Finite Group Databasebeta

← #27306367

Subgroups — #27306367

Order 13568.

1774 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810522C211yesmaximal, characteristic
2C2×#16810521C211yesmaximal, characteristic
3C2×#16810519C211yesmaximal, characteristic
4C2×#16810492C211yesmaximal, characteristic
5C2×#16810492C212yesmaximal
6C2×C4⋊C4×Dic53C211yesmaximal, characteristic
7C2×C4×#11719919C211yesmaximal, characteristic
8#20272979C212yesmaximal
9#20272978C212yesmaximal
10#20272943C212yesmaximal
11C2×C53×#389C211yesmaximal, characteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2212yes—
14C22×C4⋊Dic53C2211yescharacteristic
15C22×#11719919C2212yes—
16C22×#11719919C2212yes—
17C22×#11719919C2212yes—
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2212yes—
21C22×C4×Dic53C2211yescharacteristic
22C22×C4×Dic53C2212yes—
23C22×C4×Dic53C2211yescharacteristic
24#16810522—24no—
25#16810521—24no—
26#16810519—24no—
27#16810492—28no—
28#16810492—24no—
29C4⋊C4×Dic53C418yescomplemented
30C4×#11719919—24no—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2212yes—
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2212yes—
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C53×#389—24no—
42C2×#95×C53C2212yes—
43C23×Dic53C2312yes—
44C23×Dic53C2311yescharacteristic
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2312yes—
47C23×Dic53C2311yescharacteristic
48C23×Dic53C2311yescharacteristic
49C2×C4⋊Dic53—22no—
50C2×C4⋊Dic53—24no—
51C2×C4⋊Dic53—22no—
52C2×C4⋊Dic53—22no—
53C2×C4⋊Dic53—24no—
54C2×C4⋊Dic53—42no—
55C2×C4⋊Dic53C2×C414yes—
56C2×C4⋊Dic53D414yes—
57C2×C4⋊Dic53Q814yes—
58C2×#11719919—24no—
59C2×#11719919—22no—
60C2×#11719919—22no—
61C2×#11719919—24no—
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919—24no—
65C2×#11719919—24no—
66C2×#11719919—24no—
67C2×#11719919—22no—
68C2×#11719919—22no—
69C2×#11719919—24no—
70C2×#11719919—42no—
71C2×#11719919—42no—
72C2×#11719919—42no—
73C2×#11719919—42no—
74C2×#11719919D414yes—
75C2×#11719919Q814yes—
76C2×C4×Dic53—22no—
77C2×C4×Dic53—22no—
78C2×C4×Dic53—22no—
79C2×C4×Dic53—24no—
80C2×C4×Dic53—24no—
81C2×C4×Dic53C2×C418yes—
82C2×C4×Dic53C2×C414yes—
83C2×C4×Dic53D414yes—
84C2×C4×Dic53Q814yes—
85#13133124—24no—
86#13133124—24no—
87#13133124—24no—
88#13133124—22no—
89#13133124—22no—
90#13133124C2×C418yes—
91C23×C4×C53C2312yes—
92C23×C4×C53C2311yescharacteristic
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2312yes—
95C23×C4×C53C2311yescharacteristic
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53—24no—
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53—24no—
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—42no—
102C2×C4⋊C4×C53C2×C414yes—
103C2×C4⋊C4×C53D414yes—
104C2×C4⋊C4×C53Q814yes—
105C2×C42×C53—22no—
106C2×C42×C53—22no—
107C2×C42×C53—22no—
108#95×C53—24no—
109C24×C53C2411yescharacteristic
110C22×C4×C53—22no—
111C22×C4×C53—22no—
112C22×C4×C53—22no—
113C22×C4×C53—22no—
114C22×C4×C53—21no—
115C22×C4×C53—21no—
116C22×C4×C53—21no—
117C22×C4×C53—21no—
118C22×C4×C53—21no—
119C22×C4×C53—21no—
120C22×C4×C53—21no—
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—21no—
125C22×C4×C53—21no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53C22×C414yes—
134C22×C4×C53C22×C412yes—
135C22×C4×C53C2×D412yes—
136C22×C4×C53C2×D414yes—
137C22×C4×C53C2×D412yes—
138C22×C4×C53C2×D412yes—
139C22×C4×C53C2×D412yes—
140C22×C4×C53C2×Q812yes—
141C22×C4×C53C2×Q814yes—
142C22×C4×C53C2×Q812yes—
143C22×C4×C53C2×Q812yes—
144C22×C4×C53C2×Q812yes—
145C22×Dic53—22no—
146C22×Dic53—22no—
147C22×Dic53—21no—
148C22×Dic53—21no—
149C22×Dic53—22no—
150C22×Dic53—21no—
151C22×Dic53—21no—
152C22×Dic53—22no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—21no—
157C22×Dic53—21no—
158C22×Dic53—21no—
159C22×Dic53—21no—
160C22×Dic53—21no—
161C22×Dic53—21no—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53C22×C412yes—
173C22×Dic53C22×C414yes—
174C22×Dic53C22×C412yes—
175C22×Dic53C2×D412yes—
176C22×Dic53C2×D412yes—
177C22×Dic53C2×D414yes—
178C22×Dic53C2×D412yes—
179C22×Dic53C2×D412yes—
180C22×Dic53C2×Q812yes—
181C22×Dic53C2×Q812yes—
182C22×Dic53C2×Q814yes—
183C22×Dic53C2×Q812yes—
184C22×Dic53C2×Q812yes—
185C22×Dic53#4112yes—
186C22×Dic53#4112yes—
187C4⋊C4×C53—48no—
188C4⋊C4×C53—44no—
189C4⋊C4×C53C4⋊C4116yescomplemented
190C42×C53—44no—
191C4⋊Dic53—48no—
192C4⋊Dic53—44no—
193C4⋊Dic53C4⋊C4116yescomplemented
194#11719919—28no—
195#11719919—28no—
196#11719919—48no—
197#11719919—48no—
198#11719919—48no—
199#11719919—48no—
200C4×Dic53—216no—
201C4×Dic53—44no—
202C4×Dic53C4⋊C4116yescomplemented
203C23×C53C23×C411yescharacteristic
204C23×C53C22×D411yescharacteristic
205C23×C53C22×D411yescharacteristic
206C23×C53C22×D411yescharacteristic
207C23×C53C22×D411yescharacteristic
208C23×C53C22×Q811yescharacteristic
209C23×C53C22×Q811yescharacteristic
210C23×C53C22×Q811yescharacteristic
211C23×C53C22×Q811yescharacteristic
212C23×C53C2×#4111yescharacteristic
213C23×C53C2×#4111yescharacteristic
214C23×C53H(5,𝔽2)11yescharacteristic
215C23×C53H(5,𝔽2)11yescharacteristic
216C23×C532−1+411yescharacteristic
217C23×C532−1+411yescharacteristic
218C2×C4×C53—24no—
219C2×C4×C53—24no—
220C2×C4×C53—24no—
221C2×C4×C53—24no—
222C2×C4×C53—24no—
223C2×C4×C53—24no—
224C2×C4×C53—22no—
225C2×C4×C53—22no—
226C2×C4×C53—22no—
227C2×C4×C53—22no—
228C2×C4×C53—22no—
229C2×C4×C53—22no—
230C2×C4×C53—41no—
231C2×C4×C53—41no—
232C2×C4×C53—41no—
233C2×C4×C53—41no—
234C2×C4×C53—41no—
235C2×C4×C53—41no—
236C2×C4×C53—41no—
237C2×C4×C53—41no—
238C2×C4×C53—42no—
239C2×C4×C53—42no—
240C2×C4×C53—42no—
241C2×C4×C53—42no—
242C2×C4×C53—42no—
243C2×C4×C53—42no—
244C2×C4×C53—42no—
245C2×C4×C53C2×C4⋊C414yes—
246C2×C4×C53C2×C4⋊C414yes—
247C2×C4×C53C2×C4⋊C418yes—
248C2×C4×C53C2×C4⋊C414yes—
249C2×C4×C53#12714yes—
250C2×C4×C53C4⋊Q814yes—
251C2×C4×C53C4⋊Q814yes—
252C2×C4×C53C4⋊Q814yes—
253C2×Dic53—24no—
254C2×Dic53—22no—
255C2×Dic53—22no—
256C2×Dic53—24no—
257C2×Dic53—22no—
258C2×Dic53—22no—
259C2×Dic53—22no—
260C2×Dic53—22no—
261C2×Dic53—24no—
262C2×Dic53—24no—
263C2×Dic53—24no—
264C2×Dic53—24no—
265C2×Dic53—22no—
266C2×Dic53—22no—
267C2×Dic53—22no—
268C2×Dic53—22no—
269C2×Dic53—22no—
270C2×Dic53—22no—
271C2×Dic53—41no—
272C2×Dic53—41no—
273C2×Dic53—41no—
274C2×Dic53—41no—
275C2×Dic53—41no—
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×Dic53C2×C4⋊C414yes—
287C2×Dic53C2×C4⋊C418yes—
288C2×Dic53C2×C4⋊C414yes—
289C2×Dic53C4×D414yes—
290C2×Dic53C4×Q814yes—
291C2×Dic53#12114yes—
292C2×Dic53C22⋊Q814yes—
293C2×Dic53#12514yes—
294C2×Dic53C4⋊Q814yes—
295#13910—531nomaximal, Sylow
296C22×C53C22×C4⋊C411yescharacteristic
297C22×C53C22×C4⋊C411yescharacteristic
298C22×C53C22×C4⋊C411yescharacteristic
299C22×C53C2×C4×D411yescharacteristic
300C22×C53C2×C4×Q811yescharacteristic
301C22×C53#52011yescharacteristic
302C22×C53#52011yescharacteristic
303C22×C53C2×#12111yescharacteristic
304C22×C53C2×C22⋊Q811yescharacteristic
305C22×C53C2×#12511yescharacteristic
306C22×C53C2×#12711yescharacteristic
307C22×C53C2×C4⋊Q811yescharacteristic
308C22×C53C2×C4⋊Q811yescharacteristic
309C22×C53C2×C4⋊Q811yescharacteristic
310C22×C53C2×C4⋊Q811yescharacteristic
311C22×C53#53511yescharacteristic
312C22×C53#53611yescharacteristic
313C22×C53#54411yescharacteristic
314C22×C53#54411yescharacteristic
315C22×C53D4211yescharacteristic
316C22×C53D4211yescharacteristic
317C22×C53#54711yescharacteristic
318C22×C53#54711yescharacteristic
319C22×C53D4×Q811yescharacteristic
320C22×C53D4×Q811yescharacteristic
321C22×C53D4×Q811yescharacteristic
322C22×C53D4×Q811yescharacteristic
323C22×C53#55011yescharacteristic
324C22×C53#55011yescharacteristic
325C22×C53#55411yescharacteristic
326C22×C53#55411yescharacteristic
327C22×C53#55711yescharacteristic
328C22×C53#55711yescharacteristic
329C22×C53Q8211yescharacteristic
330C22×C53Q8211yescharacteristic
331C4×C53—28no—
332C4×C53—42no—
333C4×C53—42no—
334C4×C53—82no—
335C4×C53#38418yescomplemented
336Dic53—24no—
337Dic53—28no—
338Dic53—42no—
339Dic53—42no—
340Dic53—82no—
341Dic53#38918yescomplemented
342C2×#389—531no—
343C2×#389—531no—
344C2×#389—531no—
345C2×#389D5311yescharacteristic
346C2×#384—532no—
347C2×#384—531no—
348C2×C4×C4⋊C4—531no—
349C2×C4×C4⋊C4—531no—
350#1444—532no—
351#1444—532no—
352C4⋊#95—532no—
353C2×C53C2×#38411yescharacteristic
354C2×C53C2×#38911yescharacteristic
355C2×C53#231711yescharacteristic
356C2×C53D4×C4⋊C411yescharacteristic
357C2×C53D4×C4⋊C411yescharacteristic
358C2×C53Q8×C4⋊C411yescharacteristic
359C2×C53Q8×C4⋊C411yescharacteristic
360C2×C53#254111yescharacteristic
361C2×C53#254211yescharacteristic
362C2×C53#254611yescharacteristic
363C2×C53#255111yescharacteristic
364C2×C53#255111yescharacteristic
365C2×C53#255211yescharacteristic
366C2×C53#255211yescharacteristic
367C2×C53#256711yescharacteristic
368C22×C4⋊C4—531no—
369C22×C4⋊C4—531no—
370C22×C4⋊C4—531no—
371C22×C4⋊C4—532no—
372C22×C4⋊C4—531no—
373C22×C4⋊C4—532no—
374C22×C4⋊C4—532no—
375C22×C4⋊C4—532no—
376C22×C4⋊C4—532no—
377C22×C4⋊C4C2×D5311yescharacteristic
378C22×C4⋊C4C2×D5312yes—
379C22×C4⋊C4C2×D5311yescharacteristic
380C22×C42—531no—
381C22×C42—532no—
382C22×C42—531no—
383C22×C42C2×D5311yescharacteristic
384#389—24no—
385#389—1064no—
386#389—1064no—
387#389—1064no—
388#384—1064no—
389#384—1068no—
390C4×C4⋊C4—538no—
391C4×C4⋊C4—1064no—
392C2×#95—532no—
393C2×#95—532no—
394C2×#95—532no—
395C2×#95—532no—
396C2×#95—531no—
397C2×#95—531no—
398C2×#95C2×D5312yes—
399C53#1391011yescharacteristic, complemented, Sylow
400C23×C4—531no—
401C23×C4—532no—
402C23×C4—531no—
403C23×C4—531no—
404C23×C4—531no—
405C23×C4—532no—
406C23×C4C22×D5312yes—
407C23×C4C22×D5311yescharacteristic
408C23×C4C22×D5311yescharacteristic
409C23×C4C22×D5312yes—
410C23×C4C22×D5311yescharacteristic
411C2×C4⋊C4—24no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—534no—
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—1064no—
427C2×C4⋊C4—1064no—
428C2×C4⋊C4—1064no—
429C2×C4⋊C4—1064no—
430C2×C4⋊C4—1064no—
431C2×C4⋊C4—1064no—
432C2×C4⋊C4—1064no—
433C2×C4⋊C4—1064no—
434C2×C4⋊C4—1064no—
435C2×C4⋊C4—1062no—
436C2×C4⋊C4—1062no—
437C2×C4⋊C4—1064no—
438C2×C4⋊C4—1062no—
439C2×C4⋊C4—2122no—
440C2×C4⋊C4—2122no—
441C2×C4⋊C4—2122no—
442C2×C4⋊C4—2122no—
443C2×C4⋊C4—2122no—
444C2×C4⋊C4Dic10614yes—
445C2×C4⋊C4C4×D5314yes—
446C2×C4⋊C4C22⋊D5314yes—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—534no—
451C2×C42—534no—
452C2×C42—534no—
453C2×C42—538no—
454C2×C42—1064no—
455C2×C42—1064no—
456C2×C42—1062no—
457C2×C42—1062no—
458C2×C42—1062no—
459#95—24no—
460#95—538no—
461#95—1062no—
462#95—1062no—
463#95—1064no—
464#95—1064no—
465#95—1064no—
466C24C23×D5311yescharacteristic
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
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—532no—
500C22×C4—534no—
501C22×C4—532no—
502C22×C4—534no—
503C22×C4—532no—
504C22×C4—532no—
505C22×C4—1062no—
506C22×C4—1062no—
507C22×C4—1061no—
508C22×C4—1062no—
509C22×C4—1061no—
510C22×C4—1061no—
511C22×C4—1062no—
512C22×C4—1061no—
513C22×C4—1061no—
514C22×C4—1061no—
515C22×C4—1061no—
516C22×C4—1061no—
517C22×C4—1061no—
518C22×C4—1061no—
519C22×C4—1061no—
520C22×C4—1061no—
521C22×C4—1061no—
522C22×C4—1061no—
523C22×C4—1061no—
524C22×C4—1061no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4C2×Dic10614yes—
533C22×C4C2×Dic10612yes—
534C22×C4C2×C4×D5314yes—
535C22×C4C2×C4×D5312yes—
536C22×C4D4×D5312yes—
537C22×C4D4×D5312yes—
538C22×C4D4×D5312yes—
539C22×C4Q8×D5312yes—
540C22×C4Q8×D5312yes—
541C22×C4Q8×D5312yes—
542C22×C4C2×C22⋊D5314yes—
543C22×C4C2×C22⋊D5312yes—
544C4⋊C4—48no—
545C4⋊C4—44no—
546C4⋊C4—5316no—
547C4⋊C4—1068no—
548C4⋊C4—1068no—
549C4⋊C4—2128no—
550C4⋊C4—2128no—
551C4⋊C4—2128no—
552C4⋊C4—2128no—
553C4⋊C4—2128no—
554C4⋊C4—2124no—
555C4⋊C4#11719919116yescomplemented
556C42—44no—
557C42—5316no—
558C42—10616no—
559C42—2124no—
560C23C22×C4×D5311yescharacteristic
561C23C2×D4×D5311yescharacteristic
562C23C2×D4×D5311yescharacteristic
563C23C2×D4×D5311yescharacteristic
564C23C22×C22⋊D5311yescharacteristic
565C23C2×Q8×D5311yescharacteristic
566C23C2×Q8×D5311yescharacteristic
567C23C2×Q8×D5311yescharacteristic
568C23C22×Dic10611yescharacteristic
569C23#41×D5311yescharacteristic
570C23#41×D5311yescharacteristic
571C23#1313326211yescharacteristic
572C23#1313326311yescharacteristic
573C23#1313326411yescharacteristic
574C23#1313326511yescharacteristic
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—534no—
603C2×C4—534no—
604C2×C4—534no—
605C2×C4—534no—
606C2×C4—534no—
607C2×C4—534no—
608C2×C4—534no—
609C2×C4—534no—
610C2×C4—538no—
611C2×C4—1064no—
612C2×C4—1064no—
613C2×C4—1064no—
614C2×C4—1064no—
615C2×C4—1062no—
616C2×C4—1062no—
617C2×C4—1064no—
618C2×C4—1062no—
619C2×C4—1062no—
620C2×C4—1062no—
621C2×C4—1062no—
622C2×C4—1064no—
623C2×C4—1062no—
624C2×C4—1062no—
625C2×C4—1062no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—1062no—
629C2×C4—2122no—
630C2×C4—2122no—
631C2×C4—2122no—
632C2×C4—2122no—
633C2×C4—2122no—
634C2×C4—2122no—
635C2×C4—2122no—
636C2×C4—2121no—
637C2×C4—2121no—
638C2×C4—2121no—
639C2×C4—2121no—
640C2×C4—2121no—
641C2×C4—2121no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4C4⋊C4×D5314yes—
645C2×C4C4⋊C4×D5314yes—
646C2×C4C2×#1171991918yes—
647C2×C4C2×#1171991914yes—
648C2×C4#1313321314yes—
649C2×C4#1313321514yes—
650C2×C4#1313321614yes—
651C2×C4#1313321614yes—
652C22C2×C4⋊C4×D5311yescharacteristic
653C22C2×C4⋊C4×D5311yescharacteristic
654C22C22×#1171991911yescharacteristic
655C22C4×D4×D5311yescharacteristic
656C22C4×Q8×D5311yescharacteristic
657C22#1681110211yescharacteristic
658C22#1681110511yescharacteristic
659C22#121×D5311yescharacteristic
660C22C22⋊Q8×D5311yescharacteristic
661C22#125×D5311yescharacteristic
662C22C2×#1313321311yescharacteristic
663C22C4⋊Q8×D5311yescharacteristic
664C22C2×#1313321511yescharacteristic
665C22C2×#1313321611yescharacteristic
666C22C2×#1313321611yescharacteristic
667C22#1681118911yescharacteristic
668C22#1681119611yescharacteristic
669C22#1681125011yescharacteristic
670C22#1681125311yescharacteristic
671C22D4×C22⋊D5311yescharacteristic
672C22#1681125711yescharacteristic
673C22#1681127211yescharacteristic
674C22#1681127511yescharacteristic
675C22#1681128611yescharacteristic
676C22Q8×C22⋊D5311yescharacteristic
677C22#1681128811yescharacteristic
678C22D4×Dic10611yescharacteristic
679C22#1681129111yescharacteristic
680C22#1681129211yescharacteristic
681C22#1681132911yescharacteristic
682C22#1681133211yescharacteristic
683C22#1681134911yescharacteristic
684C22#1681135011yescharacteristic
685C22#1681135311yescharacteristic
686C22Q8×Dic10611yescharacteristic
687C4—28no—
688C4—42no—
689C4—42no—
690C4—82no—
691C4—538no—
692C4—1064no—
693C4—1068no—
694C4—4242no—
695C4—2122no—
696C4—2122no—
697C4#1681049218yescomplemented
698C2C2×#1681049211yescharacteristic
699C2#389×D5311yescharacteristic
700C2#2027733711yescharacteristic
701C2D4×#1171991911yescharacteristic
702C2#2027761611yescharacteristic
703C2Q8×#1171991911yescharacteristic
704C2#2027762911yescharacteristic
705C2#2027965811yescharacteristic
706C2#2027966511yescharacteristic
707C2#2027970211yescharacteristic
708C2#2027974211yescharacteristic
709C2#2027974311yescharacteristic
710C2#2027974711yescharacteristic
711C2#2027975211yescharacteristic
712C2#2027992211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#389C2
socle, prime radical, cosocleC24×C53C24
hypercenterC2×#389D53
hypocenterC53#13910
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
29. C4⋊C4×Dic53C4semidirect
189. C4⋊C4×C53C4⋊C4semidirect
193. C4⋊Dic53C4⋊C4semidirect
202. C4×Dic53C4⋊C4semidirect
335. C4×C53#384semidirect
341. Dic53#389semidirect
399. C53#13910semidirect
555. C4⋊C4#11719919semidirect
697. C4#16810492semidirect

Maximal subgroups

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

subgroupindex
C2×#168105222
C2×#168105212
C2×#168105192
C2×#168104922
C2×C4⋊C4×Dic532
C2×C4×#117199192
#202729792
#202729782
#202729432
C2×C53×#3892
#1391053