Finite Group Databasebeta

← #27401468

Subgroups — #27401468

Order 13568.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283369C211yesmaximal, characteristic, complemented
2#20283235C211yesmaximal, characteristic
3#20283161C211yesmaximal, characteristic
4#20275426C211yesmaximal, characteristic, complemented
5#20275419C211yesmaximal, characteristic, complemented
6#20275364C211yesmaximal, characteristic, complemented
7#20275364C211yesmaximal, characteristic, complemented
8#20274993C211yesmaximal, characteristic, complemented
9#20274993C211yesmaximal, characteristic, complemented
10#20274815C211yesmaximal, characteristic, complemented
11#20274757C211yesmaximal, characteristic, complemented
12#20274660C211yesmaximal, characteristic
13#20274559C211yesmaximal, characteristic, complemented
14#20274552C211yesmaximal, characteristic, complemented
15C53×#1753C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133223C2211yescharacteristic
18C2×#13133223C2211yescharacteristic
19C2×#13133176C2211yescharacteristic
20#16810681—21no—
21#16810681—21no—
22#16810677—21no—
23#16810673—21no—
24C2×#13133153C2211yescharacteristic, complemented
25C2×#13133153C2211yescharacteristic, complemented
26#16810649C2211yescharacteristic, complemented
27#16810649C2211yescharacteristic, complemented
28C2×#13133145C2211yescharacteristic
29C2×#13133145C2211yescharacteristic
30C2×#13133145C2211yescharacteristic
31C2×#13133145C2211yescharacteristic
32#16810633C411yescharacteristic, complemented
33#16810633C411yescharacteristic, complemented
34#16810629C411yescharacteristic, complemented
35#16810629C411yescharacteristic, complemented
36#16810625C411yescharacteristic, complemented
37#16810625C411yescharacteristic, complemented
38#16810625C411yescharacteristic, complemented
39#16810625C411yescharacteristic, complemented
40#16810620C2211yescharacteristic
41#16810620C2211yescharacteristic
42#16810620C2211yescharacteristic
43#16810620C2211yescharacteristic
44#16810589C2211yescharacteristic
45#16810589C2211yescharacteristic
46#16810588—21no—
47#16810588—21no—
48#16810587C2211yescharacteristic
49#16810587C2211yescharacteristic
50#16810585—21no—
51C22⋊C8×D53—21no—
52#16810578C2211yescharacteristic, complemented
53#16810578C2211yescharacteristic, complemented
54#16810388C2211yescharacteristic, complemented
55#16810388C2211yescharacteristic, complemented
56#16810383C2211yescharacteristic, complemented
57#16810383C2211yescharacteristic, complemented
58#16810383C2211yescharacteristic, complemented
59#16810383C2211yescharacteristic, complemented
60C22×M16×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C2×#97×C53C2211yescharacteristic, complemented
63C2×C4×C8×C53C2211yescharacteristic, complemented
64C4×C22⋊C4×C53C2211yescharacteristic
65C53×#336C2211yescharacteristic, complemented
66C53×#336C2211yescharacteristic, complemented
67C2×#11719945—21no—
68C2×#11719945—21no—
69C2×#11719945—22no—
70C2×#11719945—22no—
71C2×#11719945—41no—
72C2×#11719945—41no—
73C2×#11719945C2×C411yescharacteristic
74C2×#11719945C2×C411yescharacteristic
75C2×#11719945C2311yescharacteristic
76C2×#11719945C2311yescharacteristic
77C22×Dic106C2×C411yescharacteristic
78C22×D212C2×C411yescharacteristic
79C22×C22⋊D53—21no—
80C22×C4×D53—21no—
81#13133223—22no—
82#13133223—22no—
83#13133223—41no—
84#13133223—41no—
85C2×#11719917C2311yescharacteristic
86C2×#11719917C2311yescharacteristic
87C2×#11719917C2311yescharacteristic
88C2×#11719917C2311yescharacteristic
89C2×#11719912—21no—
90C2×#11719912—21no—
91C2×C8×D53—21no—
92C2×C8×D53—21no—
93#13133176—21no—
94#13133176—21no—
95#13133176C2×C411yescharacteristic
96#13133176C2×C411yescharacteristic
97#13133176C2311yescharacteristic
98#13133176C2311yescharacteristic
99C2×C4⋊Dic53C2×C411yescharacteristic
100C2×C4⋊Dic53C2×C411yescharacteristic
101C2×C22⋊Dic53—21no—
102C2×C4×Dic53—21no—
103#13133153—41no—
104#13133153—41no—
105#13133146—21no—
106#13133146—21no—
107#13133146—21no—
108#13133146—21no—
109#13133145—22no—
110#13133145—22no—
111#13133145—41no—
112#13133145—41no—
113#13133142C2×C411yescharacteristic
114#13133142C2×C411yescharacteristic
115#13133142C2×C411yescharacteristic
116#13133142C2×C411yescharacteristic
117#13133142C2×C411yescharacteristic
118#13133142C2×C411yescharacteristic
119#13133142C2×C411yescharacteristic
120#13133142C2×C411yescharacteristic
121#13133139C2×C411yescharacteristic
122#13133139C2×C411yescharacteristic
123#13133139C2×C411yescharacteristic
124#13133139C2×C411yescharacteristic
125#13133139C2×C411yescharacteristic
126#13133139C2×C411yescharacteristic
127#13133139C2×C411yescharacteristic
128#13133139C2×C411yescharacteristic
129C22⋊#88322—21no—
130C22⋊#88322—21no—
131C22⋊#88322—21no—
132C22⋊#88322—21no—
133#13133129—21no—
134#13133129—21no—
135#13133129—21no—
136#13133129—21no—
137#13133127—21no—
138#13133127—21no—
139C8×Dic53—21no—
140C8×Dic53—21no—
141C23×C4×C53C2311yescharacteristic
142C2×M16×C53—41no—
143C2×M16×C53—41no—
144C2×M16×C53C2×C411yescharacteristic
145C2×M16×C53C2×C411yescharacteristic
146C2×M16×C53C2×C411yescharacteristic
147C2×M16×C53C2×C411yescharacteristic
148C22×C8×C53C2311yescharacteristic
149C22×C8×C53C2311yescharacteristic
150C22×C8×C53C2311yescharacteristic
151C22×C8×C53C2311yescharacteristic
152C2×C22⋊C4×C53—21no—
153C2×C42×C53C2311yescharacteristic
154C2×C42×C53C2311yescharacteristic
155C22⋊C8×C53D411yescharacteristic
156C22⋊C8×C53D411yescharacteristic
157C22⋊C8×C53D411yescharacteristic
158C22⋊C8×C53D411yescharacteristic
159#97×C53—41no—
160C4×C8×C53—41no—
161#95×C53—21no—
162C24×C53#4111yescharacteristic
163C23×D53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C2×D411yescharacteristic
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53#4111yescharacteristic
175C22×C4×C53C2411yescharacteristic
176C2×C22⋊D53—21no—
177C2×C22⋊D53—21no—
178C2×C22⋊D53—21no—
179C2×C22⋊D53—21no—
180C2×C22⋊D53—42no—
181C2×C22⋊D53—42no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—21no—
185#11719945—21no—
186#11719945—21no—
187#11719945—21no—
188#11719945—21no—
189#11719945—21no—
190#11719945—21no—
191#11719945—22no—
192#11719945—22no—
193#11719945—41no—
194#11719945—41no—
195#11719945—42no—
196#11719945—42no—
197#11719945—42no—
198#11719945—42no—
199#11719945#4112yes—
200#11719945#4112yes—
201C2×D212—22no—
202C2×D212—21no—
203C2×D212—41no—
204C2×D212C22×C411yescharacteristic
205C2×D212C22×C411yescharacteristic
206C2×C4×D53—21no—
207C2×C4×D53—21no—
208C2×C4×D53—21no—
209C2×C4×D53—21no—
210C2×C4×D53—42no—
211C2×C4×D53—42no—
212C2×Dic106—22no—
213C2×Dic106—21no—
214C2×Dic106—41no—
215C2×Dic106C22×C411yescharacteristic
216C2×Dic106C22×C411yescharacteristic
217M16×C53—41no—
218M16×C53—41no—
219M16×C53—41no—
220M16×C53—41no—
221C2×C8×C53—21no—
222C2×C8×C53—21no—
223C2×C8×C53—21no—
224C2×C8×C53—21no—
225C2×C8×C53—21no—
226C2×C8×C53—21no—
227C2×C8×C53—21no—
228C2×C8×C53—21no—
229C2×C8×C53C22×C411yescharacteristic
230C2×C8×C53C22×C411yescharacteristic
231C2×C8×C53C22×C411yescharacteristic
232C2×C8×C53C22×C411yescharacteristic
233C2×C8×C53C2×D411yescharacteristic
234C2×C8×C53C2×D411yescharacteristic
235C2×C8×C53C2×D411yescharacteristic
236C2×C8×C53C2×D411yescharacteristic
237C22⋊C4×C53—42no—
238C42×C53—21no—
239C42×C53—21no—
240C42×C53—21no—
241C42×C53—21no—
242C22⋊Dic53—21no—
243C22⋊Dic53—21no—
244C22⋊Dic53—21no—
245C22⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53—21no—
248C4⋊Dic53C22×C411yescharacteristic
249C4⋊Dic53C22×C411yescharacteristic
250C4⋊Dic53C22×C411yescharacteristic
251C4⋊Dic53C22×C411yescharacteristic
252C4×Dic53—21no—
253C4×Dic53—21no—
254C4×Dic53—21no—
255C4×Dic53—21no—
256#11719917—21no—
257#11719917—21no—
258#11719917—21no—
259#11719917—21no—
260#11719917—21no—
261#11719917—21no—
262#11719917—21no—
263#11719917—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268#11719912—42no—
269#11719912—42no—
270C8×D53—42no—
271C8×D53—42no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53—41no—
275C23×C53—41no—
276C23×C53C4×D411yescharacteristic
277C23×C53C4×D411yescharacteristic
278C23×C53C2×#4111yescharacteristic
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—42no—
282C22×D53—42no—
283C22×D53—81no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—22no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53C4×D411yescharacteristic
301C2×C4×C53C4×D411yescharacteristic
302C2×C4×C53C23×C411yescharacteristic
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53H(5,𝔽2)11yescharacteristic
307C2×C4×C53H(5,𝔽2)11yescharacteristic
308C22⋊D53—22no—
309C22⋊D53—22no—
310C22⋊D53—42no—
311C22⋊D53—42no—
312C22⋊D53—41no—
313C22⋊D53—41no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—21no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—81no—
323D212—21no—
324D212—21no—
325D212—21no—
326D212—42no—
327D212#11712yes—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—42no—
331C4×D53—42no—
332C4×D53—41no—
333C4×D53—41no—
334Dic106—21no—
335Dic106—21no—
336Dic106—21no—
337Dic106—42no—
338Dic106#11712yes—
339C8×C53—21no—
340C8×C53—21no—
341C8×C53—21no—
342C8×C53—21no—
343C8×C53—21no—
344C8×C53—21no—
345C8×C53—21no—
346C8×C53—21no—
347#88322—41no—
348#88322—41no—
349#88322—41no—
350#88322—41no—
351#22588—531nomaximal, Sylow
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—81no—
361C22×C53—81no—
362C22×C53C2×C4×D411yescharacteristic
363C22×C53#55111yescharacteristic
364C22×C53#55111yescharacteristic
365C2×D53—22no—
366C2×D53—41no—
367C2×D53—41no—
368C2×D53—41no—
369C2×D53—41no—
370C2×D53—41no—
371C2×D53—84no—
372C4×C53—21no—
373C4×C53—21no—
374C4×C53—42no—
375C4×C53—81no—
376C4×C53C2×#11711yescharacteristic
377C4×C53#51811yescharacteristic
378C4×C53#54611yescharacteristic
379C4×C53#54611yescharacteristic
380Dic53—22no—
381Dic53—41no—
382Dic53—41no—
383Dic53—41no—
384Dic53—41no—
385Dic53—41no—
386#2924—531no—
387#2896—531no—
388#2880—531no—
389#1938—531no—
390#1937—531no—
391#1929—531no—
392#1929—531no—
393#1866—531no—
394#1866—531no—
395#1826—531no—
396#1811—531no—
397#1789—531no—
398#1765—531no—
399#1764—531no—
400#1753D5311yescharacteristic, complemented
401C2×C53—21no—
402C2×C53—21no—
403C2×C53—41no—
404C2×C53—41no—
405C2×C53#234211yescharacteristic
406C2×C53#295511yescharacteristic
407C2×C53#295611yescharacteristic
408D53—42no—
409D53—81no—
410C22×#41—531no—
411C2×#131—531no—
412C2×#131—531no—
413C22×M16C2×D5311yescharacteristic
414C2×#117—531no—
415#433—1061no—
416#433—1061no—
417#432—1061no—
418#431—1061no—
419C2×#108—531no—
420C2×#108—531no—
421#424—531no—
422#424—531no—
423C2×#104—531no—
424C2×#104—531no—
425C2×#104—531no—
426C2×#104—531no—
427#419—531no—
428#419—531no—
429#418—531no—
430#418—531no—
431#417—531no—
432#417—531no—
433#417—531no—
434#417—531no—
435#416—531no—
436#416—531no—
437#416—531no—
438#416—531no—
439#408—531no—
440#408—531no—
441#408—1061no—
442#408—1061no—
443#407—531no—
444#407—531no—
445#407—1061no—
446C2×C22⋊C8—1061no—
447C2×C22⋊C8C2×D5311yescharacteristic
448#405—531no—
449#405—531no—
450C2×#97C2×D5311yescharacteristic, complemented
451C2×C4×C8C2×D5311yescharacteristic, complemented
452C4×C22⋊C4C2×D5311yescharacteristic
453#341—531no—
454#341—531no—
455#339—531no—
456#339—531no—
457#339—531no—
458#339—531no—
459#336C2×D5311yescharacteristic, complemented
460#336C2×D5311yescharacteristic, complemented
461C53#2258811yescharacteristic, complemented, Sylow
462C2×#41—531no—
463C2×#41—531no—
464C2×#41—531no—
465C2×#41—531no—
466C2×#41—1062no—
467C2×#41—1062no—
468C2×#41—1061no—
469C2×#41—1061no—
470C2×#41—2121no—
471C2×#41—2121no—
472C22×Q8—531no—
473C22×D4—531no—
474C22×D4—1061no—
475C23×C4—1061no—
476C23×C4C22×D5311yescharacteristic
477#131—1062no—
478#131—1062no—
479#131—2121no—
480#131—2121no—
481C2×M16—41no—
482C2×M16—41no—
483C2×M16—531no—
484C2×M16—531no—
485C2×M16—531no—
486C2×M16—531no—
487C2×M16—1061no—
488C2×M16—1061no—
489C2×M16C4×D5311yescharacteristic
490C2×M16C4×D5311yescharacteristic
491C2×M16C4×D5311yescharacteristic
492C2×M16C4×D5311yescharacteristic
493C22×C8—1061no—
494C22×C8—1061no—
495C22×C8C22×D5311yescharacteristic
496C22×C8C22×D5311yescharacteristic
497C22×C8C22×D5311yescharacteristic
498C22×C8C22×D5311yescharacteristic
499#117—531no—
500#117—531no—
501#117—531no—
502#117—531no—
503#117—1061no—
504#117—1061no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1061no—
509C2×C42—1061no—
510C2×C42C22×D5311yescharacteristic
511C2×C42C22×D5311yescharacteristic
512#108—2121no—
513#108—2121no—
514C4⋊C8—1061no—
515C4⋊C8—1061no—
516C4⋊C8—1061no—
517C4⋊C8—1061no—
518#104—1062no—
519#104—1062no—
520#104—2121no—
521#104—2121no—
522#103—531no—
523#103—531no—
524#103—531no—
525#103—531no—
526#103—531no—
527#103—531no—
528#103—531no—
529#103—531no—
530#102—531no—
531#102—531no—
532#102—531no—
533#102—531no—
534#102—531no—
535#102—531no—
536#102—531no—
537#102—531no—
538C22⋊C8—1061no—
539C22⋊C8—1061no—
540C22⋊C8—1061no—
541C22⋊C8—1061no—
542C22⋊C8—1061no—
543C22⋊C8—1061no—
544C22⋊C8—1061no—
545C22⋊C8—1061no—
546C22⋊C8D21211yescharacteristic
547C22⋊C8D21211yescharacteristic
548C22⋊C8D21211yescharacteristic
549C22⋊C8D21211yescharacteristic
550#97—41no—
551#97—1061no—
552#97—1061no—
553C4×C8—41no—
554C4×C8—1061no—
555C4×C8—1061no—
556#95—21no—
557C24—1061no—
558C24#1171994511yescharacteristic
559#41—532no—
560#41—532no—
561#41—1062no—
562#41—1062no—
563#41—1061no—
564#41—1061no—
565#41—1061no—
566#41—1061no—
567#41—1061no—
568#41—1061no—
569#41—2122no—
570#41—2122no—
571#41—2121no—
572#41—2121no—
573#41—2122no—
574#41—2122no—
575C2×Q8—531no—
576C2×Q8—531no—
577C2×Q8—1062no—
578C2×Q8—1061no—
579C2×Q8—2121no—
580C2×D4—531no—
581C2×D4—531no—
582C2×D4—1062no—
583C2×D4—1061no—
584C2×D4—1061no—
585C2×D4—1061no—
586C2×D4—1061no—
587C2×D4—1061no—
588C2×D4—2121no—
589C2×D4—2122no—
590C2×D4—2122no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—2122no—
605C22×C4—2122no—
606C22×C4C2×C4×D5311yescharacteristic
607C22×C4C2×C4×D5311yescharacteristic
608C22×C4C2×D21211yescharacteristic
609C22×C4C2×D21211yescharacteristic
610C22×C4#1171994511yescharacteristic
611C22×C4C23×D5311yescharacteristic
612M16—41no—
613M16—41no—
614M16—41no—
615M16—41no—
616M16—1061no—
617M16—1061no—
618M16—1061no—
619M16—1061no—
620M16—1061no—
621M16—1061no—
622M16—1061no—
623M16—1061no—
624M16—2122no—
625M16—2122no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—2122no—
639C2×C8—2122no—
640C2×C8C2×C4×D5311yescharacteristic
641C2×C8C2×C4×D5311yescharacteristic
642C2×C8C2×C4×D5311yescharacteristic
643C2×C8C2×C4×D5311yescharacteristic
644C2×C8C2×D21211yescharacteristic
645C2×C8C2×D21211yescharacteristic
646C2×C8C2×D21211yescharacteristic
647C2×C8C2×D21211yescharacteristic
648C4⋊C4—531no—
649C4⋊C4—531no—
650C4⋊C4—531no—
651C4⋊C4—531no—
652C4⋊C4—1061no—
653C4⋊C4—1061no—
654C22⋊C4—42no—
655C22⋊C4—1061no—
656C22⋊C4—1061no—
657C22⋊C4—1061no—
658C22⋊C4—1061no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—1061no—
664C42—1061no—
665C42—1061no—
666C42—1061no—
667C23—21no—
668C23—21no—
669C23—41no—
670C23—41no—
671C23—1061no—
672C23—1061no—
673C23—4241no—
674C23—2122no—
675C23—2122no—
676C23C4×D21211yescharacteristic
677C23C4×D21211yescharacteristic
678C23C2×#1171994511yescharacteristic
679Q8—532no—
680Q8—1061no—
681Q8—1061no—
682Q8—1061no—
683Q8—2122no—
684D4—532no—
685D4—1062no—
686D4—1062no—
687D4—1061no—
688D4—1061no—
689D4—1061no—
690D4—2122no—
691D4—2122no—
692D4—2122no—
693D4—2121no—
694D4—2121no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—1061no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1061no—
715C2×C4—1061no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—1061no—
719C2×C4—4241no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4C4×D21211yescharacteristic
727C2×C4C4×D21211yescharacteristic
728C2×C4C22×C4×D5311yescharacteristic
729C2×C4C22×D21211yescharacteristic
730C2×C4#41×D5311yescharacteristic
731C2×C4#41×D5311yescharacteristic
732C2×C4#1313326211yescharacteristic
733C2×C4#1313326211yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—2121no—
743C8—2121no—
744C8—2121no—
745C8—2121no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—81no—
755C22—81no—
756C22—1062no—
757C22—4244no—
758C22—2121no—
759C22—2121no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22C2×C4×D21211yescharacteristic
764C22#1681130211yescharacteristic
765C22#1681130211yescharacteristic
766C4—21no—
767C4—21no—
768C4—42no—
769C4—81no—
770C4—1062no—
771C4—2121no—
772C4—2121no—
773C4—2121no—
774C4—2121no—
775C4—2121no—
776C4#117×D5311yescharacteristic
777C4#1681109611yescharacteristic
778C4#1681126811yescharacteristic
779C4#1681126811yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—4241no—
785C2—2122no—
786C2#2027756711yescharacteristic
787C2#2028361911yescharacteristic
788C2#2028362611yescharacteristic
subgroupG/H
centerC2×C4C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1753C2
socleC22×C53C2×C4×D4
prime radicalC22×#11719945C22
cosocleC22×C4×C53C24
hypercenter#1753D53
hypocenterC53#22588
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1753

Complements

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

NH ≅ G/Ntype
1. #20283369C2semidirect
4. #20275426C2semidirect
5. #20275419C2semidirect
6. #20275364C2semidirect
7. #20275364C2semidirect
8. #20274993C2semidirect
9. #20274993C2semidirect
10. #20274815C2semidirect
11. #20274757C2semidirect
13. #20274559C2semidirect
14. #20274552C2semidirect
15. C53×#1753C2semidirect
24. C2×#13133153C22semidirect
25. C2×#13133153C22semidirect
26. #16810649C22semidirect
27. #16810649C22semidirect
32. #16810633C4semidirect
33. #16810633C4semidirect
34. #16810629C4semidirect
35. #16810629C4semidirect
36. #16810625C4semidirect
37. #16810625C4semidirect
38. #16810625C4semidirect
39. #16810625C4semidirect
52. #16810578C22semidirect
53. #16810578C22semidirect
54. #16810388C22semidirect
55. #16810388C22semidirect
56. #16810383C22semidirect
57. #16810383C22semidirect
58. #16810383C22semidirect
59. #16810383C22semidirect
62. C2×#97×C53C22semidirect
63. C2×C4×C8×C53C22semidirect
65. C53×#336C22semidirect
66. C53×#336C22semidirect
400. #1753D53semidirect
450. C2×#97C2×D53semidirect
451. C2×C4×C8C2×D53semidirect
459. #336C2×D53semidirect
460. #336C2×D53semidirect
461. C53#22588semidirect

Maximal subgroups

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

subgroupindex
#202833692
#202832352
#202831612
#202754262
#202754192
#202753642
#202749932
#202748152
#202747572
#202746602
#202745592
#202745522
C53×#17532
#2258853