Finite Group Databasebeta

← #27320643

Subgroups — #27320643

Order 13568.

2038 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133216C211yesmaximal, characteristic, complemented
2C2×#16810535C212yesmaximal
3C2×#16810483C211yesmaximal, characteristic
4C2×C4×C22⋊Dic53C211yesmaximal, characteristic
5#20272985C212yesmaximal, complemented
6#20272973C212yesmaximal, complemented
7#20272958C212yesmaximal
8#20272944C211yesmaximal, characteristic, complemented
9#20272944C211yesmaximal, characteristic, complemented
10#20272944C211yesmaximal, characteristic, complemented
11C2×C53×#380C211yesmaximal, characteristic
12C23×Dic106C2212yes—
13C2×#13133216—24no—
14C2×#13133216—24no—
15C2×#13133216—24no—
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2212yes—
19C22×C22⋊Dic53C2212yes—
20C22×C22⋊Dic53C2211yescharacteristic
21C22×C22⋊Dic53C2211yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24#16810535—28no—
25#16810483—24no—
26C4×C22⋊Dic53—24no—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C24×C4×C53C2211yescharacteristic
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2212yes—
40C53×#380—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⋊Dic53—22no—
61C2×C4⋊Dic53D414yes—
62C2×#11719919—24no—
63C2×#11719919—24no—
64C2×#11719919—24no—
65C2×C22⋊Dic53—24no—
66C2×C22⋊Dic53—22no—
67C2×C22⋊Dic53—22no—
68C2×C22⋊Dic53—24no—
69C2×C22⋊Dic53—22no—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—42no—
72C2×C22⋊Dic53D414yes—
73C2×C22⋊Dic53Q814yescomplemented
74C2×C4×Dic53—22no—
75C2×C4×Dic53—22no—
76C2×C4×Dic53—22no—
77C2×C4×Dic53—22no—
78C2×C4×Dic53—22no—
79C2×C4×Dic53D414yes—
80#13133124—24no—
81#13133124—24no—
82#13133124—24no—
83#13133124—22no—
84#13133124—22no—
85#13133124—24no—
86#13133124—24no—
87#13133124—42no—
88#13133124—42no—
89C25×C53C2311yescharacteristic
90C23×C4×C53—22no—
91C23×C4×C53—22no—
92C23×C4×C53—22no—
93C23×C4×C53—22no—
94C23×C4×C53—22no—
95C23×C4×C53—22no—
96C23×C4×C53Q814yescomplemented
97C23×C4×C53C2312yes—
98C23×C4×C53C2312yes—
99C23×C4×C53C2311yescharacteristic
100C23×C4×C53C2311yescharacteristic
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53—22no—
106C2×C4⋊C4×C53D414yes—
107C2×C22⋊C4×C53—24no—
108C2×C22⋊C4×C53—24no—
109C2×C22⋊C4×C53—42no—
110#95×C53—24no—
111C24×C53—21no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53—21no—
115C24×C53—21no—
116C24×C53—21no—
117C24×C53—21no—
118C24×C53—21no—
119C24×C53—21no—
120C24×C53—21no—
121C24×C53—21no—
122C24×C53—21no—
123C24×C53C2×D412yes—
124C24×C53C2×Q812yes—
125C24×C53C2×Q812yes—
126C24×C53C2411yescharacteristic
127C22×C4×C53—21no—
128C22×C4×C53—22no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
131C22×C4×C53—21no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—28no—
140C22×C4×C53—28no—
141C22×C4×C53—28no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—44no—
150C22×C4×C53—44no—
151C22×C4×C53—44no—
152C22×C4×C53—44no—
153C22×C4×C53C2×D414yes—
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×Q812yes—
158C22×C4×C53C2×Q812yes—
159C22×C4×C53#4112yes—
160C22×C4×C53#4112yes—
161C22×C4×C53#4112yes—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—21no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—22no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—22no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53C2×D412yes—
196C22×Dic53C2×D414yes—
197C22×Dic53C2×D412yes—
198C22×Dic53C2×D412yes—
199C22×Dic53C2×D412yes—
200C22×Dic53C2×Q812yes—
201C22×Dic53C2×Q812yes—
202C22×Dic53#4112yes—
203C22×Dic53#4112yes—
204C2×Dic106—216no—
205C2×Dic106—48no—
206C2×Dic106—48no—
207C2×Dic106—48no—
208C2×Dic106—48no—
209C2×Dic106—48no—
210C2×Dic106—48no—
211C4⋊C4×C53—28no—
212C4⋊C4×C53—44no—
213C22⋊C4×C53—48no—
214C22⋊Dic53—28no—
215C22⋊Dic53—28no—
216C22⋊Dic53—48no—
217C4⋊Dic53—28no—
218C4⋊Dic53—44no—
219#11719919—216no—
220C4×Dic53—28no—
221C4×Dic53—44no—
222C23×C53—22no—
223C23×C53—22no—
224C23×C53—22no—
225C23×C53—22no—
226C23×C53—22no—
227C23×C53—22no—
228C23×C53—22no—
229C23×C53—22no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—22no—
233C23×C53—22no—
234C23×C53—22no—
235C23×C53—22no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—41no—
241C23×C53—41no—
242C23×C53—41no—
243C23×C53—41no—
244C23×C53—41no—
245C23×C53—41no—
246C23×C53—41no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53C4⋊Q814yescomplemented
257C23×C53C22×D411yescharacteristic
258C23×C53C22×D411yescharacteristic
259C23×C53C22×D411yescharacteristic
260C23×C53C22×D411yescharacteristic
261C23×C53C22×Q811yescharacteristic
262C23×C53C22×Q811yescharacteristic
263C23×C53C2×#4111yescharacteristic
264C23×C53C2×#4111yescharacteristic
265C23×C53C2×#4111yescharacteristic
266C23×C53C2×#4111yescharacteristic
267C23×C53C2×#4111yescharacteristic
268C23×C53H(5,𝔽2)11yescharacteristic
269C23×C53H(5,𝔽2)11yescharacteristic
270C23×C532−1+411yescharacteristic
271C23×C532−1+411yescharacteristic
272C2×C4×C53—24no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—41no—
279C2×C4×C53—42no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—42no—
284C2×C4×C53—42no—
285C2×C4×C53—42no—
286C2×C4×C53—416no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53#12014yes—
295C2×C4×C53C22⋊Q814yes—
296C2×C4×C53C22⋊Q814yes—
297C2×C4×C53C22⋊Q814yes—
298C2×C4×C53#12414yes—
299C2×C4×C53#12414yes—
300C2×C4×C53#12414yes—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—24no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—24no—
317C2×Dic53—24no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—42no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—42no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53#12114yes—
342C2×Dic53C22⋊Q814yes—
343Dic106—432no—
344#15125—531nomaximal, Sylow
345C22×C53—24no—
346C22×C53—24no—
347C22×C53—24no—
348C22×C53—42no—
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53C2×#12011yescharacteristic
361C22×C53C2×#12111yescharacteristic
362C22×C53C2×C22⋊Q811yescharacteristic
363C22×C53C2×C22⋊Q811yescharacteristic
364C22×C53C2×C22⋊Q811yescharacteristic
365C22×C53C2×C22⋊Q811yescharacteristic
366C22×C53C2×#12411yescharacteristic
367C22×C53C2×#12411yescharacteristic
368C22×C53C2×#12411yescharacteristic
369C22×C53C2×C4⋊Q811yescharacteristic
370C22×C53#53211yescharacteristic
371C22×C53#53311yescharacteristic
372C22×C53#53311yescharacteristic
373C22×C53#53511yescharacteristic
374C22×C53#53611yescharacteristic
375C22×C53#54211yescharacteristic
376C22×C53#54211yescharacteristic
377C22×C53#54411yescharacteristic
378C22×C53#54411yescharacteristic
379C22×C53D4211yescharacteristic
380C22×C53D4211yescharacteristic
381C22×C53#54611yescharacteristic
382C22×C53#54611yescharacteristic
383C22×C53#54711yescharacteristic
384C22×C53#54711yescharacteristic
385C22×C53#54811yescharacteristic
386C22×C53#54811yescharacteristic
387C22×C53D4×Q811yescharacteristic
388C22×C53D4×Q811yescharacteristic
389C22×C53#55411yescharacteristic
390C22×C53#55411yescharacteristic
391C22×C53#55511yescharacteristic
392C22×C53#55511yescharacteristic
393C22×C53#55611yescharacteristic
394C22×C53#55611yescharacteristic
395C4×C53—42no—
396C4×C53—44no—
397C4×C53—82no—
398C4×C53#39318yescomplemented
399Dic53—24no—
400Dic53—24no—
401Dic53—42no—
402Dic53—44no—
403Dic53—42no—
404Dic53—82no—
405C22×C4⋊Q8—531no—
406C2×#393—532no—
407C2×#380—531no—
408C2×#380D5311yescharacteristic
409C2×C4×C22⋊C4—531no—
410#1446—532no—
411#1442—532no—
412#1439—532no—
413C4⋊#95—531no—
414C4⋊#95—531no—
415C4⋊#95—531no—
416C2×C53—44no—
417C2×C53C2×#39311yescharacteristic
418C2×C53#240811yescharacteristic
419C2×C53#240911yescharacteristic
420C2×C53#243911yescharacteristic
421C2×C53#243911yescharacteristic
422C2×C53#244011yescharacteristic
423C2×C53#244011yescharacteristic
424C2×C53#249111yescharacteristic
425C2×C53#249111yescharacteristic
426C2×C53#249211yescharacteristic
427C2×C53#249211yescharacteristic
428C2×C53#254711yescharacteristic
429C2×C53#256311yescharacteristic
430C2×C53#262811yescharacteristic
431C2×C53#285711yescharacteristic
432C23×Q8—532no—
433C24×C4C2×D5311yescharacteristic
434C2×C4⋊Q8—1064no—
435C2×C4⋊Q8—1064no—
436C2×C4⋊Q8—1064no—
437C22×C4⋊C4—531no—
438C22×C4⋊C4—532no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4C2×D5311yescharacteristic
441C22×C4⋊C4C2×D5311yescharacteristic
442C22×C22⋊C4—531no—
443C22×C22⋊C4—531no—
444C22×C22⋊C4—532no—
445C22×C22⋊C4C2×D5312yes—
446C22×C42—531no—
447C22×C42—531no—
448#393—1068no—
449#380—24no—
450#380—1064no—
451C4×C22⋊C4—1064no—
452C2×#95—532no—
453C2×#95—532no—
454C2×#95—532no—
455C2×#95—532no—
456C2×#95—531no—
457C2×#95—532no—
458C2×#95—531no—
459C2×#95—532no—
460C2×#95—532no—
461C2×#95C2×D5312yes—
462C53#1512511yescharacteristic, complemented, Sylow
463C25C22×D5311yescharacteristic
464C22×Q8—1064no—
465C22×Q8—1064no—
466C22×Q8—1064no—
467C22×Q8—1064no—
468C22×Q8—1064no—
469C22×Q8—2122no—
470C22×Q8—2122no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—531no—
478C23×C4—531no—
479C23×C4—532no—
480C23×C4—531no—
481C23×C4—531no—
482C23×C4—532no—
483C23×C4Dic10614yescomplemented
484C23×C4C22×D5312yes—
485C23×C4C22×D5311yescharacteristic
486C23×C4C22×D5312yes—
487C23×C4C22×D5311yescharacteristic
488C4⋊Q8—10632no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—534no—
495C2×C4⋊C4—1064no—
496C2×C4⋊C4—1064no—
497C2×C4⋊C4—1062no—
498C2×C4⋊C4—1064no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1062no—
501C2×C4⋊C4—1062no—
502C2×C4⋊C4—1062no—
503C2×C4⋊C4C22⋊D5314yes—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—534no—
508C2×C22⋊C4—534no—
509C2×C22⋊C4—1062no—
510C2×C22⋊C4—1062no—
511C2×C22⋊C4—1062no—
512C2×C22⋊C4—1062no—
513C2×C22⋊C4—1064no—
514C2×C22⋊C4—1064no—
515C2×C22⋊C4—2122no—
516C2×C42—534no—
517C2×C42—1062no—
518C2×C42—1062no—
519C2×C42—1062no—
520C2×C42—1062no—
521C2×C42—1062no—
522#95—24no—
523#95—1064no—
524#95—1062no—
525#95—1062no—
526#95—1064no—
527#95—1064no—
528#95—1064no—
529#95—1064no—
530#95—2122no—
531#95—2122no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24C2×Dic10612yes—
545C24D4×D5312yes—
546C24Q8×D5312yes—
547C24C23×D5311yescharacteristic
548C2×Q8—10616no—
549C2×Q8—2128no—
550C2×Q8—2128no—
551C2×Q8—2128no—
552C2×Q8—2128no—
553C2×Q8—2128no—
554C2×Q8—2128no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—532no—
587C22×C4—532no—
588C22×C4—534no—
589C22×C4—532no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1062no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1062no—
612C22×C4—1061no—
613C22×C4—1062no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4C2×Dic10612yes—
624C22×C4C2×Dic10612yes—
625C22×C4#1171994512yes—
626C22×C4D4×D5312yes—
627C22×C4D4×D5312yes—
628C22×C4#1171994712yes—
629C22×C4#1171994712yes—
630C22×C4C2×C22⋊D5314yes—
631C22×C4C2×C22⋊D5312yes—
632C4⋊C4—28no—
633C4⋊C4—44no—
634C4⋊C4—10616no—
635C4⋊C4—1068no—
636C4⋊C4—2124no—
637C22⋊C4—48no—
638C22⋊C4—1068no—
639C22⋊C4—1068no—
640C22⋊C4—2128no—
641C42—1068no—
642C42—2124no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23#1313321614yescomplemented
678C23C2×D4×D5311yescharacteristic
679C23C2×D4×D5311yescharacteristic
680C23C2×D4×D5311yescharacteristic
681C23C22×C22⋊D5311yescharacteristic
682C23C2×Q8×D5311yescharacteristic
683C23C22×Dic10611yescharacteristic
684C23#41×D5311yescharacteristic
685C23#41×D5311yescharacteristic
686C23C2×#1171994711yescharacteristic
687C23C2×#1171994711yescharacteristic
688C23C2×#1171994511yescharacteristic
689C23#1313326211yescharacteristic
690C23#1313326311yescharacteristic
691C23#1313326411yescharacteristic
692C23#1313326511yescharacteristic
693Q8—21232no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—416no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—534no—
717C2×C4—534no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1064no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1064no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—1064no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2121no—
747C2×C4—2121no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2122no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2122no—
755C2×C4—2121no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4#1313318514yes—
759C2×C4#1313319414yes—
760C2×C4#1313319414yes—
761C2×C4#1313319614yes—
762C2×C4#1313320314yes—
763C2×C4#1313320314yes—
764C2×C4#1313320414yes—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22C2×#1313318511yescharacteristic
781C22#121×D5311yescharacteristic
782C22C22⋊Q8×D5311yescharacteristic
783C22C2×#1313319411yescharacteristic
784C22C2×#1313319411yescharacteristic
785C22C2×#1313319611yescharacteristic
786C22C2×#1313320311yescharacteristic
787C22C2×#1313320311yescharacteristic
788C22C2×#1313320411yescharacteristic
789C22C2×#1313321611yescharacteristic
790C22#1681116811yescharacteristic
791C22#1681117511yescharacteristic
792C22#1681117611yescharacteristic
793C22#1681118911yescharacteristic
794C22#1681119611yescharacteristic
795C22#1681124011yescharacteristic
796C22#1681124611yescharacteristic
797C22#1681125111yescharacteristic
798C22#1681125411yescharacteristic
799C22D4×C22⋊D5311yescharacteristic
800C22#1681125711yescharacteristic
801C22#1681126111yescharacteristic
802C22#1681127011yescharacteristic
803C22#1681127311yescharacteristic
804C22#1681127411yescharacteristic
805C22#1681128011yescharacteristic
806C22#1681128311yescharacteristic
807C22#1681128611yescharacteristic
808C22Q8×C22⋊D5311yescharacteristic
809C22#1681132811yescharacteristic
810C22#1681133111yescharacteristic
811C22#1681133611yescharacteristic
812C22#1681133711yescharacteristic
813C22#1681134111yescharacteristic
814C22#1681134411yescharacteristic
815C4—44no—
816C4—42no—
817C4—82no—
818C4—1064no—
819C4—1064no—
820C4—4242no—
821C4—2124no—
822C4—2122no—
823C4—2122no—
824C4#1681053518yescomplemented
825C2—44no—
826C2C2×#1681053511yescharacteristic
827C2#2027806711yescharacteristic
828C2#2027807611yescharacteristic
829C2#2027840011yescharacteristic
830C2#2027840711yescharacteristic
831C2#2027841111yescharacteristic
832C2#2027841811yescharacteristic
833C2#2027907411yescharacteristic
834C2#2027908011yescharacteristic
835C2#2027908511yescharacteristic
836C2#2027909111yescharacteristic
837C2#2027970911yescharacteristic
838C2#2027988511yescharacteristic
839C2#2028054011yescharacteristic
840C2#2028306511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC2×C53×#380C2
prime radicalC25×C53C23
hypercenterC2×#380D53
hypocenterC53#15125
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#13133216C2semidirect
5. #20272985C2semidirect
6. #20272973C2semidirect
8. #20272944C2semidirect
9. #20272944C2semidirect
10. #20272944C2semidirect
73. C2×C22⋊Dic53Q8semidirect
96. C23×C4×C53Q8semidirect
256. C23×C53C4⋊Q8semidirect
398. C4×C53#393semidirect
462. C53#15125semidirect
483. C23×C4Dic106semidirect
677. C23#13133216semidirect
824. C4#16810535semidirect

Maximal subgroups

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

subgroupindex
C22×#131332162
C2×#168105352
C2×#168104832
C2×C4×C22⋊Dic532
#202729852
#202729732
#202729582
#202729442
C2×C53×#3802
#1512553