
460C59C2×#310211yescharacteristic, complemented, Sylow
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D5914yes—
465C22×Q8C22×D5911yescharacteristic
466C22×Q8C22×D5911yescharacteristic
467C22×D4—21no—
468C22×D4—591no—
469C22×D4—1181no—
470C22×D4C22×D5911yescharacteristic
471C23×C4—21no—
472C23×C4—591no—
473C23×C4—591no—
474C23×C4—1181no—
475C23×C4—1181no—
476C23×C4—1181no—
477C23×C4C22×D5911yescharacteristic
478C2×Q16—24no—
479C2×Q16C22×D5914yes—
480C2×SD16—24no—
481C2×SD16—594no—
482C2×SD16—1184no—
483C2×SD16C22×D5914yes—
484C2×D8—594no—
485C2×D8—1184no—
486C22×C8—591no—
487C22×C8—591no—
488C22×C8C22×D5911yescharacteristic
489C22×C8C22×D5911yescharacteristic
490#126—1188no—
491#125—594no—
492#125—1182no—
493#124—594no—
494#124—1182no—
495#123—1188no—
496C22⋊Q8—22no—
497C22⋊Q8C22×D5914yes—
498#121—594no—
499#121—1182no—
500C4×Q8—594no—
501C4×Q8—594no—
502C4×Q8—594no—
503C4×Q8—1182no—
504C4×Q8—1182no—
505C4×Q8—1182no—
506C4×D4—594no—
507C4×D4—594no—
508C4×D4—594no—
509C4×D4—1182no—
510C4×D4—1182no—
511C4×D4—1182no—
512C4×D4—1188no—
513C4×D4—1188no—
514C4×D4—1188no—
515#117—594no—
516#117—1188no—
517#117—1188no—
518#117—1182no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—591no—
521C2×C4⋊C4—591no—
522C2×C4⋊C4—591no—
523C2×C4⋊C4—1181no—
524C2×C4⋊C4—1181no—
525C2×C4⋊C4—1181no—
526C2×C4⋊C4—1181no—
527C2×C4⋊C4—1181no—
528C2×C4⋊C4C22×D5911yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—1181no—
531C2×C22⋊C4—1181no—
532C2×C22⋊C4—1181no—
533C2×C22⋊C4—1181no—
534C2×C22⋊C4—1181no—
535C2×C22⋊C4—1181no—
536C2×C22⋊C4—1181no—
537C2×C42—591no—
538C2×C42—591no—
539C2×C42—594no—
540C2×C42—591no—
541C2×C42—591no—
542C2×C42—594no—
543C2×C42—1188no—
544C2×C42—1181no—
545C2×C42—1181no—
546C2×C42—1181no—
547C2×C42—1181no—
548#107—594no—
549#107—594no—
550#106—594no—
551#106—594no—
552C4⋊C8—594no—
553C4⋊C8—594no—
554#103—594no—
555#103—594no—
556#103—594no—
557#103C22×D5914yes—
558#102—594no—
559#102—594no—
560#102—594no—
561#102C22×D5914yes—
562C22⋊C8—594no—
563C22⋊C8C22×D5914yes—
564C4×C8—594no—
565C4×C8—594no—
566C24—21no—
567C24—1181no—
568C24D4×D5911yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8#1174568714yes—
578C2×Q8C23×D5912yes—
579C2×Q8C23×D5912yes—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—592no—
585C2×D4—1184no—
586C2×D4—1181no—
587C2×D4—1182no—
588C2×D4—1182no—
589C2×D4—2364no—
590C2×D4#1174568714yes—
591C2×D4C23×D5912yes—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—591no—
600C22×C4—594no—
601C22×C4—591no—
602C22×C4—591no—
603C22×C4—591no—
604C22×C4—594no—
605C22×C4—1184no—
606C22×C4—1184no—
607C22×C4—1184no—
608C22×C4—1184no—
609C22×C4—1181no—
610C22×C4—1181no—
611C22×C4—1181no—
612C22×C4—2364no—
613C22×C4—2364no—
614C22×C4—2362no—
615C22×C4—2364no—
616C22×C4D4×D5912yes—
617C22×C4D4×D5911yescharacteristic
618C22×C4C23×D5912yes—
619C22×C4C23×D5911yescharacteristic
620Q16—28no—
621SD16—28no—
622SD16—1188no—
623D8—1188no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—592no—
627C2×C8—592no—
628C2×C8—1182no—
629C2×C8—1182no—
630C2×C8C23×D5912yes—
631C2×C8C23×D5912yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—592no—
635C4⋊C4—592no—
636C4⋊C4—592no—
637C4⋊C4—1184no—
638C4⋊C4—1184no—
639C4⋊C4—1184no—
640C4⋊C4—1184no—
641C4⋊C4—1184no—
642C4⋊C4—1181no—
643C4⋊C4—1181no—
644C4⋊C4—1181no—
645C4⋊C4C23×D5912yes—
646C22⋊C4—24no—
647C22⋊C4—1184no—
648C22⋊C4—1184no—
649C22⋊C4—1184no—
650C22⋊C4—1184no—
651C22⋊C4—1184no—
652C22⋊C4—1184no—
653C22⋊C4—1184no—
654C42—594no—
655C42—594no—
656C42—592no—
657C42—592no—
658C42—592no—
659C42—592no—
660C42—1184no—
661C42—1184no—
662C42—1184no—
663C42—1184no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—1182no—
672C23—2362no—
673C23—2362no—
674C23—2362no—
675C23C2×D4×D5912yes—
676C23C2×D4×D5911yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—22no—
680Q8—22no—
681Q8—42no—
682Q8C2×#1174568714yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—1182no—
687D4—1182no—
688D4—2368no—
689D4—2362no—
690D4C2×#1174568714yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—594no—
703C2×C4—592no—
704C2×C4—592no—
705C2×C4—592no—
706C2×C4—592no—
707C2×C4—1188no—
708C2×C4—1182no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—2368no—
715C2×C4—2368no—
716C2×C4—2364no—
717C2×C4—2368no—
718C2×C4—2362no—
719C2×C4—2362no—
720C2×C4—2362no—
721C2×C4C2×D4×D5912yes—
722C2×C4C2×D4×D5911yescharacteristic
723C2×C4C2×#1174568712yes—
724C2×C4C2×#1174568712yes—
725C2×C4C24×D5911yescharacteristic
726C8—22no—
727C8—22no—
728C8—1182no—
729C8—1182no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—4724no—
739C22—2362no—
740C22—2362no—
741C22—2362no—
742C22#1683790812yes—
743C22#135×D5912yes—
744C22#1683820112yes—
745C22C22×D4×D5911yescharacteristic
746C4—22no—
747C4—24no—
748C4—42no—
749C4—42no—
750C4—594no—
751C4—1182no—
752C4—1182no—
753C4—1182no—
754C4—2362no—
755C4—2362no—
756C4—2362no—
757C4#1683790812yes—
758C4C22×#1174568711yescharacteristic
759C4C22×#1174568711yescharacteristic
760C2—42no—
761C2—44no—
762C2—4722no—
763C2#2143411514yesdirect product factor
764C2C2×#1683790811yescharacteristic
765C2C2×#135×D5911yescharacteristic
766C2C2×#1683820111yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#452C2
socleC23×C59C22×D4
prime radicalC2×#16837547C2
hypercenterC2×#452D59
hypocenterC59C2×#3102
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16837938C2semidirect
2. C2×#41×Dic59C2semidirect
3. #21434115C2direct (N × H)
4. C2×#16837740C2semidirect
5. C2×#16837727C2semidirect
6. C2×#16837707C2semidirect
7. C2×#16837700C2semidirect
8. C2×#16837626C2semidirect
9. C2×#16837619C2semidirect
11. C2×Q16×Dic59C2semidirect
12. C2×SD16×Dic59C2semidirect
13. C2×#16837487C2semidirect
14. C2×#16837482C2semidirect
15. C2×#16837452C2semidirect
16. C2×C59×#452C2semidirect
20. #16837938C22semidirect
27. #41×Dic59C22semidirect
42. #16837740C22semidirect
43. #16837727C22semidirect
44. #16837707C22semidirect
45. #16837700C22semidirect
46. #16837626C22semidirect
47. #16837619C22semidirect
49. Q16×Dic59C22semidirect
50. SD16×Dic59C22semidirect
51. #16837487C22semidirect
52. #16837482C22semidirect
53. #16837452C22semidirect
73. C59×#452C22semidirect
386. C2×#452D59semidirect
395. C2×C59#3102semidirect
435. #452C2×D59semidirect
460. C59C2×#3102semidirect
763. C2#21434115direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168379382
C2×#41×Dic592
#214341152
C2×#168377402
C2×#168377272
C2×#168377072
C2×#168377002
C2×#168376262
C2×#168376192
C2×#168375472
C2×Q16×Dic592
C2×SD16×Dic592
C2×#168374872
C2×#168374822
C2×#168374522
C2×C59×#4522
C2×#310259