Finite Group Databasebeta

← #27290895

Subgroups — #27290895

Order 13568.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11719913C211yesmaximal, characteristic
2C22×#13133140C211yesmaximal, characteristic, complemented
3C22×#13133137C211yesmaximal, characteristic
4C2×#16810528C211yesmaximal, characteristic, complemented
5C2×#16810524C211yesmaximal, characteristic
6C2×#16810377C211yesmaximal, characteristic, complemented
7C2×C53×#340C211yesmaximal, characteristic, complemented
8C23×Dic106C2211yescharacteristic
9C23×D212C2211yescharacteristic
10C22×#11719913—22no—
11C22×#11719913—22no—
12C22×#11719913—22no—
13C22×#11719913—22no—
14C22×#11719913—22no—
15C22×#11719913—22no—
16C22×#11719913C414yescomplemented
17C23×#88322C2211yescharacteristic
18C22×#11719921—22no—
19C22×C4×Dic53C2211yescharacteristic
20C2×#13133140—22no—
21C2×#13133140—22no—
22C2×#13133140—22no—
23C2×#13133137—22no—
24C2×#13133137—22no—
25C2×#13133137—22no—
26#16810528—22no—
27#16810528—22no—
28#16810524—22no—
29#16810524—22no—
30C2×#13133124—22no—
31#16810377—22no—
32C23×C8×C53C2211yescharacteristic
33C22×C4⋊C4×C53C2211yescharacteristic
34C22×C4⋊C4×C53C2211yescharacteristic
35C53×#340—22no—
36C24×D53—21no—
37C22×Dic106—21no—
38C22×Dic106—21no—
39C22×Dic106—21no—
40C22×Dic106—21no—
41C22×Dic106—21no—
42C22×Dic106—21no—
43C22×Dic106—21no—
44C22×Dic106—21no—
45C22×Dic106—21no—
46C22×Dic106—21no—
47C22×Dic106—21no—
48C22×Dic106C2×C412yes—
49C22×Dic106D412yes—
50C22×Dic106D412yes—
51C22×D212—21no—
52C22×D212—21no—
53C22×D212—21no—
54C22×D212—21no—
55C22×D212—21no—
56C22×D212—21no—
57C22×D212—21no—
58C22×D212—21no—
59C22×D212—21no—
60C22×D212—21no—
61C22×D212—21no—
62C22×D212C2×C412yes—
63C22×D212D412yes—
64C22×D212D412yes—
65C23×Dic53—21no—
66C23×Dic53D412yes—
67C2×#11719913—28no—
68C2×#11719913—28no—
69C2×#11719913—28no—
70C2×#11719913—28no—
71C2×#11719913—28no—
72C2×#11719913—28no—
73C2×#11719913—28no—
74C22×#88322—21no—
75C22×#88322—21no—
76C22×#88322—21no—
77C22×#88322—21no—
78C22×#88322—21no—
79C22×#88322—21no—
80C22×#88322D412yes—
81C2×#11719921—28no—
82C2×#11719921—44no—
83C2×#11719921—44no—
84C2×C4×Dic53—21no—
85C2×C4×Dic53—21no—
86C2×C4×Dic53—21no—
87C2×C4×Dic53—21no—
88C2×C4×Dic53—21no—
89C2×C4×Dic53—21no—
90#13133140—28no—
91#13133137—28no—
92#13133124—28no—
93C23×C4×C53—21no—
94C23×C4×C53—21no—
95C23×C4×C53C2311yescharacteristic
96C22×C8×C53—21no—
97C22×C8×C53—21no—
98C22×C8×C53—21no—
99C22×C8×C53—21no—
100C22×C8×C53C2×C412yes—
101C22×C8×C53D412yes—
102C22×C8×C53D412yes—
103C2×C4⋊C4×C53—21no—
104C2×C4⋊C4×C53—21no—
105C2×C4⋊C4×C53—21no—
106C2×C4⋊C4×C53—21no—
107C2×C4⋊C4×C53—21no—
108C2×C4⋊C4×C53—21no—
109C2×C4⋊C4×C53—21no—
110C2×C4⋊C4×C53—21no—
111C2×C4⋊C4×C53—21no—
112C2×C4⋊C4×C53—21no—
113C2×C4⋊C4×C53D412yes—
114C2×C4⋊C4×C53D412yes—
115C24×C53C2×D411yescharacteristic
116C23×D53—22no—
117C23×D53—22no—
118C23×D53—22no—
119C23×D53—41no—
120C23×D53—41no—
121C23×D53—41no—
122C23×D53—41no—
123C23×D53—42no—
124C23×D53—42no—
125C23×D53—42no—
126C23×D53—42no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—41no—
130C22×C4×C53—41no—
131C22×C4×C53—41no—
132C22×C4×C53—41no—
133C22×C4×C53—42no—
134C22×C4×C53—42no—
135C22×C4×C53—42no—
136C22×C4×C53—42no—
137C22×C4×C53C22×C411yescharacteristic
138C22×C4×C53C2×D411yescharacteristic
139C22×C4×C53C2×D411yescharacteristic
140C22×C4×C53C2×D411yescharacteristic
141C22×C4×C53C2×D411yescharacteristic
142C22×C4×C53C2×D411yescharacteristic
143C22×C4×C53C2×D411yescharacteristic
144C22×C4×C53C2×D411yescharacteristic
145C22×C4×C53C2×D411yescharacteristic
146C22×C4×C53C2×D411yescharacteristic
147C22×C4×C53#4111yescharacteristic
148C22×C4×C53#4111yescharacteristic
149C22×C4×C53#4111yescharacteristic
150C22×C4×C53#4111yescharacteristic
151C22×Dic53—22no—
152C22×Dic53—22no—
153C22×Dic53—22no—
154C22×Dic53—22no—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—41no—
161C22×Dic53—41no—
162C22×Dic53—41no—
163C22×Dic53—41no—
164C22×Dic53SD1614yescomplemented
165C2×D212—22no—
166C2×D212—22no—
167C2×D212—22no—
168C2×D212—22no—
169C2×D212—22no—
170C2×D212—22no—
171C2×D212—22no—
172C2×D212—22no—
173C2×D212—22no—
174C2×D212—22no—
175C2×D212—22no—
176C2×D212—22no—
177C2×D212—22no—
178C2×D212—22no—
179C2×D212—22no—
180C2×D212—41no—
181C2×D212—41no—
182C2×D212—41no—
183C2×D212—41no—
184C2×D212—41no—
185C2×D212—41no—
186C2×D212—41no—
187C2×D212—41no—
188C2×D212—41no—
189C2×D212—41no—
190C2×D212—41no—
191C2×D212—41no—
192C2×D212C22⋊C414yes—
193C2×Dic106—22no—
194C2×Dic106—22no—
195C2×Dic106—22no—
196C2×Dic106—22no—
197C2×Dic106—22no—
198C2×Dic106—22no—
199C2×Dic106—22no—
200C2×Dic106—22no—
201C2×Dic106—22no—
202C2×Dic106—22no—
203C2×Dic106—22no—
204C2×Dic106—22no—
205C2×Dic106—22no—
206C2×Dic106—22no—
207C2×Dic106—22no—
208C2×Dic106—41no—
209C2×Dic106—41no—
210C2×Dic106—41no—
211C2×Dic106—41no—
212C2×Dic106—41no—
213C2×Dic106—41no—
214C2×Dic106—41no—
215C2×Dic106—41no—
216C2×Dic106—41no—
217C2×Dic106—41no—
218C2×Dic106—41no—
219C2×Dic106—41no—
220C2×Dic106C22⋊C414yescomplemented
221C2×C8×C53—22no—
222C2×C8×C53—22no—
223C2×C8×C53—22no—
224C2×C8×C53—22no—
225C2×C8×C53—22no—
226C2×C8×C53—22no—
227C2×C8×C53C22⋊C414yescomplemented
228C4⋊C4×C53—22no—
229C4⋊C4×C53—22no—
230C4⋊C4×C53—22no—
231C4⋊C4×C53—22no—
232C4⋊C4×C53—41no—
233C4⋊C4×C53—41no—
234C4⋊C4×C53—41no—
235C4⋊C4×C53—41no—
236#11719921—416no—
237C4×Dic53—41no—
238C4×Dic53—41no—
239C4×Dic53—41no—
240C4×Dic53—41no—
241C2×#88322—22no—
242C2×#88322—22no—
243C2×#88322—22no—
244C2×#88322—41no—
245C2×#88322—41no—
246C2×#88322—41no—
247C2×#88322—41no—
248#11719913—232no—
249C23×C53C4×D411yescharacteristic
250C23×C53#12011yescharacteristic
251C23×C53#12011yescharacteristic
252C23×C53#12111yescharacteristic
253C23×C53#12111yescharacteristic
254C23×C53#12111yescharacteristic
255C23×C53#12711yescharacteristic
256C23×C53C2×SD1612yes—
257C23×C53#13512yes—
258C23×C53AGL(1,ℤ/8)12yes—
259C23×C53#13712yes—
260C22×D53—24no—
261C22×D53—42no—
262C22×D53—42no—
263C22×D53—42no—
264C22×D53—42no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53—44no—
268C22×D53—44no—
269C22×D53—44no—
270C22×D53—44no—
271C22×D53—44no—
272C22×D53—44no—
273C22×D53—82no—
274C22×D53—82no—
275C22×D53—82no—
276C22×D53—82no—
277C22×D53—82no—
278C22×D53—82no—
279C22×D53—81no—
280C22×D53—81no—
281C22×D53—81no—
282C22×D53—81no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—44no—
286C2×C4×C53—44no—
287C2×C4×C53—82no—
288C2×C4×C53—82no—
289C2×C4×C53—81no—
290C2×C4×C53—81no—
291C2×C4×C53—81no—
292C2×C4×C53—81no—
293C2×C4×C53C2×C22⋊C411yescharacteristic
294C2×C4×C53C2×C22⋊C411yescharacteristic
295C2×C4×C53C2×C22⋊C411yescharacteristic
296C2×C4×C53C4×D411yescharacteristic
297C2×C4×C53C4×D411yescharacteristic
298C2×C4×C53C4×D411yescharacteristic
299C2×C4×C53#12011yescharacteristic
300C2×C4×C53#12011yescharacteristic
301C2×C4×C53#12011yescharacteristic
302C2×C4×C53#12011yescharacteristic
303C2×C4×C53#12011yescharacteristic
304C2×C4×C53#12011yescharacteristic
305C2×C4×C53#12111yescharacteristic
306C2×C4×C53#12111yescharacteristic
307C2×C4×C53#12111yescharacteristic
308C2×C4×C53#12111yescharacteristic
309C2×C4×C53#12111yescharacteristic
310C2×C4×C53#12111yescharacteristic
311C2×C4×C53#12111yescharacteristic
312C2×C4×C53#12111yescharacteristic
313C2×C4×C53#12111yescharacteristic
314C2×C4×C53#12311yescharacteristic
315C2×C4×C53#12311yescharacteristic
316C2×C4×C53#12311yescharacteristic
317C2×C4×C53#12311yescharacteristic
318C2×C4×C53#12411yescharacteristic
319C2×C4×C53#12411yescharacteristic
320C2×C4×C53#12711yescharacteristic
321C2×Dic53—24no—
322C2×Dic53—24no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335D212—24no—
336D212—24no—
337D212—42no—
338D212—42no—
339D212—42no—
340D212—42no—
341D212—42no—
342D212—42no—
343Dic106—24no—
344Dic106—24no—
345Dic106—42no—
346Dic106—42no—
347Dic106—42no—
348Dic106—42no—
349Dic106—42no—
350Dic106—42no—
351C8×C53—24no—
352#88322—42no—
353#11023—531nomaximal, Sylow
354C22×C53#38611yescharacteristic
355C22×C53#38611yescharacteristic
356C22×C53#39011yescharacteristic
357C22×C53#39211yescharacteristic
358C22×C53#39211yescharacteristic
359C22×C53#39211yescharacteristic
360C22×C53#39411yescharacteristic
361C22×C53C4×SD1612yes—
362C22×C53#44012yes—
363C22×C53#44812yes—
364C22×C53#44912yes—
365C22×C53#45012yes—
366C22×C53#45212yes—
367C22×C53#46012yes—
368C22×C53#46112yes—
369C22×C53#46312yes—
370C22×C53#46412yes—
371C22×C53#46512yes—
372C22×C53#46812yes—
373C22×C53#49211yescharacteristic
374C22×C53#49511yescharacteristic
375C22×C53#49611yescharacteristic
376C22×C53#49711yescharacteristic
377C2×D53—48no—
378C2×D53—44no—
379C2×D53—84no—
380C2×D53—84no—
381C2×D53—82no—
382C2×D53—82no—
383C2×D53—84no—
384C2×D53—82no—
385C2×D53—82no—
386C2×D53—82no—
387C2×D53—82no—
388C4×C53—82no—
389C4×C53—82no—
390C4×C53#37911yescharacteristic
391C4×C53#38611yescharacteristic
392C4×C53#38611yescharacteristic
393C4×C53#39011yescharacteristic
394C4×C53#39211yescharacteristic
395C4×C53#39411yescharacteristic
396C4×C53#39411yescharacteristic
397C4×C53#39411yescharacteristic
398Dic53—44no—
399Dic53—44no—
400C23×SD16—531no—
401C22×#103—531no—
402C22×#102—531no—
403C2×#391—531no—
404C2×#390—531no—
405C2×#340D5311yescharacteristic, complemented
406C2×#336—531no—
407C2×C53#143811yescharacteristic
408C2×C53#187712yes—
409C2×C53#188012yes—
410C2×C53#196811yescharacteristic
411C2×C53#197311yescharacteristic
412C2×C53#200012yes—
413C2×C53#201211yescharacteristic
414C2×C53#201311yescharacteristic
415C2×C53#201411yescharacteristic
416C2×C53#201511yescharacteristic
417C2×C53#205512yes—
418D53—84no—
419C23×Q8—531no—
420C23×D4—531no—
421C22×SD16—534no—
422C22×SD16—1062no—
423C22×SD16—1062no—
424C22×SD16—1062no—
425C22×SD16—1062no—
426C22×SD16—1062no—
427C22×SD16—1062no—
428C23×C8—531no—
429C23×C8C2×D5311yescharacteristic
430C22×C4⋊C4C2×D5311yescharacteristic
431C22×C4⋊C4C2×D5311yescharacteristic
432C22×C22⋊C4—1062no—
433C22×C42—531no—
434C2×#103—1062no—
435C2×#103—1062no—
436C2×#103—1062no—
437C2×#102—1062no—
438C2×#102—1062no—
439C2×#102—1062no—
440#391—1062no—
441#391—1062no—
442#390—1062no—
443#390—1062no—
444C2×#95—1062no—
445#340—22no—
446#336—1062no—
447C53#1102311yescharacteristic, complemented, Sylow
448C25—1061no—
449C22×Q8—532no—
450C22×Q8—532no—
451C22×Q8—532no—
452C22×Q8—1061no—
453C22×Q8—1061no—
454C22×Q8—1061no—
455C22×Q8—1061no—
456C22×Q8—1061no—
457C22×Q8—1061no—
458C22×Q8—1061no—
459C22×Q8—1061no—
460C22×Q8—1061no—
461C22×Q8—1061no—
462C22×Q8—1061no—
463C22×D4—532no—
464C22×D4—532no—
465C22×D4—532no—
466C22×D4—1061no—
467C22×D4—1061no—
468C22×D4—1061no—
469C22×D4—1061no—
470C22×D4—1061no—
471C22×D4—1061no—
472C22×D4—1061no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4—1061no—
476C22×D4—1061no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—532no—
480C23×C4—1061no—
481C23×C4C22×D5311yescharacteristic
482C2×SD16—1068no—
483C2×SD16—1068no—
484C2×SD16—1068no—
485C2×SD16—1068no—
486C2×SD16—1068no—
487C2×SD16—1068no—
488C2×SD16—1068no—
489C22×C8—21no—
490C22×C8—21no—
491C22×C8—21no—
492C22×C8—21no—
493C22×C8—532no—
494C22×C8—1061no—
495C22×C8—1061no—
496C22×C8—1061no—
497C22×C8—1061no—
498C22×C8—1061no—
499C22×C8—1061no—
500C22×C8C4×D5312yes—
501C22×C8D21212yes—
502C22×C8C22⋊D5312yes—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4D21212yes—
514C2×C4⋊C4D21212yes—
515C2×C22⋊C4—1068no—
516C2×C22⋊C4—2124no—
517C2×C22⋊C4—2124no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42—1061no—
521C2×C42—1061no—
522C2×C42—1061no—
523C2×C42—1061no—
524#103—1068no—
525#102—1068no—
526#95—1068no—
527C24—1062no—
528C24—1062no—
529C24—1062no—
530C24—2121no—
531C24—2121no—
532C24—2121no—
533C24—2121no—
534C24—2122no—
535C24—2122no—
536C24—2122no—
537C24—2122no—
538C24D4×D5311yescharacteristic
539C2×Q8—534no—
540C2×Q8—1062no—
541C2×Q8—1062no—
542C2×Q8—1062no—
543C2×Q8—1062no—
544C2×Q8—1062no—
545C2×Q8—1062no—
546C2×Q8—1062no—
547C2×Q8—1062no—
548C2×Q8—1062no—
549C2×Q8—1062no—
550C2×Q8—1062no—
551C2×Q8—1062no—
552C2×Q8—1062no—
553C2×Q8—1062no—
554C2×Q8—1062no—
555C2×Q8—2121no—
556C2×Q8—2121no—
557C2×Q8—2121no—
558C2×Q8—2121no—
559C2×Q8—2121no—
560C2×Q8—2121no—
561C2×Q8—2121no—
562C2×Q8—2121no—
563C2×Q8—2121no—
564C2×Q8—2121no—
565C2×Q8—2121no—
566C2×Q8—2121no—
567C2×D4—534no—
568C2×D4—1062no—
569C2×D4—1062no—
570C2×D4—1062no—
571C2×D4—1062no—
572C2×D4—1062no—
573C2×D4—1062no—
574C2×D4—1062no—
575C2×D4—1062no—
576C2×D4—1062no—
577C2×D4—1062no—
578C2×D4—1062no—
579C2×D4—1062no—
580C2×D4—1062no—
581C2×D4—1062no—
582C2×D4—1062no—
583C2×D4—2121no—
584C2×D4—2121no—
585C2×D4—2121no—
586C2×D4—2121no—
587C2×D4—2121no—
588C2×D4—2121no—
589C2×D4—2121no—
590C2×D4—2121no—
591C2×D4—2121no—
592C2×D4—2121no—
593C2×D4—2121no—
594C2×D4—2121no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—534no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—2121no—
616C22×C4—2121no—
617C22×C4—2121no—
618C22×C4—2121no—
619C22×C4C2×C4×D5311yescharacteristic
620C22×C4C2×D21211yescharacteristic
621C22×C4C2×D21211yescharacteristic
622C22×C4C2×D21211yescharacteristic
623C22×C4#1171994511yescharacteristic
624C22×C4#1171994511yescharacteristic
625C22×C4D4×D5311yescharacteristic
626C22×C4D4×D5311yescharacteristic
627C22×C4D4×D5311yescharacteristic
628C22×C4D4×D5311yescharacteristic
629C22×C4D4×D5311yescharacteristic
630C22×C4#1171994911yescharacteristic
631C22×C4#1171994911yescharacteristic
632C22×C4C2×C22⋊D5311yescharacteristic
633SD16—10632no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—1062no—
641C2×C8—1062no—
642C2×C8—1062no—
643C2×C8—2121no—
644C2×C8—2121no—
645C2×C8—2121no—
646C2×C8—2121no—
647C2×C8#1171992114yescomplemented
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—41no—
653C4⋊C4—41no—
654C4⋊C4—41no—
655C4⋊C4—41no—
656C22⋊C4—21216no—
657C42—2121no—
658C42—2121no—
659C42—2121no—
660C42—2121no—
661C23—1064no—
662C23—4241no—
663C23—4241no—
664C23—4242no—
665C23—4242no—
666C23—4242no—
667C23—4242no—
668C23—4242no—
669C23—4242no—
670C23—4241no—
671C23—4241no—
672C23—2122no—
673C23—2124no—
674C23—2122no—
675C23—2122no—
676C23—2122no—
677C23—2124no—
678C23—2122no—
679C23—2122no—
680C23—2124no—
681C23—2124no—
682C23—2124no—
683C23—2124no—
684C23#1313317911yescharacteristic
685C23#1313318711yescharacteristic
686C23#1313318711yescharacteristic
687C23#1313319011yescharacteristic
688C23#1313319011yescharacteristic
689C23#1313319211yescharacteristic
690C23#1313321311yescharacteristic
691C23SD16×D5312yes—
692C23#1313323812yes—
693C23#1313324112yes—
694C23#1313324912yes—
695Q8—1064no—
696Q8—1064no—
697Q8—2122no—
698Q8—2122no—
699Q8—2122no—
700Q8—2122no—
701Q8—2122no—
702Q8—2122no—
703D4—1064no—
704D4—1064no—
705D4—2122no—
706D4—2122no—
707D4—2122no—
708D4—2122no—
709D4—2122no—
710D4—2122no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—82no—
718C2×C4—82no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—1064no—
722C2×C4—1064no—
723C2×C4—1064no—
724C2×C4—1064no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2122no—
735C2×C4C22⋊C4×D5311yescharacteristic
736C2×C4C22⋊C4×D5311yescharacteristic
737C2×C4C2×#1171992111yescharacteristic
738C2×C4#1313317911yescharacteristic
739C2×C4C4×D21211yescharacteristic
740C2×C4C4×D21211yescharacteristic
741C2×C4#1313318511yescharacteristic
742C2×C4#1313318511yescharacteristic
743C2×C4#1313318711yescharacteristic
744C2×C4#1313318711yescharacteristic
745C2×C4#1313318711yescharacteristic
746C2×C4#1313318711yescharacteristic
747C2×C4#1313319011yescharacteristic
748C2×C4#1313319011yescharacteristic
749C2×C4#1313319111yescharacteristic
750C2×C4#1313319111yescharacteristic
751C2×C4#1313319211yescharacteristic
752C2×C4#1313319211yescharacteristic
753C2×C4#1313319211yescharacteristic
754C2×C4#1313319211yescharacteristic
755C2×C4#1313319211yescharacteristic
756C2×C4#1313320211yescharacteristic
757C2×C4#1313320211yescharacteristic
758C2×C4#1313320211yescharacteristic
759C2×C4#1313320211yescharacteristic
760C2×C4#1313320511yescharacteristic
761C2×C4#1313320611yescharacteristic
762C2×C4#1313321411yescharacteristic
763C8—24no—
764C8—2122no—
765C22—4244no—
766C22—4244no—
767C22—4242no—
768C22—4242no—
769C22—4242no—
770C22—4242no—
771C22—4242no—
772C22—4244no—
773C22—4242no—
774C22—2124no—
775C22—2128no—
776C22#1681050111yescharacteristic
777C22#1681050111yescharacteristic
778C22#1681052411yescharacteristic
779C22#1681053211yescharacteristic
780C22#1681053211yescharacteristic
781C22#1681053311yescharacteristic
782C22#1681054111yescharacteristic
783C22#1681071012yes—
784C22#1681072212yes—
785C22#1681076312yes—
786C22#1681076912yes—
787C22#1681077512yes—
788C22#1681078812yes—
789C22#1681082212yes—
790C22#1681082712yes—
791C22#1681083712yes—
792C22#1681084812yes—
793C22#1681085312yes—
794C22#1681087012yes—
795C22#1681099411yescharacteristic
796C22#1681100411yescharacteristic
797C22#1681101111yescharacteristic
798C22#1681101611yescharacteristic
799C4—82no—
800C4—82no—
801C4—2124no—
802C4—2124no—
803C4#1681047811yescharacteristic
804C4#1681050111yescharacteristic
805C4#1681050111yescharacteristic
806C4#1681052511yescharacteristic
807C4#1681053311yescharacteristic
808C4#1681054011yescharacteristic
809C4#1681054011yescharacteristic
810C4#1681054111yescharacteristic
811C2—4244no—
812C2#2027295511yescharacteristic
813C2#2027505012yes—
814C2#2027507112yes—
815C2#2027556711yescharacteristic
816C2#2027559411yescharacteristic
817C2#2027572112yes—
818C2#2027579411yescharacteristic
819C2#2027579911yescharacteristic
820C2#2027580411yescharacteristic
821C2#2027581011yescharacteristic
822C2#2027603412yes—
subgroupG/H
centerC24D4×D53
commutatorC22×C4×C53C22×C4
FrattiniC23×C4C22×D53
FittingC2×C53×#340C2
socleC24×C53C2×D4
prime radicalC23×D212C22
cosocleC23×C4×C53C23
hypercenterC2×#340D53
hypocenterC53#11023
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#13133140C2semidirect
4. C2×#16810528C2semidirect
6. C2×#16810377C2semidirect
7. C2×C53×#340C2semidirect
16. C22×#11719913C4semidirect
164. C22×Dic53SD16semidirect
220. C2×Dic106C22⋊C4semidirect
227. C2×C8×C53C22⋊C4semidirect
405. C2×#340D53semidirect
447. C53#11023semidirect
647. C2×C8#11719921semidirect

Maximal subgroups

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

subgroupindex
C23×#117199132
C22×#131331402
C22×#131331372
C2×#168105282
C2×#168105242
C2×#168103772
C2×C53×#3402
#1102353