Finite Group Databasebeta

← #27400273

Subgroups — #27400273

Order 13568.

1132 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic
2D4×#11719917C211yesmaximal, characteristic, complemented
3#20275708C211yesmaximal, characteristic, complemented
4#20275707C211yesmaximal, characteristic, complemented
5#20275178C211yesmaximal, characteristic, complemented
6#20275178C211yesmaximal, characteristic, complemented
7#20275176C211yesmaximal, characteristic, complemented
8#20275176C211yesmaximal, characteristic, complemented
9#20274796C211yesmaximal, characteristic, complemented
10#20274793C211yesmaximal, characteristic, complemented
11#20274704C211yesmaximal, characteristic, complemented
12C4×#13133133C211yesmaximal, characteristic, complemented
13#20274453C211yesmaximal, characteristic, complemented
14C2×#16810391C211yesmaximal, characteristic, complemented
15D4×M16×C53C211yesmaximal, characteristic, complemented
16C22×#11719917C2211yescharacteristic
17C22×#11719917C2211yescharacteristic
18#16811319—21no—
19#16811319—21no—
20#16811319—21no—
21#16811319—21no—
22#16811319—21no—
23#16811319—21no—
24#16811319—21no—
25#16811319—21no—
26C2×#13133212C412yes—
27C2×#13133209C2211yescharacteristic
28C2×#13133199C412yes—
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133189C412yes—
32C2×C4×D212C2211yescharacteristic
33C2×#13133177C412yes—
34C2×#13133176C2211yescharacteristic
35C22×C4⋊Dic53C2211yescharacteristic
36#16810701—21no—
37#16810695—21no—
38#16810695—21no—
39D4×#88322—21no—
40#16810647C2211yescharacteristic
41C2×#13133133C2211yescharacteristic
42C2×#13133133C2211yescharacteristic
43C2×#13133133C2211yescharacteristic
44C2×#13133133C2211yescharacteristic
45#16810587C2211yescharacteristic
46#16810587C2211yescharacteristic
47C4×#11719917C2211yescharacteristic
48#16810391C2211yescharacteristic
49#16810391C2211yescharacteristic
50#16810391C2211yescharacteristic
51#16810391C2211yescharacteristic
52#16810391C2211yescharacteristic
53#16810391C2211yescharacteristic
54#16810391C2211yescharacteristic
55#16810391C2211yescharacteristic
56#16810391C2211yescharacteristic
57#16810391C2211yescharacteristic
58#16810391C2211yescharacteristic
59#16810391C2211yescharacteristic
60C22×M16×C53C2211yescharacteristic
61C22×M16×C53C2211yescharacteristic
62C2×C4×D4×C53C2211yescharacteristic
63C53×#436—21no—
64C53×#435—21no—
65C53×#435—21no—
66C8×D4×C53—21no—
67C53×#423C2211yescharacteristic
68C53×#407C2211yescharacteristic
69C53×#407C2211yescharacteristic
70C4×M16×C53C2211yescharacteristic
71C22×D212C2311yescharacteristic
72C22×C22⋊D53C2×C412yes—
73C22×C22⋊D53C2×C412yes—
74C23×Dic53C2×C412yes—
75C22×C4×D53C2×C412yes—
76C2×#11719917—22no—
77C2×#11719917—22no—
78C2×#11719917—21no—
79C2×#11719917—21no—
80C2×#11719917—41no—
81C2×#11719917—41no—
82C2×#11719917C2311yescharacteristic
83C2×#11719917C2311yescharacteristic
84C2×#11719917C2311yescharacteristic
85C2×#11719917C2311yescharacteristic
86C22×#88322—21no—
87C22×#88322—21no—
88#13133212—22no—
89#13133212—22no—
90#13133212—22no—
91#13133212—22no—
92#13133209—21no—
93#13133209—21no—
94#13133209—21no—
95#13133209—21no—
96#13133199—22no—
97#13133199—22no—
98#13133199—22no—
99#13133199—22no—
100#13133191—21no—
101#13133191—21no—
102#13133191—21no—
103#13133191—21no—
104#13133191—21no—
105#13133191—21no—
106#13133191—21no—
107#13133191—21no—
108#13133189—22no—
109#13133189—22no—
110#13133189—22no—
111#13133189—22no—
112C4×D212—21no—
113C4×D212—21no—
114C4×D212—21no—
115C4×D212—21no—
116#13133177—22no—
117#13133177—22no—
118#13133177—22no—
119#13133177—22no—
120#13133176—21no—
121#13133176—21no—
122#13133176—21no—
123#13133176—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53C2×C412yes—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919C2×C412yes—
133C2×#11719919C2×C412yes—
134C2×C22⋊Dic53C2×C412yes—
135C2×#11719921C2×C412yes—
136C2×#11719921C2×C412yes—
137C2×#11719921C2×C412yes—
138C2×C4×Dic53C2×C412yes—
139C4⋊#88322—21no—
140C4⋊#88322—21no—
141#13133133—22no—
142#13133133—22no—
143#13133133—41no—
144#13133133—41no—
145C22⋊#88322—21no—
146C22⋊#88322—21no—
147C22⋊#88322—21no—
148C22⋊#88322—21no—
149#13133128—21no—
150C4×#88322—21no—
151C22×D4×C53C2×C411yescharacteristic
152C23×C4×C53C2311yescharacteristic
153C23×C4×C53C2311yescharacteristic
154C2×M16×C53—22no—
155C2×M16×C53—22no—
156C2×M16×C53—21no—
157C2×M16×C53—21no—
158C2×M16×C53—41no—
159C2×M16×C53—41no—
160C2×M16×C53C2311yescharacteristic
161C2×M16×C53C2311yescharacteristic
162C2×M16×C53C2311yescharacteristic
163C2×M16×C53C2311yescharacteristic
164C22×C8×C53—21no—
165C22×C8×C53—21no—
166C4×D4×C53D411yescharacteristic
167C4×D4×C53D411yescharacteristic
168C4×D4×C53D411yescharacteristic
169C4×D4×C53D411yescharacteristic
170C4×D4×C53D411yescharacteristic
171C4×D4×C53D411yescharacteristic
172C4×D4×C53D411yescharacteristic
173C4×D4×C53D411yescharacteristic
174C2×C4⋊C4×C53C2×C411yescharacteristic
175C2×C22⋊C4×C53C2×C411yescharacteristic
176C2×C22⋊C4×C53C2×C411yescharacteristic
177C2×C42×C53C2311yescharacteristic
178C4⋊C8×C53—21no—
179C4⋊C8×C53—21no—
180C22⋊C8×C53—21no—
181C22⋊C8×C53—21no—
182C22⋊C8×C53—21no—
183C22⋊C8×C53—21no—
184#97×C53—21no—
185C4×C8×C53—21no—
186C24×C53C22×C411yescharacteristic
187C24×C53C22×C411yescharacteristic
188C23×D53C22×C412yes—
189C2×D4×C53—42no—
190C2×D4×C53C22⋊C411yescharacteristic
191C2×D4×C53C22⋊C411yescharacteristic
192C2×D4×C53C22⋊C411yescharacteristic
193C2×D4×C53C22⋊C411yescharacteristic
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53C22×C411yescharacteristic
203C22×C4×C53C22×C411yescharacteristic
204C22×C4×C53C22×C411yescharacteristic
205C22×C4×C53C22×C411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2411yescharacteristic
215C2×C22⋊D53—22no—
216C2×C22⋊D53—22no—
217C2×C22⋊D53—22no—
218C2×C22⋊D53—22no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—82no—
221C22×Dic53—22no—
222C22×Dic53—22no—
223C22×Dic53—82no—
224C22×Dic53C22×C412yes—
225C22×Dic53C22×C412yes—
226C22×Dic53C22×C412yes—
227C2×D212—21no—
228C2×D212—21no—
229C2×D212—21no—
230C2×D212—21no—
231C2×D212—21no—
232C2×D212—21no—
233C2×C4×D53—22no—
234C2×C4×D53—22no—
235C2×C4×D53—82no—
236M16×C53—21no—
237M16×C53—21no—
238M16×C53—21no—
239M16×C53—21no—
240M16×C53—21no—
241M16×C53—21no—
242M16×C53—21no—
243M16×C53—42no—
244M16×C53—42no—
245M16×C53#4112yes—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—21no—
250C2×C8×C53—42no—
251C2×C8×C53—42no—
252C4⋊C4×C53C22⋊C411yescharacteristic
253C4⋊C4×C53C22⋊C411yescharacteristic
254C4⋊C4×C53C22⋊C411yescharacteristic
255C4⋊C4×C53C22⋊C411yescharacteristic
256C22⋊C4×C53C22⋊C411yescharacteristic
257C22⋊C4×C53C22⋊C411yescharacteristic
258C22⋊C4×C53C22⋊C411yescharacteristic
259C22⋊C4×C53C22⋊C411yescharacteristic
260C22⋊C4×C53C22⋊C411yescharacteristic
261C22⋊C4×C53C22⋊C411yescharacteristic
262C22⋊C4×C53C22⋊C411yescharacteristic
263C22⋊C4×C53C22⋊C411yescharacteristic
264C42×C53C2×D411yescharacteristic
265C42×C53C2×D411yescharacteristic
266C42×C53C2×D411yescharacteristic
267C42×C53C2×D411yescharacteristic
268C22⋊Dic53—22no—
269C22⋊Dic53—22no—
270#11719921—22no—
271#11719921—22no—
272#11719921—22no—
273#11719921—22no—
274#11719921—22no—
275#11719921—22no—
276C4⋊Dic53—22no—
277C4⋊Dic53—22no—
278C4⋊Dic53—21no—
279C4⋊Dic53—21no—
280C4⋊Dic53—21no—
281C4⋊Dic53—21no—
282C4⋊Dic53—21no—
283C4⋊Dic53—21no—
284#11719919—22no—
285#11719919—22no—
286#11719919—22no—
287#11719919—22no—
288C4×Dic53—22no—
289C4×Dic53—22no—
290#11719917—21no—
291#11719917—21no—
292#11719917—21no—
293#11719917—21no—
294#11719917—21no—
295#11719917—21no—
296#11719917—21no—
297#11719917—42no—
298#11719917—42no—
299#11719917#4112yes—
300C2×#88322—21no—
301C2×#88322—21no—
302C2×#88322—21no—
303C2×#88322—21no—
304C2×#88322—42no—
305C2×#88322—42no—
306C23×C53—21no—
307C23×C53—21no—
308C23×C53—22no—
309C23×C53—21no—
310C23×C53—21no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53C2×C22⋊C411yescharacteristic
315C23×C53C2×C22⋊C411yescharacteristic
316C23×C53C2×C22⋊C411yescharacteristic
317C23×C53C2×C22⋊C411yescharacteristic
318C23×C53C23×C411yescharacteristic
319C22×D53—22no—
320C22×D53—22no—
321C22×D53—22no—
322C22×D53—42no—
323C22×D53—42no—
324D4×C53—22no—
325D4×C53—22no—
326D4×C53—41no—
327D4×C53—41no—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—21no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—21no—
341C2×C4×C53—21no—
342C2×C4×C53—21no—
343C2×C4×C53—21no—
344C2×C4×C53—21no—
345C2×C4×C53—21no—
346C2×C4×C53—21no—
347C2×C4×C53—21no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53C2×C22⋊C411yescharacteristic
351C2×C4×C53C2×C22⋊C411yescharacteristic
352C2×C4×C53C2×C22⋊C411yescharacteristic
353C2×C4×C53C2×C22⋊C411yescharacteristic
354C2×C4×C53C2×C22⋊C411yescharacteristic
355C2×C4×C53C2×C22⋊C411yescharacteristic
356C2×C4×C53C2×C22⋊C411yescharacteristic
357C2×C4×C53C2×C22⋊C411yescharacteristic
358C2×C4×C53C22×D411yescharacteristic
359C2×C4×C53C22×D411yescharacteristic
360C2×C4×C53C2×#4111yescharacteristic
361C2×C4×C53C2×#4111yescharacteristic
362C2×C4×C53H(5,𝔽2)11yescharacteristic
363C2×C4×C532−1+411yescharacteristic
364C22⋊D53—44no—
365C22⋊D53—44no—
366C22⋊D53—82no—
367C22⋊D53—82no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—42no—
372C2×Dic53—42no—
373C2×Dic53—42no—
374C2×Dic53—82no—
375C2×Dic53—82no—
376D212—41no—
377D212—41no—
378D212—41no—
379D212—41no—
380C4×D53—82no—
381C4×D53—82no—
382C8×C53—22no—
383C8×C53—41no—
384C8×C53—41no—
385C8×C53—41no—
386#88322—22no—
387#88322—41no—
388#88322—41no—
389#88322—41no—
390#22482—531nomaximal, Sylow
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—21no—
394C22×C53—21no—
395C22×C53—21no—
396C22×C53—21no—
397C22×C53—21no—
398C22×C53—21no—
399C22×C53—21no—
400C22×C53—21no—
401C22×C53—21no—
402C22×C53—21no—
403C22×C53—21no—
404C22×C53—42no—
405C22×C53—42no—
406C22×C53—81no—
407C22×C53—81no—
408C22×C53#41312yes—
409C22×C53C22×C22⋊C411yescharacteristic
410C22×C53C4×#4111yescharacteristic
411C22×C53#52011yescharacteristic
412C2×D53—42no—
413C2×D53—42no—
414C2×D53—42no—
415C2×D53—82no—
416C2×D53—82no—
417C4×C53—21no—
418C4×C53—21no—
419C4×C53—21no—
420C4×C53—21no—
421C4×C53—21no—
422C4×C53—21no—
423C4×C53—21no—
424C4×C53—21no—
425C4×C53#54611yescharacteristic
426C4×C53#54611yescharacteristic
427C4×C53#54711yescharacteristic
428C4×C53#54711yescharacteristic
429Dic53—42no—
430Dic53—42no—
431Dic53—42no—
432C2×#553—531no—
433D4×M16—531no—
434D4×M16D5311yescharacteristic, complemented
435#1998—531no—
436#1998—531no—
437#1900—531no—
438#1900—531no—
439#1900—531no—
440#1900—531no—
441#1822—531no—
442#1821—531no—
443#1800—531no—
444C4×#100—531no—
445#1742—531no—
446C2×#343—531no—
447C2×C53—21no—
448C2×C53—21no—
449C2×C53—22no—
450C2×C53—41no—
451C2×C53—41no—
452C2×C53—41no—
453C2×C53#233911yescharacteristic
454C2×C53C2×#41311yescharacteristic
455C2×C53#288811yescharacteristic
456D53—82no—
457C22×M16—531no—
458C22×M16—531no—
459C22×M16C2×D5311yescharacteristic
460C22×M16C2×D5311yescharacteristic
461#553—1061no—
462#553—1061no—
463#553—1061no—
464#553—1061no—
465#553—1061no—
466#553—1061no—
467#553—1061no—
468#553—1061no—
469C2×#126—532no—
470C2×#125—531no—
471C2×#123—532no—
472C2×#121—532no—
473C2×#121—531no—
474C2×#121—531no—
475C2×C4×D4—532no—
476C2×C4×D4—531no—
477C2×C4×D4C2×D5311yescharacteristic
478C2×#117—531no—
479C22×C4⋊C4—531no—
480#436—21no—
481#436—1061no—
482#435—21no—
483#435—21no—
484#435—1061no—
485#435—1061no—
486C8×D4—21no—
487C8×D4—1061no—
488#423—531no—
489#423C2×D5311yescharacteristic
490C2×#100—531no—
491C2×#100—531no—
492C2×#100—531no—
493C2×#100—531no—
494#407—531no—
495#407—531no—
496#407C2×D5311yescharacteristic
497#407C2×D5311yescharacteristic
498C4×M16—531no—
499C4×M16C2×D5311yescharacteristic
500#343—531no—
501#343—531no—
502#343—531no—
503#343—531no—
504#343—531no—
505#343—531no—
506#343—531no—
507#343—531no—
508#343—531no—
509#343—531no—
510#343—531no—
511#343—531no—
512C53#2248211yescharacteristic, complemented, Sylow
513C22×D4—532no—
514C22×D4—532no—
515C22×D4—531no—
516C22×D4C4×D5311yescharacteristic
517C23×C4—532no—
518C23×C4—532no—
519C23×C4C22×D5311yescharacteristic
520C23×C4C22×D5311yescharacteristic
521C2×M16—21no—
522C2×M16—21no—
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—531no—
528C2×M16—531no—
529C2×M16—531no—
530C2×M16—531no—
531C2×M16—1061no—
532C2×M16—1061no—
533C2×M16—1062no—
534C2×M16—1062no—
535C2×M16—2121no—
536C2×M16—2121no—
537C2×M16C22×D5311yescharacteristic
538C2×M16C22×D5311yescharacteristic
539C2×M16C22×D5311yescharacteristic
540C2×M16C22×D5311yescharacteristic
541C22×C8—21no—
542C22×C8—21no—
543C22×C8—1061no—
544C22×C8—1061no—
545#126—1062no—
546#126—1062no—
547#126—1062no—
548#126—1062no—
549#125—1061no—
550#125—1061no—
551#125—1061no—
552#125—1061no—
553#123—1062no—
554#123—1062no—
555#123—1062no—
556#123—1062no—
557#121—1062no—
558#121—1062no—
559#121—1062no—
560#121—1062no—
561#121—1061no—
562#121—1061no—
563#121—1061no—
564#121—1061no—
565#121—1061no—
566#121—1061no—
567#121—1061no—
568#121—1061no—
569C4×D4—1062no—
570C4×D4—1062no—
571C4×D4—1062no—
572C4×D4—1062no—
573C4×D4—1061no—
574C4×D4—1061no—
575C4×D4—1061no—
576C4×D4—1061no—
577C4×D4D21211yescharacteristic
578C4×D4D21211yescharacteristic
579C4×D4D21211yescharacteristic
580C4×D4D21211yescharacteristic
581C4×D4C22⋊D5311yescharacteristic
582C4×D4C22⋊D5311yescharacteristic
583C4×D4C22⋊D5311yescharacteristic
584C4×D4C22⋊D5311yescharacteristic
585#117—1061no—
586#117—1061no—
587#117—1061no—
588#117—1061no—
589C2×C4⋊C4—532no—
590C2×C4⋊C4—532no—
591C2×C4⋊C4—532no—
592C2×C4⋊C4—531no—
593C2×C4⋊C4—531no—
594C2×C4⋊C4—531no—
595C2×C4⋊C4—1061no—
596C2×C4⋊C4—1061no—
597C2×C4⋊C4—1061no—
598C2×C4⋊C4—1061no—
599C2×C4⋊C4C4×D5311yescharacteristic
600C2×C22⋊C4—532no—
601C2×C22⋊C4—532no—
602C2×C22⋊C4—532no—
603C2×C22⋊C4—532no—
604C2×C22⋊C4C4×D5311yescharacteristic
605C2×C22⋊C4C4×D5311yescharacteristic
606C2×C42—532no—
607C2×C42C22×D5311yescharacteristic
608C4⋊C8—21no—
609C4⋊C8—21no—
610C4⋊C8—1061no—
611C4⋊C8—1061no—
612#100—1062no—
613#100—1062no—
614#100—2121no—
615#100—2121no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—21no—
620C22⋊C8—1061no—
621C22⋊C8—1061no—
622C22⋊C8—1061no—
623C22⋊C8—1061no—
624#97—21no—
625#97—1061no—
626C4×C8—21no—
627C4×C8—1061no—
628C24—532no—
629C24C2×C4×D5311yescharacteristic
630C24C2×C4×D5311yescharacteristic
631C2×D4—42no—
632C2×D4—1062no—
633C2×D4—1062no—
634C2×D4—1062no—
635C2×D4—1062no—
636C2×D4—1061no—
637C2×D4—1061no—
638C2×D4—1061no—
639C2×D4—1061no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—4242no—
643C2×D4—2124no—
644C2×D4#1171992111yescharacteristic
645C2×D4#1171992111yescharacteristic
646C2×D4#1171992111yescharacteristic
647C2×D4#1171992111yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—532no—
657C22×C4—532no—
658C22×C4—532no—
659C22×C4—1062no—
660C22×C4—1062no—
661C22×C4—1062no—
662C22×C4—1062no—
663C22×C4—4242no—
664C22×C4—4242no—
665C22×C4C2×C4×D5311yescharacteristic
666C22×C4C2×C4×D5311yescharacteristic
667C22×C4C2×C4×D5311yescharacteristic
668C22×C4C2×C4×D5311yescharacteristic
669C22×C4C2×D21211yescharacteristic
670C22×C4C2×D21211yescharacteristic
671C22×C4C2×D21211yescharacteristic
672C22×C4C2×D21211yescharacteristic
673C22×C4C2×C22⋊D5311yescharacteristic
674C22×C4C2×C22⋊D5311yescharacteristic
675C22×C4C2×C22⋊D5311yescharacteristic
676C22×C4C2×C22⋊D5311yescharacteristic
677C22×C4C23×D5311yescharacteristic
678M16—21no—
679M16—21no—
680M16—21no—
681M16—21no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—42no—
687M16—532no—
688M16—1061no—
689M16—1061no—
690M16—1061no—
691M16—1061no—
692M16—1061no—
693M16—1061no—
694M16—1061no—
695M16—2122no—
696M16—2122no—
697M16#1171994712yes—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—42no—
703C2×C8—42no—
704C2×C8—1061no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—2122no—
709C2×C8—2122no—
710C4⋊C4—1062no—
711C4⋊C4—1062no—
712C4⋊C4—1062no—
713C4⋊C4—1062no—
714C4⋊C4—1062no—
715C4⋊C4—1062no—
716C4⋊C4—1061no—
717C4⋊C4—1061no—
718C4⋊C4—1061no—
719C4⋊C4—1061no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C4⋊C4#1171992111yescharacteristic
723C4⋊C4#1171992111yescharacteristic
724C4⋊C4#1171992111yescharacteristic
725C4⋊C4#1171992111yescharacteristic
726C22⋊C4—1062no—
727C22⋊C4—1062no—
728C22⋊C4—1062no—
729C22⋊C4—1062no—
730C22⋊C4—1062no—
731C22⋊C4—1062no—
732C22⋊C4—1062no—
733C22⋊C4—1062no—
734C22⋊C4#1171992111yescharacteristic
735C22⋊C4#1171992111yescharacteristic
736C22⋊C4#1171992111yescharacteristic
737C22⋊C4#1171992111yescharacteristic
738C22⋊C4#1171992111yescharacteristic
739C22⋊C4#1171992111yescharacteristic
740C22⋊C4#1171992111yescharacteristic
741C22⋊C4#1171992111yescharacteristic
742C42—1062no—
743C42—1062no—
744C42C2×D21211yescharacteristic
745C42C2×D21211yescharacteristic
746C42C2×C22⋊D5311yescharacteristic
747C42C2×C22⋊D5311yescharacteristic
748C23—21no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—21no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—1062no—
757C23—1062no—
758C23—1062no—
759C23—2122no—
760C23—2122no—
761C23C2×#1171992111yescharacteristic
762C23C2×#1171992111yescharacteristic
763C23C2×#1171992111yescharacteristic
764C23C2×#1171992111yescharacteristic
765C23C22×C4×D5311yescharacteristic
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—4242no—
771D4—4242no—
772D4—2124no—
773D4—2124no—
774D4—2121no—
775D4—2121no—
776D4—2121no—
777D4—2121no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—1062no—
801C2×C4—1062no—
802C2×C4—1062no—
803C2×C4—4242no—
804C2×C4—4242no—
805C2×C4—4242no—
806C2×C4—4242no—
807C2×C4—2122no—
808C2×C4—2122no—
809C2×C4—2122no—
810C2×C4C2×#1171992111yescharacteristic
811C2×C4C2×#1171992111yescharacteristic
812C2×C4C2×#1171992111yescharacteristic
813C2×C4C2×#1171992111yescharacteristic
814C2×C4C2×#1171992111yescharacteristic
815C2×C4C2×#1171992111yescharacteristic
816C2×C4C2×#1171992111yescharacteristic
817C2×C4C2×#1171992111yescharacteristic
818C2×C4C22×C22⋊D5311yescharacteristic
819C2×C4C22×D21211yescharacteristic
820C2×C4#41×D5311yescharacteristic
821C2×C4C2×#1171994711yescharacteristic
822C2×C4#1313326211yescharacteristic
823C2×C4#1313326411yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C8—1062no—
829C8—2121no—
830C8—2121no—
831C8—2121no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—42no—
846C22—42no—
847C22—81no—
848C22—81no—
849C22—4242no—
850C22—4242no—
851C22—2122no—
852C22—2122no—
853C22—2122no—
854C22#1681060512yes—
855C22C22×#1171992111yescharacteristic
856C22C4×#1171994711yescharacteristic
857C22#1681110211yescharacteristic
858C4—21no—
859C4—21no—
860C4—21no—
861C4—21no—
862C4—21no—
863C4—21no—
864C4—21no—
865C4—21no—
866C4—2122no—
867C4—2122no—
868C4—2122no—
869C4#1681126711yescharacteristic
870C4#1681126811yescharacteristic
871C4#1681127211yescharacteristic
872C4#1681127711yescharacteristic
873C2—21no—
874C2—21no—
875C2—22no—
876C2—41no—
877C2—41no—
878C2—41no—
879C2—4242no—
880C2#2027754011yescharacteristic
881C2C2×#1681060511yescharacteristic
882C2#2028319311yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC23×C53C23×C4
FrattiniC22×C4C23×D53
FittingD4×M16×C53C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811319C2
cosocleC22×C4×C53C24
hypercenterD4×M16D53
hypocenterC53#22482
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#11719917C2semidirect
3. #20275708C2semidirect
4. #20275707C2semidirect
5. #20275178C2semidirect
6. #20275178C2semidirect
7. #20275176C2semidirect
8. #20275176C2semidirect
9. #20274796C2semidirect
10. #20274793C2semidirect
11. #20274704C2semidirect
12. C4×#13133133C2semidirect
13. #20274453C2semidirect
14. C2×#16810391C2semidirect
15. D4×M16×C53C2semidirect
434. D4×M16D53semidirect
512. C53#22482semidirect

Maximal subgroups

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

subgroupindex
C2×#168113192
D4×#117199172
#202757082
#202757072
#202751782
#202751762
#202747962
#202747932
#202747042
C4×#131331332
#202744532
C2×#168103912
D4×M16×C532
#2248253