Finite Group Databasebeta

← C2×#21434329 #29456972

Subgroups — C2×#21434329 #29456972

Order 15104.

2058 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838024C211yesmaximal, characteristic
2C2×#16837878C211yesmaximal, characteristic, complemented
3#21434329C2116yesmaximal, direct product factor
4C2×#16837742C211yesmaximal, characteristic, complemented
5C2×#16837728C211yesmaximal, characteristic
6C2×#16837695C211yesmaximal, characteristic, complemented
7C2×#16837686C211yesmaximal, characteristic, complemented
8C2×#16837627C211yesmaximal, characteristic, complemented
9C2×#16837626C211yesmaximal, characteristic, complemented
10C2×#16837556C211yesmaximal, characteristic, complemented
11C2×#16837542C211yesmaximal, characteristic
12C2×#16837504C211yesmaximal, characteristic, complemented
13C2×C4×#11745672C211yesmaximal, characteristic, complemented
14C2×C4×#11745671C211yesmaximal, characteristic, complemented
15C2×#16837464C211yesmaximal, characteristic, complemented
16C2×C59×#441C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745671C2211yescharacteristic
21#16838024—24no—
22#16838024C2218yes—
23C2×#14273726C2211yescharacteristic
24C2×#14273721—21no—
25C2×#14273716C2211yescharacteristic
26C2×#14273715—21no—
27C2×#14273712—21no—
28C2×#14273705—21no—
29C2×#14273703C2211yescharacteristic
30C2×#14273702C2211yescharacteristic
31#16837878—24no—
32#16837878C2218yescomplemented
33C2×Q8×Dic59C2211yescharacteristic
34C2×C4×Dic118—21no—
35C2×C4×Dic118C2211yescharacteristic
36C2×#14273692—21no—
37C2×#14273692C2211yescharacteristic
38C2×C4×D236C2211yescharacteristic
39C2×#14273685—21no—
40C2×#14273685C2211yescharacteristic
41C2×#14273684—21no—
42C2×#14273684C2211yescharacteristic
43#16837742C2218yescomplemented
44#16837728C2218yes—
45#16837695C2218yescomplemented
46#16837686C2218yescomplemented
47#16837627C2218yescomplemented
48#16837626C2218yescomplemented
49#16837556C2218yescomplemented
50#16837542C2218yes—
51#16837504C2218yescomplemented
52C4×#11745672C2218yescomplemented
53C4×#11745671C2218yescomplemented
54#16837464C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
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
72C59×#441C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#97×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C2×Q8×D59—24no—
81C2×Q8×D59—22no—
82C2×Q8×D59—24no—
83C2×Q8×D59C2314yes—
84C22×D236—21no—
85C22×D236C2311yescharacteristic
86C22×C4×D59—21no—
87C22×C4×D59—21no—
88C22×C4×D59C2311yescharacteristic
89C2×#11745672—24no—
90C2×#11745672C2314yes—
91C2×#11745660—24no—
92C2×#11745660C2314yes—
93C2×#11745671—24no—
94C2×#11745671C2314yes—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97#14273726—22no—
98#14273726C2314yes—
99#14273721—28no—
100#14273716—22no—
101#14273716C2314yes—
102#14273715—28no—
103#14273712—28no—
104#14273705—28no—
105#14273703—22no—
106#14273703C2314yes—
107#14273702—22no—
108#14273702C2314yes—
109Q8×Dic59—22no—
110Q8×Dic59C2314yes—
111C4×Dic118—22no—
112C4×Dic118—28no—
113C4×Dic118C2314yes—
114#14273692—28no—
115#14273692—22no—
116#14273692C2314yes—
117C4×D236—22no—
118C4×D236C2314yes—
119#14273685—22no—
120#14273685—28no—
121#14273685C2314yes—
122#14273684—28no—
123#14273684D414yes—
124#14273684C2314yes—
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⋊C4D411yescharacteristic
133C2×Dic59⋊C4D411yescharacteristic
134C2×(C2×D59)⋊C4—21no—
135C2×(C2×D59)⋊C4—21no—
136C2×(C2×D59)⋊C4—21no—
137C2×(C2×D59)⋊C4—21no—
138C2×(C2×D59)⋊C4—21no—
139C2×(C2×D59)⋊C4—21no—
140C2×(C2×D59)⋊C4D411yescharacteristic
141C2×(C2×D59)⋊C4D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59C2311yescharacteristic
147#14273661C2314yes—
148#14273660C2314yes—
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#106×C59C2314yes—
179#103×C59C2314yes—
180#103×C59C2314yes—
181#97×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
205Q8×D59—216no—
206Q8×D59—28no—
207Q8×D59—28no—
208C2×D236—22no—
209C2×D236—22no—
210C2×D236—21no—
211C2×D236—24no—
212C2×D236—82no—
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—82no—
220C2×C4×D59C2×D412yes—
221C2×C4×D59C2412yes—
222C2×Dic118—28no—
223C2×Dic118—21no—
224C2×Dic118—22no—
225C2×Dic118—24no—
226C2×Dic118—24no—
227C2×Dic118—82no—
228C2×Dic118#4114yes—
229C2×Dic118C2412yes—
230Q16×C59—28no—
231C2×C8×C59—22no—
232C2×C8×C59—22no—
233C2×C8×C59C2412yes—
234C2×C8×C59C2412yes—
235C4⋊C4×C59—24no—
236C4⋊C4×C59—24no—
237C4⋊C4×C59—21no—
238C4⋊C4×C59—21no—
239C4⋊C4×C59C2412yes—
240C4⋊C4×C59C2412yes—
241C42×C59—24no—
242C42×C59—24no—
243C42×C59C2×D412yes—
244C42×C59C2412yes—
245#11745672—28no—
246#11745671—28no—
247(C2×D59)⋊C4—24no—
248(C2×D59)⋊C4—24no—
249(C2×D59)⋊C4—24no—
250(C2×D59)⋊C4—24no—
251(C2×D59)⋊C4—24no—
252(C2×D59)⋊C4—24no—
253(C2×D59)⋊C4C2×D414yes—
254(C2×D59)⋊C4C2×D414yes—
255C4⋊Dic59—21no—
256C4⋊Dic59—21no—
257C4⋊Dic59—24no—
258C4⋊Dic59C2412yes—
259C4⋊Dic59C2412yes—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262Dic59⋊C4—24no—
263Dic59⋊C4—24no—
264Dic59⋊C4C2×D414yes—
265Dic59⋊C4C2×D414yes—
266C4×Dic59—24no—
267C4×Dic59—24no—
268C4×Dic59—24no—
269C4×Dic59—24no—
270C4×Dic59C2×D412yes—
271C4×Dic59C2412yes—
272C2×C59⋊C8—22no—
273C2×C59⋊C8—22no—
274C2×C59⋊C8C2412yes—
275C2×C59⋊C8C2412yes—
276#11745660—28no—
277C23×C59C22×D411yescharacteristic
278C22×D59—22no—
279C22×D59—22no—
280C22×D59—22no—
281C22×D59—22no—
282C22×D59—42no—
283C22×D59—42no—
284C22×D59—42no—
285C22×D59C22×D412yes—
286Q8×C59—24no—
287Q8×C59—22no—
288Q8×C59—22no—
289Q8×C59—22no—
290Q8×C59—42no—
291Q8×C59C2×#4114yes—
292C2×C4×C59—24no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—22no—
298C2×C4×C59—22no—
299C2×C4×C59—42no—
300C2×C4×C59—42no—
301C2×C4×C59—42no—
302C2×C4×C59C22×D412yes—
303C2×C4×C59C22×D412yes—
304C2×C4×C59C22×D411yescharacteristic
305C2×C4×C59C2×#4112yes—
306C2×C4×C59C2×#4112yes—
307C2×C4×C59C2511yescharacteristic
308C2×Dic59—22no—
309C2×Dic59—24no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—42no—
316C2×Dic59—42no—
317C2×Dic59C22×D412yes—
318C2×Dic59C22×D412yes—
319C2×Dic59C22×D412yes—
320D236—22no—
321D236—22no—
322D236—42no—
323D236—84no—
324C4×D59—216no—
325C4×D59—24no—
326C4×D59—22no—
327C4×D59—22no—
328C4×D59—84no—
329Dic118—216no—
330Dic118—24no—
331Dic118—22no—
332Dic118—84no—
333Dic118C2×#4114yes—
334C8×C59—22no—
335C8×C59—22no—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C2×#3121—591nomaximal, Sylow
339C22×C59#52512yes—
340C22×C59#57712yes—
341C22×C59#57812yes—
342C22×C59C23×D411yescharacteristic
343C2×D59—22no—
344C2×D59—22no—
345C2×D59—22no—
346C2×D59—44no—
347C2×D59—42no—
348C2×D59—42no—
349C2×D59—42no—
350C2×D59—84no—
351C4×C59—24no—
352C4×C59—22no—
353C4×C59—22no—
354C4×C59—42no—
355C4×C59—42no—
356C4×C59—42no—
357C4×C59#52512yes—
358C4×C59C22×#4111yescharacteristic
359C4×C59C22×#4111yescharacteristic
360Dic59—22no—
361Dic59—24no—
362Dic59—22no—
363Dic59—22no—
364Dic59—42no—
365Dic59—42no—
366C2×#542—591no—
367C2×#519—591no—
368#3121—5916no—
369C2×#485—591no—
370C2×#482—591no—
371C2×#477—591no—
372C2×#475—591no—
373C2×#464—591no—
374C2×#464—591no—
375C2×#451—591no—
376C2×#448—591no—
377C2×#441D5911yescharacteristic, complemented
378C2×#440—591no—
379C2×C4×Q16—591no—
380C2×C4×SD16—591no—
381C2×#433—591no—
382C2×C59#312114yescomplemented
383C2×C59C2×#52511yescharacteristic
384C2×C59C2×#57711yescharacteristic
385C2×C59C2×#57811yescharacteristic
386D59—42no—
387D59—82no—
388C23×Q8—591no—
389C22×Q16—591no—
390C22×Q16C2×D5911yescharacteristic
391C22×SD16—591no—
392C22×SD16—591no—
393#542—598no—
394#542—1184no—
395C2×C4⋊Q8—591no—
396C2×#126—1181no—
397C2×#124—591no—
398C2×#124—1181no—
399C2×#123—1181no—
400C2×C22⋊Q8—591no—
401C2×C22⋊Q8—1181no—
402C2×#121—591no—
403#519—598no—
404#519—1184no—
405C2×C4×Q8—591no—
406C2×C4×Q8—591no—
407C2×C4×Q8—591no—
408C2×C4×Q8—1181no—
409C2×C4×Q8—1181no—
410C2×C4×Q8C2×D5911yescharacteristic
411C2×C4×Q8C2×D5911yescharacteristic
412C2×C4×D4—591no—
413C2×#117—591no—
414C2×#117—591no—
415C2×#117—1181no—
416C2×#117—1181no—
417#485—598no—
418#482—598no—
419#477—598no—
420#475—598no—
421#464—598no—
422#464—598no—
423#451—598no—
424#448—598no—
425#441C2×D5918yescomplemented
426#440—598no—
427C4×Q16—598no—
428C4×SD16—598no—
429#433—598no—
430C2×#107—591no—
431C2×#107—591no—
432C2×#106—591no—
433C2×#106C2×D5911yescharacteristic
434C2×C4⋊C8—591no—
435C2×C4⋊C8—591no—
436C2×#103—591no—
437C2×#103—591no—
438C2×#103—591no—
439C2×#103—591no—
440C2×#103C2×D5911yescharacteristic
441C2×#103C2×D5911yescharacteristic
442C2×#102—591no—
443C2×#102—591no—
444C2×C22⋊C8—591no—
445C2×C22⋊C8—591no—
446C2×#97C2×D5911yescharacteristic
447C2×C4×C8—591no—
448C59C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—594no—
450C22×Q8—591no—
451C22×Q8—1181no—
452C22×Q8—1181no—
453C22×Q8—1182no—
454C22×Q8—1184no—
455C22×Q8—1184no—
456C22×Q8C22×D5911yescharacteristic
457C22×Q8C22×D5911yescharacteristic
458C22×D4—591no—
459C22×D4—1181no—
460C23×C4—591no—
461C23×C4—1181no—
462C23×C4—1181no—
463C2×Q16—24no—
464C2×Q16—594no—
465C2×Q16—1184no—
466C2×Q16C22×D5914yes—
467C2×SD16—594no—
468C2×SD16—594no—
469C2×SD16—1184no—
470C2×SD16—1184no—
471C22×C8—591no—
472C22×C8—591no—
473C22×C8C22×D5911yescharacteristic
474C22×C8C22×D5911yescharacteristic
475C4⋊Q8—594no—
476C4⋊Q8—1182no—
477#126—1188no—
478#124—594no—
479#124—1188no—
480#124—1182no—
481#123—1188no—
482C22⋊Q8—594no—
483C22⋊Q8—1188no—
484C22⋊Q8—1182no—
485#121—594no—
486#121—1182no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—594no—
490C4×Q8—594no—
491C4×Q8—594no—
492C4×Q8—1188no—
493C4×Q8—1182no—
494C4×Q8—1182no—
495C4×Q8—1188no—
496C4×Q8—1182no—
497C4×Q8C22×D5914yes—
498C4×Q8C22×D5914yes—
499C4×D4—594no—
500C4×D4—1182no—
501#117—594no—
502#117—594no—
503#117—594no—
504#117—1188no—
505#117—1188no—
506#117—1182no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—591no—
511C2×C4⋊C4—591no—
512C2×C4⋊C4—591no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4—1181no—
518C2×C4⋊C4C22×D5911yescharacteristic
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C22⋊C4—591no—
521C2×C22⋊C4—591no—
522C2×C22⋊C4—1181no—
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—1181no—
532C2×C42—1181no—
533C2×C42—1181no—
534C2×C42—1181no—
535C2×C42C22×D5911yescharacteristic
536#107—594no—
537#107—594no—
538#106—594no—
539#106C22×D5914yes—
540C4⋊C8—594no—
541C4⋊C8—594no—
542#103—594no—
543#103—594no—
544#103—594no—
545#103—594no—
546#103C22×D5914yes—
547#103C22×D5914yes—
548#102—594no—
549#102—594no—
550C22⋊C8—594no—
551C22⋊C8—594no—
552#97C22×D5914yes—
553C4×C8—594no—
554C24—591no—
555C24—1181no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8—22no—
561C2×Q8—594no—
562C2×Q8—592no—
563C2×Q8—1184no—
564C2×Q8—1184no—
565C2×Q8—1188no—
566C2×Q8—1188no—
567C2×Q8—11816no—
568C2×Q8—1188no—
569C2×Q8—1181no—
570C2×Q8—1182no—
571C2×Q8—4722no—
572C2×Q8#1174568514yes—
573C2×Q8C23×D5912yes—
574C2×Q8C23×D5912yes—
575C2×D4—592no—
576C2×D4—1184no—
577C2×D4—1181no—
578C2×D4—1182no—
579C2×D4—1182no—
580C2×D4—4722no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—591no—
586C22×C4—591no—
587C22×C4—591no—
588C22×C4—592no—
589C22×C4—592no—
590C22×C4—1184no—
591C22×C4—1188no—
592C22×C4—1181no—
593C22×C4—1182no—
594C22×C4—1182no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—1184no—
598C22×C4—4722no—
599C22×C4D4×D5911yescharacteristic
600C22×C4D4×D5911yescharacteristic
601C22×C4C23×D5911yescharacteristic
602Q16—28no—
603Q16—1188no—
604SD16—1188no—
605SD16—1188no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—592no—
609C2×C8—592no—
610C2×C8—1182no—
611C2×C8—1182no—
612C2×C8C23×D5912yes—
613C2×C8C23×D5912yes—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—594no—
619C4⋊C4—594no—
620C4⋊C4—592no—
621C4⋊C4—592no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1181no—
627C4⋊C4—1181no—
628C4⋊C4—1184no—
629C4⋊C4C23×D5912yes—
630C4⋊C4C23×D5912yes—
631C22⋊C4—594no—
632C22⋊C4—594no—
633C22⋊C4—1184no—
634C22⋊C4—1184no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C42—24no—
640C42—24no—
641C42—592no—
642C42—592no—
643C42—1184no—
644C42—1184no—
645C42—1184no—
646C42—1184no—
647C42D4×D5912yes—
648C42C23×D5912yes—
649C23—592no—
650C23—1182no—
651C23—1182no—
652C23—1182no—
653C23—1182no—
654C23—2362no—
655C23—2362no—
656C23—2362no—
657C23C2×D4×D5911yescharacteristic
658Q8—24no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—594no—
664Q8—11816no—
665Q8—1184no—
666Q8—1182no—
667Q8—4724no—
668Q8C2×#1174568514yes—
669D4—1182no—
670D4—1182no—
671D4—4724no—
672D4—2362no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—592no—
684C2×C4—592no—
685C2×C4—592no—
686C2×C4—11816no—
687C2×C4—1182no—
688C2×C4—1184no—
689C2×C4—1182no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1184no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—4724no—
698C2×C4—2362no—
699C2×C4—2362no—
700C2×C4C2×D4×D5912yes—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4C2×#1174568512yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1182no—
709C8—1182no—
710C22—1182no—
711C22—1182no—
712C22—1182no—
713C22—4724no—
714C22—2362no—
715C22—2362no—
716C22—2362no—
717C22—2364no—
718C22#1683791112yes—
719C22#1683821112yes—
720C22#1683821812yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—22no—
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—1182no—
729C4—1182no—
730C4—1182no—
731C4—1184no—
732C4—2362no—
733C4—2362no—
734C4#1683791112yes—
735C4C2×#41×D5911yescharacteristic
736C4C22×#1174568511yescharacteristic
737C2—4722no—
738C2—2362no—
739C2#2143432914yesdirect product factor
740C2C2×#1683791111yescharacteristic
741C2C2×#1683821111yescharacteristic
742C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#441C2
socleC23×C59C22×D4
prime radicalC2×#14273702C22
hypercenterC2×#441D59
hypocenterC59C2×#3121
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
2. C2×#16837878C2semidirect
3. #21434329C2direct (N × H)
4. C2×#16837742C2semidirect
6. C2×#16837695C2semidirect
7. C2×#16837686C2semidirect
8. C2×#16837627C2semidirect
9. C2×#16837626C2semidirect
10. C2×#16837556C2semidirect
12. C2×#16837504C2semidirect
13. C2×C4×#11745672C2semidirect
14. C2×C4×#11745671C2semidirect
15. C2×#16837464C2semidirect
16. C2×C59×#441C2semidirect
32. #16837878C22semidirect
43. #16837742C22semidirect
45. #16837695C22semidirect
46. #16837686C22semidirect
47. #16837627C22semidirect
48. #16837626C22semidirect
49. #16837556C22semidirect
51. #16837504C22semidirect
52. C4×#11745672C22semidirect
53. C4×#11745671C22semidirect
54. #16837464C22semidirect
72. C59×#441C22semidirect
377. C2×#441D59semidirect
382. C2×C59#3121semidirect
425. #441C2×D59semidirect
448. C59C2×#3121semidirect
739. C2#21434329direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380242
C2×#168378782
#214343292
C2×#168377422
C2×#168377282
C2×#168376952
C2×#168376862
C2×#168376272
C2×#168376262
C2×#168375562
C2×#168375422
C2×#168375042
C2×C4×#117456722
C2×C4×#117456712
C2×#168374642
C2×C59×#4412
C2×#312159