Finite Group Databasebeta

← #27351583

Subgroups — #27351583

Order 13568.

1510 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic
2C2×#16810483C211yesmaximal, characteristic, complemented
3#20273288C212yesmaximal, complemented
4#20273284C212yesmaximal, complemented
5#20273259C214yesmaximal, complemented
6#20273220C214yesmaximal, complemented
7C2×C53×#407C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9#16811134—21no—
10#16811134—21no—
11#16811134—21no—
12#16811134—21no—
13#16811134C412yescomplemented
14#16811134C412yescomplemented
15#16811134C2212yes—
16#16811134C2212yes—
17C2×#13133200—21no—
18C2×#13133196C411yescharacteristic, complemented
19C2×#13133196C2211yescharacteristic
20C2×#13133191C411yescharacteristic, complemented
21C2×#13133191C2211yescharacteristic
22C2×#13133186—21no—
23C2×C4×C22⋊D53—21no—
24C2×C4×C22⋊D53—21no—
25C2×#13133176C411yescharacteristic, complemented
26C22×C4⋊Dic53—21no—
27C22×C22⋊Dic53—21no—
28#16810483—21no—
29#16810483—21no—
30#16810483C2212yes—
31#16810483C2212yescomplemented
32C2×#13133124C2212yescomplemented
33#16810361C2218yescomplemented
34#16810358C2218yescomplemented
35C24×C4×C53C2211yescharacteristic
36C22×M16×C53—21no—
37C53×#407—21no—
38C53×#407—21no—
39C53×#407C2212yescomplemented
40C53×#407C2212yescomplemented
41C2×C22⋊C8×C53—21no—
42C2×C22⋊C8×C53C2212yes—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—44no—
46C2×#11719945C2×C412yes—
47C2×#11719945C2×C412yescomplemented
48C22×Dic106C2×C411yescharacteristic, complemented
49C22×D212C2×C411yescharacteristic, complemented
50C22×C22⋊D53—21no—
51C22×C22⋊D53—21no—
52C22×C22⋊D53—21no—
53C23×Dic53—22no—
54C22×C4×D53—21no—
55#13133200—22no—
56#13133200—22no—
57#13133200—22no—
58#13133200—22no—
59#13133196—21no—
60#13133196—21no—
61#13133196—21no—
62#13133196—21no—
63#13133196C2×C412yes—
64#13133196C2×C412yescomplemented
65#13133196C2×C412yescomplemented
66#13133196C2312yes—
67#13133191—21no—
68#13133191—21no—
69#13133191—21no—
70#13133191—21no—
71#13133191C2×C412yes—
72#13133191C2×C412yescomplemented
73#13133191C2×C412yescomplemented
74#13133191C2312yes—
75#13133186—22no—
76#13133186—22no—
77#13133186—22no—
78#13133186—22no—
79C4×C22⋊D53—22no—
80C4×C22⋊D53—22no—
81C4×C22⋊D53—22no—
82C4×C22⋊D53—22no—
83C4×C22⋊D53—22no—
84C4×C22⋊D53—22no—
85C4×C22⋊D53—22no—
86C4×C22⋊D53—22no—
87#13133176—21no—
88#13133176—21no—
89#13133176C2×C412yes—
90#13133176C2×C412yescomplemented
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53—22no—
93C2×C4⋊Dic53—44no—
94C2×C4⋊Dic53C2×C411yescharacteristic, complemented
95C2×C4⋊Dic53C2×C411yescharacteristic, complemented
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×C22⋊Dic53—22no—
102C2×C22⋊Dic53—22no—
103C2×C22⋊Dic53—44no—
104C2×#11719921—21no—
105C2×#11719921—21no—
106C2×C4×Dic53—21no—
107#13133124—22no—
108#13133124C2314yes—
109C25×C53D411yescharacteristic
110C23×C4×C53—44no—
111C23×C4×C53C2×C411yescharacteristic
112C23×C4×C53C2×C411yescharacteristic
113C23×C4×C53C2×C411yescharacteristic
114C23×C4×C53C2×C411yescharacteristic
115C23×C4×C53D411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53D411yescharacteristic
118C23×C4×C53D411yescharacteristic
119C23×C4×C53D411yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53D411yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C2×M16×C53—22no—
126C2×M16×C53—22no—
127C2×M16×C53—44no—
128C22×C8×C53—22no—
129C22⋊C8×C53—22no—
130C22⋊C8×C53—22no—
131C22⋊C8×C53—22no—
132C22⋊C8×C53C2314yes—
133C24×C53—22no—
134C24×C53—22no—
135C24×C53—42no—
136C24×C53—42no—
137C24×C53C22⋊C411yescharacteristic
138C24×C53C22⋊C411yescharacteristic
139C24×C53C22⋊C411yescharacteristic
140C24×C53C22⋊C411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C24×C53C2×D411yescharacteristic
144C23×D53—21no—
145C22×C4×C53—24no—
146C22×C4×C53—24no—
147C22×C4×C53—24no—
148C22×C4×C53—42no—
149C22×C4×C53—42no—
150C22×C4×C53—42no—
151C22×C4×C53—42no—
152C22×C4×C53—42no—
153C22×C4×C53—42no—
154C22×C4×C53—42no—
155C22×C4×C53—42no—
156C22×C4×C53—42no—
157C22×C4×C53—42no—
158C22×C4×C53—42no—
159C22×C4×C53C22⋊C411yescharacteristic
160C22×C4×C53C22⋊C411yescharacteristic
161C22×C4×C53C22⋊C411yescharacteristic
162C22×C4×C53C22⋊C411yescharacteristic
163C22×C4×C53C22⋊C411yescharacteristic
164C22×C4×C53C22⋊C411yescharacteristic
165C22×C4×C53C22⋊C411yescharacteristic
166C22×C4×C53C22⋊C411yescharacteristic
167C22×C4×C53C22⋊C411yescharacteristic
168C22×C4×C53C22⋊C411yescharacteristic
169C22×C4×C53C22⋊C411yescharacteristic
170C22×C4×C53C22⋊C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C22×C411yescharacteristic
173C22×C4×C53C22×C411yescharacteristic
174C22×C4×C53C22×C411yescharacteristic
175C22×C4×C53C22×C411yescharacteristic
176C22×C4×C53C22×C411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2411yescharacteristic
187C2×C22⋊D53—22no—
188C2×C22⋊D53—22no—
189C2×C22⋊D53—22no—
190C2×C22⋊D53—22no—
191C2×C22⋊D53—22no—
192C2×C22⋊D53—22no—
193C2×C22⋊D53—44no—
194C2×C22⋊D53—44no—
195C2×C22⋊D53—42no—
196C2×C22⋊D53—42no—
197C22×Dic53—21no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—24no—
201C22×Dic53—44no—
202C22×Dic53—44no—
203C22×Dic53—44no—
204#11719945—44no—
205#11719945—44no—
206#11719945—44no—
207#11719945—44no—
208C2×D212—21no—
209C2×D212—42no—
210C2×D212C22×C412yes—
211C2×C4×D53—22no—
212C2×C4×D53—22no—
213C2×C4×D53—44no—
214C2×Dic106—21no—
215C2×Dic106—42no—
216C2×Dic106C22×C412yes—
217M16×C53—44no—
218M16×C53—44no—
219C2×C8×C53—24no—
220C2×C8×C53—44no—
221C22⋊Dic53—22no—
222C22⋊Dic53—22no—
223C22⋊Dic53—22no—
224C22⋊Dic53—22no—
225C22⋊Dic53—22no—
226C22⋊Dic53—22no—
227C22⋊Dic53—44no—
228C22⋊Dic53—44no—
229#11719921—22no—
230#11719921—22no—
231#11719921—22no—
232#11719921—22no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—44no—
236C4⋊Dic53—44no—
237C4⋊Dic53C22×C412yes—
238C4⋊Dic53C22×C412yes—
239#11719919—22no—
240#11719919—22no—
241#11719919—22no—
242#11719919—22no—
243C4×Dic53—22no—
244C4×Dic53—22no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—41no—
260C23×C53—41no—
261C23×C53—41no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—48no—
268C23×C53—48no—
269C23×C53C2×C22⋊C411yescharacteristic
270C23×C53C2×C22⋊C411yescharacteristic
271C23×C53C2×C22⋊C411yescharacteristic
272C23×C53C2×C22⋊C411yescharacteristic
273C23×C53C2×C22⋊C411yescharacteristic
274C23×C53C2×C22⋊C411yescharacteristic
275C23×C53AGL(1,ℤ/8)12yes—
276C23×C53#13712yes—
277C23×C53C22×D411yescharacteristic
278C22×D53—22no—
279C22×D53—42no—
280C22×D53—42no—
281C22×D53—42no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53#9914yes—
310C2×C4×C53C2×C22⋊C411yescharacteristic
311C2×C4×C53C2×C22⋊C411yescharacteristic
312C2×C4×C53C2×C22⋊C411yescharacteristic
313C2×C4×C53C2×C22⋊C411yescharacteristic
314C2×C4×C53C2×C22⋊C411yescharacteristic
315C2×C4×C53C2×C22⋊C411yescharacteristic
316C2×C4×C53C23×C411yescharacteristic
317C2×C4×C53C22×D411yescharacteristic
318C22⋊D53—44no—
319C22⋊D53—44no—
320C22⋊D53—42no—
321C22⋊D53—42no—
322C22⋊D53—44no—
323C22⋊D53—44no—
324C22⋊D53—44no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—44no—
332C2×Dic53—44no—
333C2×Dic53—44no—
334C2×Dic53—88no—
335D212—42no—
336D212—42no—
337C4×D53—44no—
338C4×D53—44no—
339Dic106—42no—
340Dic106—42no—
341C8×C53—44no—
342#17592—531nomaximal, Sylow
343C22×C53—24no—
344C22×C53—24no—
345C22×C53—21no—
346C22×C53—21no—
347C22×C53—21no—
348C22×C53—21no—
349C22×C53—21no—
350C22×C53—21no—
351C22×C53—21no—
352C22×C53—21no—
353C22×C53—21no—
354C22×C53—21no—
355C22×C53—21no—
356C22×C53—21no—
357C22×C53—21no—
358C22×C53—21no—
359C22×C53—21no—
360C22×C53—21no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53—44no—
366C22×C53—44no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53C2×#9912yes—
370C22×C53#41712yes—
371C22×C53#41712yes—
372C22×C53#42112yes—
373C22×C53C22×C22⋊C411yescharacteristic
374C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
375C22×C53C2×#13711yescharacteristic
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—84no—
380C4×C53—21no—
381C4×C53—21no—
382C4×C53—21no—
383C4×C53—21no—
384C4×C53—21no—
385C4×C53—21no—
386C4×C53C2×#9912yes—
387C4×C53C2×#9912yes—
388Dic53—42no—
389Dic53—42no—
390Dic53—42no—
391Dic53—84no—
392C2×#525—531no—
393C2×#407D5311yescharacteristic, complemented
394C2×#380—531no—
395#1520—532no—
396#1519—532no—
397#1513—534no—
398#1504—534no—
399C2×C53—21no—
400C2×C53—22no—
401C2×C53—21no—
402C2×C53—22no—
403C2×C53—22no—
404C2×C53—22no—
405C2×C53—41no—
406C2×C53—41no—
407C2×C53C22×#9911yescharacteristic
408C2×C53C2×#41711yescharacteristic
409C2×C53C2×#42111yescharacteristic
410D53—82no—
411C22×#41—531no—
412C24×C4C2×D5311yescharacteristic
413C22×M16—21no—
414#525—532no—
415#525—532no—
416#525—532no—
417#525—532no—
418#525—1061no—
419#525—1061no—
420#525—1061no—
421#525—1061no—
422C2×#123—1061no—
423C2×C22⋊Q8—531no—
424C2×C22⋊Q8—531no—
425C2×#121—531no—
426C2×#121—531no—
427C2×#120—1061no—
428C2×C4×D4—1061no—
429C2×C4×D4—1061no—
430C2×#117—531no—
431C22×C4⋊C4—1061no—
432C22×C22⋊C4—1061no—
433#407—21no—
434#407—21no—
435#407C2×D5312yescomplemented
436#407C2×D5312yescomplemented
437C2×C22⋊C8—21no—
438C2×C22⋊C8C2×D5312yes—
439#380—532no—
440#380—532no—
441#380—1061no—
442#380—1061no—
443C2×#95—532no—
444#328—538no—
445#327—538no—
446C53#1759211yescharacteristic, complemented, Sylow
447C25D21211yescharacteristic
448C2×#41—532no—
449C2×#41—532no—
450C2×#41—1061no—
451C2×#41—1061no—
452C2×#41—2124no—
453C22×Q8—531no—
454C22×D4—531no—
455C22×D4—1061no—
456C22×D4—1061no—
457C22×D4—1061no—
458C23×C4—44no—
459C23×C4—1061no—
460C23×C4—1062no—
461C23×C4C4×D5311yescharacteristic
462C23×C4C4×D5311yescharacteristic
463C23×C4C4×D5311yescharacteristic
464C23×C4C4×D5311yescharacteristic
465C23×C4D21211yescharacteristic
466C23×C4D21211yescharacteristic
467C23×C4D21211yescharacteristic
468C23×C4C22⋊D5311yescharacteristic
469C23×C4C22⋊D5311yescharacteristic
470C23×C4C22⋊D5311yescharacteristic
471C23×C4C22⋊D5311yescharacteristic
472C23×C4C22×D5311yescharacteristic
473C23×C4C22×D5311yescharacteristic
474C23×C4C22×D5311yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—44no—
478C22×C8—22no—
479#123—1062no—
480#123—1062no—
481#123—1062no—
482#123—1062no—
483C22⋊Q8—532no—
484C22⋊Q8—532no—
485C22⋊Q8—532no—
486C22⋊Q8—532no—
487C22⋊Q8—1061no—
488C22⋊Q8—1061no—
489C22⋊Q8—1061no—
490C22⋊Q8—1061no—
491#121—532no—
492#121—532no—
493#121—532no—
494#121—532no—
495#121—1061no—
496#121—1061no—
497#121—1061no—
498#121—1061no—
499#120—1062no—
500#120—1062no—
501#120—1062no—
502#120—1062no—
503C4×D4—1062no—
504C4×D4—1062no—
505C4×D4—1062no—
506C4×D4—1062no—
507C4×D4—1062no—
508C4×D4—1062no—
509C4×D4—1062no—
510C4×D4—1062no—
511#117—532no—
512#117—532no—
513#117—1061no—
514#117—1061no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—531no—
517C2×C4⋊C4—1061no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4—1062no—
520C2×C4⋊C4—1062no—
521C2×C4⋊C4—2124no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4—1061no—
527C2×C22⋊C4—1062no—
528C2×C22⋊C4—1062no—
529C2×C22⋊C4—2124no—
530C2×C42—1061no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8C22×D5314yes—
535#95—534no—
536#95—1062no—
537C24—22no—
538C24—22no—
539C24—42no—
540C24—42no—
541C24—1061no—
542C24#1171992111yescharacteristic
543C24#1171992111yescharacteristic
544C24#1171992111yescharacteristic
545C24#1171992111yescharacteristic
546C24C2×D21211yescharacteristic
547C24C2×D21211yescharacteristic
548C24C2×D21211yescharacteristic
549#41—2124no—
550#41—2124no—
551#41—2124no—
552#41—2124no—
553C2×Q8—532no—
554C2×Q8—1061no—
555C2×Q8—2122no—
556C2×D4—532no—
557C2×D4—1062no—
558C2×D4—1062no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—1061no—
564C2×D4—2122no—
565C2×D4—2124no—
566C2×D4—2124no—
567C2×D4—2122no—
568C2×D4—2122no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1064no—
589C22×C4—2124no—
590C22×C4—2124no—
591C22×C4—2124no—
592C22×C4—2124no—
593C22×C4#1171992111yescharacteristic
594C22×C4#1171992111yescharacteristic
595C22×C4#1171992111yescharacteristic
596C22×C4#1171992111yescharacteristic
597C22×C4#1171992111yescharacteristic
598C22×C4#1171992111yescharacteristic
599C22×C4#1171992111yescharacteristic
600C22×C4#1171992111yescharacteristic
601C22×C4#1171992111yescharacteristic
602C22×C4#1171992111yescharacteristic
603C22×C4#1171992111yescharacteristic
604C22×C4#1171992111yescharacteristic
605C22×C4C2×C4×D5311yescharacteristic
606C22×C4C2×C4×D5311yescharacteristic
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4C2×C4×D5311yescharacteristic
609C22×C4C2×C4×D5311yescharacteristic
610C22×C4C2×C4×D5311yescharacteristic
611C22×C4C2×D21211yescharacteristic
612C22×C4C2×D21211yescharacteristic
613C22×C4C2×D21211yescharacteristic
614C22×C4C2×C22⋊D5311yescharacteristic
615C22×C4C2×C22⋊D5311yescharacteristic
616C22×C4C2×C22⋊D5311yescharacteristic
617C22×C4C2×C22⋊D5311yescharacteristic
618C22×C4C2×C22⋊D5311yescharacteristic
619C22×C4C2×C22⋊D5311yescharacteristic
620C22×C4C23×D5311yescharacteristic
621M16—44no—
622M16—44no—
623C2×C8—24no—
624C2×C8—44no—
625C4⋊C4—532no—
626C4⋊C4—532no—
627C4⋊C4—1061no—
628C4⋊C4—1061no—
629C4⋊C4—1062no—
630C4⋊C4—1062no—
631C4⋊C4—1062no—
632C4⋊C4—1062no—
633C4⋊C4—2124no—
634C4⋊C4—2124no—
635C22⋊C4—1062no—
636C22⋊C4—1062no—
637C22⋊C4—1062no—
638C22⋊C4—1062no—
639C22⋊C4—1062no—
640C22⋊C4—1062no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C22⋊C4—2124no—
646C22⋊C4—2124no—
647C42—1062no—
648C42—1062no—
649C23—22no—
650C23—22no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—48no—
672C23—48no—
673C23—1062no—
674C23—2122no—
675C23—2122no—
676C23—2122no—
677C23C2×#1171992111yescharacteristic
678C23C2×#1171992111yescharacteristic
679C23C2×#1171992111yescharacteristic
680C23C2×#1171992111yescharacteristic
681C23C2×#1171992111yescharacteristic
682C23C2×#1171992111yescharacteristic
683C23#1313324512yes—
684C23#1313325012yes—
685C23C22×D21211yescharacteristic
686Q8—2122no—
687Q8—2122no—
688D4—2122no—
689D4—2124no—
690D4—2124no—
691D4—2124no—
692D4—2124no—
693D4—2124no—
694D4—2122no—
695D4—2122no—
696D4—2122no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—4248no—
728C2×C4—2124no—
729C2×C4—2124no—
730C2×C4—2124no—
731C2×C4—2124no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2122no—
735C2×C4—2124no—
736C2×C4#1313313114yes—
737C2×C4C2×#1171992111yescharacteristic
738C2×C4C2×#1171992111yescharacteristic
739C2×C4C2×#1171992111yescharacteristic
740C2×C4C2×#1171992111yescharacteristic
741C2×C4C2×#1171992111yescharacteristic
742C2×C4C2×#1171992111yescharacteristic
743C2×C4C22×C4×D5311yescharacteristic
744C2×C4C22×C22⋊D5311yescharacteristic
745C8—44no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—4244no—
773C22—2122no—
774C22—2122no—
775C22—2122no—
776C22C2×#1313313112yes—
777C22#1681062512yes—
778C22#1681062512yes—
779C22#1681063912yes—
780C22C22×#1171992111yescharacteristic
781C22C2×#1313324511yescharacteristic
782C22C2×#1313325011yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—4244no—
790C4—2122no—
791C4—2122no—
792C4—2122no—
793C4C2×#1313313112yes—
794C4C2×#1313313112yes—
795C2—21no—
796C2—22no—
797C2—22no—
798C2—21no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—4242no—
804C2C22×#1313313111yescharacteristic
805C2C2×#1681062511yescharacteristic
806C2C2×#1681063911yescharacteristic
subgroupG/H
centerC22C22×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#407C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811134C2
cosocleC22×C4×C53C24
hypercenterC2×#407D53
hypocenterC53#17592
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#16810483C2semidirect
3. #20273288C2semidirect
4. #20273284C2semidirect
5. #20273259C2semidirect
6. #20273220C2semidirect
7. C2×C53×#407C2semidirect
8. C22×#11719945C4semidirect
13. #16811134C4semidirect
14. #16811134C4semidirect
18. C2×#13133196C4semidirect
20. C2×#13133191C4semidirect
25. C2×#13133176C4semidirect
31. #16810483C22semidirect
32. C2×#13133124C22semidirect
33. #16810361C22semidirect
34. #16810358C22semidirect
39. C53×#407C22semidirect
40. C53×#407C22semidirect
47. C2×#11719945C2×C4semidirect
48. C22×Dic106C2×C4semidirect
49. C22×D212C2×C4semidirect
64. #13133196C2×C4semidirect
65. #13133196C2×C4semidirect
72. #13133191C2×C4semidirect
73. #13133191C2×C4semidirect
90. #13133176C2×C4semidirect
94. C2×C4⋊Dic53C2×C4semidirect
95. C2×C4⋊Dic53C2×C4semidirect
393. C2×#407D53semidirect
435. #407C2×D53semidirect
436. #407C2×D53semidirect
446. C53#17592semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
C2×#168104832
#202732882
#202732842
#202732592
#202732202
C2×C53×#4072
#1759253