Finite Group Databasebeta

← #27395511

Subgroups — #27395511

Order 13568.

900 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283933C211yesmaximal, characteristic
2#20283414C211yesmaximal, characteristic, complemented
3#20283160C211yesmaximal, characteristic, complemented
4#20275605C211yesmaximal, characteristic, complemented
5#20275600C211yesmaximal, characteristic, complemented
6#20275423C211yesmaximal, characteristic, complemented
7#20275416C211yesmaximal, characteristic, complemented
8#20275366C211yesmaximal, characteristic, complemented
9#20275366C211yesmaximal, characteristic, complemented
10#20275039C211yesmaximal, characteristic, complemented
11#20275039C211yesmaximal, characteristic, complemented
12#20275015C211yesmaximal, characteristic, complemented
13#20274919C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#1789C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133225C2211yescharacteristic, complemented
19C22×#11719917C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21#16811134C2211yescharacteristic
22#16810785C411yescharacteristic, complemented
23#16810785C411yescharacteristic, complemented
24#16810779C411yescharacteristic, complemented
25#16810774C411yescharacteristic, complemented
26#16810768C411yescharacteristic, complemented
27#16810768C411yescharacteristic, complemented
28#16810762C411yescharacteristic, complemented
29#16810757C411yescharacteristic, complemented
30#16810698—21no—
31#16810698—21no—
32#16810697—21no—
33#16810697—21no—
34C2×#13133152C2211yescharacteristic, complemented
35C2×#13133152C2211yescharacteristic, complemented
36#16810651C2211yescharacteristic, complemented
37C2×#13133145C2211yescharacteristic, complemented
38C2×#13133145C2211yescharacteristic, complemented
39#16810619C2211yescharacteristic
40#16810619C2211yescharacteristic
41#16810591C2211yescharacteristic, complemented
42#16810590—21no—
43#16810590—21no—
44#16810590C2211yescharacteristic
45#16810590C2211yescharacteristic
46#16810590C2211yescharacteristic
47#16810590C2211yescharacteristic
48#16810587—21no—
49#16810587—21no—
50C2×C22⋊#88322C2211yescharacteristic
51#16810581C2211yescharacteristic, complemented
52C2×#13133128C2211yescharacteristic, complemented
53C2×C4×#88322C2211yescharacteristic, complemented
54#16810387C2211yescharacteristic, complemented
55#16810387C2211yescharacteristic, complemented
56#16810383C2211yescharacteristic, complemented
57#16810383C2211yescharacteristic, complemented
58#16810378C2211yescharacteristic, complemented
59#16810378C2211yescharacteristic, complemented
60C22×#41×C53C2211yescharacteristic
61C2×#104×C53C2211yescharacteristic
62C2×#104×C53C2211yescharacteristic
63C2×#104×C53C2211yescharacteristic
64C2×#104×C53C2211yescharacteristic
65C53×#407C2211yescharacteristic
66C4×C22⋊C4×C53C2211yescharacteristic
67C2×#11719945C2311yescharacteristic
68#13133237—41no—
69#13133237—41no—
70#13133237—41no—
71#13133237—41no—
72C2×#11719925C2×C411yescharacteristic
73C2×#11719925C2×C411yescharacteristic
74C2×#11719923C2×C411yescharacteristic
75C2×#11719923C2×C411yescharacteristic
76C2×#11719924C2×C411yescharacteristic
77C2×#11719924C2×C411yescharacteristic
78C2×#11719922C2×C411yescharacteristic
79C2×#11719922C2×C411yescharacteristic
80#13133225—41no—
81#13133225—41no—
82C2×#11719917—21no—
83C2×#11719917—41no—
84C2×#11719917—41no—
85C2×#11719917—41no—
86C2×#11719917—41no—
87C2×#11719917D411yescharacteristic
88C2×#11719917D411yescharacteristic
89C2×#11719917D411yescharacteristic
90C2×#11719917D411yescharacteristic
91C2×#11719917C2311yescharacteristic
92C2×#11719917C2311yescharacteristic
93C2×#11719912—21no—
94C22×#88322—21no—
95C22×#88322C2311yescharacteristic
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—21no—
100#13133200—21no—
101#13133196C2×C411yescharacteristic
102#13133196C2×C411yescharacteristic
103#13133191C2×C411yescharacteristic
104#13133191C2×C411yescharacteristic
105#13133186—21no—
106C4×C22⋊D53—21no—
107C4×C22⋊D53—21no—
108#13133176C2311yescharacteristic
109#13133152—41no—
110#13133152—41no—
111#13133146—21no—
112#13133146—21no—
113#13133145—41no—
114#13133145—41no—
115#13133141C2×C411yescharacteristic
116#13133141C2×C411yescharacteristic
117#13133141C2×C411yescharacteristic
118#13133141C2×C411yescharacteristic
119#13133138C2×C411yescharacteristic
120#13133138C2×C411yescharacteristic
121#13133138C2×C411yescharacteristic
122#13133138C2×C411yescharacteristic
123C22⋊#88322—21no—
124C22⋊#88322—21no—
125C22⋊#88322—21no—
126C22⋊#88322—21no—
127C22⋊#88322—21no—
128C22⋊#88322—21no—
129C22⋊#88322—21no—
130C22⋊#88322—21no—
131C22⋊#88322C2×C411yescharacteristic
132C22⋊#88322C2×C411yescharacteristic
133C22⋊#88322C2×C411yescharacteristic
134C22⋊#88322C2×C411yescharacteristic
135#13133129—21no—
136#13133129—21no—
137#13133128—41no—
138#13133127—21no—
139C4×#88322—41no—
140C8×Dic53—21no—
141C2×#41×C53—21no—
142C2×#41×C53—21no—
143C2×#41×C53—41no—
144C2×#41×C53—41no—
145C2×#41×C53—41no—
146C2×#41×C53—41no—
147C2×#41×C53C2×C411yescharacteristic
148C2×#41×C53C2×C411yescharacteristic
149C2×#41×C53C2311yescharacteristic
150C2×#41×C53C2311yescharacteristic
151C22×Q8×C53C2×C411yescharacteristic
152C22×D4×C53—21no—
153C22×D4×C53C2×C411yescharacteristic
154C23×C4×C53—21no—
155C23×C4×C53C2311yescharacteristic
156C2×M16×C53C2311yescharacteristic
157C2×M16×C53C2311yescharacteristic
158C2×C22⋊C4×C53—21no—
159C2×C42×C53C2311yescharacteristic
160C2×C42×C53C2311yescharacteristic
161#104×C53—41no—
162#104×C53—41no—
163#104×C53—41no—
164#104×C53—41no—
165C22⋊C8×C53—21no—
166C22⋊C8×C53—21no—
167#95×C53—21no—
168C24×C53—21no—
169C24×C53#4111yescharacteristic
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—21no—
173#41×C53—21no—
174#41×C53—21no—
175#41×C53—21no—
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—41no—
179#41×C53—41no—
180#41×C53—41no—
181#41×C53—41no—
182#41×C53—42no—
183#41×C53—42no—
184#41×C53—42no—
185#41×C53—42no—
186C2×Q8×C53—21no—
187C2×Q8×C53—41no—
188C2×Q8×C53—41no—
189C2×Q8×C53C22×C411yescharacteristic
190C2×Q8×C53C22×C411yescharacteristic
191C2×D4×C53—21no—
192C2×D4×C53—21no—
193C2×D4×C53—21no—
194C2×D4×C53—21no—
195C2×D4×C53—21no—
196C2×D4×C53—41no—
197C2×D4×C53—41no—
198C2×D4×C53—42no—
199C2×D4×C53—42no—
200C2×D4×C53C22×C411yescharacteristic
201C2×D4×C53C22×C411yescharacteristic
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—42no—
214C22×C4×C53—42no—
215C22×C4×C53C22×C411yescharacteristic
216C22×C4×C53C22×C411yescharacteristic
217C22×C4×C53C2×D411yescharacteristic
218C22×C4×C53C2×D411yescharacteristic
219C22×C4×C53#4111yescharacteristic
220C22×C4×C53C2411yescharacteristic
221C2×C22⋊D53—21no—
222C2×C22⋊D53—21no—
223C2×C22⋊D53—21no—
224#11719945—21no—
225#11719945—21no—
226#11719945—21no—
227#11719945—21no—
228C2×D212C22×C411yescharacteristic
229C2×C4×D53—21no—
230C2×Dic106C22×C411yescharacteristic
231M16×C53—21no—
232M16×C53—21no—
233M16×C53—21no—
234M16×C53—21no—
235C2×C8×C53—21no—
236C2×C8×C53—21no—
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—
245#11719925—41no—
246#11719925—41no—
247#11719924—41no—
248#11719924—41no—
249#11719923—41no—
250#11719923—41no—
251#11719922—41no—
252#11719922—41no—
253#11719921—21no—
254#11719921—21no—
255C4⋊Dic53C22×C411yescharacteristic
256C4⋊Dic53C22×C411yescharacteristic
257#11719919—21no—
258#11719919—21no—
259C4×Dic53—21no—
260#11719917—21no—
261#11719917—21no—
262#11719917—21no—
263#11719917—21no—
264#11719917—41no—
265#11719917—41no—
266#11719917—41no—
267#11719917—41no—
268#11719917—42no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—42no—
280C2×#88322C22×C411yescharacteristic
281C2×#88322C22×C411yescharacteristic
282C2×#88322C22×C411yescharacteristic
283C2×#88322C22×C411yescharacteristic
284C2×#88322C2×D411yescharacteristic
285C2×#88322C2×D411yescharacteristic
286C2×#88322C2×D411yescharacteristic
287C2×#88322C2×D411yescharacteristic
288#11719912—42no—
289C8×D53—42no—
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—21no—
294C23×C53—41no—
295C23×C53—41no—
296C23×C53—42no—
297C23×C53—81no—
298C23×C53—81no—
299C23×C53C4×D411yescharacteristic
300C23×C53C4×D411yescharacteristic
301C23×C53C2×#4111yescharacteristic
302C22×D53—21no—
303Q8×C53—21no—
304Q8×C53—21no—
305Q8×C53—21no—
306Q8×C53—21no—
307Q8×C53—42no—
308D4×C53—21no—
309D4×C53—21no—
310D4×C53—21no—
311D4×C53—21no—
312D4×C53—42no—
313D4×C53—42no—
314D4×C53—42no—
315D4×C53—41no—
316D4×C53—41no—
317D4×C53—41no—
318D4×C53—41no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—21no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—21no—
326C2×C4×C53—21no—
327C2×C4×C53—21no—
328C2×C4×C53—21no—
329C2×C4×C53—22no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—42no—
333C2×C4×C53—42no—
334C2×C4×C53—41no—
335C2×C4×C53—42no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53C4×D411yescharacteristic
345C2×C4×C53C4×D411yescharacteristic
346C2×C4×C53C23×C411yescharacteristic
347C2×C4×C53C22×D411yescharacteristic
348C2×C4×C53H(5,𝔽2)11yescharacteristic
349C2×C4×C53H(5,𝔽2)11yescharacteristic
350C2×C4×C53H(5,𝔽2)11yescharacteristic
351C2×C4×C53H(5,𝔽2)11yescharacteristic
352C22⋊D53—41no—
353C22⋊D53—41no—
354C22⋊D53—81no—
355C22⋊D53—81no—
356C2×Dic53—21no—
357C2×Dic53—21no—
358C2×Dic53—21no—
359D212—21no—
360D212—21no—
361C4×D53—41no—
362C4×D53—41no—
363Dic106—21no—
364Dic106—21no—
365C8×C53—41no—
366C8×C53—41no—
367#88322—21no—
368#88322—21no—
369#88322—21no—
370#88322—21no—
371#88322—21no—
372#88322—21no—
373#88322—21no—
374#88322—21no—
375#88322—41no—
376#88322—41no—
377#22062—531nomaximal, Sylow
378C22×C53—21no—
379C22×C53—21no—
380C22×C53—21no—
381C22×C53—21no—
382C22×C53—21no—
383C22×C53—21no—
384C22×C53—21no—
385C22×C53—21no—
386C22×C53—41no—
387C22×C53—41no—
388C22×C53—41no—
389C22×C53—41no—
390C22×C53—41no—
391C22×C53—41no—
392C22×C53—81no—
393C22×C53—81no—
394C22×C53—84no—
395C22×C53C2×C4×D411yescharacteristic
396C22×C53#53811yescharacteristic
397C22×C53#53811yescharacteristic
398C2×D53—41no—
399C2×D53—41no—
400C2×D53—41no—
401C4×C53—21no—
402C4×C53—21no—
403C4×C53—42no—
404C4×C53—41no—
405C4×C53—41no—
406C4×C53—81no—
407C4×C53#51811yescharacteristic
408C4×C53#51811yescharacteristic
409C4×C53#53411yescharacteristic
410C4×C53#53511yescharacteristic
411Dic53—41no—
412Dic53—41no—
413Dic53—41no—
414#3002—531no—
415#2930—531no—
416#2879—531no—
417#1975—531no—
418#1974—531no—
419#1938—531no—
420#1937—531no—
421#1929—531no—
422#1929—531no—
423#1876—531no—
424#1876—531no—
425#1871—531no—
426#1855—531no—
427#1789D5311yescharacteristic, complemented
428#1753—531no—
429C2×C53—21no—
430C2×C53—21no—
431C2×C53—41no—
432C2×C53—41no—
433C2×C53—81no—
434C2×C53—81no—
435C2×C53#232111yescharacteristic
436C2×C53#295611yescharacteristic
437C2×C53#295711yescharacteristic
438D53—81no—
439C22×#41C2×D5311yescharacteristic
440C2×#135—531no—
441C2×#135—531no—
442C2×#131—531no—
443C22×M16—531no—
444C22×M16—531no—
445#525—531no—
446#452—531no—
447#452—531no—
448#451—531no—
449#450—531no—
450#449—531no—
451#449—531no—
452#448—531no—
453#447—531no—
454#436—1061no—
455#436—1061no—
456#435—1061no—
457#435—1061no—
458C2×#108—531no—
459C2×#108—531no—
460#424—531no—
461C2×#104—531no—
462C2×#104—531no—
463C2×#104C2×D5311yescharacteristic
464C2×#104C2×D5311yescharacteristic
465C2×#104C2×D5311yescharacteristic
466C2×#104C2×D5311yescharacteristic
467#416—531no—
468#416—531no—
469#408—531no—
470#408—531no—
471#408—531no—
472#408—531no—
473#408—531no—
474#408—1061no—
475#408—1061no—
476#407—1061no—
477#407—1061no—
478#407C2×D5311yescharacteristic
479C2×C22⋊C8—531no—
480#405—531no—
481C2×#97—531no—
482C2×C4×C8—531no—
483C4×C22⋊C4C2×D5311yescharacteristic
484#341—531no—
485#341—531no—
486#339—531no—
487#339—531no—
488#336—531no—
489#336—531no—
490C53#2206211yescharacteristic, complemented, Sylow
491C2×#41—21no—
492C2×#41—21no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—531no—
498C2×#41C4×D5311yescharacteristic
499C2×#41C4×D5311yescharacteristic
500C2×#41C22×D5311yescharacteristic
501C2×#41C22×D5311yescharacteristic
502C22×Q8C4×D5311yescharacteristic
503C22×D4—21no—
504C22×D4C4×D5311yescharacteristic
505C23×C4—21no—
506C23×C4C22×D5311yescharacteristic
507#135—2121no—
508#135—2121no—
509#135—2121no—
510#135—2121no—
511C2×Q16—531no—
512C2×Q16—531no—
513C2×SD16—531no—
514C2×SD16—531no—
515C2×SD16—531no—
516C2×SD16—531no—
517C2×D8—531no—
518C2×D8—531no—
519#131—2121no—
520#131—2121no—
521C2×M16—531no—
522C2×M16—531no—
523C2×M16—531no—
524C2×M16—531no—
525C2×M16—531no—
526C2×M16—531no—
527C2×M16—1061no—
528C2×M16—1061no—
529C2×M16—2121no—
530C2×M16—2121no—
531C2×M16—2121no—
532C2×M16—2121no—
533C2×M16C22×D5311yescharacteristic
534C2×M16C22×D5311yescharacteristic
535C22×C8—531no—
536C22×C8—531no—
537C22×C8—531no—
538C22×C8—531no—
539C22×C8—1061no—
540C22×C8—1061no—
541#123—1061no—
542C22⋊Q8—531no—
543C22⋊Q8—531no—
544#121—531no—
545#121—531no—
546#120—1061no—
547C4×D4—1061no—
548C4×D4—1061no—
549#117—531no—
550C2×C22⋊C4—21no—
551C2×C42C22×D5311yescharacteristic
552C2×C42C22×D5311yescharacteristic
553#108—2121no—
554#108—2121no—
555C4⋊C8—1061no—
556C4⋊C8—1061no—
557#104—41no—
558#104—41no—
559#104—41no—
560#104—41no—
561#104—2121no—
562#104—2121no—
563#103—531no—
564#103—531no—
565#103—531no—
566#103—531no—
567#102—531no—
568#102—531no—
569#102—531no—
570#102—531no—
571C22⋊C8—21no—
572C22⋊C8—21no—
573C22⋊C8—531no—
574C22⋊C8—531no—
575C22⋊C8—531no—
576C22⋊C8—531no—
577C22⋊C8—1061no—
578C22⋊C8—1061no—
579C22⋊C8—1061no—
580C22⋊C8—1061no—
581C22⋊C8—1061no—
582C22⋊C8—1061no—
583C22⋊C8—1061no—
584C22⋊C8—1061no—
585C22⋊C8—1061no—
586C22⋊C8—1061no—
587#97—1061no—
588#97—2121no—
589C4×C8—1061no—
590C4×C8—2121no—
591#95—21no—
592C24—21no—
593C24#1171994711yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—41no—
603#41—41no—
604#41—41no—
605#41—41no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—1061no—
611#41—1061no—
612#41—1061no—
613#41—1061no—
614C2×Q8—21no—
615C2×Q8—41no—
616C2×Q8—41no—
617C2×Q8—531no—
618C2×Q8C2×C4×D5311yescharacteristic
619C2×Q8C2×C4×D5311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4—531no—
630C2×D4—1061no—
631C2×D4—1061no—
632C2×D4—1061no—
633C2×D4C2×C4×D5311yescharacteristic
634C2×D4C2×C4×D5311yescharacteristic
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—1061no—
649C22×C4C2×C4×D5311yescharacteristic
650C22×C4C2×C4×D5311yescharacteristic
651C22×C4D4×D5311yescharacteristic
652C22×C4D4×D5311yescharacteristic
653C22×C4#1171994711yescharacteristic
654C22×C4C23×D5311yescharacteristic
655Q16—2121no—
656Q16—2121no—
657SD16—2121no—
658SD16—2121no—
659SD16—2121no—
660SD16—2121no—
661D8—2121no—
662D8—2121no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—1061no—
668M16—1061no—
669M16—1061no—
670M16—1061no—
671M16—2122no—
672M16—2121no—
673M16—2121no—
674M16—2121no—
675M16—2121no—
676M16—2122no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—531no—
680C2×C8—531no—
681C2×C8—531no—
682C2×C8—531no—
683C2×C8—531no—
684C2×C8—531no—
685C2×C8—531no—
686C2×C8—531no—
687C2×C8—1061no—
688C2×C8—1061no—
689C2×C8—1061no—
690C2×C8—1061no—
691C2×C8—1061no—
692C2×C8—1061no—
693C2×C8—1061no—
694C2×C8—1061no—
695C2×C8—1061no—
696C2×C8—1061no—
697C2×C8—2122no—
698C2×C8—2122no—
699C4⋊C4—531no—
700C4⋊C4—531no—
701C4⋊C4—1061no—
702C4⋊C4—1061no—
703C22⋊C4—42no—
704C22⋊C4—1061no—
705C22⋊C4—1061no—
706C22⋊C4—1061no—
707C22⋊C4—1061no—
708C22⋊C4—1061no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—1061no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—81no—
722C23—81no—
723C23—1061no—
724C23#1313317711yescharacteristic
725C23#1313317711yescharacteristic
726C23C2×#1171994711yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—21no—
730Q8—21no—
731Q8—42no—
732Q8—1061no—
733Q8—1061no—
734D4—21no—
735D4—21no—
736D4—21no—
737D4—21no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—1061no—
746D4—1061no—
747D4—4241no—
748D4—4241no—
749D4—2121no—
750D4—2121no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—1061no—
777C2×C4—1061no—
778C2×C4—1061no—
779C2×C4—2121no—
780C2×C4—2121no—
781C2×C4#1313317711yescharacteristic
782C2×C4#1313317711yescharacteristic
783C2×C4C22×C4×D5311yescharacteristic
784C2×C4C2×D4×D5311yescharacteristic
785C2×C4#1313326211yescharacteristic
786C2×C4#1313326211yescharacteristic
787C2×C4#1313326211yescharacteristic
788C2×C4#1313326211yescharacteristic
789C8—41no—
790C8—41no—
791C8—1061no—
792C8—1061no—
793C8—1061no—
794C8—1061no—
795C8—1061no—
796C8—1061no—
797C8—1061no—
798C8—1061no—
799C8—2121no—
800C8—2121no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—81no—
816C22—81no—
817C22—84no—
818C22—2121no—
819C22—2121no—
820C22—2121no—
821C22C2×#1313317711yescharacteristic
822C22#1681120811yescharacteristic
823C22#1681120811yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—81no—
830C4—2121no—
831C4—2121no—
832C4—2121no—
833C4#1681109611yescharacteristic
834C4#1681109611yescharacteristic
835C4#1681118311yescharacteristic
836C4#1681118811yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—81no—
843C2—4241no—
844C2#2027737011yescharacteristic
845C2#2028362111yescharacteristic
846C2#2028362811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1789C2
socleC22×C53C2×C4×D4
prime radical#20283933C2
cosocleC22×C4×C53C24
hypercenter#1789D53
hypocenterC53#22062
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #20283414C2semidirect
3. #20283160C2semidirect
4. #20275605C2semidirect
5. #20275600C2semidirect
6. #20275423C2semidirect
7. #20275416C2semidirect
8. #20275366C2semidirect
9. #20275366C2semidirect
10. #20275039C2semidirect
11. #20275039C2semidirect
12. #20275015C2semidirect
13. #20274919C2semidirect
14. #20274499C2semidirect
15. C53×#1789C2semidirect
18. C2×#13133225C22semidirect
22. #16810785C4semidirect
23. #16810785C4semidirect
24. #16810779C4semidirect
25. #16810774C4semidirect
26. #16810768C4semidirect
27. #16810768C4semidirect
28. #16810762C4semidirect
29. #16810757C4semidirect
34. C2×#13133152C22semidirect
35. C2×#13133152C22semidirect
36. #16810651C22semidirect
37. C2×#13133145C22semidirect
38. C2×#13133145C22semidirect
41. #16810591C22semidirect
51. #16810581C22semidirect
52. C2×#13133128C22semidirect
53. C2×C4×#88322C22semidirect
54. #16810387C22semidirect
55. #16810387C22semidirect
56. #16810383C22semidirect
57. #16810383C22semidirect
58. #16810378C22semidirect
59. #16810378C22semidirect
427. #1789D53semidirect
490. C53#22062semidirect

Maximal subgroups

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

subgroupindex
#202839332
#202834142
#202831602
#202756052
#202756002
#202754232
#202754162
#202753662
#202750392
#202750152
#202749192
#202744992
C53×#17892
#2206253