Finite Group Databasebeta

← #27320670

Subgroups — #27320670

Order 13568.

1822 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133216C211yesmaximal, characteristic
2C2×#16810543C212yesmaximal
3C2×#16810521C211yesmaximal, characteristic
4C2×C4×#11719919C211yesmaximal, characteristic
5#20272985C212yesmaximal
6#20272978C212yesmaximal
7#20272966C212yesmaximal
8#20272944C211yesmaximal, characteristic
9#20272944C211yesmaximal, characteristic
10#20272944C211yesmaximal, characteristic
11C2×C53×#389C211yesmaximal, characteristic
12C23×Dic106C2212yes—
13C2×#13133216—24no—
14C2×#13133216—24no—
15C2×#13133216—24no—
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2212yes—
19C22×#11719919C2212yes—
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24#16810543—28no—
25#16810521—24no—
26C4×#11719919—24no—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C22×C4⋊C4×C53C2212yes—
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C53×#389—24no—
41C2×#95×C53C2212yes—
42C22×Dic106—24no—
43C22×Dic106—24no—
44C22×Dic106—24no—
45C22×Dic106—24no—
46C22×Dic106—24no—
47C22×Dic106—42no—
48C22×Dic106—42no—
49C23×Dic53C2312yes—
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2312yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2311yescharacteristic
55#13133216—232no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—22no—
59C2×C4⋊Dic53—22no—
60C2×C4⋊Dic53D414yes—
61C2×C4⋊Dic53Q814yescomplemented
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919—24no—
65C2×#11719919—24no—
66C2×#11719919—22no—
67C2×#11719919—22no—
68C2×#11719919—24no—
69C2×#11719919—22no—
70C2×#11719919—22no—
71C2×#11719919—42no—
72C2×#11719919D414yes—
73C2×#11719919Q814yescomplemented
74C2×C4×Dic53—22no—
75C2×C4×Dic53—22no—
76C2×C4×Dic53—22no—
77C2×C4×Dic53—22no—
78C2×C4×Dic53D414yes—
79C2×C4×Dic53Q814yescomplemented
80#13133124—24no—
81#13133124—24no—
82#13133124—24no—
83#13133124—24no—
84#13133124—22no—
85#13133124—22no—
86#13133124—24no—
87#13133124—42no—
88#13133124—42no—
89C23×C4×C53C2311yescharacteristic
90C23×C4×C53C2312yes—
91C23×C4×C53C2311yescharacteristic
92C23×C4×C53C2312yes—
93C23×C4×C53C2311yescharacteristic
94C2×C4⋊C4×C53—22no—
95C2×C4⋊C4×C53—22no—
96C2×C4⋊C4×C53—22no—
97C2×C4⋊C4×C53—24no—
98C2×C4⋊C4×C53—24no—
99C2×C4⋊C4×C53—22no—
100C2×C4⋊C4×C53—42no—
101C2×C4⋊C4×C53D414yes—
102C2×C4⋊C4×C53Q814yescomplemented
103C2×C42×C53—22no—
104C2×C42×C53—22no—
105C2×C42×C53—22no—
106#95×C53—24no—
107C24×C53C2411yescharacteristic
108C22×C4×C53—21no—
109C22×C4×C53—22no—
110C22×C4×C53—21no—
111C22×C4×C53—21no—
112C22×C4×C53—21no—
113C22×C4×C53—21no—
114C22×C4×C53—21no—
115C22×C4×C53—22no—
116C22×C4×C53—22no—
117C22×C4×C53—22no—
118C22×C4×C53—22no—
119C22×C4×C53—22no—
120C22×C4×C53—22no—
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—22no—
124C22×C4×C53—21no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—22no—
132C22×C4×C53C2×D412yes—
133C22×C4×C53C2×D414yes—
134C22×C4×C53C2×D412yes—
135C22×C4×C53C2×D412yes—
136C22×C4×C53C2×D412yes—
137C22×C4×C53C2×Q814yes—
138C22×C4×C53C2×Q812yes—
139C22×C4×C53C2×Q812yes—
140C22×C4×C53C2×Q812yes—
141C22×C4×C53C2×Q812yes—
142C22×C4×C53#4112yes—
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—21no—
152C22×Dic53—21no—
153C22×Dic53—21no—
154C22×Dic53—21no—
155C22×Dic53—21no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—21no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—22no—
173C22×Dic53C2×D414yes—
174C22×Dic53C2×D412yes—
175C22×Dic53C2×D412yes—
176C22×Dic53C2×D412yes—
177C22×Dic53C2×D412yes—
178C22×Dic53C2×Q812yes—
179C22×Dic53C2×Q814yes—
180C22×Dic53C2×Q812yes—
181C22×Dic53C2×Q812yes—
182C22×Dic53C2×Q812yes—
183C22×Dic53#4112yes—
184C22×Dic53#4112yes—
185C2×Dic106—216no—
186C2×Dic106—48no—
187C2×Dic106—48no—
188C2×Dic106—48no—
189C2×Dic106—48no—
190C2×Dic106—48no—
191C2×Dic106—48no—
192C4⋊C4×C53—28no—
193C4⋊C4×C53—28no—
194C4⋊C4×C53—48no—
195C42×C53—44no—
196C4⋊Dic53—28no—
197C4⋊Dic53—28no—
198#11719919—216no—
199#11719919—28no—
200#11719919—28no—
201#11719919—48no—
202C4×Dic53—28no—
203C4×Dic53—28no—
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×C53C2×#4111yescharacteristic
215C23×C53H(5,𝔽2)11yescharacteristic
216C23×C53H(5,𝔽2)11yescharacteristic
217C23×C532−1+411yescharacteristic
218C23×C532−1+411yescharacteristic
219C2×C4×C53—24no—
220C2×C4×C53—22no—
221C2×C4×C53—22no—
222C2×C4×C53—24no—
223C2×C4×C53—24no—
224C2×C4×C53—22no—
225C2×C4×C53—22no—
226C2×C4×C53—24no—
227C2×C4×C53—22no—
228C2×C4×C53—22no—
229C2×C4×C53—24no—
230C2×C4×C53—24no—
231C2×C4×C53—41no—
232C2×C4×C53—41no—
233C2×C4×C53—42no—
234C2×C4×C53—42no—
235C2×C4×C53—42no—
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—41no—
243C2×C4×C53—41no—
244C2×C4×C53—41no—
245C2×C4×C53—42no—
246C2×C4×C53—41no—
247C2×C4×C53#12014yes—
248C2×C4×C53C22⋊Q814yes—
249C2×C4×C53C22⋊Q814yes—
250C2×C4×C53C22⋊Q814yes—
251C2×C4×C53C4⋊Q814yes—
252C2×C4×C53C4⋊Q814yes—
253C2×C4×C53C4⋊Q814yes—
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—22no—
271C2×Dic53—22no—
272C2×Dic53—24no—
273C2×Dic53—22no—
274C2×Dic53—24no—
275C2×Dic53—22no—
276C2×Dic53—22no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—24no—
280C2×Dic53—24no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—41no—
285C2×Dic53—41no—
286C2×Dic53—41no—
287C2×Dic53—41no—
288C2×Dic53—42no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53#12114yes—
294C2×Dic53C22⋊Q814yes—
295C2×Dic53C4⋊Q814yescomplemented
296Dic106—432no—
297#15128—531nomaximal, Sylow
298C22×C53C2×#12011yescharacteristic
299C22×C53C2×#12111yescharacteristic
300C22×C53C2×C22⋊Q811yescharacteristic
301C22×C53C2×C22⋊Q811yescharacteristic
302C22×C53C2×C22⋊Q811yescharacteristic
303C22×C53C2×C22⋊Q811yescharacteristic
304C22×C53C2×C4⋊Q811yescharacteristic
305C22×C53C2×C4⋊Q811yescharacteristic
306C22×C53C2×C4⋊Q811yescharacteristic
307C22×C53C2×C4⋊Q811yescharacteristic
308C22×C53#53211yescharacteristic
309C22×C53#53311yescharacteristic
310C22×C53#53311yescharacteristic
311C22×C53#53511yescharacteristic
312C22×C53#53611yescharacteristic
313C22×C53#54211yescharacteristic
314C22×C53#54211yescharacteristic
315C22×C53#54411yescharacteristic
316C22×C53#54411yescharacteristic
317C22×C53D4211yescharacteristic
318C22×C53D4211yescharacteristic
319C22×C53#54611yescharacteristic
320C22×C53#54611yescharacteristic
321C22×C53#54811yescharacteristic
322C22×C53#54811yescharacteristic
323C22×C53D4×Q811yescharacteristic
324C22×C53D4×Q811yescharacteristic
325C22×C53D4×Q811yescharacteristic
326C22×C53D4×Q811yescharacteristic
327C22×C53#55411yescharacteristic
328C22×C53#55411yescharacteristic
329C22×C53#55711yescharacteristic
330C22×C53#55711yescharacteristic
331C22×C53Q8211yescharacteristic
332C22×C53Q8211yescharacteristic
333C4×C53—44no—
334C4×C53—42no—
335C4×C53—42no—
336C4×C53—44no—
337C4×C53#39518yescomplemented
338Dic53—24no—
339Dic53—24no—
340Dic53—24no—
341Dic53—42no—
342Dic53—44no—
343Dic53—44no—
344C22×C4⋊Q8—531no—
345C2×#395—532no—
346C2×#389—531no—
347C2×#389D5311yescharacteristic
348C2×C4×C4⋊C4—531no—
349#1446—532no—
350#1444—532no—
351#1441—532no—
352C4⋊#95—531no—
353C4⋊#95—531no—
354C4⋊#95—531no—
355C2×C53C2×#39511yescharacteristic
356C2×C53#240811yescharacteristic
357C2×C53#240911yescharacteristic
358C2×C53#245111yescharacteristic
359C2×C53#245111yescharacteristic
360C2×C53#245211yescharacteristic
361C2×C53#245211yescharacteristic
362C2×C53#254611yescharacteristic
363C2×C53#255011yescharacteristic
364C2×C53#255011yescharacteristic
365C2×C53#255111yescharacteristic
366C2×C53#255111yescharacteristic
367C2×C53#256711yescharacteristic
368C2×C53#262811yescharacteristic
369C2×C53#285711yescharacteristic
370C23×Q8—532no—
371C2×C4⋊Q8—1064no—
372C2×C4⋊Q8—1064no—
373C2×C4⋊Q8—1064no—
374C22×C4⋊C4—531no—
375C22×C4⋊C4—531no—
376C22×C4⋊C4—531no—
377C22×C4⋊C4—531no—
378C22×C4⋊C4—532no—
379C22×C4⋊C4—532no—
380C22×C4⋊C4C2×D5312yes—
381C22×C4⋊C4C2×D5311yescharacteristic
382C22×C4⋊C4C2×D5311yescharacteristic
383C22×C42—531no—
384C22×C42—531no—
385C22×C42C2×D5311yescharacteristic
386#395—1068no—
387#389—24no—
388#389—1064no—
389C4×C4⋊C4—1064no—
390C2×#95—532no—
391C2×#95—532no—
392C2×#95—532no—
393C2×#95—532no—
394C2×#95—532no—
395C2×#95—531no—
396C2×#95—531no—
397C2×#95—532no—
398C2×#95—532no—
399C2×#95C2×D5312yes—
400C53#1512811yescharacteristic, complemented, Sylow
401C22×Q8—1064no—
402C22×Q8—1064no—
403C22×Q8—1064no—
404C22×Q8—1064no—
405C22×Q8—1064no—
406C22×Q8—2122no—
407C22×Q8—2122no—
408C23×C4—531no—
409C23×C4—531no—
410C23×C4—531no—
411C23×C4—532no—
412C23×C4—532no—
413C23×C4—531no—
414C23×C4C22×D5312yes—
415C23×C4C22×D5311yescharacteristic
416C23×C4C22×D5311yescharacteristic
417C23×C4C22×D5312yes—
418C23×C4C22×D5311yescharacteristic
419C4⋊Q8—10632no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—24no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—534no—
428C2×C4⋊C4—534no—
429C2×C4⋊C4—534no—
430C2×C4⋊C4—534no—
431C2×C4⋊C4—1064no—
432C2×C4⋊C4—1064no—
433C2×C4⋊C4—1062no—
434C2×C4⋊C4—1062no—
435C2×C4⋊C4—1062no—
436C2×C4⋊C4—1062no—
437C2×C4⋊C4—1062no—
438C2×C4⋊C4—1062no—
439C2×C4⋊C4—1062no—
440C2×C4⋊C4—1064no—
441C2×C4⋊C4—1062no—
442C2×C4⋊C4—1064no—
443C2×C4⋊C4—1064no—
444C2×C4⋊C4—2122no—
445C2×C4⋊C4Dic10614yescomplemented
446C2×C4⋊C4C22⋊D5314yes—
447C2×C42—22no—
448C2×C42—22no—
449C2×C42—22no—
450C2×C42—534no—
451C2×C42—534no—
452C2×C42—1062no—
453C2×C42—1062no—
454C2×C42—1062no—
455C2×C42—1062no—
456#95—24no—
457#95—1064no—
458#95—1062no—
459#95—1062no—
460#95—1064no—
461#95—1064no—
462#95—1064no—
463#95—1064no—
464#95—2122no—
465#95—2122no—
466C24C23×D5311yescharacteristic
467C2×Q8—10616no—
468C2×Q8—2128no—
469C2×Q8—2128no—
470C2×Q8—2128no—
471C2×Q8—2128no—
472C2×Q8—2128no—
473C2×Q8—2128no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—532no—
499C22×C4—532no—
500C22×C4—532no—
501C22×C4—532no—
502C22×C4—532no—
503C22×C4—532no—
504C22×C4—532no—
505C22×C4—532no—
506C22×C4—532no—
507C22×C4—534no—
508C22×C4—532no—
509C22×C4—534no—
510C22×C4—1061no—
511C22×C4—1061no—
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—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1061no—
531C22×C4—1062no—
532C22×C4—1061no—
533C22×C4—1062no—
534C22×C4—1061no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1061no—
538C22×C4—1062no—
539C22×C4—1061no—
540C22×C4C2×Dic10614yes—
541C22×C4C2×Dic10612yes—
542C22×C4#1171994512yes—
543C22×C4D4×D5312yes—
544C22×C4D4×D5312yes—
545C22×C4D4×D5312yes—
546C22×C4Q8×D5312yes—
547C22×C4Q8×D5312yes—
548C22×C4Q8×D5312yes—
549C22×C4C2×C22⋊D5314yes—
550C22×C4C2×C22⋊D5312yes—
551C4⋊C4—28no—
552C4⋊C4—28no—
553C4⋊C4—48no—
554C4⋊C4—1068no—
555C4⋊C4—1068no—
556C4⋊C4—10616no—
557C4⋊C4—1068no—
558C4⋊C4—1068no—
559C4⋊C4—2128no—
560C42—44no—
561C42—1068no—
562C42—1068no—
563C23C2×D4×D5311yescharacteristic
564C23C2×D4×D5311yescharacteristic
565C23C2×D4×D5311yescharacteristic
566C23C22×C22⋊D5311yescharacteristic
567C23C2×Q8×D5311yescharacteristic
568C23C2×Q8×D5311yescharacteristic
569C23C2×Q8×D5311yescharacteristic
570C23C22×Dic10611yescharacteristic
571C23#41×D5311yescharacteristic
572C23#41×D5311yescharacteristic
573C23C2×#1171994511yescharacteristic
574C23#1313326211yescharacteristic
575C23#1313326311yescharacteristic
576C23#1313326411yescharacteristic
577C23#1313326511yescharacteristic
578Q8—21232no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—24no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—41no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—534no—
608C2×C4—534no—
609C2×C4—534no—
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—1062no—
619C2×C4—1062no—
620C2×C4—1062no—
621C2×C4—1062no—
622C2×C4—1062no—
623C2×C4—1062no—
624C2×C4—1062no—
625C2×C4—1062no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—1064no—
629C2×C4—1064no—
630C2×C4—1064no—
631C2×C4—1064no—
632C2×C4—1062no—
633C2×C4—1064no—
634C2×C4—1062no—
635C2×C4—1062no—
636C2×C4—1064no—
637C2×C4—2122no—
638C2×C4—2122no—
639C2×C4—2122no—
640C2×C4—2121no—
641C2×C4—2122no—
642C2×C4—2121no—
643C2×C4—2121no—
644C2×C4—2122no—
645C2×C4—2121no—
646C2×C4—2122no—
647C2×C4—2122no—
648C2×C4—2122no—
649C2×C4#1313318514yes—
650C2×C4#1313319514yes—
651C2×C4#1313319514yes—
652C2×C4#1313319614yes—
653C2×C4#1313321514yes—
654C2×C4#1313321614yes—
655C2×C4#1313321614yes—
656C22C2×#1313318511yescharacteristic
657C22#121×D5311yescharacteristic
658C22C22⋊Q8×D5311yescharacteristic
659C22C2×#1313319511yescharacteristic
660C22C2×#1313319511yescharacteristic
661C22C2×#1313319611yescharacteristic
662C22C4⋊Q8×D5311yescharacteristic
663C22C2×#1313321511yescharacteristic
664C22C2×#1313321611yescharacteristic
665C22C2×#1313321611yescharacteristic
666C22#1681117011yescharacteristic
667C22#1681117711yescharacteristic
668C22#1681117911yescharacteristic
669C22#1681118911yescharacteristic
670C22#1681119611yescharacteristic
671C22#1681123811yescharacteristic
672C22#1681124511yescharacteristic
673C22#1681125011yescharacteristic
674C22#1681125311yescharacteristic
675C22D4×C22⋊D5311yescharacteristic
676C22#1681125711yescharacteristic
677C22#1681126111yescharacteristic
678C22#1681127011yescharacteristic
679C22#1681128011yescharacteristic
680C22#1681128311yescharacteristic
681C22#1681128611yescharacteristic
682C22Q8×C22⋊D5311yescharacteristic
683C22#1681128811yescharacteristic
684C22D4×Dic10611yescharacteristic
685C22#1681132911yescharacteristic
686C22#1681133211yescharacteristic
687C22#1681134911yescharacteristic
688C22#1681135011yescharacteristic
689C22#1681135311yescharacteristic
690C22Q8×Dic10611yescharacteristic
691C4—44no—
692C4—42no—
693C4—44no—
694C4—42no—
695C4—1064no—
696C4—1064no—
697C4—1064no—
698C4—2124no—
699C4—2124no—
700C4—2122no—
701C4#1681054318yescomplemented
702C2C2×#1681054311yescharacteristic
703C2#2027806711yescharacteristic
704C2#2027807611yescharacteristic
705C2#2027854811yescharacteristic
706C2#2027855511yescharacteristic
707C2#2027855911yescharacteristic
708C2#2027856611yescharacteristic
709C2#2027970211yescharacteristic
710C2#2027973411yescharacteristic
711C2#2027973911yescharacteristic
712C2#2027974211yescharacteristic
713C2#2027974311yescharacteristic
714C2#2027992211yescharacteristic
715C2#2028054211yescharacteristic
716C2#2028306611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, prime radical, cosocleC24×C53C24
FittingC2×C53×#389C2
hypercenterC2×#389D53
hypocenterC53#15128
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
61. C2×C4⋊Dic53Q8semidirect
73. C2×#11719919Q8semidirect
79. C2×C4×Dic53Q8semidirect
102. C2×C4⋊C4×C53Q8semidirect
295. C2×Dic53C4⋊Q8semidirect
337. C4×C53#395semidirect
400. C53#15128semidirect
445. C2×C4⋊C4Dic106semidirect
701. C4#16810543semidirect

Maximal subgroups

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

subgroupindex
C22×#131332162
C2×#168105432
C2×#168105212
C2×C4×#117199192
#202729852
#202729782
#202729662
#202729442
C2×C53×#3892
#1512853