Finite Group Databasebeta

← #27389867

Subgroups — #27389867

Order 13568.

1400 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811100C211yesmaximal, characteristic, complemented
2C2×#16810761C211yesmaximal, characteristic
3C2×#16810723C211yesmaximal, characteristic, complemented
4C2×C4×#11719923C211yesmaximal, characteristic, complemented
5#20275073C211yesmaximal, characteristic, complemented
6#20275073C211yesmaximal, characteristic, complemented
7#20275038C211yesmaximal, characteristic
8#20274982C211yesmaximal, characteristic, complemented
9#20274968C211yesmaximal, characteristic, complemented
10#20274912C211yesmaximal, characteristic, complemented
11#20274649C211yesmaximal, characteristic, complemented
12#20274548C211yesmaximal, characteristic, complemented
13C4×#13133140C211yesmaximal, characteristic, complemented
14#20274481C211yesmaximal, characteristic, complemented
15C53×#2324C211yesmaximal, characteristic
16C23×Dic106C2211yescharacteristic
17C22×#11719923C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19#16811100—24no—
20#16811100—24no—
21C2×C4×Dic106C2211yescharacteristic
22C2×C4×Dic106C2211yescharacteristic
23C2×C4×Dic106C2211yescharacteristic
24C2×C4×Dic106C2211yescharacteristic
25C2×#13133182—21no—
26C2×#13133182—21no—
27C2×#13133176C2211yescharacteristic
28C2×#13133173—21no—
29C2×#13133173—21no—
30#16810761C418yescomplemented
31#16810723—24no—
32C4×#11719923—24no—
33C2×#13133150C2211yescharacteristic
34C2×#13133148C2211yescharacteristic
35C2×#13133140C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37C2×#13133140C2211yescharacteristic
38C2×#13133140C2211yescharacteristic
39C2×#13133140C2211yescharacteristic
40C2×#13133140C2211yescharacteristic
41C2×#13133138C2211yescharacteristic
42C2×#13133138C2211yescharacteristic
43C2×C22⋊#88322C2211yescharacteristic
44C2×C22⋊#88322C2211yescharacteristic
45C2×#13133128C2211yescharacteristic
46C2×C4×#88322C2211yescharacteristic
47#16810385C2211yescharacteristic
48#16810385C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810378C2211yescharacteristic
52#16810378C2211yescharacteristic
53C2×#121×C53C2211yescharacteristic
54C2×C4×D4×C53C2211yescharacteristic
55C2×#117×C53C2211yescharacteristic
56C53×#390—21no—
57C53×#390C2211yescharacteristic
58C53×#389C2211yescharacteristic
59C53×#388—21no—
60C53×#386—21no—
61C53×#385—21no—
62C53×#380C2211yescharacteristic
63C4×C4⋊C4×C53C2211yescharacteristic
64C22×Dic106—21no—
65C22×Dic106—22no—
66C22×Dic106—22no—
67C22×Dic106—22no—
68C22×Dic106—22no—
69C22×Dic106—22no—
70C22×Dic106C2×C414yescomplemented
71C22×Dic106C2311yescharacteristic
72C22×Dic106C2311yescharacteristic
73C23×Dic53—21no—
74C2×#11719923—22no—
75C2×#11719923—22no—
76C2×#11719923—22no—
77C2×#11719923—22no—
78C2×#11719923C2×C414yes—
79C2×#11719923C2×C414yes—
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84C4×Dic106—22no—
85C4×Dic106—22no—
86C4×Dic106—22no—
87C4×Dic106—22no—
88C4×Dic106—22no—
89C4×Dic106—22no—
90C4×Dic106D414yescomplemented
91C4×Dic106D414yescomplemented
92#13133182—28no—
93#13133182—28no—
94#13133176—22no—
95#13133176—22no—
96#13133173—28no—
97#13133173—28no—
98C2×C4⋊Dic53C2311yescharacteristic
99C2×C4⋊Dic53C2311yescharacteristic
100C2×#11719919—21no—
101C2×#11719919—21no—
102C2×#11719919—21no—
103C2×#11719919—21no—
104C2×C22⋊Dic53—21no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53—21no—
108C2×C4×Dic53—21no—
109C2×C4×Dic53—21no—
110#13133150—22no—
111#13133148—22no—
112#13133140—22no—
113#13133140—22no—
114#13133140—22no—
115#13133140—22no—
116#13133140C2×C414yescomplemented
117#13133140C2×C414yescomplemented
118#13133138—22no—
119#13133138—22no—
120C22⋊#88322—22no—
121C22⋊#88322C2×C414yescomplemented
122#13133128—22no—
123C4×#88322—22no—
124C22×D4×C53—21no—
125C22×D4×C53C2311yescharacteristic
126C23×C4×C53—21no—
127C23×C4×C53C2311yescharacteristic
128#121×C53—22no—
129#121×C53C2×C414yes—
130C4×D4×C53—22no—
131C4×D4×C53—22no—
132#117×C53—22no—
133#117×C53—22no—
134C2×C4⋊C4×C53—21no—
135C2×C4⋊C4×C53D411yescharacteristic
136C2×C4⋊C4×C53D411yescharacteristic
137C2×C4⋊C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53C2311yescharacteristic
139C2×C4⋊C4×C53C2311yescharacteristic
140C2×C22⋊C4×C53—21no—
141C2×C22⋊C4×C53—21no—
142C2×C22⋊C4×C53—21no—
143C2×C22⋊C4×C53—21no—
144C2×C22⋊C4×C53—21no—
145C2×C22⋊C4×C53D411yescharacteristic
146C2×C22⋊C4×C53D411yescharacteristic
147C2×C42×C53—21no—
148C2×C42×C53C2311yescharacteristic
149C2×C42×C53C2311yescharacteristic
150#95×C53—21no—
151#95×C53—21no—
152#95×C53—21no—
153C24×C53—21no—
154C24×C53C2×D411yescharacteristic
155C2×D4×C53—24no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—21no—
161C2×D4×C53—81no—
162C2×D4×C53—81no—
163C2×D4×C53C22×C412yes—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—42no—
172C22×C4×C53—81no—
173C22×C4×C53—81no—
174C22×C4×C53C22×C412yes—
175C22×C4×C53C2×D411yescharacteristic
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53#4112yes—
181C22×C4×C53C2411yescharacteristic
182C22×Dic53—24no—
183C22×Dic53—24no—
184C22×Dic53—24no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—21no—
189C2×Dic106—24no—
190C2×Dic106—24no—
191C2×Dic106—28no—
192C2×Dic106—28no—
193C2×Dic106—24no—
194C2×Dic106—21no—
195C2×Dic106—21no—
196C2×Dic106—21no—
197C2×Dic106—21no—
198C2×Dic106—21no—
199C2×Dic106—21no—
200C2×Dic106—28no—
201C2×Dic106—28no—
202C2×Dic106C22×C412yes—
203C2×Dic106C22×C412yes—
204C2×Dic106C2×D412yes—
205C2×Dic106C2×D412yes—
206C2×Dic106#4112yes—
207C2×Dic106#4112yes—
208C4⋊C4×C53—22no—
209C4⋊C4×C53—22no—
210C4⋊C4×C53—21no—
211C4⋊C4×C53—21no—
212C4⋊C4×C53—21no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—81no—
216C4⋊C4×C53C22×C412yes—
217C22⋊C4×C53—24no—
218C22⋊C4×C53—22no—
219C22⋊C4×C53—22no—
220C22⋊C4×C53—42no—
221C22⋊C4×C53—81no—
222C22⋊C4×C53—81no—
223C22⋊C4×C53—81no—
224C42×C53—21no—
225C42×C53—21no—
226C42×C53—81no—
227C42×C53C2×D412yes—
228C42×C53C2×D412yes—
229C22⋊Dic53—24no—
230#11719923—28no—
231#11719923—28no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53C2×D412yes—
235C4⋊Dic53C2×D412yes—
236#11719919—24no—
237#11719919—24no—
238#11719919—24no—
239#11719919—24no—
240C4×Dic53—24no—
241C4×Dic53—24no—
242C4×Dic53—24no—
243C4×Dic53—24no—
244C4×Dic53—24no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322C22×C412yes—
256C2×#88322C22×C412yes—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—22no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53C4×D412yes—
271C23×C53C22×D411yescharacteristic
272D4×C53—22no—
273D4×C53—22no—
274D4×C53—41no—
275D4×C53—41no—
276D4×C53—84no—
277C2×C4×C53—21no—
278C2×C4×C53—21no—
279C2×C4×C53—21no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—84no—
303C2×C4×C53C4×D412yes—
304C2×C4×C53#12012yes—
305C2×C4×C53#12012yes—
306C2×C4×C53C23×C411yescharacteristic
307C2×C4×C53C22×D411yescharacteristic
308C2×C4×C53C22×D411yescharacteristic
309C2×C4×C53C2×#4111yescharacteristic
310C2×C4×C53C2×#4111yescharacteristic
311C2×C4×C53C2×#4111yescharacteristic
312C2×Dic53—216no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325Dic106—216no—
326Dic106—22no—
327Dic106—22no—
328Dic106—22no—
329Dic106—22no—
330Dic106—22no—
331Dic106—22no—
332Dic106C4×D414yes—
333Dic106C4×D414yes—
334#88322—22no—
335#88322—22no—
336#88322—41no—
337#88322—41no—
338#21462—531nomaximal, Sylow
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—41no—
343C22×C53—41no—
344C22×C53—41no—
345C22×C53—41no—
346C22×C53—42no—
347C22×C53—42no—
348C22×C53—42no—
349C22×C53—81no—
350C22×C53—81no—
351C22×C53—81no—
352C22×C53—81no—
353C22×C53C2×C4×D411yescharacteristic
354C22×C53C2×#12011yescharacteristic
355C22×C53#52511yescharacteristic
356C22×C53#57711yescharacteristic
357C22×C53#57711yescharacteristic
358C22×C53#57711yescharacteristic
359C22×C53#57811yescharacteristic
360C4×C53—22no—
361C4×C53—22no—
362C4×C53—22no—
363C4×C53—42no—
364C4×C53—41no—
365C4×C53—41no—
366C4×C53—81no—
367C4×C53—81no—
368C4×C53C2×C4×D411yescharacteristic
369C4×C53C2×C4×D411yescharacteristic
370C4×C53#52511yescharacteristic
371C4×C53#52511yescharacteristic
372Dic53—24no—
373Dic53—24no—
374Dic53—42no—
375Dic53—42no—
376C2×#519—531no—
377C2×#448—531no—
378C2×#440—531no—
379C2×C4×SD16—531no—
380#2324D5311yescharacteristic
381#1880—531no—
382#1880—531no—
383#1875—531no—
384#1865—531no—
385#1863—531no—
386#1854—531no—
387#1787—531no—
388#1763—531no—
389C4×#103—531no—
390#1750—531no—
391C2×C53—42no—
392C2×C53—82no—
393C2×C53C4×#12011yescharacteristic
394C2×C53#294711yescharacteristic
395C2×C53#294911yescharacteristic
396C2×C53#301011yescharacteristic
397C2×C53#301311yescharacteristic
398C2×C53#312111yescharacteristic
399C2×C53#312611yescharacteristic
400C23×Q8—531no—
401C22×SD16—531no—
402C22×SD16—531no—
403C2×#121C2×D5311yescharacteristic
404#519—1064no—
405#519—1064no—
406C2×C4×Q8—531no—
407C2×C4×Q8—531no—
408C2×C4×Q8—531no—
409C2×C4×Q8—531no—
410C2×C4×Q8—1061no—
411C2×C4×Q8—1061no—
412C2×C4×D4C2×D5311yescharacteristic
413C2×#117—531no—
414C2×#117—1061no—
415C2×#117—1061no—
416C2×#117C2×D5311yescharacteristic
417#448—538no—
418#440—1064no—
419C4×SD16—1064no—
420C2×#107—531no—
421C2×#106—531no—
422C2×#103—531no—
423C2×#103—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×C22⋊C8—531no—
431C2×C22⋊C8—531no—
432C2×#97—531no—
433C2×C4×C8—531no—
434#390—21no—
435#390C2×D5311yescharacteristic
436#389C2×D5311yescharacteristic
437#388—21no—
438#386—21no—
439#385—21no—
440#380C2×D5311yescharacteristic
441C4×C4⋊C4C2×D5311yescharacteristic
442#340—531no—
443#340—531no—
444#340—531no—
445#340—531no—
446#336—531no—
447#336—531no—
448C53#2146211yescharacteristic, complemented, Sylow
449C22×Q8—534no—
450C22×Q8—531no—
451C22×Q8—531no—
452C22×Q8—1062no—
453C22×Q8—1062no—
454C22×Q8—1062no—
455C22×Q8—1062no—
456C22×Q8—1062no—
457C22×Q8—1061no—
458C22×D4—21no—
459C22×D4C22×D5311yescharacteristic
460C23×C4—21no—
461C23×C4—1061no—
462C23×C4C22×D5311yescharacteristic
463C2×SD16—534no—
464C2×SD16—534no—
465C2×SD16—1062no—
466C2×SD16—1062no—
467C2×SD16—1062no—
468C2×SD16—1062no—
469C22×C8—531no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473#121—22no—
474#121C4×D5314yes—
475C4×Q8—534no—
476C4×Q8—534no—
477C4×Q8—1062no—
478C4×Q8—1062no—
479C4×Q8—1062no—
480C4×Q8—1062no—
481C4×Q8—1068no—
482C4×Q8—1068no—
483C4×Q8—1062no—
484C4×Q8—1062no—
485C4×D4—22no—
486C4×D4—22no—
487#117—22no—
488#117—22no—
489#117—1068no—
490#117—1068no—
491#117—1062no—
492#117—1062no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4C22⋊D5311yescharacteristic
501C2×C4⋊C4C22⋊D5311yescharacteristic
502C2×C4⋊C4C22×D5311yescharacteristic
503C2×C4⋊C4C22×D5311yescharacteristic
504C2×C4⋊C4C22×D5311yescharacteristic
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4C22⋊D5311yescharacteristic
512C2×C22⋊C4C22⋊D5311yescharacteristic
513C2×C42—21no—
514C2×C42—1061no—
515C2×C42—1061no—
516C2×C42—1061no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42C22×D5311yescharacteristic
520C2×C42C22×D5311yescharacteristic
521#107—1062no—
522#106—1062no—
523#103—534no—
524#103—534no—
525#103—1062no—
526#103—1062no—
527#103—1062no—
528#103—1062no—
529#102—1062no—
530#102—1062no—
531C22⋊C8—534no—
532C22⋊C8—1062no—
533#97—1062no—
534C4×C8—1062no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×C22⋊D5311yescharacteristic
540C2×Q8—532no—
541C2×Q8—532no—
542C2×Q8—532no—
543C2×Q8—532no—
544C2×Q8—532no—
545C2×Q8—532no—
546C2×Q8—1068no—
547C2×Q8—1068no—
548C2×Q8—1064no—
549C2×Q8—1064no—
550C2×Q8—1068no—
551C2×Q8—1068no—
552C2×Q8—1064no—
553C2×Q8—1061no—
554C2×Q8—1061no—
555C2×Q8—1061no—
556C2×Q8—1061no—
557C2×Q8—1061no—
558C2×Q8—1061no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—81no—
566C2×D4—81no—
567C2×D4C2×C4×D5312yes—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—81no—
577C22×C4—81no—
578C22×C4—1064no—
579C22×C4—1064no—
580C22×C4—1064no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4C2×C4×D5312yes—
586C22×C4#1171994512yes—
587C22×C4C2×C22⋊D5311yescharacteristic
588C22×C4C2×C22⋊D5311yescharacteristic
589C22×C4C2×C22⋊D5311yescharacteristic
590C22×C4C2×C22⋊D5311yescharacteristic
591C22×C4C2×C22⋊D5311yescharacteristic
592C22×C4C23×D5311yescharacteristic
593SD16—1068no—
594SD16—1068no—
595C2×C8—532no—
596C2×C8—532no—
597C2×C8—1061no—
598C2×C8—1061no—
599C2×C8—1061no—
600C2×C8—1061no—
601C2×C8—1061no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—1061no—
605C2×C8—1061no—
606C2×C8—1061no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—81no—
615C4⋊C4—532no—
616C4⋊C4—532no—
617C4⋊C4—1064no—
618C4⋊C4—1064no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4C2×C4×D5312yes—
624C22⋊C4—24no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—42no—
628C22⋊C4—81no—
629C22⋊C4—81no—
630C22⋊C4—81no—
631C22⋊C4—1064no—
632C42—21no—
633C42—21no—
634C42—81no—
635C42—1064no—
636C42—1064no—
637C42—1064no—
638C42—1064no—
639C42—1064no—
640C42D4×D5312yes—
641C42D4×D5312yes—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—22no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23C4×C22⋊D5312yes—
656C23C22×C22⋊D5311yescharacteristic
657Q8—534no—
658Q8—534no—
659Q8—10616no—
660Q8—1062no—
661Q8—1062no—
662Q8—1062no—
663Q8—1062no—
664Q8—1062no—
665Q8—1062no—
666D4—22no—
667D4—22no—
668D4—41no—
669D4—41no—
670D4—84no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—84no—
697C2×C4—10616no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—2121no—
707C2×C4—2121no—
708C2×C4—2121no—
709C2×C4—2121no—
710C2×C4C4×C22⋊D5312yes—
711C2×C4#1313318512yes—
712C2×C4#1313318512yes—
713C2×C4C22×C4×D5311yescharacteristic
714C2×C4C2×D4×D5311yescharacteristic
715C2×C4C2×D4×D5311yescharacteristic
716C2×C4#41×D5311yescharacteristic
717C2×C4#41×D5311yescharacteristic
718C2×C4C2×#1171994511yescharacteristic
719C8—1062no—
720C8—1062no—
721C8—2121no—
722C8—2121no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22C2×C4×C22⋊D5311yescharacteristic
738C22C2×#1313318511yescharacteristic
739C22#1681113011yescharacteristic
740C22#1681143411yescharacteristic
741C22#1681143411yescharacteristic
742C22#1681143411yescharacteristic
743C22#1681143811yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—41no—
748C4—41no—
749C4—42no—
750C4—81no—
751C4—81no—
752C4—1064no—
753C4—1064no—
754C4—2122no—
755C4—2122no—
756C4C4×D4×D5311yescharacteristic
757C4C4×D4×D5311yescharacteristic
758C4#1681113211yescharacteristic
759C4#1681113211yescharacteristic
760C2—42no—
761C2—82no—
762C2C4×#1313318511yescharacteristic
763C2#2028355411yescharacteristic
764C2#2028357211yescharacteristic
765C2#2028399911yescharacteristic
766C2#2028402711yescharacteristic
767C2#2028493811yescharacteristic
768C2#2028500111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2324C2
socleC23×C53C22×D4
prime radicalC2×#121×C53C22
cosocleC22×C4×C53C24
hypercenter#2324D53
hypocenterC53#21462
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#16811100C2semidirect
3. C2×#16810723C2semidirect
4. C2×C4×#11719923C2semidirect
5. #20275073C2semidirect
6. #20275073C2semidirect
8. #20274982C2semidirect
9. #20274968C2semidirect
10. #20274912C2semidirect
11. #20274649C2semidirect
12. #20274548C2semidirect
13. C4×#13133140C2semidirect
14. #20274481C2semidirect
30. #16810761C4semidirect
70. C22×Dic106C2×C4semidirect
90. C4×Dic106D4semidirect
91. C4×Dic106D4semidirect
116. #13133140C2×C4semidirect
117. #13133140C2×C4semidirect
121. C22⋊#88322C2×C4semidirect
448. C53#21462semidirect

Maximal subgroups

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

subgroupindex
C2×#168111002
C2×#168107612
C2×#168107232
C2×C4×#117199232
#202750732
#202750382
#202749822
#202749682
#202749122
#202746492
#202745482
C4×#131331402
#202744812
C53×#23242
#2146253