Finite Group Databasebeta

← #27320645

Subgroups — #27320645

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×#16810536C212yesmaximal
3C2×#16810480C211yesmaximal, characteristic
4C2×#16810480C211yesmaximal, characteristic
5C2×C4×#11719921C211yesmaximal, characteristic
6#20272985C212yesmaximal, complemented
7#20272970C212yesmaximal, complemented
8#20272959C212yesmaximal
9#20272945C211yesmaximal, characteristic, complemented
10#20272944C211yesmaximal, characteristic, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×Dic106C2212yes—
13C23×C4×D53C2211yescharacteristic
14C2×#13133216—24no—
15C2×#13133216—24no—
16C2×#13133216—24no—
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×#11719921C2212yes—
21C22×#11719921C2212yes—
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25#16810536—28no—
26#16810480—24no—
27#16810480—24no—
28C4×#11719921—24no—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C2×#95×C53C2212yes—
42C24×D53C2311yescharacteristic
43C22×Dic106—24no—
44C22×Dic106—24no—
45C22×Dic106—24no—
46C22×Dic106—24no—
47C22×Dic106—24no—
48C22×Dic106—42no—
49C22×Dic106—42no—
50C23×Dic53C2312yes—
51C23×Dic53C2312yes—
52C23×Dic53C2311yescharacteristic
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2311yescharacteristic
55C22×C4×D53—22no—
56C22×C4×D53—22no—
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53Q814yescomplemented
62#13133216—232no—
63C2×C4⋊Dic53—22no—
64C2×C4⋊Dic53—22no—
65C2×C4⋊Dic53—22no—
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53D414yes—
69C2×#11719919—24no—
70C2×#11719919—24no—
71C2×#11719919—24no—
72C2×#11719921—24no—
73C2×#11719921—24no—
74C2×#11719921—24no—
75C2×#11719921—22no—
76C2×#11719921—22no—
77C2×#11719921—24no—
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—42no—
81C2×#11719921—42no—
82C2×#11719921D414yes—
83C2×#11719921Q814yescomplemented
84C2×C4×Dic53—22no—
85C2×C4×Dic53—22no—
86C2×C4×Dic53D414yes—
87#13133124—24no—
88#13133124—24no—
89#13133124—24no—
90#13133124—22no—
91#13133124—22no—
92#13133124—24no—
93#13133124—24no—
94#13133124—42no—
95C23×C4×C53C2312yes—
96C23×C4×C53C2311yescharacteristic
97C23×C4×C53C2312yes—
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2311yescharacteristic
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53D414yes—
106C2×C42×C53—22no—
107C2×C42×C53—22no—
108C2×C42×C53—22no—
109#95×C53—24no—
110#95×C53—42no—
111C24×C53C2411yescharacteristic
112C23×D53—21no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—21no—
117C23×D53—21no—
118C23×D53—21no—
119C23×D53—21no—
120C23×D53—21no—
121C23×D53—21no—
122C23×D53—21no—
123C23×D53—21no—
124C23×D53C2×D412yes—
125C23×D53C2×Q812yes—
126C23×D53C2×Q812yes—
127C22×C4×C53—22no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—22no—
131C22×C4×C53—22no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—21no—
136C22×C4×C53—21no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—21no—
140C22×C4×C53—22no—
141C22×C4×C53—21no—
142C22×C4×C53—22no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53C2×D414yes—
153C22×C4×C53C2×D412yes—
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—21no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53C2×D414yes—
190C22×Dic53C2×D412yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×D412yes—
193C22×Dic53C2×Q812yes—
194C22×Dic53C2×Q812yes—
195C22×Dic53#4112yes—
196C22×Dic53#4112yes—
197C2×C4×D53—28no—
198C2×C4×D53—28no—
199C2×C4×D53—28no—
200C2×C4×D53—44no—
201C2×C4×D53—44no—
202C2×C4×D53—44no—
203C2×C4×D53—44no—
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—
213C42×C53—44no—
214#11719921—28no—
215#11719921—28no—
216#11719921—48no—
217#11719921—48no—
218C4⋊Dic53—28no—
219C4⋊Dic53—44no—
220#11719919—216no—
221C4×Dic53—28no—
222C23×C53C22×D411yescharacteristic
223C23×C53C22×D411yescharacteristic
224C23×C53C22×D411yescharacteristic
225C23×C53C22×D411yescharacteristic
226C23×C53C22×Q811yescharacteristic
227C23×C53C22×Q811yescharacteristic
228C23×C53C2×#4111yescharacteristic
229C23×C53C2×#4111yescharacteristic
230C23×C53C2×#4111yescharacteristic
231C23×C53C2×#4111yescharacteristic
232C23×C53C2×#4111yescharacteristic
233C23×C53H(5,𝔽2)11yescharacteristic
234C23×C53H(5,𝔽2)11yescharacteristic
235C23×C532−1+411yescharacteristic
236C23×C532−1+411yescharacteristic
237C22×D53—22no—
238C22×D53—22no—
239C22×D53—22no—
240C22×D53—22no—
241C22×D53—22no—
242C22×D53—22no—
243C22×D53—22no—
244C22×D53—22no—
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—22no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53C4⋊Q814yescomplemented
272C2×C4×C53—24no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—42no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—42no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53—42no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53#12014yes—
301C2×C4×C53C22⋊Q814yes—
302C2×C4×C53C22⋊Q814yes—
303C2×C4×C53C22⋊Q814yes—
304C2×C4×C53#12414yes—
305C2×C4×C53#12414yes—
306C2×C4×C53#12414yes—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—24no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—24no—
324C2×Dic53—24no—
325C2×Dic53—41no—
326C2×Dic53—42no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—41no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53#12114yes—
341C2×Dic53C22⋊Q814yes—
342C4×D53—416no—
343Dic106—432no—
344#15125—531nomaximal, Sylow
345C22×C53C2×#12011yescharacteristic
346C22×C53C2×#12111yescharacteristic
347C22×C53C2×C22⋊Q811yescharacteristic
348C22×C53C2×C22⋊Q811yescharacteristic
349C22×C53C2×C22⋊Q811yescharacteristic
350C22×C53C2×C22⋊Q811yescharacteristic
351C22×C53C2×#12411yescharacteristic
352C22×C53C2×#12411yescharacteristic
353C22×C53C2×#12411yescharacteristic
354C22×C53C2×C4⋊Q811yescharacteristic
355C22×C53#53211yescharacteristic
356C22×C53#53311yescharacteristic
357C22×C53#53311yescharacteristic
358C22×C53#53511yescharacteristic
359C22×C53#53611yescharacteristic
360C22×C53#54211yescharacteristic
361C22×C53#54211yescharacteristic
362C22×C53#54411yescharacteristic
363C22×C53#54411yescharacteristic
364C22×C53D4211yescharacteristic
365C22×C53D4211yescharacteristic
366C22×C53#54611yescharacteristic
367C22×C53#54611yescharacteristic
368C22×C53#54711yescharacteristic
369C22×C53#54711yescharacteristic
370C22×C53#54811yescharacteristic
371C22×C53#54811yescharacteristic
372C22×C53D4×Q811yescharacteristic
373C22×C53D4×Q811yescharacteristic
374C22×C53#55411yescharacteristic
375C22×C53#55411yescharacteristic
376C22×C53#55511yescharacteristic
377C22×C53#55511yescharacteristic
378C22×C53#55611yescharacteristic
379C22×C53#55611yescharacteristic
380C2×D53—24no—
381C2×D53—24no—
382C2×D53—24no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C4×C53—42no—
396C4×C53—44no—
397C4×C53—42no—
398C4×C53—82no—
399C4×C53#39318yescomplemented
400Dic53—24no—
401Dic53—24no—
402Dic53—42no—
403Dic53—44no—
404Dic53—82no—
405C22×C4⋊Q8—531no—
406C2×#393—532no—
407C2×#380—531no—
408C2×#380—531no—
409C2×C4×C22⋊C4—531no—
410#1446—532no—
411#1442—532no—
412#1439—532no—
413C4⋊#95—531no—
414C4⋊#95—531no—
415C4⋊#95D5311yescharacteristic, complemented
416C2×C53C2×#39311yescharacteristic
417C2×C53#240811yescharacteristic
418C2×C53#240911yescharacteristic
419C2×C53#243911yescharacteristic
420C2×C53#243911yescharacteristic
421C2×C53#244011yescharacteristic
422C2×C53#244011yescharacteristic
423C2×C53#249111yescharacteristic
424C2×C53#249111yescharacteristic
425C2×C53#249211yescharacteristic
426C2×C53#249211yescharacteristic
427C2×C53#254711yescharacteristic
428C2×C53#256311yescharacteristic
429C2×C53#262811yescharacteristic
430C2×C53#285711yescharacteristic
431D53—44no—
432C23×Q8—532no—
433C24×C4—531no—
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⋊C4—532no—
446C22×C42—531no—
447C22×C42C2×D5311yescharacteristic
448#393—1068no—
449#380—1064no—
450#380—1064no—
451C4×C22⋊C4—1064no—
452C2×#95—532no—
453C2×#95—532no—
454C2×#95—532no—
455C2×#95—531no—
456C2×#95—532no—
457C2×#95—532no—
458C2×#95—531no—
459C2×#95—532no—
460C2×#95C2×D5312yes—
461C2×#95C2×D5312yes—
462C53#1512511yescharacteristic, complemented, Sylow
463C25—531no—
464C22×Q8—1064no—
465C22×Q8—1064no—
466C22×Q8—1064no—
467C22×Q8—1064no—
468C22×Q8—1064no—
469C22×Q8—2122no—
470C22×Q8—2122no—
471C23×C4—531no—
472C23×C4—531no—
473C23×C4—532no—
474C23×C4—531no—
475C23×C4—534no—
476C23×C4—532no—
477C23×C4—1062no—
478C23×C4—1062no—
479C23×C4—1062no—
480C23×C4—1062no—
481C23×C4—1062no—
482C23×C4—1062no—
483C23×C4C22×D5312yes—
484C23×C4C22×D5312yes—
485C23×C4C22×D5311yescharacteristic
486C23×C4C22×D5311yescharacteristic
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—1064no—
498C2×C4⋊C4—1062no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1062no—
501C2×C4⋊C4—1062no—
502C2×C4⋊C4—1062no—
503C2×C4⋊C4D21214yes—
504C2×C22⋊C4—534no—
505C2×C22⋊C4—534no—
506C2×C22⋊C4—1062no—
507C2×C22⋊C4—1062no—
508C2×C22⋊C4—1062no—
509C2×C22⋊C4—1062no—
510C2×C22⋊C4—1064no—
511C2×C22⋊C4—1064no—
512C2×C22⋊C4—1064no—
513C2×C22⋊C4—1064no—
514C2×C22⋊C4—2122no—
515C2×C22⋊C4—2122no—
516C2×C42—22no—
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—534no—
520C2×C42—1062no—
521C2×C42—1062no—
522#95—24no—
523#95—42no—
524#95—1064no—
525#95—1062no—
526#95—1062no—
527#95—1064no—
528#95—1064no—
529#95—1064no—
530#95—1064no—
531#95—2122no—
532C24—532no—
533C24—532no—
534C24—532no—
535C24—1061no—
536C24—1061no—
537C24—1061no—
538C24—1061no—
539C24—1061no—
540C24—1061no—
541C24—1061no—
542C24—1061no—
543C24—1061no—
544C24—1061no—
545C24—1061no—
546C24—1061no—
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—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—532no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—534no—
587C22×C4—532no—
588C22×C4—1061no—
589C22×C4—1061no—
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—1062no—
599C22×C4—1062no—
600C22×C4—1061no—
601C22×C4—1062no—
602C22×C4—1062no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1068no—
609C22×C4—1068no—
610C22×C4—1068no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—2124no—
619C22×C4—2124no—
620C22×C4—2124no—
621C22×C4—2124no—
622C22×C4C2×D21214yes—
623C22×C4C2×D21212yes—
624C22×C4#1171994512yes—
625C22×C4#1171994512yes—
626C22×C4D4×D5312yes—
627C22×C4D4×D5312yes—
628C22×C4D4×D5312yes—
629C22×C4#1171994712yes—
630C22×C4Q8×D5312yes—
631C22×C4Q8×D5312yes—
632C4⋊C4—28no—
633C4⋊C4—44no—
634C4⋊C4—10616no—
635C4⋊C4—1068no—
636C4⋊C4—2124no—
637C22⋊C4—1068no—
638C22⋊C4—1068no—
639C22⋊C4—2128no—
640C22⋊C4—2128no—
641C42—44no—
642C42—1068no—
643C23—534no—
644C23—1062no—
645C23—1062no—
646C23—1062no—
647C23—1062no—
648C23—1062no—
649C23—1062no—
650C23—1062no—
651C23—1062no—
652C23—1062no—
653C23—1062no—
654C23—1062no—
655C23—1062no—
656C23—1062no—
657C23—1062no—
658C23—1062no—
659C23—1062no—
660C23—1062no—
661C23—1062no—
662C23—2121no—
663C23—2121no—
664C23—2121no—
665C23—2121no—
666C23—2121no—
667C23—2121no—
668C23—2121no—
669C23—2121no—
670C23—2121no—
671C23—2121no—
672C23—2121no—
673C23—2121no—
674C23—2121no—
675C23—2121no—
676C23—2121no—
677C23—2121no—
678C23C2×D4×D5311yescharacteristic
679C23C2×D4×D5311yescharacteristic
680C23C2×D4×D5311yescharacteristic
681C23C22×D21211yescharacteristic
682C23C2×Q8×D5311yescharacteristic
683C23C2×Q8×D5311yescharacteristic
684C23#41×D5311yescharacteristic
685C23#41×D5311yescharacteristic
686C23C2×#1171994711yescharacteristic
687C23C2×#1171994511yescharacteristic
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—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—534no—
723C2×C4—534no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1064no—
737C2×C4—1064no—
738C2×C4—1062no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1064no—
742C2×C4—2122no—
743C2×C4—2122no—
744C2×C4—2122no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4—2122no—
750C2×C4—2121no—
751C2×C4—2122no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2121no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—21216no—
758C2×C4#1313318714yes—
759C2×C4#1313319514yes—
760C2×C4#1313319514yes—
761C2×C4#1313319714yes—
762C2×C4#1313320314yes—
763C2×C4#1313320314yes—
764C2×C4#1313320514yes—
765C22—1064no—
766C22—1064no—
767C22—1064no—
768C22—2122no—
769C22—2122no—
770C22—2122no—
771C22—2122no—
772C22—2122no—
773C22—2122no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22—2122no—
778C22—2122no—
779C22—2122no—
780C22C2×#1313318711yescharacteristic
781C22#121×D5311yescharacteristic
782C22C22⋊Q8×D5311yescharacteristic
783C22C2×#1313319511yescharacteristic
784C22C2×#1313319511yescharacteristic
785C22C2×#1313319711yescharacteristic
786C22C2×#1313320311yescharacteristic
787C22C2×#1313320311yescharacteristic
788C22C2×#1313320511yescharacteristic
789C22C4⋊Q8×D5311yescharacteristic
790C22#1681117011yescharacteristic
791C22#1681117711yescharacteristic
792C22#1681117911yescharacteristic
793C22#1681118911yescharacteristic
794C22#1681119611yescharacteristic
795C22#1681123811yescharacteristic
796C22#1681124511yescharacteristic
797C22#1681125011yescharacteristic
798C22#1681125311yescharacteristic
799C22#1681125811yescharacteristic
800C22D4×D21211yescharacteristic
801C22#1681126611yescharacteristic
802C22#1681126811yescharacteristic
803C22#1681127311yescharacteristic
804C22#1681127411yescharacteristic
805C22#1681128111yescharacteristic
806C22#1681128511yescharacteristic
807C22#1681128811yescharacteristic
808C22Q8×D21211yescharacteristic
809C22#1681132811yescharacteristic
810C22#1681133111yescharacteristic
811C22#1681133611yescharacteristic
812C22#1681133711yescharacteristic
813C22#1681134111yescharacteristic
814C22#1681134411yescharacteristic
815C4—44no—
816C4—42no—
817C4—42no—
818C4—82no—
819C4—1064no—
820C4—1064no—
821C4—4242no—
822C4—2124no—
823C4—2122no—
824C4#1681053618yescomplemented
825C2—2124no—
826C2C2×#1681053611yescharacteristic
827C2#2027806911yescharacteristic
828C2#2027807811yescharacteristic
829C2#2027840411yescharacteristic
830C2#2027840911yescharacteristic
831C2#2027841511yescharacteristic
832C2#2027842011yescharacteristic
833C2#2027907211yescharacteristic
834C2#2027907911yescharacteristic
835C2#2027908311yescharacteristic
836C2#2027909011yescharacteristic
837C2#2027970911yescharacteristic
838C2#2027988511yescharacteristic
839C2#2028054211yescharacteristic
840C2#2028306611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutator, socle, cosocleC24×C53C24
FittingC53×C4⋊#95C2
prime radicalC24×D53C23
hypercenterC4⋊#95D53
hypocenterC53#15125
LCSG ▷ C24×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C22×#13133216C2semidirect
6. #20272985C2semidirect
7. #20272970C2semidirect
9. #20272945C2semidirect
10. #20272944C2semidirect
11. C53×C4⋊#95C2semidirect
61. C22×C4×D53Q8semidirect
83. C2×#11719921Q8semidirect
271. C22×D53C4⋊Q8semidirect
399. C4×C53#393semidirect
415. C4⋊#95D53semidirect
462. C53#15125semidirect
824. C4#16810536semidirect

Maximal subgroups

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

subgroupindex
C22×#131332162
C2×#168105362
C2×#168104802
C2×C4×#117199212
#202729852
#202729702
#202729592
#202729452
#202729442
C53×C4⋊#952
#1512553