Finite Group Databasebeta

← #27306498

Subgroups — #27306498

Order 13568.

1710 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic106C211yesmaximal, characteristic
2C2×#16810488C211yesmaximal, characteristic
3C2×C4⋊C4×Dic53C211yesmaximal, characteristic
4#20272985C212yesmaximal
5#20272981C212yesmaximal
6#20272949C212yesmaximal
7#20272946C212yesmaximal
8#20272945C211yesmaximal, characteristic
9#20272944C211yesmaximal, characteristic
10#20272944C211yesmaximal, characteristic
11C53×C4⋊#95C211yesmaximal, characteristic
12C23×Dic106C2211yescharacteristic
13C2×C4×Dic106—24no—
14C2×C4×Dic106—24no—
15C2×C4×Dic106C418yescomplemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×C4×Dic53C2211yescharacteristic
22C22×C4×Dic53C2212yes—
23C22×C4×Dic53C2211yescharacteristic
24#16810488—24no—
25C4⋊C4×Dic53—24no—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C22×C4⋊C4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C42×C53C2211yescharacteristic
38C2×#95×C53C2212yes—
39C2×#95×C53C2212yes—
40C22×Dic106—22no—
41C22×Dic106—22no—
42C22×Dic106—22no—
43C22×Dic106—22no—
44C22×Dic106—22no—
45C22×Dic106—22no—
46C22×Dic106C2×C414yes—
47C23×Dic53C2312yes—
48C23×Dic53C2311yescharacteristic
49C23×Dic53C2312yes—
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2311yescharacteristic
53C4×Dic106—232no—
54C2×C4⋊Dic53—22no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—22no—
59C2×C4⋊Dic53—22no—
60C2×C4⋊Dic53—22no—
61C2×C4⋊Dic53C2×C414yes—
62C2×C4⋊Dic53Q814yescomplemented
63C2×#11719919—22no—
64C2×#11719919—22no—
65C2×#11719919—22no—
66C2×#11719919—22no—
67C2×#11719919C2×C414yes—
68C2×#11719919C2×C414yes—
69C2×C4×Dic53—22no—
70C2×C4×Dic53—22no—
71C2×C4×Dic53—24no—
72C2×C4×Dic53—42no—
73C2×C4×Dic53—42no—
74C2×C4×Dic53C2×C414yes—
75C2×C4×Dic53C2×C414yes—
76C2×C4×Dic53D414yes—
77C2×C4×Dic53D414yes—
78#13133124—24no—
79#13133124—24no—
80#13133124—24no—
81#13133124—24no—
82#13133124—24no—
83#13133124—24no—
84#13133124—42no—
85#13133124—42no—
86#13133124—42no—
87C23×C4×C53C2312yes—
88C23×C4×C53C2311yescharacteristic
89C23×C4×C53C2312yes—
90C23×C4×C53C2311yescharacteristic
91C23×C4×C53C2311yescharacteristic
92C2×C4⋊C4×C53—22no—
93C2×C4⋊C4×C53—22no—
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53Q814yescomplemented
98C2×C42×C53—22no—
99C2×C42×C53—22no—
100C2×C42×C53C2×C414yes—
101#95×C53—24no—
102#95×C53—42no—
103C24×C53C2411yescharacteristic
104C22×C4×C53—21no—
105C22×C4×C53—21no—
106C22×C4×C53—21no—
107C22×C4×C53—21no—
108C22×C4×C53—21no—
109C22×C4×C53—21no—
110C22×C4×C53—22no—
111C22×C4×C53—22no—
112C22×C4×C53—22no—
113C22×C4×C53—22no—
114C22×C4×C53—21no—
115C22×C4×C53—22no—
116C22×C4×C53—21no—
117C22×C4×C53—22no—
118C22×C4×C53—21no—
119C22×C4×C53—21no—
120C22×C4×C53—22no—
121C22×C4×C53—22no—
122C22×C4×C53—22no—
123C22×C4×C53—22no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53C22×C412yes—
128C22×C4×C53C22×C412yes—
129C22×C4×C53C22×C412yes—
130C22×C4×C53C2×D412yes—
131C22×C4×C53C2×D412yes—
132C22×C4×C53C2×Q814yes—
133C22×C4×C53C2×Q812yes—
134C22×C4×C53C2×Q812yes—
135C22×C4×C53#4112yes—
136C22×C4×C53#4112yes—
137C22×C4×C53#4112yes—
138C22×C4×C53#4112yes—
139C22×Dic53—21no—
140C22×Dic53—21no—
141C22×Dic53—21no—
142C22×Dic53—21no—
143C22×Dic53—21no—
144C22×Dic53—21no—
145C22×Dic53—21no—
146C22×Dic53—21no—
147C22×Dic53—21no—
148C22×Dic53—21no—
149C22×Dic53—21no—
150C22×Dic53—21no—
151C22×Dic53—22no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—22no—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53C22×C412yes—
171C22×Dic53C22×C412yes—
172C22×Dic53C22×C412yes—
173C22×Dic53C22×C412yes—
174C22×Dic53C2×D412yes—
175C22×Dic53C2×D412yes—
176C22×Dic53C2×D412yes—
177C22×Dic53C2×D412yes—
178C22×Dic53C2×Q814yes—
179C22×Dic53#4112yes—
180C22×Dic53#4112yes—
181C2×Dic106—28no—
182C2×Dic106—28no—
183C2×Dic106—28no—
184C2×Dic106—28no—
185C2×Dic106—28no—
186C2×Dic106—28no—
187C2×Dic106—28no—
188C4⋊C4×C53—28no—
189C4⋊C4×C53—44no—
190C42×C53—28no—
191C4⋊Dic53—28no—
192C4⋊Dic53—28no—
193C4⋊Dic53—44no—
194#11719919—28no—
195#11719919—28no—
196C4×Dic53—28no—
197C4×Dic53—48no—
198C4×Dic53C22⋊C4116yes—
199C23×C53C23×C411yescharacteristic
200C23×C53C22×D411yescharacteristic
201C23×C53C22×D411yescharacteristic
202C23×C53C22×Q811yescharacteristic
203C23×C53C22×Q811yescharacteristic
204C23×C53C2×#4111yescharacteristic
205C23×C53C2×#4111yescharacteristic
206C23×C53C2×#4111yescharacteristic
207C23×C53C2×#4111yescharacteristic
208C23×C53C2×#4111yescharacteristic
209C23×C53C2×#4111yescharacteristic
210C23×C53H(5,𝔽2)11yescharacteristic
211C23×C53H(5,𝔽2)11yescharacteristic
212C23×C532−1+411yescharacteristic
213C23×C532−1+411yescharacteristic
214C2×C4×C53—22no—
215C2×C4×C53—22no—
216C2×C4×C53—22no—
217C2×C4×C53—22no—
218C2×C4×C53—22no—
219C2×C4×C53—22no—
220C2×C4×C53—22no—
221C2×C4×C53—22no—
222C2×C4×C53—22no—
223C2×C4×C53—24no—
224C2×C4×C53—24no—
225C2×C4×C53—24no—
226C2×C4×C53—42no—
227C2×C4×C53—41no—
228C2×C4×C53—42no—
229C2×C4×C53—41no—
230C2×C4×C53—41no—
231C2×C4×C53—41no—
232C2×C4×C53—42no—
233C2×C4×C53—42no—
234C2×C4×C53—42no—
235C2×C4×C53—42no—
236C2×C4×C53—42no—
237C2×C4×C53—42no—
238C2×C4×C53—42no—
239C2×C4×C53—42no—
240C2×C4×C53—42no—
241C2×C4×C53C2×C22⋊C414yes—
242C2×C4×C53#11714yes—
243C2×C4×C53C4×Q814yes—
244C2×C4×C53C4×Q814yes—
245C2×C4×C53C22⋊Q814yes—
246C2×C4×C53C22⋊Q814yes—
247C2×C4×C53#12414yes—
248C2×C4×C53C4⋊Q814yes—
249C2×Dic53—22no—
250C2×Dic53—22no—
251C2×Dic53—22no—
252C2×Dic53—22no—
253C2×Dic53—22no—
254C2×Dic53—22no—
255C2×Dic53—22no—
256C2×Dic53—22no—
257C2×Dic53—22no—
258C2×Dic53—22no—
259C2×Dic53—22no—
260C2×Dic53—22no—
261C2×Dic53—22no—
262C2×Dic53—22no—
263C2×Dic53—22no—
264C2×Dic53—22no—
265C2×Dic53—22no—
266C2×Dic53—22no—
267C2×Dic53—22no—
268C2×Dic53—22no—
269C2×Dic53—22no—
270C2×Dic53—24no—
271C2×Dic53—24no—
272C2×Dic53—24no—
273C2×Dic53—42no—
274C2×Dic53—41no—
275C2×Dic53—42no—
276C2×Dic53—41no—
277C2×Dic53—41no—
278C2×Dic53—41no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53C2×C22⋊C414yes—
289C2×Dic53C2×C22⋊C414yes—
290C2×Dic53#11714yes—
291Dic106—232no—
292#13925—531nomaximal, Sylow
293C22×C53C22×C22⋊C411yescharacteristic
294C22×C53C2×#11711yescharacteristic
295C22×C53C2×#11711yescharacteristic
296C22×C53C2×C4×Q811yescharacteristic
297C22×C53C2×C4×Q811yescharacteristic
298C22×C53#52011yescharacteristic
299C22×C53#52011yescharacteristic
300C22×C53C2×C22⋊Q811yescharacteristic
301C22×C53C2×C22⋊Q811yescharacteristic
302C22×C53#52511yescharacteristic
303C22×C53#52511yescharacteristic
304C22×C53#52511yescharacteristic
305C22×C53#52511yescharacteristic
306C22×C53C2×#12411yescharacteristic
307C22×C53C2×C4⋊Q811yescharacteristic
308C22×C53#53511yescharacteristic
309C22×C53#53611yescharacteristic
310C22×C53#53711yescharacteristic
311C22×C53#53711yescharacteristic
312C22×C53#55411yescharacteristic
313C22×C53#55411yescharacteristic
314C22×C53#55411yescharacteristic
315C22×C53#55411yescharacteristic
316C22×C53#55611yescharacteristic
317C22×C53#55611yescharacteristic
318C22×C53#55611yescharacteristic
319C22×C53#55611yescharacteristic
320C22×C53#55711yescharacteristic
321C22×C53#55711yescharacteristic
322C22×C53#55711yescharacteristic
323C22×C53#55711yescharacteristic
324C22×C53#55911yescharacteristic
325C22×C53#55911yescharacteristic
326C22×C53#55911yescharacteristic
327C22×C53#55911yescharacteristic
328C4×C53—24no—
329C4×C53—42no—
330C4×C53—44no—
331C4×C53—82no—
332C4×C53#39118yes—
333Dic53—24no—
334Dic53—24no—
335Dic53—24no—
336Dic53—42no—
337Dic53—44no—
338Dic53—82no—
339C22×C4×Q8—531no—
340C2×#382—531no—
341C2×C4×C4⋊C4—531no—
342#1446—532no—
343#1445—532no—
344#1436—532no—
345#1436—532no—
346C4⋊#95—531no—
347C4⋊#95—531no—
348C4⋊#95—531no—
349C4⋊#95D5311yescharacteristic
350C2×C53#228011yescharacteristic
351C2×C53C2×#39111yescharacteristic
352C2×C53#231111yescharacteristic
353C2×C53#235511yescharacteristic
354C2×C53#235511yescharacteristic
355C2×C53#235511yescharacteristic
356C2×C53#235511yescharacteristic
357C2×C53#258011yescharacteristic
358C2×C53#258011yescharacteristic
359C2×C53#258111yescharacteristic
360C2×C53#258111yescharacteristic
361C2×C53#258411yescharacteristic
362C2×C53#258411yescharacteristic
363C2×C53#259211yescharacteristic
364C2×C53#259211yescharacteristic
365C23×Q8—531no—
366C2×C4×Q8—538no—
367C2×C4×Q8—1064no—
368C2×C4×Q8—1064no—
369C22×C4⋊C4—531no—
370C22×C4⋊C4—531no—
371C22×C4⋊C4—531no—
372C22×C4⋊C4—531no—
373C22×C4⋊C4—531no—
374C22×C4⋊C4C2×D5311yescharacteristic
375C22×C4⋊C4C2×D5311yescharacteristic
376C22×C42—531no—
377C22×C42—531no—
378C22×C42—532no—
379C22×C42C2×D5311yescharacteristic
380#382—1064no—
381C4×C4⋊C4—1064no—
382C2×#95—532no—
383C2×#95—532no—
384C2×#95—532no—
385C2×#95—532no—
386C2×#95—532no—
387C2×#95—532no—
388C2×#95—532no—
389C2×#95—532no—
390C2×#95—532no—
391C2×#95C2×D5312yes—
392C2×#95C2×D5312yes—
393C53#1392511yescharacteristic, complemented, Sylow
394C22×Q8—534no—
395C22×Q8—1062no—
396C22×Q8—1062no—
397C22×Q8—1062no—
398C22×Q8—1062no—
399C22×Q8—1062no—
400C22×Q8—1062no—
401C23×C4—531no—
402C23×C4—531no—
403C23×C4—531no—
404C23×C4—531no—
405C23×C4—532no—
406C23×C4—532no—
407C23×C4C22×D5312yes—
408C23×C4C22×D5312yes—
409C23×C4C22×D5311yescharacteristic
410C23×C4C22×D5311yescharacteristic
411C23×C4C22×D5311yescharacteristic
412C4×Q8—10632no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—534no—
419C2×C4⋊C4—534no—
420C2×C4⋊C4—534no—
421C2×C4⋊C4—534no—
422C2×C4⋊C4—1062no—
423C2×C4⋊C4—1062no—
424C2×C4⋊C4—1062no—
425C2×C4⋊C4—1062no—
426C2×C4⋊C4—1062no—
427C2×C4⋊C4—1062no—
428C2×C4⋊C4—1062no—
429C2×C4⋊C4—1062no—
430C2×C4⋊C4—1062no—
431C2×C4⋊C4—1062no—
432C2×C4⋊C4—1062no—
433C2×C4⋊C4Dic10614yescomplemented
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—534no—
437C2×C42—534no—
438C2×C42—534no—
439C2×C42—534no—
440C2×C42—1062no—
441C2×C42—1062no—
442C2×C42—1064no—
443C2×C42—2122no—
444C2×C42—2122no—
445C2×C42C4×D5314yes—
446#95—24no—
447#95—42no—
448#95—1064no—
449#95—1064no—
450#95—1064no—
451#95—1064no—
452#95—1064no—
453#95—1064no—
454#95—2122no—
455#95—2122no—
456#95—2122no—
457C24C23×D5311yescharacteristic
458C2×Q8—1068no—
459C2×Q8—1068no—
460C2×Q8—1068no—
461C2×Q8—1068no—
462C2×Q8—1068no—
463C2×Q8—1068no—
464C2×Q8—1068no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—532no—
489C22×C4—532no—
490C22×C4—532no—
491C22×C4—532no—
492C22×C4—532no—
493C22×C4—532no—
494C22×C4—532no—
495C22×C4—532no—
496C22×C4—532no—
497C22×C4—532no—
498C22×C4—534no—
499C22×C4—1061no—
500C22×C4—1061no—
501C22×C4—1061no—
502C22×C4—1061no—
503C22×C4—1061no—
504C22×C4—1061no—
505C22×C4—1061no—
506C22×C4—1061no—
507C22×C4—1061no—
508C22×C4—1061no—
509C22×C4—1061no—
510C22×C4—1061no—
511C22×C4—1062no—
512C22×C4—1061no—
513C22×C4—1061no—
514C22×C4—1062no—
515C22×C4—1062no—
516C22×C4—1062no—
517C22×C4—1061no—
518C22×C4—1062no—
519C22×C4—1061no—
520C22×C4—1062no—
521C22×C4—1061no—
522C22×C4—1061no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4C2×Dic10614yes—
531C22×C4C2×Dic10612yes—
532C22×C4C2×C4×D5312yes—
533C22×C4C2×C4×D5312yes—
534C22×C4C2×C4×D5312yes—
535C22×C4#1171994512yes—
536C22×C4D4×D5312yes—
537C22×C4D4×D5312yes—
538C22×C4#1171994712yes—
539C22×C4#1171994712yes—
540C22×C4Q8×D5312yes—
541C22×C4#1171994912yes—
542C4⋊C4—28no—
543C4⋊C4—44no—
544C4⋊C4—1068no—
545C4⋊C4—1068no—
546C4⋊C4—1068no—
547C4⋊C4—1068no—
548C4⋊C4—2124no—
549C42—28no—
550C42—5316no—
551C42—1068no—
552C42—2128no—
553C23C22×C4×D5311yescharacteristic
554C23C2×D4×D5311yescharacteristic
555C23C2×D4×D5311yescharacteristic
556C23C2×Q8×D5311yescharacteristic
557C23C22×Dic10611yescharacteristic
558C23#41×D5311yescharacteristic
559C23#41×D5311yescharacteristic
560C23C2×#1171994711yescharacteristic
561C23C2×#1171994711yescharacteristic
562C23C2×#1171994511yescharacteristic
563C23C2×#1171994911yescharacteristic
564C23#1313326211yescharacteristic
565C23#1313326311yescharacteristic
566C23#1313326411yescharacteristic
567C23#1313326511yescharacteristic
568Q8—10632no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—534no—
597C2×C4—534no—
598C2×C4—534no—
599C2×C4—1062no—
600C2×C4—1062no—
601C2×C4—1062no—
602C2×C4—1062no—
603C2×C4—1062no—
604C2×C4—1062no—
605C2×C4—1062no—
606C2×C4—1062no—
607C2×C4—1062no—
608C2×C4—1062no—
609C2×C4—1062no—
610C2×C4—1062no—
611C2×C4—1062no—
612C2×C4—1062no—
613C2×C4—1062no—
614C2×C4—1062no—
615C2×C4—1062no—
616C2×C4—1062no—
617C2×C4—1062no—
618C2×C4—1064no—
619C2×C4—1064no—
620C2×C4—1062no—
621C2×C4—1062no—
622C2×C4—1064no—
623C2×C4—2122no—
624C2×C4—2122no—
625C2×C4—2122no—
626C2×C4—2122no—
627C2×C4—2122no—
628C2×C4—2122no—
629C2×C4—2122no—
630C2×C4—2122no—
631C2×C4—2122no—
632C2×C4—2122no—
633C2×C4—2122no—
634C2×C4—2121no—
635C2×C4—2121no—
636C2×C4—2121no—
637C2×C4—2121no—
638C2×C4C22⋊C4×D5314yes—
639C2×C4#1313317514yes—
640C2×C4#1313318214yes—
641C2×C4C4×Dic10614yes—
642C2×C4#1313319414yes—
643C2×C4#1313319514yes—
644C2×C4#1313320314yes—
645C2×C4#1313321614yes—
646C22C2×C22⋊C4×D5311yescharacteristic
647C22#117×D5311yescharacteristic
648C22C2×#1313317511yescharacteristic
649C22C2×#1313318211yescharacteristic
650C22C2×C4×Dic10611yescharacteristic
651C22#1681110311yescharacteristic
652C22#1681110411yescharacteristic
653C22C2×#1313319411yescharacteristic
654C22C2×#1313319511yescharacteristic
655C22#1681113311yescharacteristic
656C22#1681113311yescharacteristic
657C22#1681113611yescharacteristic
658C22#1681113611yescharacteristic
659C22C2×#1313320311yescharacteristic
660C22C2×#1313321611yescharacteristic
661C22#1681118911yescharacteristic
662C22#1681119611yescharacteristic
663C22#1681120211yescharacteristic
664C22#1681120311yescharacteristic
665C22#1681132911yescharacteristic
666C22#1681133011yescharacteristic
667C22#1681133211yescharacteristic
668C22#1681133411yescharacteristic
669C22#1681134211yescharacteristic
670C22#1681134311yescharacteristic
671C22#1681134511yescharacteristic
672C22#1681134711yescharacteristic
673C22#1681134811yescharacteristic
674C22#1681134911yescharacteristic
675C22#1681135011yescharacteristic
676C22#1681135211yescharacteristic
677C22#1681135511yescharacteristic
678C22#1681135611yescharacteristic
679C22#1681135811yescharacteristic
680C22#1681135911yescharacteristic
681C4—24no—
682C4—44no—
683C4—42no—
684C4—82no—
685C4—1064no—
686C4—1064no—
687C4—1064no—
688C4—4242no—
689C4—2124no—
690C4—2122no—
691C4#1681052718yes—
692C2#2027709711yescharacteristic
693C2C2×#1681052711yescharacteristic
694C2#2027730411yescharacteristic
695C2#2027766711yescharacteristic
696C2#2027767011yescharacteristic
697C2#2027767311yescharacteristic
698C2#2027767411yescharacteristic
699C2#2028007111yescharacteristic
700C2#2028007511yescharacteristic
701C2#2028007911yescharacteristic
702C2#2028008311yescharacteristic
703C2#2028010011yescharacteristic
704C2#2028010211yescharacteristic
705C2#2028020011yescharacteristic
706C2#2028020211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, prime radical, cosocleC24×C53C24
hypercenterC4⋊#95D53
hypocenterC53#13925
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic106C4semidirect
62. C2×C4⋊Dic53Q8semidirect
97. C2×C4⋊C4×C53Q8semidirect
393. C53#13925semidirect
433. C2×C4⋊C4Dic106semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic1062
C2×#168104882
C2×C4⋊C4×Dic532
#202729852
#202729812
#202729492
#202729462
#202729452
#202729442
C53×C4⋊#952
#1392553