Finite Group Databasebeta

← #27351448

Subgroups — #27351448

Order 13568.

1470 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811134C211yesmaximal, characteristic
2C22×C22⋊#88322C211yesmaximal, characteristic, complemented
3#20273286C212yesmaximal, complemented
4#20273282C212yesmaximal, complemented
5#20273269C214yesmaximal, complemented
6#20273204C214yesmaximal, complemented
7C53×#2280C211yesmaximal, characteristic, complemented
8C22×#11719945C411yescharacteristic, complemented
9C23×#88322—21no—
10#16811134—21no—
11#16811134—21no—
12#16811134—21no—
13#16811134—21no—
14#16811134C412yescomplemented
15#16811134C412yescomplemented
16#16811134C2212yes—
17#16811134C2212yes—
18C2×#13133200—21no—
19C2×#13133196C411yescharacteristic, complemented
20C2×#13133196C2211yescharacteristic
21C2×#13133191C411yescharacteristic, complemented
22C2×#13133191C2211yescharacteristic
23C2×#13133186—21no—
24C2×C4×C22⋊D53—21no—
25C2×C4×C22⋊D53—21no—
26C2×#13133176C411yescharacteristic, complemented
27C2×C22⋊#88322—21no—
28C2×C22⋊#88322—21no—
29C2×C22⋊#88322—21no—
30C2×C22⋊#88322C2212yes—
31C2×C22⋊#88322C2212yescomplemented
32C2×C22⋊#88322C2212yescomplemented
33#16810359C2218yescomplemented
34#16810356C2218yescomplemented
35C24×C4×C53C2211yescharacteristic
36C2×#117×C53—21no—
37C53×#381C2212yescomplemented
38C53×#380—21no—
39C53×#380C2212yes—
40C53×#379—21no—
41C4×C22⋊C4×C53—21no—
42C4×C22⋊C4×C53C2212yescomplemented
43C2×#11719945—21no—
44C2×#11719945—21no—
45C2×#11719945—44no—
46C2×#11719945C2×C412yes—
47C2×#11719945C2×C412yes—
48C22×Dic106C2×C411yescharacteristic
49C22×D212C2×C411yescharacteristic
50C22×C22⋊D53—21no—
51C22×C22⋊D53—21no—
52C22×C22⋊D53—21no—
53C22×C4×D53—21no—
54C22×#88322—22no—
55C22×#88322—22no—
56C22×#88322—22no—
57C22×#88322—44no—
58#13133200—22no—
59#13133200—22no—
60#13133200—22no—
61#13133200—22no—
62#13133196—21no—
63#13133196—21no—
64#13133196—21no—
65#13133196—21no—
66#13133196C2×C412yes—
67#13133196C2×C412yes—
68#13133196C2×C412yes—
69#13133196C2312yes—
70#13133191—21no—
71#13133191—21no—
72#13133191—21no—
73#13133191—21no—
74#13133191C2×C412yes—
75#13133191C2×C412yes—
76#13133191C2×C412yes—
77#13133191C2312yes—
78#13133186—22no—
79#13133186—22no—
80#13133186—22no—
81#13133186—22no—
82C4×C22⋊D53—22no—
83C4×C22⋊D53—22no—
84C4×C22⋊D53—22no—
85C4×C22⋊D53—22no—
86C4×C22⋊D53—22no—
87C4×C22⋊D53—22no—
88C4×C22⋊D53—22no—
89C4×C22⋊D53—22no—
90#13133176—21no—
91#13133176—21no—
92#13133176C2×C412yes—
93#13133176C2×C412yes—
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×C4⋊Dic53C2×C411yescharacteristic
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×#11719921—21no—
102C2×#11719921—21no—
103C2×C4×Dic53—21no—
104C22⋊#88322—22no—
105C22⋊#88322—22no—
106C22⋊#88322—22no—
107C22⋊#88322C2314yes—
108C25×C53D411yescharacteristic
109C23×C4×C53—44no—
110C23×C4×C53C2×C411yescharacteristic
111C23×C4×C53C2×C411yescharacteristic
112C23×C4×C53C2×C411yescharacteristic
113C23×C4×C53C2×C411yescharacteristic
114C23×C4×C53D411yescharacteristic
115C23×C4×C53D411yescharacteristic
116C23×C4×C53D411yescharacteristic
117C23×C4×C53D411yescharacteristic
118C23×C4×C53D411yescharacteristic
119C23×C4×C53D411yescharacteristic
120C23×C4×C53D411yescharacteristic
121C23×C4×C53C2311yescharacteristic
122C23×C4×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124#117×C53—44no—
125C2×C4⋊C4×C53—22no—
126C2×C22⋊C4×C53—22no—
127C2×C22⋊C4×C53—22no—
128C2×C22⋊C4×C53—22no—
129C2×C42×C53—22no—
130#95×C53—22no—
131#95×C53C2314yes—
132C24×C53—24no—
133C24×C53—42no—
134C24×C53—42no—
135C24×C53C22⋊C411yescharacteristic
136C24×C53C22⋊C411yescharacteristic
137C24×C53C22⋊C411yescharacteristic
138C24×C53C22⋊C411yescharacteristic
139C24×C53C2×D411yescharacteristic
140C24×C53C2×D411yescharacteristic
141C24×C53C2×D411yescharacteristic
142C23×D53—21no—
143C22×C4×C53—24no—
144C22×C4×C53—24no—
145C22×C4×C53—24no—
146C22×C4×C53—24no—
147C22×C4×C53—42no—
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×C53C22⋊C411yescharacteristic
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×C53C2×D411yescharacteristic
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×C53C2411yescharacteristic
186C2×C22⋊D53—22no—
187C2×C22⋊D53—22no—
188C2×C22⋊D53—22no—
189C2×C22⋊D53—22no—
190C2×C22⋊D53—22no—
191C2×C22⋊D53—22no—
192C2×C22⋊D53—44no—
193C2×C22⋊D53—44no—
194C2×C22⋊D53—44no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198#11719945—44no—
199#11719945—44no—
200#11719945—44no—
201#11719945—44no—
202C2×D212—21no—
203C2×D212—42no—
204C2×D212C22×C412yes—
205C2×C4×D53—22no—
206C2×C4×D53—22no—
207C2×C4×D53—44no—
208C2×Dic106—21no—
209C2×Dic106—42no—
210C2×Dic106C22×C412yes—
211C4⋊C4×C53—44no—
212C22⋊C4×C53—44no—
213C22⋊C4×C53—44no—
214C22⋊C4×C53—44no—
215C42×C53—44no—
216C22⋊Dic53—22no—
217C22⋊Dic53—22no—
218C22⋊Dic53—22no—
219C22⋊Dic53—22no—
220C22⋊Dic53—22no—
221C22⋊Dic53—22no—
222#11719921—22no—
223#11719921—22no—
224#11719921—22no—
225#11719921—22no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53C22×C412yes—
229C4⋊Dic53C22×C412yes—
230#11719919—22no—
231#11719919—22no—
232#11719919—22no—
233#11719919—22no—
234C4×Dic53—22no—
235C4×Dic53—22no—
236C2×#88322—24no—
237C2×#88322—44no—
238C2×#88322—44no—
239C2×#88322—44no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—41no—
253C23×C53—41no—
254C23×C53—41no—
255C23×C53—41no—
256C23×C53—41no—
257C23×C53—41no—
258C23×C53—41no—
259C23×C53—41no—
260C23×C53—416no—
261C23×C53C2×C22⋊C411yescharacteristic
262C23×C53C2×C22⋊C411yescharacteristic
263C23×C53C2×C22⋊C411yescharacteristic
264C23×C53C2×C22⋊C411yescharacteristic
265C23×C53C2×C22⋊C411yescharacteristic
266C23×C53C2×C22⋊C411yescharacteristic
267C23×C53#13514yes—
268C23×C53C22×D411yescharacteristic
269C22×D53—22no—
270C22×D53—42no—
271C22×D53—42no—
272C22×D53—42no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
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—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—44no—
301C2×C4×C53—44no—
302C2×C4×C53—44no—
303C2×C4×C53#9914yes—
304C2×C4×C53C2×C22⋊C411yescharacteristic
305C2×C4×C53C2×C22⋊C411yescharacteristic
306C2×C4×C53C2×C22⋊C411yescharacteristic
307C2×C4×C53C2×C22⋊C411yescharacteristic
308C2×C4×C53C2×C22⋊C411yescharacteristic
309C2×C4×C53C2×C22⋊C411yescharacteristic
310C2×C4×C53C23×C411yescharacteristic
311C2×C4×C53C22×D411yescharacteristic
312C22⋊D53—44no—
313C22⋊D53—44no—
314C22⋊D53—44no—
315C22⋊D53—44no—
316C22⋊D53—44no—
317C22⋊D53—44no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324D212—42no—
325D212—42no—
326C4×D53—44no—
327C4×D53—44no—
328Dic106—42no—
329Dic106—42no—
330#88322—44no—
331#17572—531nomaximal, Sylow
332C22×C53—28no—
333C22×C53—21no—
334C22×C53—21no—
335C22×C53—21no—
336C22×C53—21no—
337C22×C53—21no—
338C22×C53—21no—
339C22×C53—21no—
340C22×C53—21no—
341C22×C53—21no—
342C22×C53—21no—
343C22×C53—21no—
344C22×C53—21no—
345C22×C53—21no—
346C22×C53—21no—
347C22×C53—21no—
348C22×C53—21no—
349C22×C53—44no—
350C22×C53—44no—
351C22×C53—44no—
352C22×C53—44no—
353C22×C53—44no—
354C22×C53—44no—
355C22×C53C2×#9912yes—
356C22×C53#41612yes—
357C22×C53#41612yes—
358C22×C53#42112yes—
359C22×C53C22×C22⋊C411yescharacteristic
360C22×C53C2×#13512yes—
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—84no—
365C4×C53—21no—
366C4×C53—21no—
367C4×C53—21no—
368C4×C53—21no—
369C4×C53—21no—
370C4×C53—21no—
371C4×C53—84no—
372C4×C53C2×#9912yes—
373C4×C53C2×#9912yes—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377C2×#525—531no—
378C22×C22⋊C8—531no—
379#2280D5311yescharacteristic, complemented
380#1520—532no—
381#1519—532no—
382#1516—534no—
383#1501—534no—
384C2×C53—22no—
385C2×C53—22no—
386C2×C53—22no—
387C2×C53—22no—
388C2×C53—22no—
389C2×C53—41no—
390C2×C53—41no—
391C2×C53C22×#9911yescharacteristic
392C2×C53C2×#41611yescharacteristic
393C2×C53C2×#42111yescharacteristic
394D53—82no—
395C22×#41—531no—
396C24×C4C2×D5311yescharacteristic
397C23×C8—1061no—
398#525—532no—
399#525—532no—
400#525—532no—
401#525—532no—
402#525—1061no—
403#525—1061no—
404#525—1061no—
405#525—1061no—
406C2×#123—1061no—
407C2×C22⋊Q8—531no—
408C2×C22⋊Q8—531no—
409C2×#121—531no—
410C2×#121—531no—
411C2×#120—1061no—
412C2×C4×D4—1061no—
413C2×C4×D4—1061no—
414C2×#117—21no—
415C2×#117—531no—
416C2×C22⋊C8—532no—
417C2×C22⋊C8—532no—
418C2×C22⋊C8—532no—
419C2×C22⋊C8—1061no—
420C2×C22⋊C8—1061no—
421C2×C22⋊C8—1061no—
422#381C2×D5312yescomplemented
423#380—21no—
424#380C2×D5312yes—
425#379—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4C2×D5312yescomplemented
428#328—538no—
429#327—538no—
430C53#1757211yescharacteristic, complemented, Sylow
431C25C22⋊D5311yescharacteristic
432C2×#41—532no—
433C2×#41—532no—
434C2×#41—1061no—
435C2×#41—1061no—
436C2×#41—2124no—
437C22×Q8—531no—
438C22×D4—531no—
439C22×D4—1061no—
440C22×D4—1061no—
441C22×D4—1061no—
442C23×C4—44no—
443C23×C4—1061no—
444C23×C4C4×D5311yescharacteristic
445C23×C4C4×D5311yescharacteristic
446C23×C4C4×D5311yescharacteristic
447C23×C4C4×D5311yescharacteristic
448C23×C4D21211yescharacteristic
449C23×C4D21211yescharacteristic
450C23×C4D21211yescharacteristic
451C23×C4D21211yescharacteristic
452C23×C4C22⋊D5311yescharacteristic
453C23×C4C22⋊D5311yescharacteristic
454C23×C4C22⋊D5311yescharacteristic
455C23×C4C22×D5311yescharacteristic
456C23×C4C22×D5311yescharacteristic
457C23×C4C22×D5311yescharacteristic
458C22×C8—1062no—
459C22×C8—1062no—
460C22×C8—1062no—
461C22×C8—2124no—
462#123—1062no—
463#123—1062no—
464#123—1062no—
465#123—1062no—
466C22⋊Q8—532no—
467C22⋊Q8—532no—
468C22⋊Q8—532no—
469C22⋊Q8—532no—
470C22⋊Q8—1061no—
471C22⋊Q8—1061no—
472C22⋊Q8—1061no—
473C22⋊Q8—1061no—
474#121—532no—
475#121—532no—
476#121—532no—
477#121—532no—
478#121—1061no—
479#121—1061no—
480#121—1061no—
481#121—1061no—
482#120—1062no—
483#120—1062no—
484#120—1062no—
485#120—1062no—
486C4×D4—1062no—
487C4×D4—1062no—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—1062no—
491C4×D4—1062no—
492C4×D4—1062no—
493C4×D4—1062no—
494#117—44no—
495#117—532no—
496#117—532no—
497#117—1061no—
498#117—1061no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—1061no—
508C2×C22⋊C4—1061no—
509C2×C22⋊C4—1061no—
510C2×C22⋊C4—1061no—
511C2×C22⋊C4—1061no—
512C2×C42—22no—
513C2×C42—1061no—
514C22⋊C8—534no—
515C22⋊C8—1062no—
516C22⋊C8—1062no—
517C22⋊C8—1062no—
518#95—22no—
519#95C22×D5314yes—
520C24—24no—
521C24—42no—
522C24—42no—
523C24—1061no—
524C24#1171992111yescharacteristic
525C24#1171992111yescharacteristic
526C24#1171992111yescharacteristic
527C24#1171992111yescharacteristic
528C24C2×C22⋊D5311yescharacteristic
529C24C2×C22⋊D5311yescharacteristic
530C24C2×C22⋊D5311yescharacteristic
531#41—2124no—
532#41—2124no—
533#41—2124no—
534#41—2124no—
535C2×Q8—532no—
536C2×Q8—1061no—
537C2×Q8—2122no—
538C2×D4—532no—
539C2×D4—1062no—
540C2×D4—1062no—
541C2×D4—1062no—
542C2×D4—1062no—
543C2×D4—1062no—
544C2×D4—1062no—
545C2×D4—1061no—
546C2×D4—2122no—
547C2×D4—2124no—
548C2×D4—2124no—
549C2×D4—2124no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—2124no—
571C22×C4#1171992111yescharacteristic
572C22×C4#1171992111yescharacteristic
573C22×C4#1171992111yescharacteristic
574C22×C4#1171992111yescharacteristic
575C22×C4#1171992111yescharacteristic
576C22×C4#1171992111yescharacteristic
577C22×C4#1171992111yescharacteristic
578C22×C4#1171992111yescharacteristic
579C22×C4#1171992111yescharacteristic
580C22×C4#1171992111yescharacteristic
581C22×C4#1171992111yescharacteristic
582C22×C4#1171992111yescharacteristic
583C22×C4C2×C4×D5311yescharacteristic
584C22×C4C2×C4×D5311yescharacteristic
585C22×C4C2×C4×D5311yescharacteristic
586C22×C4C2×C4×D5311yescharacteristic
587C22×C4C2×C4×D5311yescharacteristic
588C22×C4C2×C4×D5311yescharacteristic
589C22×C4C2×D21211yescharacteristic
590C22×C4C2×D21211yescharacteristic
591C22×C4C2×D21211yescharacteristic
592C22×C4C2×D21211yescharacteristic
593C22×C4C2×D21211yescharacteristic
594C22×C4C2×D21211yescharacteristic
595C22×C4C2×C22⋊D5311yescharacteristic
596C22×C4C2×C22⋊D5311yescharacteristic
597C22×C4C2×C22⋊D5311yescharacteristic
598C22×C4C23×D5311yescharacteristic
599C2×C8—1064no—
600C2×C8—2124no—
601C2×C8—2124no—
602C2×C8—2124no—
603C4⋊C4—44no—
604C4⋊C4—532no—
605C4⋊C4—532no—
606C4⋊C4—1061no—
607C4⋊C4—1061no—
608C4⋊C4—1062no—
609C4⋊C4—1062no—
610C4⋊C4—1062no—
611C4⋊C4—1062no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—1062no—
616C22⋊C4—1062no—
617C22⋊C4—1062no—
618C22⋊C4—1062no—
619C22⋊C4—1062no—
620C22⋊C4—1062no—
621C22⋊C4—1062no—
622C22⋊C4—1062no—
623C22⋊C4—1062no—
624C22⋊C4—1062no—
625C42—44no—
626C42—1062no—
627C42—1062no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—416no—
649C23—1062no—
650C23—2122no—
651C23—2122no—
652C23—2122no—
653C23C2×#1171992111yescharacteristic
654C23C2×#1171992111yescharacteristic
655C23C2×#1171992111yescharacteristic
656C23C2×#1171992111yescharacteristic
657C23C2×#1171992111yescharacteristic
658C23C2×#1171992111yescharacteristic
659C23#1313323714yes—
660C23C22×C22⋊D5311yescharacteristic
661Q8—2122no—
662Q8—2122no—
663D4—2122no—
664D4—2124no—
665D4—2124no—
666D4—2124no—
667D4—2124no—
668D4—2124no—
669D4—2124no—
670D4—2122no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—44no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—2124no—
705C2×C4—2122no—
706C2×C4—2122no—
707C2×C4—2122no—
708C2×C4—2124no—
709C2×C4#1313313114yes—
710C2×C4C2×#1171992111yescharacteristic
711C2×C4C2×#1171992111yescharacteristic
712C2×C4C2×#1171992111yescharacteristic
713C2×C4C2×#1171992111yescharacteristic
714C2×C4C2×#1171992111yescharacteristic
715C2×C4C2×#1171992111yescharacteristic
716C2×C4C22×C4×D5311yescharacteristic
717C2×C4C22×D21211yescharacteristic
718C8—2124no—
719C22—28no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—44no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—4244no—
743C22—2122no—
744C22—2122no—
745C22—2122no—
746C22C2×#1313313112yes—
747C22#1681061712yes—
748C22#1681061712yes—
749C22#1681064112yes—
750C22C22×#1171992111yescharacteristic
751C22C2×#1313323712yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—84no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4C2×#1313313112yes—
763C4C2×#1313313112yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—4242no—
772C2C22×#1313313111yescharacteristic
773C2C2×#1681061711yescharacteristic
774C2C2×#1681064111yescharacteristic
subgroupG/H
centerC2×C4C2×#11719921
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2280C2
socleC22×C53C22×C22⋊C4
prime radicalC2×#16811134C2
cosocleC22×C4×C53C24
hypercenter#2280D53
hypocenterC53#17572
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
2. C22×C22⋊#88322C2semidirect
3. #20273286C2semidirect
4. #20273282C2semidirect
5. #20273269C2semidirect
6. #20273204C2semidirect
7. C53×#2280C2semidirect
8. C22×#11719945C4semidirect
14. #16811134C4semidirect
15. #16811134C4semidirect
19. C2×#13133196C4semidirect
21. C2×#13133191C4semidirect
26. C2×#13133176C4semidirect
31. C2×C22⋊#88322C22semidirect
32. C2×C22⋊#88322C22semidirect
33. #16810359C22semidirect
34. #16810356C22semidirect
37. C53×#381C22semidirect
42. C4×C22⋊C4×C53C22semidirect
379. #2280D53semidirect
422. #381C2×D53semidirect
427. C4×C22⋊C4C2×D53semidirect
430. C53#17572semidirect

Maximal subgroups

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

subgroupindex
C2×#168111342
C22×C22⋊#883222
#202732862
#202732822
#202732692
#202732042
C53×#22802
#1757253