Finite Group Databasebeta

← C2×#21434320 #29456963

Subgroups — C2×#21434320 #29456963

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×#16838019C211yesmaximal, characteristic
2C2×#16837879C211yesmaximal, characteristic, complemented
3#21434320C2116yesmaximal, direct product factor
4C2×#16837743C211yesmaximal, characteristic, complemented
5C2×#16837696C211yesmaximal, characteristic, complemented
6C2×#16837686C211yesmaximal, characteristic, complemented
7C2×#16837623C211yesmaximal, characteristic, complemented
8C2×#16837623C211yesmaximal, characteristic, complemented
9C2×#16837560C211yesmaximal, characteristic, complemented
10C2×#16837540C211yesmaximal, characteristic
11C2×#16837508C211yesmaximal, characteristic, complemented
12C2×#16837499C211yesmaximal, characteristic, complemented
13C2×#16837496C211yesmaximal, characteristic, complemented
14C2×#16837493C211yesmaximal, characteristic, complemented
15C2×#16837460C211yesmaximal, characteristic, complemented
16C2×C59×#482C211yesmaximal, characteristic
17C23×Dic118C2211yescharacteristic
18C22×Dic236C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×#11745670C2211yescharacteristic
21C22×#11745670C2211yescharacteristic
22#16838019—24no—
23#16838019C2218yes—
24C2×#14273726C2211yescharacteristic
25C2×#14273720—21no—
26C2×#14273714—21no—
27C2×#14273714C2211yescharacteristic
28C2×#14273708—21no—
29C2×#14273706C2211yescharacteristic
30C2×#14273704—21no—
31#16837879—24no—
32#16837879C2218yescomplemented
33C2×C4×Dic118—21no—
34C2×C4×Dic118—21no—
35C2×#14273692C2211yescharacteristic
36C2×#14273692C2211yescharacteristic
37C2×#14273692C2211yescharacteristic
38C2×#14273692C2211yescharacteristic
39C2×#14273692C2211yescharacteristic
40C2×D4×Dic59C2211yescharacteristic
41C2×#14273686C2211yescharacteristic
42C2×#14273683—21no—
43C2×#14273683—21no—
44#16837743C2218yescomplemented
45#16837696C2218yescomplemented
46#16837686C2218yescomplemented
47#16837623C2218yescomplemented
48#16837623C2218yescomplemented
49#16837560C2218yescomplemented
50#16837540C2218yes—
51#16837508C2218yescomplemented
52#16837499C2218yescomplemented
53#16837496C2218yescomplemented
54#16837493C2218yescomplemented
55#16837460C2218yescomplemented
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58C2×Dic59⋊C8C2211yescharacteristic
59C2×Dic59⋊C8C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×C22⋊(C59⋊C8)C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C2×#121×C59C2211yescharacteristic
70C2×#117×C59C2211yescharacteristic
71C59×#482C2218yes—
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—22no—
79C22×Dic118—24no—
80C22×Dic118—24no—
81C22×Dic118—21no—
82C22×Dic118C2311yescharacteristic
83C22×Dic118C2314yes—
84C22×Dic118C2311yescharacteristic
85C22×Dic118C2311yescharacteristic
86C23×Dic59—21no—
87C23×Dic59—21no—
88C2×Dic236—24no—
89C2×Dic236—24no—
90C2×Dic236C2314yes—
91C2×Dic236C2314yes—
92C2×#11745670—24no—
93C2×#11745670—24no—
94C2×#11745670C2314yes—
95C2×#11745670C2314yes—
96C22×C59⋊C8C2311yescharacteristic
97C22×C59⋊C8C2311yescharacteristic
98#14273726—22no—
99#14273726C2314yes—
100#14273720—28no—
101#14273714—28no—
102#14273714—22no—
103#14273714C2314yes—
104#14273708—28no—
105#14273706—22no—
106#14273706C2314yes—
107#14273704—28no—
108C4×Dic118—28no—
109C4×Dic118—28no—
110#14273692—22no—
111#14273692—22no—
112#14273692—22no—
113#14273692—22no—
114#14273692—22no—
115#14273692C2314yes—
116#14273692C2314yes—
117#14273692C2314yes—
118#14273692C2314yes—
119#14273692C2314yes—
120D4×Dic59—22no—
121D4×Dic59C2314yes—
122#14273686D414yes—
123#14273686C2314yes—
124#14273683—28no—
125#14273683—28no—
126C2×C4⋊Dic59D411yescharacteristic
127C2×C4⋊Dic59D411yescharacteristic
128C2×C4⋊Dic59C2311yescharacteristic
129C2×Dic59⋊C4—21no—
130C2×Dic59⋊C4—21no—
131C2×Dic59⋊C4—21no—
132C2×Dic59⋊C4—21no—
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×C22⋊Dic59—21no—
137C2×C22⋊Dic59—21no—
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59D411yescharacteristic
141C2×C22⋊Dic59D411yescharacteristic
142C2×C4×Dic59—21no—
143C2×C4×Dic59—21no—
144C2×C4×Dic59—21no—
145C2×C4×Dic59—21no—
146C2×C4×Dic59—21no—
147C2×C4×Dic59C2311yescharacteristic
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yes—
150#14273658C2314yes—
151Dic59⋊C8C2314yes—
152Dic59⋊C8C2314yes—
153#14273652C2314yes—
154#14273652C2314yes—
155#14273650C2314yes—
156#14273650C2314yes—
157#14273650C2314yes—
158#14273650C2314yes—
159C22⋊(C59⋊C8)C2314yes—
160#14273637C2314yes—
161C8×Dic59C2314yes—
162C22×D4×C59—21no—
163C22×D4×C59C2311yescharacteristic
164C23×C4×C59C2311yescharacteristic
165C22×C8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167#121×C59—22no—
168#121×C59C2314yes—
169#117×C59—22no—
170#117×C59C2314yes—
171C2×C4⋊C4×C59C2311yescharacteristic
172C2×C4⋊C4×C59C2311yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C22⋊C4×C59—21no—
175C2×C22⋊C4×C59—21no—
176C2×C42×C59—21no—
177#107×C59C2314yes—
178#106×C59C2314yes—
179#102×C59C2314yes—
180#102×C59C2314yes—
181C22⋊C8×C59C2314yes—
182C24×C59—21no—
183C24×C59C2×D411yescharacteristic
184C2×D4×C59—24no—
185C2×D4×C59—21no—
186C2×D4×C59—22no—
187C2×D4×C59—22no—
188C2×D4×C59—82no—
189C2×D4×C59C2412yes—
190C22×C4×C59—22no—
191C22×C4×C59—22no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D412yes—
197C22×C4×C59C2412yes—
198C22×C4×C59C2411yescharacteristic
199C22×Dic59—28no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59—24no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—24no—
206C22×Dic59—82no—
207C22×Dic59C2×D411yescharacteristic
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211C2×Dic118—28no—
212C2×Dic118—216no—
213C2×Dic118—21no—
214C2×Dic118—21no—
215C2×Dic118—24no—
216C2×Dic118—22no—
217C2×Dic118—22no—
218C2×Dic118—28no—
219C2×Dic118—28no—
220C2×Dic118—22no—
221C2×Dic118—22no—
222C2×Dic118—21no—
223C2×Dic118—24no—
224C2×Dic118—82no—
225C2×Dic118#4114yes—
226C2×Dic118#4114yes—
227C2×Dic118C2412yes—
228C2×Dic118C2412yes—
229C2×Dic118C2412yes—
230C2×C8×C59—22no—
231C2×C8×C59—22no—
232C2×C8×C59C2412yes—
233C2×C8×C59C2412yes—
234C4⋊C4×C59—21no—
235C4⋊C4×C59—21no—
236C4⋊C4×C59—21no—
237C4⋊C4×C59C2412yes—
238C4⋊C4×C59C2412yes—
239C4⋊C4×C59C2412yes—
240C22⋊C4×C59—24no—
241C22⋊C4×C59—24no—
242C42×C59—24no—
243C22⋊Dic59—24no—
244C22⋊Dic59—24no—
245C22⋊Dic59—24no—
246C22⋊Dic59—24no—
247C22⋊Dic59C2×D414yes—
248C22⋊Dic59C2×D414yes—
249#11745670—28no—
250#11745670—28no—
251C4⋊Dic59—21no—
252C4⋊Dic59C2×D414yes—
253C4⋊Dic59C2×D414yes—
254C4⋊Dic59C2412yes—
255Dic59⋊C4—24no—
256Dic59⋊C4—24no—
257Dic59⋊C4—24no—
258Dic59⋊C4—24no—
259Dic59⋊C4—24no—
260Dic59⋊C4—24no—
261Dic59⋊C4—24no—
262C4×Dic59—24no—
263C4×Dic59—24no—
264C4×Dic59—24no—
265C4×Dic59—24no—
266C4×Dic59—24no—
267C4×Dic59C2×D412yes—
268C4×Dic59C2×D412yes—
269C4×Dic59C2412yes—
270C4×Dic59C2412yes—
271C2×C59⋊C8—22no—
272C2×C59⋊C8—22no—
273C2×C59⋊C8C2412yes—
274C2×C59⋊C8C2412yes—
275Dic236—28no—
276Dic236—28no—
277C23×C59—22no—
278C23×C59—22no—
279C23×C59—22no—
280C23×C59—22no—
281C23×C59—42no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59C22×D412yes—
285C23×C59C22×D411yescharacteristic
286D4×C59—22no—
287D4×C59—22no—
288D4×C59—42no—
289D4×C59—84no—
290C2×C4×C59—22no—
291C2×C4×C59—24no—
292C2×C4×C59—22no—
293C2×C4×C59—22no—
294C2×C4×C59—22no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—42no—
298C2×C4×C59—42no—
299C2×C4×C59—42no—
300C2×C4×C59C22×D412yes—
301C2×C4×C59C22×D411yescharacteristic
302C2×C4×C59C2×#4112yes—
303C2×C4×C59C2×#4112yes—
304C2×C4×C59C2511yescharacteristic
305C2×Dic59—216no—
306C2×Dic59—24no—
307C2×Dic59—24no—
308C2×Dic59—22no—
309C2×Dic59—22no—
310C2×Dic59—22no—
311C2×Dic59—22no—
312C2×Dic59—22no—
313C2×Dic59—22no—
314C2×Dic59—22no—
315C2×Dic59—22no—
316C2×Dic59—42no—
317C2×Dic59—42no—
318C2×Dic59—84no—
319C2×Dic59C22×D412yes—
320C2×Dic59C22×D412yes—
321C2×Dic59C22×D412yes—
322C2×Dic59C22×D412yes—
323Dic118—216no—
324Dic118—24no—
325Dic118—24no—
326Dic118—22no—
327Dic118—22no—
328Dic118—22no—
329Dic118—22no—
330Dic118—42no—
331Dic118—84no—
332Dic118C2×#4114yes—
333Dic118C2×#4114yes—
334C8×C59—22no—
335C8×C59—22no—
336C59⋊C8—22no—
337C59⋊C8—22no—
338C2×#3121—591nomaximal, Sylow
339C22×C59—22no—
340C22×C59—22no—
341C22×C59—22no—
342C22×C59—44no—
343C22×C59—42no—
344C22×C59—42no—
345C22×C59—42no—
346C22×C59—84no—
347C22×C59#52512yes—
348C22×C59#57712yes—
349C22×C59#57812yes—
350C22×C59C23×D411yescharacteristic
351C4×C59—22no—
352C4×C59—42no—
353C4×C59—42no—
354C4×C59—42no—
355C4×C59#52512yes—
356C4×C59C22×#4111yescharacteristic
357C4×C59C22×#4111yescharacteristic
358Dic59—24no—
359Dic59—24no—
360Dic59—22no—
361Dic59—22no—
362Dic59—22no—
363Dic59—22no—
364Dic59—42no—
365Dic59—42no—
366C2×#542—591no—
367C2×#519—591no—
368#3121—5916no—
369C2×#485—591no—
370C2×#482D5911yescharacteristic
371C2×#477—591no—
372C2×#475—591no—
373C2×#464—591no—
374C2×#464—591no—
375C2×#451—591no—
376C2×#448—591no—
377C2×#441—591no—
378C2×#440—591no—
379C2×C4×Q16—591no—
380C2×C4×SD16—591no—
381C2×#433—591no—
382C2×C59—42no—
383C2×C59—82no—
384C2×C59#312114yescomplemented
385C2×C59C2×#52511yescharacteristic
386C2×C59C2×#57711yescharacteristic
387C2×C59C2×#57811yescharacteristic
388C23×Q8—591no—
389C22×Q16—591no—
390C22×Q16—591no—
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×#121C2×D5911yescharacteristic
403#519—598no—
404#519—1184no—
405C2×C4×Q8—591no—
406C2×C4×Q8—591no—
407C2×C4×Q8—591no—
408C2×C4×Q8—591no—
409C2×C4×Q8—591no—
410C2×C4×Q8—1181no—
411C2×C4×Q8—1181no—
412C2×C4×D4—591no—
413C2×#117—591no—
414C2×#117—1181no—
415C2×#117—1181no—
416C2×#117C2×D5911yescharacteristic
417#485—598no—
418#482C2×D5918yes—
419#477—598no—
420#475—598no—
421#464—598no—
422#464—598no—
423#451—598no—
424#448—598no—
425#441—598no—
426#440—598no—
427C4×Q16—598no—
428C4×SD16—598no—
429#433—598no—
430C2×#107—591no—
431C2×#107C2×D5911yescharacteristic
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×#103—591no—
441C2×#103—591no—
442C2×#102C2×D5911yescharacteristic
443C2×#102C2×D5911yescharacteristic
444C2×C22⋊C8—591no—
445C2×C22⋊C8C2×D5911yescharacteristic
446C2×#97—591no—
447C2×C4×C8—591no—
448C59C2×#312111yescharacteristic, complemented, Sylow
449C22×Q8—591no—
450C22×Q8—591no—
451C22×Q8—591no—
452C22×Q8—594no—
453C22×Q8—1181no—
454C22×Q8—1184no—
455C22×Q8—1184no—
456C22×Q8—1181no—
457C22×Q8—1182no—
458C22×D4—21no—
459C22×D4C22×D5911yescharacteristic
460C23×C4—1181no—
461C23×C4—1181no—
462C23×C4C22×D5911yescharacteristic
463C2×Q16—594no—
464C2×Q16—594no—
465C2×Q16—1184no—
466C2×Q16—1184no—
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—1182no—
480#124—1188no—
481#123—1188no—
482C22⋊Q8—594no—
483C22⋊Q8—1188no—
484C22⋊Q8—1182no—
485#121—22no—
486#121C22×D5914yes—
487C4×Q8—594no—
488C4×Q8—594no—
489C4×Q8—594no—
490C4×Q8—594no—
491C4×Q8—594no—
492C4×Q8—1188no—
493C4×Q8—1188no—
494C4×Q8—1182no—
495C4×Q8—1182no—
496C4×Q8—1182no—
497C4×Q8—1182no—
498C4×Q8—1182no—
499C4×D4—594no—
500C4×D4—1182no—
501#117—22no—
502#117—594no—
503#117—594no—
504#117—1188no—
505#117—1188no—
506#117C22×D5914yes—
507C2×C4⋊C4—591no—
508C2×C4⋊C4—591no—
509C2×C4⋊C4—591no—
510C2×C4⋊C4—1181no—
511C2×C4⋊C4—1181no—
512C2×C4⋊C4—1181no—
513C2×C4⋊C4—1181no—
514C2×C4⋊C4—1181no—
515C2×C4⋊C4—1181no—
516C2×C4⋊C4—1181no—
517C2×C4⋊C4C22×D5911yescharacteristic
518C2×C4⋊C4C22×D5911yescharacteristic
519C2×C4⋊C4C22×D5911yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—591no—
523C2×C22⋊C4—591no—
524C2×C22⋊C4—1181no—
525C2×C22⋊C4—1181no—
526C2×C22⋊C4—1181no—
527C2×C22⋊C4—1181no—
528C2×C42—21no—
529C2×C42—591no—
530C2×C42—591no—
531C2×C42—1181no—
532C2×C42—1181no—
533C2×C42—1181no—
534C2×C42—1181no—
535C2×C42—1181no—
536#107—594no—
537#107C22×D5914yes—
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#103—594no—
547#103—594no—
548#102C22×D5914yes—
549#102C22×D5914yes—
550C22⋊C8—594no—
551C22⋊C8C22×D5914yes—
552#97—594no—
553C4×C8—594no—
554C24—21no—
555C24D4×D5911yescharacteristic
556C2×Q8—594no—
557C2×Q8—594no—
558C2×Q8—592no—
559C2×Q8—592no—
560C2×Q8—592no—
561C2×Q8—1184no—
562C2×Q8—1188no—
563C2×Q8—1188no—
564C2×Q8—1188no—
565C2×Q8—11816no—
566C2×Q8—1184no—
567C2×Q8—1181no—
568C2×Q8—1181no—
569C2×Q8—1181no—
570C2×Q8—1182no—
571C2×Q8—1182no—
572C2×Q8—1182no—
573C2×Q8—1182no—
574C2×Q8—4722no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—82no—
580C2×D4C23×D5912yes—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—591no—
587C22×C4—591no—
588C22×C4—591no—
589C22×C4—591no—
590C22×C4—1184no—
591C22×C4—1188no—
592C22×C4—1184no—
593C22×C4—1181no—
594C22×C4—1181no—
595C22×C4—1181no—
596C22×C4—1181no—
597C22×C4—4722no—
598C22×C4D4×D5912yes—
599C22×C4D4×D5911yescharacteristic
600C22×C4C23×D5912yes—
601C22×C4C23×D5911yescharacteristic
602Q16—1188no—
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—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—594no—
618C4⋊C4—594no—
619C4⋊C4—592no—
620C4⋊C4—1184no—
621C4⋊C4—1184no—
622C4⋊C4—1184no—
623C4⋊C4—1184no—
624C4⋊C4—1184no—
625C4⋊C4—1184no—
626C4⋊C4—1181no—
627C4⋊C4—1184no—
628C4⋊C4C23×D5912yes—
629C4⋊C4C23×D5912yes—
630C4⋊C4C23×D5912yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—594no—
634C22⋊C4—594no—
635C22⋊C4—1184no—
636C22⋊C4—1184no—
637C22⋊C4—1184no—
638C22⋊C4—1184no—
639C42—24no—
640C42—592no—
641C42—592no—
642C42—592no—
643C42—592no—
644C42—1184no—
645C42—1184no—
646C42—1184no—
647C42—1184no—
648C42—1184no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C2×D4×D5912yes—
657C23C2×D4×D5911yescharacteristic
658Q8—594no—
659Q8—594no—
660Q8—11816no—
661Q8—1184no—
662Q8—1184no—
663Q8—1182no—
664Q8—1182no—
665Q8—1182no—
666Q8—1182no—
667Q8—4724no—
668Q8—2362no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—84no—
673C2×C4—22no—
674C2×C4—24no—
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—592no—
687C2×C4—11816no—
688C2×C4—1184no—
689C2×C4—1184no—
690C2×C4—1182no—
691C2×C4—1182no—
692C2×C4—1182no—
693C2×C4—1182no—
694C2×C4—1182no—
695C2×C4—1182no—
696C2×C4—1182no—
697C2×C4—1182no—
698C2×C4—4724no—
699C2×C4—2362no—
700C2×C4—2362no—
701C2×C4C2×D4×D5912yes—
702C2×C4C2×D4×D5911yescharacteristic
703C2×C4#41×D5912yes—
704C2×C4#41×D5912yes—
705C2×C4C24×D5911yescharacteristic
706C8—22no—
707C8—22no—
708C8—1182no—
709C8—1182no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—84no—
718C22#1683791012yes—
719C22#1683821212yes—
720C22#1683821612yes—
721C22C22×D4×D5911yescharacteristic
722C4—22no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—1182no—
727C4—1182no—
728C4—1182no—
729C4—1182no—
730C4—1184no—
731C4—1184no—
732C4—2362no—
733C4—2362no—
734C4#1683791012yes—
735C4C2×#41×D5911yescharacteristic
736C4C2×#41×D5911yescharacteristic
737C2—42no—
738C2—82no—
739C2#2143432014yesdirect product factor
740C2C2×#1683791011yescharacteristic
741C2C2×#1683821211yescharacteristic
742C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#482C2
socleC23×C59C22×D4
prime radicalC2×#121×C59C22
hypercenterC2×#482D59
hypocenterC59C2×#3121
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#482

Complements

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

NH ≅ G/Ntype
2. C2×#16837879C2semidirect
3. #21434320C2direct (N × H)
4. C2×#16837743C2semidirect
5. C2×#16837696C2semidirect
6. C2×#16837686C2semidirect
7. C2×#16837623C2semidirect
8. C2×#16837623C2semidirect
9. C2×#16837560C2semidirect
11. C2×#16837508C2semidirect
12. C2×#16837499C2semidirect
13. C2×#16837496C2semidirect
14. C2×#16837493C2semidirect
15. C2×#16837460C2semidirect
32. #16837879C22semidirect
44. #16837743C22semidirect
45. #16837696C22semidirect
46. #16837686C22semidirect
47. #16837623C22semidirect
48. #16837623C22semidirect
49. #16837560C22semidirect
51. #16837508C22semidirect
52. #16837499C22semidirect
53. #16837496C22semidirect
54. #16837493C22semidirect
55. #16837460C22semidirect
384. C2×C59#3121semidirect
448. C59C2×#3121semidirect
739. C2#21434320direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380192
C2×#168378792
#214343202
C2×#168377432
C2×#168376962
C2×#168376862
C2×#168376232
C2×#168375602
C2×#168375402
C2×#168375082
C2×#168374992
C2×#168374962
C2×#168374932
C2×#168374602
C2×C59×#4822
C2×#312159