Finite Group Databasebeta

← #27400397

Subgroups — #27400397

Order 13568.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811338C211yesmaximal, characteristic
2#20277644C211yesmaximal, characteristic, complemented
3#20275688C211yesmaximal, characteristic, complemented
4#20275666C211yesmaximal, characteristic, complemented
5#20275153C211yesmaximal, characteristic, complemented
6#20275143C211yesmaximal, characteristic, complemented
7#20275035C211yesmaximal, characteristic, complemented
8#20275030C211yesmaximal, characteristic, complemented
9#20274811C211yesmaximal, characteristic, complemented
10#20274811C211yesmaximal, characteristic, complemented
11#20274726C211yesmaximal, characteristic, complemented
12#20274541C211yesmaximal, characteristic, complemented
13#20274435C211yesmaximal, characteristic, complemented
14#20274432C211yesmaximal, characteristic, complemented
15C2×C53×#435C211yesmaximal, characteristic, complemented
16#16811338—24no—
17#16811338C418yescomplemented
18C2×#13133217C2211yescharacteristic
19C2×#13133203—21no—
20C2×#13133203—21no—
21C2×#13133191C2211yescharacteristic
22C2×#13133191C2211yescharacteristic
23C2×#13133188—21no—
24C2×C4×D212C2211yescharacteristic
25C2×#13133176C2211yescharacteristic
26C2×#13133176C2211yescharacteristic
27C2×#13133176C2211yescharacteristic
28C2×#13133175—21no—
29C22×C4⋊Dic53C2211yescharacteristic
30C2×#13133139C2211yescharacteristic
31C2×#13133139C2211yescharacteristic
32C2×#13133139C2211yescharacteristic
33C2×#13133139C2211yescharacteristic
34#16810516—21no—
35#16810509—21no—
36#16810503—21no—
37#16810489C2211yescharacteristic
38#16810483C2211yescharacteristic
39#16810483C2211yescharacteristic
40C4×C4⋊Dic53C2211yescharacteristic
41C22⋊C4×Dic53—21no—
42#16810386C2211yescharacteristic
43#16810386C2211yescharacteristic
44#16810386C2211yescharacteristic
45#16810386C2211yescharacteristic
46#16810386C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810386C2211yescharacteristic
50#16810386C2211yescharacteristic
51#16810386C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810386C2211yescharacteristic
54C22×M16×C53C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C2×C4×D4×C53C2211yescharacteristic
57C53×#435—24no—
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C2×#97×C53C2211yescharacteristic
62C22×Dic106—21no—
63C22×D212C2311yescharacteristic
64C22×C22⋊D53—21no—
65C22×C22⋊D53—21no—
66C23×Dic53—21no—
67C22×C4×D53—21no—
68#13133217—22no—
69#13133217C2×C414yescomplemented
70#13133203—28no—
71#13133203—28no—
72#13133191—22no—
73#13133191—22no—
74#13133191C2×C414yes—
75#13133191C2×C414yescomplemented
76#13133188—28no—
77C4×D212—22no—
78C4×D212C2×C414yescomplemented
79#13133176—22no—
80#13133176—22no—
81#13133176—22no—
82#13133176—41no—
83#13133176C2×C414yes—
84#13133176C2×C414yescomplemented
85#13133175—28no—
86C2×C4⋊Dic53—21no—
87C2×C4⋊Dic53—21no—
88C2×C4⋊Dic53—22no—
89C2×C4⋊Dic53—41no—
90C2×C4⋊Dic53C2311yescharacteristic
91C2×C4⋊Dic53C2311yescharacteristic
92C2×C4⋊Dic53C2311yescharacteristic
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×C4⋊Dic53C2311yescharacteristic
97C2×C22⋊Dic53—21no—
98C2×C22⋊Dic53—21no—
99C2×C22⋊Dic53—21no—
100C2×C22⋊Dic53—21no—
101C2×C22⋊Dic53—21no—
102C2×#11719921—21no—
103C2×#11719921—21no—
104C2×#11719921—21no—
105C2×C4×Dic53—21no—
106C2×C4×Dic53—21no—
107C2×C4×Dic53—21no—
108C2×C4×Dic53—21no—
109#13133139—22no—
110#13133139—22no—
111#13133139—41no—
112#13133139—41no—
113#13133124—21no—
114#13133124—21no—
115#13133124—21no—
116#13133124—21no—
117#13133124—21no—
118C22×D4×C53D411yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C2×M16×C53—22no—
122C2×M16×C53—22no—
123C2×M16×C53—41no—
124C22×C8×C53—22no—
125C22×C8×C53—22no—
126C22×C8×C53—41no—
127C22×C8×C53C2311yescharacteristic
128C22×C8×C53C2311yescharacteristic
129C22×C8×C53C2311yescharacteristic
130C22×C8×C53C2311yescharacteristic
131C4×D4×C53C2×C414yes—
132C4×D4×C53D414yes—
133C2×C4⋊C4×C53D411yescharacteristic
134C2×C22⋊C4×C53D411yescharacteristic
135C2×C22⋊C4×C53D411yescharacteristic
136C2×C42×C53C2311yescharacteristic
137C4⋊C8×C53—22no—
138C22⋊C8×C53—22no—
139C22⋊C8×C53—22no—
140#97×C53—22no—
141C24×C53C2×D411yescharacteristic
142C24×C53C2×D411yescharacteristic
143C23×D53—21no—
144C2×D4×C53—41no—
145C2×D4×C53—41no—
146C2×D4×C53C22⋊C414yes—
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53C22×C412yes—
156C22×C4×C53C22×C412yes—
157C22×C4×C53C2×D411yescharacteristic
158C22×C4×C53C2×D411yescharacteristic
159C22×C4×C53C2×D411yescharacteristic
160C22×C4×C53C2×D411yescharacteristic
161C22×C4×C53C2×D412yes—
162C22×C4×C53C2×D412yes—
163C22×C4×C53C2411yescharacteristic
164C2×C22⋊D53—24no—
165C2×C22⋊D53—24no—
166C2×C22⋊D53—81no—
167C2×C22⋊D53—81no—
168C2×C22⋊D53—81no—
169C2×C22⋊D53—81no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—21no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—42no—
178C22×Dic53—42no—
179C22×Dic53—81no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212—21no—
183C2×D212—21no—
184C2×D212—21no—
185C2×D212C22×C412yes—
186C2×C4×D53—24no—
187C2×C4×D53—42no—
188C2×C4×D53—42no—
189C2×Dic106—24no—
190C2×Dic106—81no—
191C2×Dic106—81no—
192M16×C53—44no—
193C2×C8×C53—21no—
194C2×C8×C53—21no—
195C2×C8×C53—21no—
196C2×C8×C53—21no—
197C2×C8×C53—21no—
198C2×C8×C53—21no—
199C2×C8×C53—21no—
200C2×C8×C53—21no—
201C2×C8×C53—21no—
202C2×C8×C53—21no—
203C2×C8×C53—21no—
204C2×C8×C53—44no—
205C2×C8×C53#4112yes—
206C4⋊C4×C53C22⋊C414yes—
207C22⋊C4×C53C22⋊C414yes—
208C22⋊C4×C53C22⋊C414yes—
209C42×C53C22×C412yes—
210C42×C53C2×D412yes—
211C22⋊Dic53—24no—
212C22⋊Dic53—24no—
213C22⋊Dic53—42no—
214C22⋊Dic53—42no—
215C22⋊Dic53—81no—
216#11719921—24no—
217#11719921—24no—
218#11719921—24no—
219C4⋊Dic53—24no—
220C4⋊Dic53—21no—
221C4⋊Dic53—21no—
222C4⋊Dic53—21no—
223C4⋊Dic53—21no—
224C4⋊Dic53—21no—
225C4⋊Dic53—21no—
226C4⋊Dic53—21no—
227C4⋊Dic53—21no—
228C4⋊Dic53—21no—
229C4⋊Dic53—21no—
230C4⋊Dic53—42no—
231C4⋊Dic53C22×C412yes—
232C4⋊Dic53C22×C412yes—
233C4⋊Dic53C22×C412yes—
234C4⋊Dic53#4112yes—
235C4×Dic53—24no—
236C4×Dic53—24no—
237C4×Dic53—42no—
238C4×Dic53—81no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—21no—
248C23×C53—21no—
249C23×C53—21no—
250C23×C53—21no—
251C23×C53C2×C22⋊C412yes—
252C23×C53C2×C22⋊C412yes—
253C23×C53C22×D411yescharacteristic
254C22×D53—22no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261D4×C53—44no—
262C2×C4×C53—21no—
263C2×C4×C53—21no—
264C2×C4×C53—21no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53C2×C22⋊C412yes—
279C2×C4×C53C2×C22⋊C412yes—
280C2×C4×C53C2×C22⋊C412yes—
281C2×C4×C53C2×C22⋊C412yes—
282C2×C4×C53C23×C411yescharacteristic
283C2×C4×C53C22×D411yescharacteristic
284C2×C4×C53C2×#4111yescharacteristic
285C2×C4×C53C2×#4111yescharacteristic
286C2×C4×C53H(5,𝔽2)11yescharacteristic
287C2×C4×C532−1+411yescharacteristic
288C22⋊D53—84no—
289C22⋊D53—84no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—41no—
295C2×Dic53—41no—
296C2×Dic53—41no—
297C2×Dic53—41no—
298C2×Dic53—41no—
299C2×Dic53—41no—
300C2×Dic53—41no—
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—84no—
312D212—22no—
313D212—22no—
314D212—41no—
315D212—41no—
316C4×D53—48no—
317Dic106—84no—
318C8×C53—22no—
319C8×C53—41no—
320C8×C53—41no—
321C8×C53—41no—
322#22492—531nomaximal, Sylow
323C22×C53—22no—
324C22×C53—22no—
325C22×C53—22no—
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—41no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—41no—
337C22×C53C22×C22⋊C411yescharacteristic
338C22×C53#54611yescharacteristic
339C22×C53#54711yescharacteristic
340C22×C53#57511yescharacteristic
341C22×C53#57511yescharacteristic
342C22×C53#57611yescharacteristic
343C22×C53#57711yescharacteristic
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C2×D53—81no—
348C2×D53—81no—
349C2×D53—81no—
350C2×D53—81no—
351C4×C53—22no—
352C4×C53—22no—
353C4×C53—22no—
354C4×C53—22no—
355C4×C53C4×#4111yescharacteristic
356C4×C53#52011yescharacteristic
357C4×C53#54611yescharacteristic
358C4×C53#54711yescharacteristic
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363Dic53—81no—
364Dic53—81no—
365Dic53—81no—
366C2×#555—531no—
367C2×#435D5311yescharacteristic, complemented
368#2352—531no—
369#1993—531no—
370#1988—531no—
371#1895—531no—
372#1893—531no—
373#1875—531no—
374#1874—531no—
375#1825—531no—
376#1825—531no—
377#1804—531no—
378#1762—531no—
379#1736—531no—
380#1735—531no—
381C2×C53—42no—
382C2×C53—42no—
383C2×C53#233911yescharacteristic
384C2×C53#289611yescharacteristic
385C2×C53#289711yescharacteristic
386C2×C53#331911yescharacteristic
387C2×C53#332111yescharacteristic
388C2×C53#334711yescharacteristic
389C2×C53#334811yescharacteristic
390D53—82no—
391C22×M16C2×D5311yescharacteristic
392C23×C8C2×D5311yescharacteristic
393#555—538no—
394#555—1064no—
395C2×C4⋊Q8—531no—
396C2×#124—1061no—
397C2×#124—1061no—
398C2×#121—531no—
399C2×#121—531no—
400C2×#121—1061no—
401C2×C4×D4—531no—
402C2×C4×D4C2×D5311yescharacteristic
403C2×#117—531no—
404C2×#117—531no—
405C2×#117—531no—
406C2×#117—1061no—
407C22×C4⋊C4—531no—
408#435—24no—
409C2×C4⋊C8C2×D5311yescharacteristic
410C2×#102—531no—
411C2×#102—531no—
412C2×#102—531no—
413C2×#102—531no—
414C2×C22⋊C8C2×D5311yescharacteristic
415C2×C22⋊C8C2×D5311yescharacteristic
416C2×#97C2×D5311yescharacteristic
417#388—1061no—
418#387—1061no—
419#386—1061no—
420#382—531no—
421#380—531no—
422#380—531no—
423C4×C4⋊C4—531no—
424C4×C22⋊C4—1061no—
425#340—531no—
426#340—531no—
427#340—531no—
428#340—531no—
429#340—531no—
430#340—531no—
431#340—531no—
432#340—531no—
433#340—531no—
434#340—531no—
435#340—531no—
436#340—531no—
437C53#2249211yescharacteristic, complemented, Sylow
438C22×Q8—1061no—
439C22×D4—531no—
440C22×D4—1061no—
441C22×D4—1061no—
442C22×D4D21211yescharacteristic
443C23×C4—1061no—
444C23×C4—1061no—
445C23×C4C22×D5311yescharacteristic
446C23×C4C22×D5311yescharacteristic
447C2×M16—22no—
448C2×M16—22no—
449C2×M16—41no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—41no—
453C22×C8C22×D5311yescharacteristic
454C22×C8C22×D5311yescharacteristic
455C22×C8C22×D5311yescharacteristic
456C22×C8C22×D5311yescharacteristic
457C4⋊Q8—534no—
458C4⋊Q8—1062no—
459#124—1068no—
460#124—1068no—
461#121—534no—
462#121—534no—
463#121—1068no—
464#121—1062no—
465#121—1062no—
466C4×D4—534no—
467C4×D4—1062no—
468C4×D4C4×D5314yes—
469C4×D4C22⋊D5314yes—
470#117—534no—
471#117—534no—
472#117—1062no—
473#117—1062no—
474#117—1068no—
475#117—1062no—
476#117—2121no—
477C2×C4⋊C4—531no—
478C2×C4⋊C4—531no—
479C2×C4⋊C4—531no—
480C2×C4⋊C4—531no—
481C2×C4⋊C4—531no—
482C2×C4⋊C4—531no—
483C2×C4⋊C4—531no—
484C2×C4⋊C4—1062no—
485C2×C4⋊C4—1061no—
486C2×C4⋊C4—1061no—
487C2×C4⋊C4—2121no—
488C2×C4⋊C4D21211yescharacteristic
489C2×C22⋊C4—1061no—
490C2×C22⋊C4—1061no—
491C2×C22⋊C4—1061no—
492C2×C22⋊C4—1061no—
493C2×C22⋊C4—1061no—
494C2×C22⋊C4—1061no—
495C2×C22⋊C4—1061no—
496C2×C22⋊C4—1061no—
497C2×C22⋊C4D21211yescharacteristic
498C2×C22⋊C4D21211yescharacteristic
499C2×C42—1061no—
500C2×C42—1061no—
501C2×C42—1061no—
502C2×C42—1061no—
503C2×C42C22×D5311yescharacteristic
504C4⋊C8—22no—
505#102—1062no—
506#102—1062no—
507#102—2121no—
508#102—2121no—
509C22⋊C8—22no—
510C22⋊C8—22no—
511#97—22no—
512#95—1061no—
513#95—1061no—
514#95—1061no—
515#95—1061no—
516#95—1061no—
517C24—1061no—
518C24C2×D21211yescharacteristic
519C24C2×D21211yescharacteristic
520C2×Q8—1064no—
521C2×Q8—4241no—
522C2×Q8—4241no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—532no—
526C2×D4—1064no—
527C2×D4—1064no—
528C2×D4—1061no—
529C2×D4—1061no—
530C2×D4—1061no—
531C2×D4—1061no—
532C2×D4—1061no—
533C2×D4—4241no—
534C2×D4—4241no—
535C2×D4—4241no—
536C2×D4—4241no—
537C2×D4#1171992114yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—1061no—
547C22×C4—1061no—
548C22×C4—1061no—
549C22×C4—1061no—
550C22×C4—1064no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—1061no—
554C22×C4—4241no—
555C22×C4—2122no—
556C22×C4—2122no—
557C22×C4—2122no—
558C22×C4—2122no—
559C22×C4C2×C4×D5312yes—
560C22×C4C2×C4×D5312yes—
561C22×C4C2×D21211yescharacteristic
562C22×C4C2×D21211yescharacteristic
563C22×C4C2×D21211yescharacteristic
564C22×C4C2×D21211yescharacteristic
565C22×C4C2×C22⋊D5312yes—
566C22×C4C2×C22⋊D5312yes—
567C22×C4C23×D5311yescharacteristic
568M16—44no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—44no—
581C2×C8#1171994712yes—
582C4⋊C4—532no—
583C4⋊C4—532no—
584C4⋊C4—532no—
585C4⋊C4—532no—
586C4⋊C4—1064no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—1061no—
590C4⋊C4—1061no—
591C4⋊C4—1061no—
592C4⋊C4—1061no—
593C4⋊C4—1061no—
594C4⋊C4—1061no—
595C4⋊C4—1061no—
596C4⋊C4—1061no—
597C4⋊C4—2122no—
598C4⋊C4#1171992114yes—
599C22⋊C4—1064no—
600C22⋊C4—1064no—
601C22⋊C4—1064no—
602C22⋊C4—1064no—
603C22⋊C4—1064no—
604C22⋊C4—4241no—
605C22⋊C4—2122no—
606C22⋊C4—2122no—
607C22⋊C4#1171992114yes—
608C22⋊C4#1171992114yes—
609C42—1064no—
610C42—1064no—
611C42—4241no—
612C42—2122no—
613C42C2×C4×D5312yes—
614C42C2×C22⋊D5312yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—1062no—
628C23—2121no—
629C23—2121no—
630C23—2121no—
631C23—2121no—
632C23—2121no—
633C23—2121no—
634C23C2×#1171992112yes—
635C23C2×#1171992112yes—
636C23C22×D21211yescharacteristic
637Q8—4244no—
638D4—44no—
639D4—1062no—
640D4—1062no—
641D4—4244no—
642D4—4244no—
643D4—2121no—
644D4—2121no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—4244no—
666C2×C4—2128no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4—2121no—
682C2×C4—2121no—
683C2×C4—2121no—
684C2×C4C2×#1171992112yes—
685C2×C4C2×#1171992112yes—
686C2×C4C2×#1171992112yes—
687C2×C4C2×#1171992112yes—
688C2×C4C22×C4×D5311yescharacteristic
689C2×C4C22×C22⋊D5311yescharacteristic
690C2×C4#41×D5311yescharacteristic
691C2×C4C2×#1171994711yescharacteristic
692C2×C4#1313326211yescharacteristic
693C2×C4#1313326411yescharacteristic
694C8—22no—
695C8—41no—
696C8—41no—
697C8—41no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—4241no—
713C22—4241no—
714C22—4241no—
715C22—4241no—
716C22—2122no—
717C22—2122no—
718C22—2122no—
719C22C22×#1171992111yescharacteristic
720C22#1681126811yescharacteristic
721C22#1681127711yescharacteristic
722C22#1681142311yescharacteristic
723C22#1681142311yescharacteristic
724C22#1681142811yescharacteristic
725C22#1681143511yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—4241no—
731C4—4241no—
732C4—4241no—
733C4—2122no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4C4×#1171994711yescharacteristic
738C4#1681110211yescharacteristic
739C4#1681126711yescharacteristic
740C4#1681127211yescharacteristic
741C2—42no—
742C2—42no—
743C2—4242no—
744C2#2027754011yescharacteristic
745C2#2028323511yescharacteristic
746C2#2028324211yescharacteristic
747C2#2028687311yescharacteristic
748C2#2028690311yescharacteristic
749C2#2028721711yescharacteristic
750C2#2028723211yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811338C2
cosocleC22×C4×C53C24
hypercenterC2×#435D53
hypocenterC53#22492
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #20277644C2semidirect
3. #20275688C2semidirect
4. #20275666C2semidirect
5. #20275153C2semidirect
6. #20275143C2semidirect
7. #20275035C2semidirect
8. #20275030C2semidirect
9. #20274811C2semidirect
10. #20274811C2semidirect
11. #20274726C2semidirect
12. #20274541C2semidirect
13. #20274435C2semidirect
14. #20274432C2semidirect
15. C2×C53×#435C2semidirect
17. #16811338C4semidirect
69. #13133217C2×C4semidirect
75. #13133191C2×C4semidirect
78. C4×D212C2×C4semidirect
84. #13133176C2×C4semidirect
367. C2×#435D53semidirect
437. C53#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#168113382
#202776442
#202756882
#202756662
#202751532
#202751432
#202750352
#202750302
#202748112
#202747262
#202745412
#202744352
#202744322
C2×C53×#4352
#2249253