Finite Group Databasebeta

← #27404829

Subgroups — #27404829

Order 13568.

1058 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20283933C211yesmaximal, characteristic
2C2×#16810742C211yesmaximal, characteristic, complemented
3#20283440C211yesmaximal, characteristic, complemented
4#20283164C211yesmaximal, characteristic, complemented
5#20275605C211yesmaximal, characteristic, complemented
6#20275423C211yesmaximal, characteristic, complemented
7#20275366C211yesmaximal, characteristic, complemented
8#20275158C211yesmaximal, characteristic, complemented
9#20275040C211yesmaximal, characteristic, complemented
10#20275039C211yesmaximal, characteristic, complemented
11#20274988C211yesmaximal, characteristic, complemented
12#20274920C211yesmaximal, characteristic, complemented
13#20274560C211yesmaximal, characteristic, complemented
14#20274477C211yesmaximal, characteristic, complemented
15C22×#104×C53C211yesmaximal, characteristic, complemented
16C2×#13133237C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133225C2211yescharacteristic, complemented
19C2×#13133224C2211yescharacteristic
20C2×#13133224C2211yescharacteristic
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#16810742—24no—
31#16810699—21no—
32#16810694—21no—
33#16810692—21no—
34C8×C22⋊D53—21no—
35C2×#13133152C2211yescharacteristic, complemented
36C2×#13133152C2211yescharacteristic, complemented
37#16810651C2211yescharacteristic, complemented
38C2×#13133145C2211yescharacteristic, complemented
39C2×#13133145C2211yescharacteristic, complemented
40#16810619C2211yescharacteristic
41#16810619C2211yescharacteristic
42#16810591C2211yescharacteristic, complemented
43#16810590—21no—
44#16810590—21no—
45#16810590C2211yescharacteristic
46#16810590C2211yescharacteristic
47#16810587—21no—
48#16810587C2211yescharacteristic
49C2×C22⋊#88322—21no—
50C2×C22⋊#88322C2211yescharacteristic
51C2×C22⋊#88322C2211yescharacteristic
52#16810581C2211yescharacteristic, complemented
53C2×#13133128C2211yescharacteristic, complemented
54C2×#13133128C2211yescharacteristic, complemented
55#16810387C2211yescharacteristic, complemented
56#16810387C2211yescharacteristic, complemented
57#16810383C2211yescharacteristic, complemented
58#16810383C2211yescharacteristic, complemented
59#16810378C2211yescharacteristic, complemented
60#16810378C2211yescharacteristic, complemented
61C22×#41×C53C2211yescharacteristic
62C22×M16×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C2×#104×C53—24no—
65C2×#104×C53C2211yescharacteristic
66C2×#104×C53C2211yescharacteristic
67C2×#104×C53C2211yescharacteristic
68C2×#104×C53C2211yescharacteristic
69C2×#11719945C2311yescharacteristic
70#13133237—22no—
71#13133237—22no—
72#13133237—41no—
73#13133237—41no—
74C2×#11719925C2×C411yescharacteristic, complemented
75C2×#11719925C2×C411yescharacteristic, complemented
76C2×#11719923C2×C411yescharacteristic, complemented
77C2×#11719923C2×C411yescharacteristic, complemented
78C2×#11719924C2×C411yescharacteristic, complemented
79C2×#11719924C2×C411yescharacteristic, complemented
80C2×#11719922C2×C411yescharacteristic, complemented
81C2×#11719922C2×C411yescharacteristic, complemented
82#13133225—22no—
83#13133225—41no—
84#13133224—22no—
85#13133224—22no—
86#13133224—41no—
87#13133224—41no—
88C2×#11719917—21no—
89C2×#11719917—21no—
90C2×#11719917C2311yescharacteristic
91C2×#11719917C2311yescharacteristic
92C2×#11719912—21no—
93C22×#88322—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—22no—
110#13133152—41no—
111#13133146—21no—
112#13133146—21no—
113#13133145—22no—
114#13133145—41no—
115#13133141C2×C411yescharacteristic, complemented
116#13133141C2×C411yescharacteristic, complemented
117#13133141C2×C411yescharacteristic, complemented
118#13133141C2×C411yescharacteristic, complemented
119#13133138C2×C411yescharacteristic, complemented
120#13133138C2×C411yescharacteristic, complemented
121#13133138C2×C411yescharacteristic, complemented
122#13133138C2×C411yescharacteristic, complemented
123C22⋊#88322—21no—
124C22⋊#88322—21no—
125C22⋊#88322—21no—
126C22⋊#88322—21no—
127C22⋊#88322—21no—
128C22⋊#88322—21no—
129C22⋊#88322C2×C411yescharacteristic
130C22⋊#88322C2×C411yescharacteristic
131C22⋊#88322C2×C411yescharacteristic
132C22⋊#88322C2×C411yescharacteristic
133C22⋊#88322D411yescharacteristic
134C22⋊#88322D411yescharacteristic
135C22⋊#88322D411yescharacteristic
136C22⋊#88322D411yescharacteristic
137#13133129—21no—
138#13133129—21no—
139#13133128—22no—
140#13133128—41no—
141#13133127—21no—
142C8×Dic53—21no—
143C2×#41×C53—21no—
144C2×#41×C53—21no—
145C2×#41×C53—22no—
146C2×#41×C53—22no—
147C2×#41×C53—41no—
148C2×#41×C53—41no—
149C2×#41×C53C2×C411yescharacteristic
150C2×#41×C53C2×C411yescharacteristic
151C2×#41×C53C2311yescharacteristic
152C2×#41×C53C2311yescharacteristic
153C22×Q8×C53C2×C411yescharacteristic
154C22×D4×C53—21no—
155C22×D4×C53C2×C411yescharacteristic
156C23×C4×C53—21no—
157C23×C4×C53—21no—
158C23×C4×C53C2311yescharacteristic
159C2×M16×C53—22no—
160C2×M16×C53—21no—
161C2×M16×C53—41no—
162C2×M16×C53C2311yescharacteristic
163C2×M16×C53C2311yescharacteristic
164C22×C8×C53—21no—
165C2×C42×C53—21no—
166C2×C42×C53—22no—
167C2×C42×C53—41no—
168C2×C42×C53C2311yescharacteristic
169C2×C42×C53C2311yescharacteristic
170#104×C53—22no—
171#104×C53—22no—
172#104×C53—22no—
173#104×C53D414yescomplemented
174C24×C53—21no—
175C24×C53#4111yescharacteristic
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—22no—
179#41×C53—22no—
180#41×C53—21no—
181#41×C53—21no—
182#41×C53—21no—
183#41×C53—21no—
184#41×C53—42no—
185#41×C53—42no—
186#41×C53—41no—
187#41×C53—41no—
188#41×C53—42no—
189#41×C53—42no—
190#41×C53C2×D412yes—
191#41×C53#4112yes—
192C2×Q8×C53—21no—
193C2×Q8×C53—22no—
194C2×Q8×C53—41no—
195C2×Q8×C53C22×C411yescharacteristic
196C2×Q8×C53C22×C411yescharacteristic
197C2×D4×C53—21no—
198C2×D4×C53—22no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—21no—
202C2×D4×C53—21no—
203C2×D4×C53—41no—
204C2×D4×C53—42no—
205C2×D4×C53—42no—
206C2×D4×C53C22×C411yescharacteristic
207C2×D4×C53C22×C411yescharacteristic
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—42no—
220C22×C4×C53—42no—
221C22×C4×C53—42no—
222C22×C4×C53—42no—
223C22×C4×C53—42no—
224C22×C4×C53C22×C411yescharacteristic
225C22×C4×C53C22×C411yescharacteristic
226C22×C4×C53C2×D411yescharacteristic
227C22×C4×C53C2×D411yescharacteristic
228C22×C4×C53#4111yescharacteristic
229C22×C4×C53C2411yescharacteristic
230C2×C22⋊D53—21no—
231C2×C22⋊D53—21no—
232C2×C22⋊D53—21no—
233#11719945—21no—
234#11719945—21no—
235#11719945—21no—
236#11719945—21no—
237C2×D212C22×C411yescharacteristic
238C2×C4×D53—21no—
239C2×Dic106C22×C411yescharacteristic
240M16×C53—21no—
241M16×C53—21no—
242M16×C53—21no—
243M16×C53—42no—
244M16×C53C2×D412yes—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—42no—
248C42×C53—21no—
249C42×C53—21no—
250C42×C53—21no—
251C42×C53—42no—
252C42×C53C2×D412yes—
253C22⋊Dic53—21no—
254C22⋊Dic53—21no—
255C22⋊Dic53—21no—
256#11719925—22no—
257#11719925—41no—
258#11719924—22no—
259#11719924—41no—
260#11719923—22no—
261#11719923—41no—
262#11719922—22no—
263#11719922—41no—
264#11719921—21no—
265#11719921—21no—
266C4⋊Dic53C22×C411yescharacteristic
267C4⋊Dic53C22×C411yescharacteristic
268#11719919—21no—
269#11719919—21no—
270C4×Dic53—21no—
271#11719917—21no—
272#11719917—21no—
273#11719917—21no—
274#11719917—21no—
275#11719917—42no—
276#11719917—42no—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—21no—
280C2×#88322—21no—
281C2×#88322—21no—
282C2×#88322—21no—
283C2×#88322—21no—
284C2×#88322—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322—42no—
288C2×#88322—42no—
289C2×#88322C22×C411yescharacteristic
290C2×#88322C22×C411yescharacteristic
291C2×#88322C22×C411yescharacteristic
292C2×#88322C22×C411yescharacteristic
293C2×#88322C2×D411yescharacteristic
294C2×#88322C2×D411yescharacteristic
295C2×#88322C2×D411yescharacteristic
296C2×#88322C2×D411yescharacteristic
297#11719912—42no—
298C8×D53—42no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—21no—
302C23×C53—22no—
303C23×C53—21no—
304C23×C53—41no—
305C23×C53—42no—
306C23×C53—42no—
307C23×C53—81no—
308C23×C53C4×D411yescharacteristic
309C23×C53C4×D411yescharacteristic
310C23×C53C2×#4111yescharacteristic
311C22×D53—21no—
312Q8×C53—21no—
313Q8×C53—21no—
314Q8×C53—21no—
315Q8×C53—42no—
316Q8×C53C4×D412yes—
317D4×C53—22no—
318D4×C53—22no—
319D4×C53—21no—
320D4×C53—21no—
321D4×C53—21no—
322D4×C53—42no—
323D4×C53—42no—
324D4×C53—42no—
325D4×C53—41no—
326D4×C53—41no—
327D4×C53C4×D412yes—
328C2×C4×C53—21no—
329C2×C4×C53—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—21no—
335C2×C4×C53—21no—
336C2×C4×C53—21no—
337C2×C4×C53—22no—
338C2×C4×C53—21no—
339C2×C4×C53—21no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—21no—
343C2×C4×C53—22no—
344C2×C4×C53—42no—
345C2×C4×C53—42no—
346C2×C4×C53—42no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—48no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53C4×D411yescharacteristic
355C2×C4×C53C4×D411yescharacteristic
356C2×C4×C53C23×C411yescharacteristic
357C2×C4×C53C22×D411yescharacteristic
358C2×C4×C53C22×D411yescharacteristic
359C2×C4×C53C2×#4111yescharacteristic
360C2×C4×C53H(5,𝔽2)11yescharacteristic
361C2×C4×C53H(5,𝔽2)11yescharacteristic
362C22⋊D53—41no—
363C22⋊D53—41no—
364C22⋊D53—42no—
365C22⋊D53—81no—
366C2×Dic53—21no—
367C2×Dic53—21no—
368C2×Dic53—21no—
369D212—21no—
370D212—21no—
371C4×D53—41no—
372C4×D53—41no—
373Dic106—21no—
374Dic106—21no—
375C8×C53—22no—
376C8×C53—41no—
377#88322—21no—
378#88322—21no—
379#88322—21no—
380#88322—21no—
381#88322—21no—
382#88322—21no—
383#88322—21no—
384#88322—21no—
385#88322—41no—
386#88322—41no—
387#22886—531nomaximal, Sylow
388C22×C53—21no—
389C22×C53—21no—
390C22×C53—21no—
391C22×C53—21no—
392C22×C53—21no—
393C22×C53—22no—
394C22×C53—21no—
395C22×C53—21no—
396C22×C53—42no—
397C22×C53—42no—
398C22×C53—41no—
399C22×C53—41no—
400C22×C53—41no—
401C22×C53—41no—
402C22×C53—41no—
403C22×C53—84no—
404C22×C53#44412yescomplemented
405C22×C53C2×C4×D411yescharacteristic
406C22×C53#54611yescharacteristic
407C22×C53#55111yescharacteristic
408C2×D53—41no—
409C2×D53—41no—
410C2×D53—41no—
411C4×C53—21no—
412C4×C53—21no—
413C4×C53—22no—
414C4×C53—42no—
415C4×C53—42no—
416C4×C53—41no—
417C4×C53C2×C4×D411yescharacteristic
418C4×C53#51811yescharacteristic
419C4×C53D4211yescharacteristic
420C4×C53#54611yescharacteristic
421Dic53—41no—
422Dic53—41no—
423Dic53—41no—
424#3002—531no—
425C2×#444—531no—
426#2933—531no—
427C22×#104D5311yescharacteristic, complemented
428#2880—531no—
429#1975—531no—
430#1938—531no—
431#1929—531no—
432#1896—531no—
433#1876—531no—
434#1876—531no—
435#1866—531no—
436#1855—531no—
437#1765—531no—
438#1749—531no—
439C2×C53—21no—
440C2×C53—22no—
441C2×C53—21no—
442C2×C53—41no—
443C2×C53—42no—
444C2×C53—81no—
445C2×C53#235811yescharacteristic
446C2×C53C2×#44411yescharacteristic
447C2×C53#295611yescharacteristic
448D53—81no—
449C22×#41C2×D5311yescharacteristic
450C2×#135—531no—
451C2×#135—531no—
452C2×#131—531no—
453C2×#131—531no—
454C2×#131—531no—
455C22×M16C2×D5311yescharacteristic
456#525—531no—
457C22×C42C2×D5311yescharacteristic
458#452—531no—
459#452—531no—
460#451—531no—
461#450—531no—
462#449—531no—
463#449—531no—
464#448—531no—
465#447—531no—
466#444—1064no—
467#436—1061no—
468#435—1061no—
469#435—1061no—
470C8×D4—1061no—
471C2×#108—531no—
472C2×#108—531no—
473#424—531no—
474C2×#104—24no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104C2×D5311yescharacteristic
478C2×#104C2×D5311yescharacteristic
479C2×#104C2×D5311yescharacteristic
480C2×#104C2×D5311yescharacteristic
481#416—531no—
482#416—531no—
483#408—531no—
484#408—531no—
485#408—531no—
486#408—1061no—
487#408—1061no—
488#407—531no—
489#407—1061no—
490C2×C22⋊C8—531no—
491C2×C22⋊C8—531no—
492C2×C22⋊C8—1061no—
493#405—531no—
494C2×#97—531no—
495C2×#97—531no—
496#341—531no—
497#341—531no—
498#339—531no—
499#339—531no—
500#336—531no—
501#336—531no—
502C53#2288611yescharacteristic, complemented, Sylow
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—531no—
510C2×#41C4×D5311yescharacteristic
511C2×#41C4×D5311yescharacteristic
512C2×#41C22×D5311yescharacteristic
513C2×#41C22×D5311yescharacteristic
514C22×Q8C4×D5311yescharacteristic
515C22×D4—21no—
516C22×D4C4×D5311yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C22×D5311yescharacteristic
520#135—1062no—
521#135—1062no—
522#135—2121no—
523#135—2121no—
524C2×Q16—531no—
525C2×Q16—531no—
526C2×SD16—531no—
527C2×SD16—531no—
528C2×SD16—531no—
529C2×SD16—531no—
530C2×D8—531no—
531C2×D8—531no—
532#131—1062no—
533#131—1062no—
534#131—1062no—
535#131—2121no—
536#131—2121no—
537#131—2121no—
538C2×M16—21no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—531no—
542C2×M16—531no—
543C2×M16—1061no—
544C2×M16—1061no—
545C2×M16—1061no—
546C2×M16C22×D5311yescharacteristic
547C2×M16C22×D5311yescharacteristic
548C22×C8—21no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—531no—
553C22×C8—1061no—
554C22×C8—1061no—
555C22×C8—1061no—
556#123—1061no—
557C22⋊Q8—531no—
558C22⋊Q8—531no—
559#121—531no—
560#121—531no—
561#120—1061no—
562C4×D4—1061no—
563C4×D4—1061no—
564#117—531no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D5311yescharacteristic
569C2×C42C22×D5311yescharacteristic
570#108—1062no—
571#108—2121no—
572C4⋊C8—1061no—
573C4⋊C8—1061no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—1062no—
578#104—2121no—
579#104C22⋊D5314yescomplemented
580#103—531no—
581#103—531no—
582#103—531no—
583#103—531no—
584#102—531no—
585#102—531no—
586#102—531no—
587#102—531no—
588C22⋊C8—531no—
589C22⋊C8—531no—
590C22⋊C8—531no—
591C22⋊C8—531no—
592C22⋊C8—531no—
593C22⋊C8—531no—
594C22⋊C8—531no—
595C22⋊C8—531no—
596C22⋊C8—1061no—
597C22⋊C8—1061no—
598C22⋊C8—1061no—
599C22⋊C8—1061no—
600C22⋊C8—1061no—
601C22⋊C8—1061no—
602C22⋊C8—1061no—
603C22⋊C8—1061no—
604#97—1061no—
605#97—1062no—
606#97—2121no—
607C4×C8—1061no—
608C24—21no—
609C24#1171994711yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41—1061no—
625#41—1061no—
626#41—1061no—
627#41—1061no—
628#41#1171994512yes—
629#41C2×C22⋊D5312yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—531no—
634C2×Q8C2×C4×D5311yescharacteristic
635C2×Q8C2×C4×D5311yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—531no—
646C2×D4—1061no—
647C2×D4—1061no—
648C2×D4—1061no—
649C2×D4C2×C4×D5311yescharacteristic
650C2×D4C2×C4×D5311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1061no—
668C22×C4C2×C4×D5311yescharacteristic
669C22×C4C2×C4×D5311yescharacteristic
670C22×C4D4×D5311yescharacteristic
671C22×C4D4×D5311yescharacteristic
672C22×C4#1171994711yescharacteristic
673C22×C4C23×D5311yescharacteristic
674Q16—1062no—
675Q16—2121no—
676SD16—1062no—
677SD16—1062no—
678SD16—2121no—
679SD16—2121no—
680D8—1062no—
681D8—2121no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—1061no—
687M16—1061no—
688M16—1061no—
689M16—1061no—
690M16—2122no—
691M16—2122no—
692M16—2122no—
693M16C2×C22⋊D5312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—42no—
697C2×C8—531no—
698C2×C8—531no—
699C2×C8—531no—
700C2×C8—531no—
701C2×C8—531no—
702C2×C8—531no—
703C2×C8—531no—
704C2×C8—531no—
705C2×C8—1061no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—1061no—
712C2×C8—1061no—
713C2×C8—1061no—
714C2×C8—1061no—
715C2×C8—2122no—
716C2×C8—2122no—
717C2×C8—2122no—
718C4⋊C4—531no—
719C4⋊C4—531no—
720C4⋊C4—1061no—
721C4⋊C4—1061no—
722C22⋊C4—1061no—
723C22⋊C4—1061no—
724C22⋊C4—1061no—
725C22⋊C4—1061no—
726C22⋊C4—1061no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1061no—
732C42C2×C22⋊D5312yes—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—1061no—
743C23#1313317711yescharacteristic
744C23#1313317711yescharacteristic
745C23C2×#1171994711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—1061no—
751Q8—1061no—
752Q8C4×C22⋊D5312yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—1061no—
764D4—1061no—
765D4—4241no—
766D4—2121no—
767D4—2121no—
768D4—2122no—
769D4C4×C22⋊D5312yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—48no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—1061no—
797C2×C4—1061no—
798C2×C4—1061no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4#1313317711yescharacteristic
802C2×C4#1313317711yescharacteristic
803C2×C4C22×C4×D5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C22×C22⋊D5311yescharacteristic
806C2×C4C2×#1171994511yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326211yescharacteristic
809C8—22no—
810C8—41no—
811C8—1061no—
812C8—1061no—
813C8—1061no—
814C8—1061no—
815C8—1061no—
816C8—1061no—
817C8—1061no—
818C8—1061no—
819C8—2121no—
820C8—2121no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—2121no—
838C22—2121no—
839C22—2121no—
840C22#1681074212yescomplemented
841C22C2×#1313317711yescharacteristic
842C22#1681126711yescharacteristic
843C22#1681129911yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—42no—
848C4—42no—
849C4—41no—
850C4—2121no—
851C4—2121no—
852C4—2121no—
853C4C2×C4×C22⋊D5311yescharacteristic
854C4#1681109611yescharacteristic
855C4D4×C22⋊D5311yescharacteristic
856C4#1681126311yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—4241no—
864C2#2027769411yescharacteristic
865C2C2×#1681074211yescharacteristic
866C2#2028362111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC22×#104×C53C2
socleC22×C53C2×C4×D4
prime radical#20283933C2
cosocleC22×C4×C53C24
hypercenterC22×#104D53
hypocenterC53#22886
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16810742C2semidirect
3. #20283440C2semidirect
4. #20283164C2semidirect
5. #20275605C2semidirect
6. #20275423C2semidirect
7. #20275366C2semidirect
8. #20275158C2semidirect
9. #20275040C2semidirect
10. #20275039C2semidirect
11. #20274988C2semidirect
12. #20274920C2semidirect
13. #20274560C2semidirect
14. #20274477C2semidirect
15. C22×#104×C53C2semidirect
18. C2×#13133225C22semidirect
22. #16810785C4semidirect
23. #16810785C4semidirect
24. #16810779C4semidirect
25. #16810774C4semidirect
26. #16810768C4semidirect
27. #16810768C4semidirect
28. #16810762C4semidirect
29. #16810757C4semidirect
35. C2×#13133152C22semidirect
36. C2×#13133152C22semidirect
37. #16810651C22semidirect
38. C2×#13133145C22semidirect
39. C2×#13133145C22semidirect
42. #16810591C22semidirect
52. #16810581C22semidirect
53. C2×#13133128C22semidirect
54. C2×#13133128C22semidirect
55. #16810387C22semidirect
56. #16810387C22semidirect
57. #16810383C22semidirect
58. #16810383C22semidirect
59. #16810378C22semidirect
60. #16810378C22semidirect
74. C2×#11719925C2×C4semidirect
75. C2×#11719925C2×C4semidirect
76. C2×#11719923C2×C4semidirect
77. C2×#11719923C2×C4semidirect
78. C2×#11719924C2×C4semidirect
79. C2×#11719924C2×C4semidirect
80. C2×#11719922C2×C4semidirect
81. C2×#11719922C2×C4semidirect
115. #13133141C2×C4semidirect
116. #13133141C2×C4semidirect
117. #13133141C2×C4semidirect
118. #13133141C2×C4semidirect
119. #13133138C2×C4semidirect
120. #13133138C2×C4semidirect
121. #13133138C2×C4semidirect
122. #13133138C2×C4semidirect
173. #104×C53D4semidirect
404. C22×C53#444semidirect
427. C22×#104D53semidirect
502. C53#22886semidirect
579. #104C22⋊D53semidirect
840. C22#16810742semidirect

Maximal subgroups

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

subgroupindex
#202839332
C2×#168107422
#202834402
#202831642
#202756052
#202754232
#202753662
#202751582
#202750402
#202750392
#202749882
#202749202
#202745602
#202744772
C22×#104×C532
#2288653