Finite Group Databasebeta

← #27389435

Subgroups — #27389435

Order 13568.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic
2#20277098C211yesmaximal, characteristic, complemented
3#20275700C212yesmaximal, complemented
4#20275551C212yesmaximal, complemented
5#20275168C214yesmaximal, complemented
6C4×#13133131C214yesmaximal, complemented
7C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9#16811134—21no—
10#16811134—21no—
11#16811134—21no—
12#16811134—21no—
13#16811134—21no—
14#16811134—21no—
15#16811134—21no—
16#16811134—21no—
17C2×#13133200C412yescomplemented
18C2×#13133196C411yescharacteristic, complemented
19C2×#13133196C2211yescharacteristic
20C2×#13133191C411yescharacteristic, complemented
21C2×#13133191C2211yescharacteristic
22C2×#13133186C2212yes—
23C2×C4×C22⋊D53C412yescomplemented
24C2×C4×C22⋊D53C2212yes—
25C2×#13133176—21no—
26C2×#13133176C411yescharacteristic, complemented
27C2×#13133131C2218yes—
28#16810486—21no—
29#16810483—21no—
30#16810483C2212yes—
31#16810479C2212yes—
32C4×C22⋊Dic53—21no—
33C4×C22⋊Dic53C2212yes—
34#16810389C2218yes—
35C24×C4×C53C2211yescharacteristic
36C22×C22⋊C4×C53C2212yes—
37C22×C42×C53—21no—
38C4×C22⋊C4×C53—21no—
39C4×C22⋊C4×C53—21no—
40C4×C22⋊C4×C53C2212yes—
41C4×C22⋊C4×C53C2212yes—
42C2×#95×C53—21no—
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—21no—
46C2×#11719945—21no—
47C2×#11719945—44no—
48C22×Dic106C2×C411yescharacteristic, complemented
49C22×D212C2×C411yescharacteristic, complemented
50C22×C22⋊D53C2×C412yes—
51C22×C22⋊D53C2×C412yes—
52C22×C22⋊D53C2312yes—
53C22×C4×D53C2×C412yescomplemented
54#13133200—22no—
55#13133200—22no—
56#13133200—22no—
57#13133200—22no—
58#13133196—21no—
59#13133196—21no—
60#13133196—21no—
61#13133196—21no—
62#13133196—21no—
63#13133196—21no—
64#13133196—21no—
65#13133196—21no—
66#13133191—21no—
67#13133191—21no—
68#13133191—21no—
69#13133191—21no—
70#13133191—21no—
71#13133191—21no—
72#13133191—21no—
73#13133191—21no—
74#13133186—22no—
75#13133186—22no—
76#13133186—22no—
77#13133186—22no—
78C4×C22⋊D53—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—
86#13133176—21no—
87#13133176—21no—
88#13133176—21no—
89#13133176—21no—
90#13133176—44no—
91C2×C4⋊Dic53—22no—
92C2×C4⋊Dic53C2×C411yescharacteristic, complemented
93C2×C4⋊Dic53C2×C411yescharacteristic, complemented
94C2×#11719919C2×C412yescomplemented
95C2×#11719919C2×C412yescomplemented
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53C2×C412yes—
99C2×C22⋊Dic53C2×C412yes—
100C2×C22⋊Dic53C2314yes—
101C2×C22⋊Dic53C2312yes—
102C2×#11719921C2×C412yescomplemented
103C2×#11719921C2×C412yescomplemented
104C2×C4×Dic53—22no—
105C2×C4×Dic53C2×C412yescomplemented
106#13133131—216no—
107#13133124—22no—
108#13133124—22no—
109C25×C53C2311yescharacteristic
110C23×C4×C53—22no—
111C23×C4×C53—44no—
112C23×C4×C53C2×C411yescharacteristic
113C23×C4×C53C2×C411yescharacteristic
114C23×C4×C53C2×C411yescharacteristic
115C23×C4×C53C2×C411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53D411yescharacteristic
118C23×C4×C53D411yescharacteristic
119C23×C4×C53D411yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53D411yescharacteristic
122C23×C4×C53D411yescharacteristic
123C23×C4×C53D411yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C2×C22⋊C4×C53—28no—
127C2×C22⋊C4×C53—22no—
128C2×C22⋊C4×C53C2314yes—
129C2×C42×C53—22no—
130C2×C42×C53—22no—
131C2×C42×C53—44no—
132#95×C53—22no—
133#95×C53—22no—
134C24×C53—24no—
135C24×C53—42no—
136C24×C53—42no—
137C24×C53C22×C411yescharacteristic
138C24×C53C22×C411yescharacteristic
139C24×C53C2×D411yescharacteristic
140C24×C53C2×D411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C24×C53C2411yescharacteristic
144C23×D53C22×C412yes—
145C22×C4×C53—24no—
146C22×C4×C53—24no—
147C22×C4×C53—24no—
148C22×C4×C53—28no—
149C22×C4×C53—24no—
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×C53—42no—
160C22×C4×C53—42no—
161C22×C4×C53—44no—
162C22×C4×C53—44no—
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×C53C22⋊C411yescharacteristic
178C22×C4×C53C22⋊C411yescharacteristic
179C22×C4×C53C22×C411yescharacteristic
180C22×C4×C53C22×C411yescharacteristic
181C22×C4×C53C22×C411yescharacteristic
182C22×C4×C53C22×C411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D411yescharacteristic
191C2×C22⋊D53—22no—
192C2×C22⋊D53—22no—
193C2×C22⋊D53—22no—
194C2×C22⋊D53—22no—
195C2×C22⋊D53—22no—
196C2×C22⋊D53—22no—
197C2×C22⋊D53—28no—
198C2×C22⋊D53—44no—
199C2×C22⋊D53—44no—
200C22×Dic53—24no—
201C22×Dic53C22×C412yes—
202C22×Dic53C22×C412yes—
203C22×Dic53C22×C412yes—
204#11719945—44no—
205#11719945—44no—
206#11719945—44no—
207#11719945—44no—
208C2×D212—21no—
209C2×D212—21no—
210C2×D212—42no—
211C2×C4×D53—22no—
212C2×C4×D53—22no—
213C2×C4×D53—44no—
214C2×Dic106—21no—
215C2×Dic106—21no—
216C2×Dic106—42no—
217C22⋊C4×C53—28no—
218C22⋊C4×C53—24no—
219C22⋊C4×C53#4118yescomplemented
220C42×C53—44no—
221C42×C53—44no—
222C22⋊Dic53—22no—
223C22⋊Dic53—22no—
224C22⋊Dic53—22no—
225C22⋊Dic53—22no—
226C22⋊Dic53—22no—
227C22⋊Dic53—22no—
228C22⋊Dic53—28no—
229C22⋊Dic53—44no—
230C22⋊Dic53—44no—
231#11719921—22no—
232#11719921—22no—
233#11719921—22no—
234#11719921—22no—
235C4⋊Dic53—21no—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53—44no—
240#11719919—22no—
241#11719919—22no—
242#11719919—22no—
243#11719919—22no—
244C4×Dic53—22no—
245C4×Dic53—22no—
246C4×Dic53—44no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
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—416no—
268C23×C53C2×C22⋊C411yescharacteristic
269C23×C53C2×C22⋊C411yescharacteristic
270C23×C53C2×C22⋊C411yescharacteristic
271C23×C53C2×C22⋊C411yescharacteristic
272C23×C53C23×C411yescharacteristic
273C23×C53C22×D411yescharacteristic
274C23×C53C22×D411yescharacteristic
275C23×C53C2×#4114yes—
276C22×D53—22no—
277C22×D53—24no—
278C22×D53—42no—
279C22×D53—42no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
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—28no—
296C2×C4×C53—41no—
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—416no—
309C2×C4×C53—44no—
310C2×C4×C53—44no—
311C2×C4×C53#9914yescomplemented
312C2×C4×C53C2×C22⋊C411yescharacteristic
313C2×C4×C53C2×C22⋊C411yescharacteristic
314C2×C4×C53C2×C22⋊C411yescharacteristic
315C2×C4×C53C2×C22⋊C411yescharacteristic
316C2×C4×C53C2×C22⋊C411yescharacteristic
317C2×C4×C53C2×C22⋊C411yescharacteristic
318C2×C4×C53C2×C22⋊C411yescharacteristic
319C2×C4×C53C2×C22⋊C411yescharacteristic
320C22⋊D53—44no—
321C22⋊D53—44no—
322C22⋊D53—44no—
323C22⋊D53—44no—
324C22⋊D53—44no—
325C22⋊D53—44no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—24no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—44no—
333C2×Dic53—44no—
334C2×Dic53—44no—
335D212—42no—
336D212—42no—
337C4×D53—44no—
338C4×D53—44no—
339Dic106—42no—
340Dic106—42no—
341#21420—531nomaximal, Sylow
342C22×C53—28no—
343C22×C53—21no—
344C22×C53—21no—
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—44no—
360C22×C53—44no—
361C22×C53—44no—
362C22×C53—44no—
363C22×C53—44no—
364C22×C53—44no—
365C22×C53C2×#9912yes—
366C22×C53#41012yes—
367C22×C53C22×C22⋊C411yescharacteristic
368C22×C53C4×#4112yes—
369C22×C53#52512yes—
370C22×C53#53212yes—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—84no—
375C4×C53—21no—
376C4×C53—21no—
377C4×C53—21no—
378C4×C53—21no—
379C4×C53—21no—
380C4×C53—21no—
381C4×C53—48no—
382C4×C53C2×#9912yes—
383C4×C53C2×#9912yes—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387Dic53—84no—
388C2×#525—531no—
389#2280—531no—
390C2×C4×C22⋊C4D5311yescharacteristic, complemented
391#1996—532no—
392#1964—532no—
393#1898—534no—
394C4×#99—534no—
395C2×C53—22no—
396C2×C53—22no—
397C2×C53—22no—
398C2×C53—22no—
399C2×C53—22no—
400C2×C53—41no—
401C2×C53—41no—
402C2×C53#229711yescharacteristic
403C2×C53C22×#9911yescharacteristic
404C2×C53C2×#41011yescharacteristic
405D53—82no—
406C22×#41—531no—
407C24×C4C2×D5311yescharacteristic
408#525—1061no—
409#525—1061no—
410#525—1061no—
411#525—1061no—
412#525—1061no—
413#525—1061no—
414#525—1061no—
415#525—1061no—
416C2×#123—532no—
417C2×C22⋊Q8—531no—
418C2×C22⋊Q8—531no—
419C2×#121—531no—
420C2×#121—531no—
421C2×#120—532no—
422C2×C4×D4—532no—
423C2×C4×D4—532no—
424C2×#117—531no—
425C2×#117—1061no—
426C22×C22⋊C4C2×D5312yes—
427C22×C42—21no—
428C2×#99—538no—
429#381—1061no—
430#380—532no—
431#380—1061no—
432#379—532no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—532no—
436C4×C22⋊C4—1061no—
437C4×C22⋊C4C2×D5312yes—
438C4×C22⋊C4C2×D5312yes—
439C2×#95—21no—
440#342—538no—
441C53#2142011yescharacteristic, complemented, Sylow
442C25C22×D5311yescharacteristic
443C2×#41—1061no—
444C2×#41—1061no—
445C2×#41—1061no—
446C2×#41—1061no—
447C2×#41—2124no—
448C22×Q8—531no—
449C22×D4—532no—
450C22×D4—532no—
451C22×D4—532no—
452C22×D4—531no—
453C23×C4—22no—
454C23×C4—44no—
455C23×C4—532no—
456C23×C4C4×D5311yescharacteristic
457C23×C4C4×D5311yescharacteristic
458C23×C4C4×D5311yescharacteristic
459C23×C4C4×D5311yescharacteristic
460C23×C4D21211yescharacteristic
461C23×C4D21211yescharacteristic
462C23×C4D21211yescharacteristic
463C23×C4D21211yescharacteristic
464C23×C4C22⋊D5311yescharacteristic
465C23×C4C22⋊D5311yescharacteristic
466C23×C4C22⋊D5311yescharacteristic
467C23×C4C22⋊D5311yescharacteristic
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470#123—1062no—
471#123—1062no—
472#123—1062no—
473#123—1062no—
474C22⋊Q8—1061no—
475C22⋊Q8—1061no—
476C22⋊Q8—1061no—
477C22⋊Q8—1061no—
478C22⋊Q8—1061no—
479C22⋊Q8—1061no—
480C22⋊Q8—1061no—
481C22⋊Q8—1061no—
482#121—1061no—
483#121—1061no—
484#121—1061no—
485#121—1061no—
486#121—1061no—
487#121—1061no—
488#121—1061no—
489#121—1061no—
490#120—1062no—
491#120—1062no—
492#120—1062no—
493#120—1062no—
494C4×D4—1062no—
495C4×D4—1062no—
496C4×D4—1062no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1062no—
500C4×D4—1062no—
501C4×D4—1062no—
502#117—1061no—
503#117—1061no—
504#117—1061no—
505#117—1061no—
506#117—2124no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—532no—
510C2×C4⋊C4—532no—
511C2×C4⋊C4—1062no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—532no—
515C2×C22⋊C4—532no—
516C2×C22⋊C4—532no—
517C2×C22⋊C4—532no—
518C2×C22⋊C4—532no—
519C2×C22⋊C4—534no—
520C2×C22⋊C4—1062no—
521C2×C22⋊C4—1062no—
522C2×C22⋊C4C22×D5314yes—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—44no—
526C2×C42—532no—
527C2×C42—1062no—
528#99—10616no—
529#95—22no—
530#95—22no—
531#95—1062no—
532#95—1062no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24—532no—
537C24C2×C4×D5311yescharacteristic
538C24C2×C4×D5311yescharacteristic
539C24C2×D21211yescharacteristic
540C24C2×D21211yescharacteristic
541C24C2×C22⋊D5311yescharacteristic
542C24C2×C22⋊D5311yescharacteristic
543C24C23×D5311yescharacteristic
544#41—2124no—
545#41—2124no—
546#41—2124no—
547#41—2124no—
548C2×Q8—1061no—
549C2×Q8—1061no—
550C2×Q8—2122no—
551C2×D4—1062no—
552C2×D4—1062no—
553C2×D4—1062no—
554C2×D4—1062no—
555C2×D4—1062no—
556C2×D4—1062no—
557C2×D4—1068no—
558C2×D4—1061no—
559C2×D4—1061no—
560C2×D4—2122no—
561C2×D4—2124no—
562C2×D4—2124no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—532no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1064no—
587C22×C4—2124no—
588C22×C4#1171992111yescharacteristic
589C22×C4#1171992111yescharacteristic
590C22×C4#1171992111yescharacteristic
591C22×C4#1171992111yescharacteristic
592C22×C4#1171992111yescharacteristic
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×C4C2×C4×D5311yescharacteristic
605C22×C4C2×C4×D5311yescharacteristic
606C22×C4C2×C4×D5311yescharacteristic
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4C2×D21211yescharacteristic
609C22×C4C2×D21211yescharacteristic
610C22×C4C2×D21211yescharacteristic
611C22×C4C2×D21211yescharacteristic
612C22×C4C2×C22⋊D5311yescharacteristic
613C22×C4C2×C22⋊D5311yescharacteristic
614C22×C4C2×C22⋊D5311yescharacteristic
615C22×C4C2×C22⋊D5311yescharacteristic
616C4⋊C4—1061no—
617C4⋊C4—1061no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4—1062no—
621C4⋊C4—1062no—
622C4⋊C4—1062no—
623C4⋊C4—1062no—
624C4⋊C4—2124no—
625C22⋊C4—28no—
626C22⋊C4—24no—
627C22⋊C4—1062no—
628C22⋊C4—1062no—
629C22⋊C4—1062no—
630C22⋊C4—1062no—
631C22⋊C4—1062no—
632C22⋊C4—1062no—
633C22⋊C4—1062no—
634C22⋊C4—1062no—
635C22⋊C4—1062no—
636C22⋊C4—1062no—
637C22⋊C4—1068no—
638C22⋊C4—2124no—
639C22⋊C4—2124no—
640C22⋊C4#1171994518yescomplemented
641C42—44no—
642C42—44no—
643C42—1062no—
644C42—1062no—
645C42—2124no—
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—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—416no—
667C23—1064no—
668C23—1062no—
669C23—2122no—
670C23—2122no—
671C23C2×#1171992111yescharacteristic
672C23C2×#1171992111yescharacteristic
673C23C2×#1171992111yescharacteristic
674C23C2×#1171992111yescharacteristic
675C23C22×C4×D5311yescharacteristic
676C23C22×C22⋊D5311yescharacteristic
677C23C22×D21211yescharacteristic
678C23C2×#1171994514yes—
679Q8—2122no—
680Q8—2122no—
681D4—2122no—
682D4—2124no—
683D4—2124no—
684D4—2124no—
685D4—2124no—
686D4—2124no—
687D4—2124no—
688D4—2122no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—28no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—44no—
718C2×C4—416no—
719C2×C4—44no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1064no—
724C2×C4—2124no—
725C2×C4—2124no—
726C2×C4—2124no—
727C2×C4—2124no—
728C2×C4—2124no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4#1313313114yescomplemented
732C2×C4C2×#1171992111yescharacteristic
733C2×C4C2×#1171992111yescharacteristic
734C2×C4C2×#1171992111yescharacteristic
735C2×C4C2×#1171992111yescharacteristic
736C2×C4C2×#1171992111yescharacteristic
737C2×C4C2×#1171992111yescharacteristic
738C2×C4C2×#1171992111yescharacteristic
739C2×C4C2×#1171992111yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—4244no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22C2×#1313313112yes—
768C22#1681059612yes—
769C22C22×#1171992111yescharacteristic
770C22C4×#1171994512yes—
771C22#1681113412yes—
772C22#1681117312yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—4244no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4C2×#1313313112yes—
785C4C2×#1313313112yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—4242no—
794C2#2027720511yescharacteristic
795C2C22×#1313313111yescharacteristic
796C2C2×#1681059611yescharacteristic
subgroupG/H
centerC2×C4C2×#11719921
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC2×C4×C22⋊C4×C53C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811134C2
cosocleC24×C53C24
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#21420
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20277098C2semidirect
3. #20275700C2semidirect
4. #20275551C2semidirect
5. #20275168C2semidirect
6. C4×#13133131C2semidirect
7. C2×C4×C22⋊C4×C53C2semidirect
8. C22×#11719945C4semidirect
17. C2×#13133200C4semidirect
18. C2×#13133196C4semidirect
20. C2×#13133191C4semidirect
23. C2×C4×C22⋊D53C4semidirect
26. C2×#13133176C4semidirect
48. C22×Dic106C2×C4semidirect
49. C22×D212C2×C4semidirect
53. C22×C4×D53C2×C4semidirect
92. C2×C4⋊Dic53C2×C4semidirect
93. C2×C4⋊Dic53C2×C4semidirect
94. C2×#11719919C2×C4semidirect
95. C2×#11719919C2×C4semidirect
102. C2×#11719921C2×C4semidirect
103. C2×#11719921C2×C4semidirect
105. C2×C4×Dic53C2×C4semidirect
219. C22⋊C4×C53#41semidirect
311. C2×C4×C53#99semidirect
390. C2×C4×C22⋊C4D53semidirect
441. C53#21420semidirect
640. C22⋊C4#11719945semidirect
731. C2×C4#13133131semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
#202770982
#202757002
#202755512
#202751682
C4×#131331312
C2×C4×C22⋊C4×C532
#2142053