Finite Group Databasebeta

← #28595156

Subgroups — #28595156

Order 15104.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837524C211yesmaximal, characteristic, complemented
2C2×#16837519C211yesmaximal, characteristic, complemented
3#21432814C211yesmaximal, characteristic, complemented
4#21432524C211yesmaximal, characteristic, complemented
5#21425016C211yesmaximal, characteristic, complemented
6#21424872C211yesmaximal, characteristic, complemented
7#21424746C211yesmaximal, characteristic, complemented
8#21424746C211yesmaximal, characteristic, complemented
9#21424425C211yesmaximal, characteristic, complemented
10#21424425C211yesmaximal, characteristic, complemented
11#21424116C211yesmaximal, characteristic, complemented
12#21423973C211yesmaximal, characteristic, complemented
13#21423943C211yesmaximal, characteristic, complemented
14#21423936C211yesmaximal, characteristic, complemented
15C59×#3035C211yesmaximal, characteristic
16C2×#14273734C2211yescharacteristic
17C2×#14273734C2211yescharacteristic
18C2×#14273734C2211yescharacteristic
19C2×#14273734C2211yescharacteristic
20#16837524—24no—
21#16837519—24no—
22#16837474—21no—
23#16837474—21no—
24#16837474—21no—
25#16837474—21no—
26C2×#14273663C2211yescharacteristic
27C2×#14273663C2211yescharacteristic
28#16837426C2211yescharacteristic
29C2×#14273654C2211yescharacteristic
30C2×#14273654C2211yescharacteristic
31C2×#14273654C2211yescharacteristic
32C2×#14273654C2211yescharacteristic
33C2×#14273654C2211yescharacteristic
34C2×#14273654C2211yescharacteristic
35#16837369C2211yescharacteristic
36#16837369C2211yescharacteristic
37#16837358—21no—
38#16837358—21no—
39#16837358C2211yescharacteristic
40#16837358C2211yescharacteristic
41C4×#11745664—21no—
42C4×#11745664C2211yescharacteristic
43C2×#14273638—21no—
44C2×#14273638C2211yescharacteristic
45C2×#14273637C2211yescharacteristic
46C2×C8×Dic59C2211yescharacteristic
47C4×C4⋊Dic59C2211yescharacteristic
48#16837167C2211yescharacteristic
49#16837167C2211yescharacteristic
50#16837161C2211yescharacteristic
51#16837161C2211yescharacteristic
52#16837156C2211yescharacteristic
53#16837156C2211yescharacteristic
54C2×#135×C59C2211yescharacteristic
55C2×#135×C59C2211yescharacteristic
56C59×#532C2211yescharacteristic
57C4×#41×C59C2211yescharacteristic
58C59×#464C411yescharacteristic, complemented
59C59×#464C411yescharacteristic, complemented
60C59×#463C411yescharacteristic, complemented
61C59×#463C411yescharacteristic, complemented
62C59×#462C411yescharacteristic, complemented
63C59×#461C411yescharacteristic, complemented
64C59×#460C411yescharacteristic, complemented
65C59×#459C411yescharacteristic, complemented
66C2×C4⋊C8×C59C2211yescharacteristic
67C59×#416C2211yescharacteristic
68C59×#416C2211yescharacteristic
69#14273734—22no—
70#14273734—22no—
71#14273734—22no—
72#14273734—22no—
73#14273734—22no—
74#14273734—22no—
75#14273734—22no—
76#14273734D414yescomplemented
77C2×#11745664—21no—
78C2×#11745664—21no—
79C2×#11745664—21no—
80C2×#11745664—21no—
81C2×#11745664C2311yescharacteristic
82C2×#11745664C2311yescharacteristic
83C2×#11745664C2311yescharacteristic
84C2×#11745664C2311yescharacteristic
85C22×C59⋊C8—21no—
86C22×C59⋊C8—21no—
87C22×C59⋊C8—21no—
88C22×C59⋊C8—21no—
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C2×C4⋊Dic59—21no—
92C2×C4×Dic59C2311yescharacteristic
93C2×C4×Dic59C2311yescharacteristic
94#14273663—22no—
95#14273663—22no—
96C4⋊(C59⋊C8)—21no—
97C4⋊(C59⋊C8)—21no—
98#14273654—22no—
99#14273654—22no—
100#14273654—22no—
101#14273654—22no—
102#14273654—22no—
103#14273654—22no—
104C22⋊(C59⋊C8)—21no—
105C22⋊(C59⋊C8)—21no—
106C22⋊(C59⋊C8)—21no—
107C22⋊(C59⋊C8)—21no—
108#14273638—21no—
109#14273638—21no—
110#14273638—21no—
111#14273638D411yescharacteristic
112#14273638D411yescharacteristic
113#14273638D411yescharacteristic
114#14273638D411yescharacteristic
115#14273637—22no—
116C4×C59⋊C8—21no—
117C4×C59⋊C8—21no—
118C4×C59⋊C8—21no—
119C8×Dic59—22no—
120C59⋊#95—21no—
121C2×#41×C59C2311yescharacteristic
122C2×#41×C59C2311yescharacteristic
123C2×#41×C59C2311yescharacteristic
124#135×C59—22no—
125#135×C59—22no—
126#135×C59—22no—
127#135×C59—22no—
128C2×Q16×C59C2×C411yescharacteristic
129C2×Q16×C59C2×C411yescharacteristic
130C2×SD16×C59C2×C411yescharacteristic
131C2×SD16×C59C2×C411yescharacteristic
132C2×SD16×C59C2×C411yescharacteristic
133C2×SD16×C59C2×C411yescharacteristic
134C2×D8×C59C2×C411yescharacteristic
135C2×D8×C59C2×C411yescharacteristic
136C22×C8×C59C2311yescharacteristic
137C22×C8×C59C2311yescharacteristic
138C4⋊Q8×C59C2×C411yescharacteristic
139#127×C59C2×C411yescharacteristic
140#124×C59C2×C411yescharacteristic
141#124×C59C2×C411yescharacteristic
142#121×C59—21no—
143#121×C59—21no—
144C4×Q8×C59C2×C411yescharacteristic
145C4×Q8×C59C2×C411yescharacteristic
146C4×D4×C59—21no—
147C4×D4×C59—21no—
148C4×D4×C59—21no—
149C4×D4×C59—21no—
150C4×D4×C59C2×C411yescharacteristic
151C4×D4×C59C2×C411yescharacteristic
152#117×C59—21no—
153#117×C59C2311yescharacteristic
154C2×C42×C59—21no—
155C2×C42×C59C2311yescharacteristic
156C4⋊C8×C59C2×C411yescharacteristic
157C4⋊C8×C59C2×C411yescharacteristic
158C4⋊C8×C59C2×C411yescharacteristic
159C4⋊C8×C59C2×C411yescharacteristic
160#103×C59C2×C411yescharacteristic
161#103×C59C2×C411yescharacteristic
162#103×C59C2×C411yescharacteristic
163#103×C59C2×C411yescharacteristic
164#102×C59C2×C411yescharacteristic
165#102×C59C2×C411yescharacteristic
166#102×C59C2×C411yescharacteristic
167#102×C59C2×C411yescharacteristic
168#41×C59—21no—
169#41×C59—21no—
170#41×C59—21no—
171#41×C59—21no—
172#41×C59—21no—
173#41×C59—21no—
174#41×C59—21no—
175#41×C59—21no—
176#41×C59—21no—
177#41×C59—21no—
178#41×C59C2×D412yes—
179#41×C59#4112yes—
180C2×Q8×C59C22×C411yescharacteristic
181C2×Q8×C59C22×C411yescharacteristic
182C2×Q8×C59C22×C411yescharacteristic
183C2×D4×C59—21no—
184C2×D4×C59—21no—
185C2×D4×C59—21no—
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59C22×C411yescharacteristic
189C2×D4×C59C22×C411yescharacteristic
190C2×D4×C59C22×C411yescharacteristic
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59#4111yescharacteristic
197C22×C4×C59#4111yescharacteristic
198C22×C4×C59C2411yescharacteristic
199C22×Dic59—21no—
200C22×Dic59—21no—
201Q16×C59—22no—
202Q16×C59—22no—
203SD16×C59—22no—
204SD16×C59—22no—
205SD16×C59—22no—
206SD16×C59—22no—
207D8×C59—22no—
208D8×C59—22no—
209C2×C8×C59—21no—
210C2×C8×C59—21no—
211C2×C8×C59—21no—
212C2×C8×C59—21no—
213C2×C8×C59C22×C411yescharacteristic
214C2×C8×C59C22×C411yescharacteristic
215C2×C8×C59C22×C411yescharacteristic
216C2×C8×C59C22×C411yescharacteristic
217C4⋊C4×C59—21no—
218C4⋊C4×C59—21no—
219C4⋊C4×C59—21no—
220C4⋊C4×C59—21no—
221C4⋊C4×C59C22×C411yescharacteristic
222C4⋊C4×C59C22×C411yescharacteristic
223C22⋊C4×C59—21no—
224C22⋊C4×C59—21no—
225C22⋊C4×C59—21no—
226C22⋊C4×C59—21no—
227C22⋊C4×C59—21no—
228C22⋊C4×C59—21no—
229C22⋊C4×C59—21no—
230C42×C59—21no—
231C42×C59—21no—
232C42×C59—21no—
233C42×C59C22×C411yescharacteristic
234C42×C59C22×C411yescharacteristic
235C42×C59C2×D411yescharacteristic
236C42×C59C2×D411yescharacteristic
237C4⋊Dic59—42no—
238C4×Dic59—21no—
239C4×Dic59—21no—
240C4×Dic59—21no—
241C4×Dic59—21no—
242#11745664—24no—
243#11745664—21no—
244#11745664—21no—
245#11745664—24no—
246#11745664—21no—
247#11745664—21no—
248#11745664—21no—
249#11745664—21no—
250#11745664—42no—
251#11745664—42no—
252#11745664C2×D412yes—
253#11745664#4112yes—
254C2×C59⋊C8—24no—
255C2×C59⋊C8—21no—
256C2×C59⋊C8—21no—
257C2×C59⋊C8—21no—
258C2×C59⋊C8—21no—
259C2×C59⋊C8—24no—
260C2×C59⋊C8—21no—
261C2×C59⋊C8—21no—
262C2×C59⋊C8—42no—
263C2×C59⋊C8—42no—
264C2×C59⋊C8C2×D411yescharacteristic
265C2×C59⋊C8C2×D411yescharacteristic
266C2×C59⋊C8C2×D412yes—
267C2×C59⋊C8C2×D411yescharacteristic
268C2×C59⋊C8C2×D411yescharacteristic
269C2×C59⋊C8#4112yes—
270C23×C59—21no—
271C23×C59—21no—
272C23×C59—21no—
273C23×C59C2×#4111yescharacteristic
274Q8×C59—21no—
275Q8×C59—21no—
276Q8×C59—21no—
277Q8×C59—21no—
278Q8×C59—21no—
279Q8×C59C4×D412yes—
280D4×C59—22no—
281D4×C59—22no—
282D4×C59—21no—
283D4×C59—21no—
284D4×C59—21no—
285D4×C59—21no—
286D4×C59—21no—
287D4×C59—41no—
288D4×C59—41no—
289D4×C59—41no—
290D4×C59—41no—
291D4×C59—81no—
292D4×C59—81no—
293D4×C59C4×D412yes—
294C2×C4×C59—21no—
295C2×C4×C59—22no—
296C2×C4×C59—22no—
297C2×C4×C59—21no—
298C2×C4×C59—21no—
299C2×C4×C59—21no—
300C2×C4×C59—21no—
301C2×C4×C59—41no—
302C2×C4×C59—41no—
303C2×C4×C59—41no—
304C2×C4×C59—41no—
305C2×C4×C59—41no—
306C2×C4×C59—41no—
307C2×C4×C59—81no—
308C2×C4×C59—81no—
309C2×C4×C59C4×D411yescharacteristic
310C2×C4×C59C4×D411yescharacteristic
311C2×C4×C59C4×D411yescharacteristic
312C2×C4×C59C4×D411yescharacteristic
313C2×C4×C59C23×C411yescharacteristic
314C2×C4×C59C22×D411yescharacteristic
315C2×C4×C59C22×D411yescharacteristic
316C2×C4×C59C2×#4111yescharacteristic
317C2×C4×C59C2×#4111yescharacteristic
318C2×C4×C59C2×#4111yescharacteristic
319C2×Dic59—22no—
320C2×Dic59—41no—
321C2×Dic59—41no—
322C2×Dic59—41no—
323C2×Dic59—41no—
324C2×Dic59—41no—
325C8×C59—21no—
326C8×C59—21no—
327C8×C59—21no—
328C8×C59—21no—
329C59⋊C8—22no—
330C59⋊C8—21no—
331C59⋊C8—22no—
332C59⋊C8—21no—
333C59⋊C8—41no—
334C59⋊C8—41no—
335C59⋊C8#12112yes—
336C59⋊C8#12112yes—
337#21519—591nomaximal, Sylow
338C22×C59—21no—
339C22×C59—21no—
340C22×C59—22no—
341C22×C59—41no—
342C22×C59—41no—
343C22×C59—41no—
344C22×C59—41no—
345C22×C59—41no—
346C22×C59—41no—
347C22×C59—41no—
348C22×C59—41no—
349C22×C59C2×C4×D411yescharacteristic
350C22×C59#52911yescharacteristic
351C22×C59#53211yescharacteristic
352C4×C59—21no—
353C4×C59—21no—
354C4×C59—21no—
355C4×C59—21no—
356C4×C59—22no—
357C4×C59—41no—
358C4×C59—41no—
359C4×C59—41no—
360C4×C59—41no—
361C4×C59C2×C4×D411yescharacteristic
362C4×C59C4×#4111yescharacteristic
363C4×C59C2×#12111yescharacteristic
364C4×C59#52511yescharacteristic
365Dic59—42no—
366Dic59—81no—
367#3035D5911yescharacteristic
368C2×#444—591no—
369C2×#443—591no—
370#2932—591no—
371#2875—591no—
372#1980—591no—
373#1950—591no—
374#1929—591no—
375#1929—591no—
376#1876—591no—
377#1876—591no—
378#1806—591no—
379#1771—591no—
380#1765—591no—
381#1764—591no—
382C2×C59—21no—
383C2×C59—21no—
384C2×C59—42no—
385C2×C59—81no—
386C2×C59—81no—
387C2×C59C4×#12111yescharacteristic
388C2×C59#295611yescharacteristic
389C2×C59#295711yescharacteristic
390C2×#135C2×D5911yescharacteristic
391C2×#135C2×D5911yescharacteristic
392C2×#131—591no—
393C2×#131—591no—
394C2×#131—591no—
395C2×#131—591no—
396#532C2×D5911yescharacteristic
397C4×#41C2×D5911yescharacteristic
398#464Dic5911yescharacteristic, complemented
399#464Dic5911yescharacteristic, complemented
400#463Dic5911yescharacteristic, complemented
401#463Dic5911yescharacteristic, complemented
402#462Dic5911yescharacteristic, complemented
403#461Dic5911yescharacteristic, complemented
404#460Dic5911yescharacteristic, complemented
405#459Dic5911yescharacteristic, complemented
406#444—1184no—
407#443—1184no—
408#435—1181no—
409#435—1181no—
410#435—1181no—
411#435—1181no—
412C2×#108—591no—
413C2×#108—591no—
414#423—591no—
415C2×C4⋊C8C2×D5911yescharacteristic
416C2×#104—591no—
417C2×#104—591no—
418C2×#104—591no—
419C2×#104—591no—
420C2×#104—591no—
421C2×#104—591no—
422#416C2×D5911yescharacteristic
423#416C2×D5911yescharacteristic
424#408—591no—
425#408—591no—
426#405—591no—
427#405—591no—
428#405—1181no—
429#405—1181no—
430C4×M16—591no—
431C4×M16—1181no—
432C2×#97—591no—
433C2×#97—591no—
434C2×#97—1181no—
435C2×C4×C8—591no—
436C4×C4⋊C4—591no—
437#341—591no—
438#341—591no—
439#339—591no—
440#339—591no—
441#336—591no—
442#336—591no—
443C59#2151911yescharacteristic, complemented, Sylow
444C2×#41C22×D5911yescharacteristic
445C2×#41C22×D5911yescharacteristic
446C2×#41C22×D5911yescharacteristic
447#135—22no—
448#135—22no—
449#135—22no—
450#135—22no—
451C2×Q16C2×Dic5911yescharacteristic
452C2×Q16C2×Dic5911yescharacteristic
453C2×SD16C2×Dic5911yescharacteristic
454C2×SD16C2×Dic5911yescharacteristic
455C2×SD16C2×Dic5911yescharacteristic
456C2×SD16C2×Dic5911yescharacteristic
457C2×D8C2×Dic5911yescharacteristic
458C2×D8C2×Dic5911yescharacteristic
459#131—594no—
460#131—1182no—
461#131—1182no—
462#131—1182no—
463#131—1182no—
464#131—1182no—
465#131—1182no—
466#131—1182no—
467C2×M16—591no—
468C2×M16—591no—
469C2×M16—591no—
470C2×M16—591no—
471C2×M16—1181no—
472C2×M16—1181no—
473C2×M16—1181no—
474C2×M16—1181no—
475C22×C8—591no—
476C22×C8—591no—
477C22×C8—1181no—
478C22×C8—1181no—
479C22×C8—1181no—
480C22×C8—1181no—
481C22×C8C22×D5911yescharacteristic
482C22×C8C22×D5911yescharacteristic
483C4⋊Q8C2×Dic5911yescharacteristic
484#127C2×Dic5911yescharacteristic
485#124C2×Dic5911yescharacteristic
486#124C2×Dic5911yescharacteristic
487#121—21no—
488#121—21no—
489C4×Q8C2×Dic5911yescharacteristic
490C4×Q8C2×Dic5911yescharacteristic
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4C2×Dic5911yescharacteristic
496C4×D4C2×Dic5911yescharacteristic
497#117—21no—
498#117C22×D5911yescharacteristic
499C2×C4⋊C4—1181no—
500C2×C42—21no—
501C2×C42—591no—
502C2×C42—591no—
503C2×C42C22×D5911yescharacteristic
504#108—1182no—
505#108—1182no—
506C4⋊C8—1181no—
507C4⋊C8—1181no—
508C4⋊C8C2×Dic5911yescharacteristic
509C4⋊C8C2×Dic5911yescharacteristic
510C4⋊C8C2×Dic5911yescharacteristic
511C4⋊C8C2×Dic5911yescharacteristic
512#104—1182no—
513#104—1182no—
514#104—1182no—
515#104—1182no—
516#104—1182no—
517#104—1182no—
518#103C2×Dic5911yescharacteristic
519#103C2×Dic5911yescharacteristic
520#103C2×Dic5911yescharacteristic
521#103C2×Dic5911yescharacteristic
522#102C2×Dic5911yescharacteristic
523#102C2×Dic5911yescharacteristic
524#102C2×Dic5911yescharacteristic
525#102C2×Dic5911yescharacteristic
526C22⋊C8—1181no—
527C22⋊C8—1181no—
528C22⋊C8—1181no—
529C22⋊C8—1181no—
530#97—591no—
531#97—591no—
532#97—591no—
533#97—591no—
534#97—1181no—
535#97—1181no—
536#97—1182no—
537#97—1181no—
538C4×C8—1181no—
539C4×C8—1181no—
540C4×C8—1182no—
541C4×C8—1181no—
542#95—1181no—
543#41—21no—
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41D4×D5912yes—
554#41#1174568712yes—
555C2×Q8C22×Dic5911yescharacteristic
556C2×Q8C22×Dic5911yescharacteristic
557C2×Q8C22×Dic5911yescharacteristic
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C22×Dic5911yescharacteristic
564C2×D4C22×Dic5911yescharacteristic
565C2×D4C22×Dic5911yescharacteristic
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—1181no—
572C22×C4—1181no—
573C22×C4#1174568711yescharacteristic
574C22×C4#1174568711yescharacteristic
575C22×C4C23×D5911yescharacteristic
576Q16—22no—
577Q16—22no—
578SD16—22no—
579SD16—22no—
580SD16—22no—
581SD16—22no—
582D8—22no—
583D8—22no—
584M16—592no—
585M16—592no—
586M16—1184no—
587M16—1184no—
588M16—1181no—
589M16—1181no—
590M16—1181no—
591M16—1181no—
592M16—1181no—
593M16—1181no—
594M16—2362no—
595M16—2362no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—592no—
601C2×C8—591no—
602C2×C8—591no—
603C2×C8—592no—
604C2×C8—591no—
605C2×C8—591no—
606C2×C8—1184no—
607C2×C8—1184no—
608C2×C8—1181no—
609C2×C8—1181no—
610C2×C8—1181no—
611C2×C8—1181no—
612C2×C8—1181no—
613C2×C8—1181no—
614C2×C8—2362no—
615C2×C8—2362no—
616C2×C8C22×Dic5911yescharacteristic
617C2×C8C22×Dic5911yescharacteristic
618C2×C8C22×Dic5911yescharacteristic
619C2×C8C22×Dic5911yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—2362no—
625C4⋊C4C22×Dic5911yescharacteristic
626C4⋊C4C22×Dic5911yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C42—21no—
635C42—21no—
636C42—21no—
637C42—1181no—
638C42—1181no—
639C42—1181no—
640C42—1181no—
641C42D4×D5911yescharacteristic
642C42D4×D5911yescharacteristic
643C42C22×Dic5911yescharacteristic
644C42C22×Dic5911yescharacteristic
645C23—21no—
646C23—21no—
647C23—21no—
648C23C2×#1174568711yescharacteristic
649Q8—21no—
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8D4×Dic5912yes—
655D4—22no—
656D4—22no—
657D4—21no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—81no—
667D4—81no—
668D4D4×Dic5912yes—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—1182no—
685C2×C4—2361no—
686C2×C4—2361no—
687C2×C4—2361no—
688C2×C4—2361no—
689C2×C4—2361no—
690C2×C4D4×Dic5911yescharacteristic
691C2×C4D4×Dic5911yescharacteristic
692C2×C4D4×Dic5911yescharacteristic
693C2×C4D4×Dic5911yescharacteristic
694C2×C4C23×Dic5911yescharacteristic
695C2×C4C2×D4×D5911yescharacteristic
696C2×C4C2×D4×D5911yescharacteristic
697C2×C4#41×D5911yescharacteristic
698C2×C4#41×D5911yescharacteristic
699C2×C4C2×#1174568711yescharacteristic
700C8—21no—
701C8—21no—
702C8—21no—
703C8—21no—
704C8—592no—
705C8—592no—
706C8—1182no—
707C8—1181no—
708C8—1181no—
709C8—1182no—
710C8—2361no—
711C8—2361no—
712C22—21no—
713C22—21no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22C2×D4×Dic5911yescharacteristic
724C22#1683793311yescharacteristic
725C22#1683794711yescharacteristic
726C4—21no—
727C4—21no—
728C4—22no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—4721no—
736C4—2362no—
737C4C2×D4×Dic5911yescharacteristic
738C4#41×Dic5911yescharacteristic
739C4#121×D5911yescharacteristic
740C4#1683791211yescharacteristic
741C2—21no—
742C2—21no—
743C2—42no—
744C2—81no—
745C2—81no—
746C2#121×Dic5911yescharacteristic
747C2#2143300611yescharacteristic
748C2#2143301311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
Fitting, prime radicalC59×#3035C2
socleC22×C59C2×C4×D4
cosocleC22×C4×C59C24
hypercenter#3035D59
hypocenterC59#21519
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. C2×#16837524C2semidirect
2. C2×#16837519C2semidirect
3. #21432814C2semidirect
4. #21432524C2semidirect
5. #21425016C2semidirect
6. #21424872C2semidirect
7. #21424746C2semidirect
8. #21424746C2semidirect
9. #21424425C2semidirect
10. #21424425C2semidirect
11. #21424116C2semidirect
12. #21423973C2semidirect
13. #21423943C2semidirect
14. #21423936C2semidirect
58. C59×#464C4semidirect
59. C59×#464C4semidirect
60. C59×#463C4semidirect
61. C59×#463C4semidirect
62. C59×#462C4semidirect
63. C59×#461C4semidirect
64. C59×#460C4semidirect
65. C59×#459C4semidirect
76. #14273734D4semidirect
398. #464Dic59semidirect
399. #464Dic59semidirect
400. #463Dic59semidirect
401. #463Dic59semidirect
402. #462Dic59semidirect
403. #461Dic59semidirect
404. #460Dic59semidirect
405. #459Dic59semidirect
443. C59#21519semidirect

Maximal subgroups

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

subgroupindex
C2×#168375242
C2×#168375192
#214328142
#214325242
#214250162
#214248722
#214247462
#214244252
#214241162
#214239732
#214239432
#214239362
C59×#30352
#2151959