Finite Group Databasebeta

← #27404830

Subgroups — #27404830

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#20283931C211yesmaximal, characteristic
2C2×#16810743C211yesmaximal, characteristic, complemented
3C22×#13133143C211yesmaximal, characteristic, complemented
4#20283161C211yesmaximal, characteristic, complemented
5#20275607C211yesmaximal, characteristic, complemented
6#20275425C211yesmaximal, characteristic, complemented
7#20275363C211yesmaximal, characteristic, complemented
8#20275159C211yesmaximal, characteristic, complemented
9#20275045C211yesmaximal, characteristic, complemented
10#20275042C211yesmaximal, characteristic, complemented
11#20274989C211yesmaximal, characteristic, complemented
12#20274920C211yesmaximal, characteristic, complemented
13#20274561C211yesmaximal, characteristic, complemented
14#20274479C211yesmaximal, characteristic, complemented
15C53×#2933C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133237C2211yescharacteristic
19C2×#13133223C2211yescharacteristic
20C2×#13133223C2211yescharacteristic
21C22×C4×Dic53C2211yescharacteristic
22#16810783C411yescharacteristic, complemented
23#16810783C411yescharacteristic, complemented
24#16810778C411yescharacteristic, complemented
25#16810773C411yescharacteristic, complemented
26#16810766C411yescharacteristic, complemented
27#16810766C411yescharacteristic, complemented
28#16810761C411yescharacteristic, complemented
29#16810756C411yescharacteristic, complemented
30#16810743—24no—
31C2×#13133152C2211yescharacteristic, complemented
32C2×#13133152C2211yescharacteristic, complemented
33C2×#13133144C2211yescharacteristic, complemented
34C2×#13133144C2211yescharacteristic, complemented
35C2×#13133143—24no—
36C2×#13133143C2211yescharacteristic
37C2×#13133143C2211yescharacteristic
38C2×#13133143C2211yescharacteristic
39C2×#13133143C2211yescharacteristic
40#16810617C2211yescharacteristic
41#16810617C2211yescharacteristic
42#16810589C2211yescharacteristic
43#16810589C2211yescharacteristic
44#16810588—21no—
45#16810588—21no—
46#16810587C2211yescharacteristic
47#16810585—21no—
48C2×C22⋊#88322C2211yescharacteristic
49C22⋊C8×D53—21no—
50C2×#13133127C2211yescharacteristic, complemented
51C2×#13133127C2211yescharacteristic, complemented
52#16810387C2211yescharacteristic, complemented
53#16810387C2211yescharacteristic, complemented
54#16810382C2211yescharacteristic, complemented
55#16810382C2211yescharacteristic, complemented
56#16810377C2211yescharacteristic, complemented
57#16810377C2211yescharacteristic, complemented
58C2×#131×C53C2211yescharacteristic, complemented
59C22×M16×C53C2211yescharacteristic
60C53×#525C2211yescharacteristic
61C53×#436—21no—
62C53×#435—21no—
63C53×#435—21no—
64C8×D4×C53—21no—
65C53×#424C2211yescharacteristic, complemented
66C53×#408C2211yescharacteristic, complemented
67C2×C22⋊C8×C53C2211yescharacteristic
68C53×#405C2211yescharacteristic, complemented
69C2×#11719945—21no—
70C2×#11719945—21no—
71C2×#11719945—22no—
72C2×#11719945—22no—
73C2×#11719945—41no—
74C2×#11719945—41no—
75C2×#11719945C2×C411yescharacteristic
76C2×#11719945C2×C411yescharacteristic
77C2×#11719945C2311yescharacteristic
78C2×#11719945C2311yescharacteristic
79C22×Dic106C2×C411yescharacteristic
80C22×D212C2×C411yescharacteristic
81C22×C22⋊D53—21no—
82C23×Dic53—21no—
83C22×C4×D53—21no—
84#13133237—22no—
85#13133237—22no—
86#13133237—41no—
87#13133237—41no—
88C2×#11719925C2×C411yescharacteristic, complemented
89C2×#11719925C2×C411yescharacteristic, complemented
90C2×#11719923C2×C411yescharacteristic, complemented
91C2×#11719923C2×C411yescharacteristic, complemented
92C2×#11719924C2×C411yescharacteristic, complemented
93C2×#11719924C2×C411yescharacteristic, complemented
94C2×#11719922C2×C411yescharacteristic, complemented
95C2×#11719922C2×C411yescharacteristic, complemented
96#13133223—22no—
97#13133223—22no—
98#13133223—41no—
99#13133223—41no—
100C2×#11719917C2311yescharacteristic
101C2×#11719917C2311yescharacteristic
102C2×#11719912—21no—
103C2×#11719912—21no—
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106C2×C8×D53—21no—
107C2×C8×D53—21no—
108C2×C4×Dic53—21no—
109C2×C4×Dic53—22no—
110C2×C4×Dic53—41no—
111C2×C4×Dic53C2311yescharacteristic
112C2×C4×Dic53C2311yescharacteristic
113#13133152—22no—
114#13133152—41no—
115#13133144—22no—
116#13133144—41no—
117#13133143—22no—
118#13133143—22no—
119#13133143—22no—
120#13133143D414yescomplemented
121#13133140C2×C411yescharacteristic, complemented
122#13133140C2×C411yescharacteristic, complemented
123#13133140C2×C411yescharacteristic, complemented
124#13133140C2×C411yescharacteristic, complemented
125#13133137C2×C411yescharacteristic, complemented
126#13133137C2×C411yescharacteristic, complemented
127#13133137C2×C411yescharacteristic, complemented
128#13133137C2×C411yescharacteristic, complemented
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#13133129—21no—
138#13133129—21no—
139#13133127—22no—
140#13133127—41no—
141C2×#41×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143#131×C53—22no—
144#131×C53—41no—
145C2×M16×C53—21no—
146C2×M16×C53—22no—
147C2×M16×C53—21no—
148C2×M16×C53—41no—
149C2×M16×C53C2311yescharacteristic
150C2×M16×C53C2311yescharacteristic
151C22×C8×C53—21no—
152C22×C8×C53—21no—
153C22×C8×C53C2311yescharacteristic
154C22×C8×C53C2311yescharacteristic
155#123×C53—21no—
156C22⋊Q8×C53C2×C411yescharacteristic
157C22⋊Q8×C53C2×C411yescharacteristic
158#121×C53C2×C411yescharacteristic
159#121×C53C2×C411yescharacteristic
160#120×C53—21no—
161C4×D4×C53—21no—
162C4×D4×C53—21no—
163#117×C53C2311yescharacteristic
164C4⋊C8×C53—21no—
165C4⋊C8×C53—21no—
166C22⋊C8×C53—21no—
167C22⋊C8×C53—21no—
168C22⋊C8×C53D411yescharacteristic
169C22⋊C8×C53D411yescharacteristic
170C22⋊C8×C53D411yescharacteristic
171C22⋊C8×C53D411yescharacteristic
172#97×C53—21no—
173C4×C8×C53—21no—
174C24×C53#4111yescharacteristic
175C23×D53—21no—
176#41×C53—21no—
177#41×C53—21no—
178#41×C53—21no—
179#41×C53—21no—
180C2×Q8×C53C22×C411yescharacteristic
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—21no—
184C2×D4×C53C22×C411yescharacteristic
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53C22×C411yescharacteristic
191C22×C4×C53C22×C411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53#4111yescharacteristic
195C22×C4×C53C2411yescharacteristic
196C2×C22⋊D53—21no—
197C2×C22⋊D53—21no—
198C2×C22⋊D53—21no—
199C2×C22⋊D53—21no—
200C2×C22⋊D53—42no—
201C2×C22⋊D53—42no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—42no—
206C22×Dic53—42no—
207C22×Dic53—42no—
208#11719945—21no—
209#11719945—21no—
210#11719945—21no—
211#11719945—21no—
212#11719945—21no—
213#11719945—21no—
214#11719945—22no—
215#11719945—22no—
216#11719945—41no—
217#11719945—41no—
218#11719945—42no—
219#11719945—42no—
220#11719945—42no—
221#11719945—42no—
222#11719945C2×D412yes—
223#11719945#4112yes—
224C2×D212—22no—
225C2×D212—21no—
226C2×D212—41no—
227C2×D212C22×C411yescharacteristic
228C2×D212C22×C411yescharacteristic
229C2×C4×D53—21no—
230C2×C4×D53—21no—
231C2×C4×D53—21no—
232C2×C4×D53—21no—
233C2×C4×D53—42no—
234C2×C4×D53—42no—
235C2×Dic106—22no—
236C2×Dic106—21no—
237C2×Dic106—41no—
238C2×Dic106C22×C411yescharacteristic
239C2×Dic106C22×C411yescharacteristic
240M16×C53—21no—
241M16×C53—21no—
242M16×C53—21no—
243M16×C53—42no—
244M16×C53—42no—
245M16×C53C2×D412yes—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—21no—
250C2×C8×C53—21no—
251C2×C8×C53—21no—
252C2×C8×C53—42no—
253C2×C8×C53—42no—
254C2×C8×C53C2×D411yescharacteristic
255C2×C8×C53C2×D411yescharacteristic
256C2×C8×C53C2×D411yescharacteristic
257C2×C8×C53C2×D411yescharacteristic
258C4⋊C4×C53—21no—
259C4⋊C4×C53—21no—
260C4⋊C4×C53C22×C411yescharacteristic
261C4⋊C4×C53C22×C411yescharacteristic
262C22⋊C4×C53—21no—
263C22⋊C4×C53—21no—
264C22⋊C4×C53—21no—
265C22⋊C4×C53—21no—
266C22⋊C4×C53—21no—
267C42×C53—21no—
268#11719925—22no—
269#11719925—41no—
270#11719924—22no—
271#11719924—41no—
272#11719923—22no—
273#11719923—41no—
274#11719922—22no—
275#11719922—41no—
276C4×Dic53—21no—
277C4×Dic53—21no—
278C4×Dic53—21no—
279C4×Dic53—42no—
280C4×Dic53C2×D412yes—
281#11719917—21no—
282#11719917—21no—
283#11719917—21no—
284#11719917—21no—
285C2×#88322—21no—
286C2×#88322—21no—
287C2×#88322—21no—
288C2×#88322—21no—
289C2×#88322—21no—
290C2×#88322—21no—
291C2×#88322C22×C411yescharacteristic
292C2×#88322C22×C411yescharacteristic
293C2×#88322C22×C411yescharacteristic
294C2×#88322C22×C411yescharacteristic
295#11719912—42no—
296#11719912—42no—
297C8×D53—42no—
298C8×D53—42no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—22no—
302C23×C53—21no—
303C23×C53—41no—
304C23×C53C4×D411yescharacteristic
305C23×C53C4×D411yescharacteristic
306C23×C53C2×#4111yescharacteristic
307C22×D53—21no—
308C22×D53—21no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—81no—
312Q8×C53—21no—
313Q8×C53—21no—
314D4×C53—21no—
315D4×C53—21no—
316D4×C53—41no—
317D4×C53—41no—
318D4×C53—42no—
319D4×C53—81no—
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—21no—
330C2×C4×C53—21no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—41no—
334C2×C4×C53—41no—
335C2×C4×C53C4×D411yescharacteristic
336C2×C4×C53C4×D411yescharacteristic
337C2×C4×C53C23×C411yescharacteristic
338C2×C4×C53C22×D411yescharacteristic
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53C2×#4111yescharacteristic
341C2×C4×C53H(5,𝔽2)11yescharacteristic
342C2×C4×C53H(5,𝔽2)11yescharacteristic
343C22⋊D53—22no—
344C22⋊D53—22no—
345C22⋊D53—42no—
346C22⋊D53—42no—
347C22⋊D53—41no—
348C22⋊D53—41no—
349C2×Dic53—21no—
350C2×Dic53—22no—
351C2×Dic53—21no—
352C2×Dic53—22no—
353C2×Dic53—42no—
354C2×Dic53—41no—
355C2×Dic53—41no—
356C2×Dic53—41no—
357C2×Dic53—48no—
358C2×Dic53—41no—
359D212—21no—
360D212—21no—
361D212—21no—
362D212—42no—
363D212C4×D412yes—
364C4×D53—22no—
365C4×D53—22no—
366C4×D53—42no—
367C4×D53—42no—
368C4×D53—41no—
369C4×D53—41no—
370Dic106—21no—
371Dic106—21no—
372Dic106—21no—
373Dic106—42no—
374Dic106C4×D412yes—
375C8×C53—21no—
376C8×C53—21no—
377C8×C53—22no—
378C8×C53—21no—
379C8×C53—21no—
380C8×C53—41no—
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—21no—
394C22×C53—21no—
395C22×C53—42no—
396C22×C53—42no—
397C22×C53—41no—
398C22×C53—41no—
399C22×C53—41no—
400C22×C53#44412yescomplemented
401C22×C53C2×C4×D411yescharacteristic
402C22×C53#54611yescharacteristic
403C22×C53#55111yescharacteristic
404C2×D53—22no—
405C2×D53—41no—
406C2×D53—41no—
407C2×D53—41no—
408C2×D53—41no—
409C2×D53—41no—
410C2×D53—84no—
411C4×C53—21no—
412C4×C53—21no—
413C4×C53—41no—
414C4×C53—41no—
415C4×C53—41no—
416C4×C53C2×C4×D411yescharacteristic
417C4×C53#51811yescharacteristic
418C4×C53D4211yescharacteristic
419C4×C53#54611yescharacteristic
420Dic53—22no—
421Dic53—42no—
422Dic53—42no—
423Dic53—41no—
424#3002—531no—
425C2×#444—531no—
426#2933D5311yescharacteristic, complemented
427C22×#104—531no—
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—81no—
444C2×C53#235811yescharacteristic
445C2×C53C2×#44411yescharacteristic
446C2×C53#295611yescharacteristic
447D53—42no—
448D53—81no—
449C22×#41—531no—
450C2×#135—531no—
451C2×#135—531no—
452C2×#131—531no—
453C2×#131—531no—
454C2×#131C2×D5311yescharacteristic, complemented
455C22×M16C2×D5311yescharacteristic
456#525C2×D5311yescharacteristic
457C22×C42—531no—
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—21no—
468#435—21no—
469#435—21no—
470C8×D4—21no—
471C2×#108—531no—
472C2×#108—531no—
473#424C2×D5311yescharacteristic, complemented
474C2×#104—531no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104—531no—
478C2×#104—531no—
479C2×#104—531no—
480C2×#104—1064no—
481#416—531no—
482#416—531no—
483#408—531no—
484#408—531no—
485#408—1061no—
486#408—1061no—
487#408C2×D5311yescharacteristic, complemented
488#407—531no—
489#407—1061no—
490C2×C22⋊C8—531no—
491C2×C22⋊C8—1061no—
492C2×C22⋊C8C2×D5311yescharacteristic
493#405C2×D5311yescharacteristic, complemented
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—531no—
504C2×#41—531no—
505C2×#41—531no—
506C2×#41—531no—
507C2×#41—1062no—
508C2×#41—1062no—
509C2×#41—1061no—
510C2×#41—1061no—
511C2×#41—2121no—
512C2×#41—2121no—
513C2×#41C22×D5311yescharacteristic
514C22×Q8—531no—
515C22×D4—531no—
516C22×D4—1061no—
517C23×C4—1061no—
518C23×C4—1061no—
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—22no—
533#131—41no—
534#131—1062no—
535#131—1062no—
536#131—2121no—
537#131—2121no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—531no—
543C2×M16—531no—
544C2×M16—1061no—
545C2×M16—1061no—
546C2×M16C22×D5311yescharacteristic
547C2×M16C22×D5311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—1061no—
553C22×C8—1061no—
554C22×C8C22×D5311yescharacteristic
555C22×C8C22×D5311yescharacteristic
556#123—21no—
557C22⋊Q8C4×D5311yescharacteristic
558C22⋊Q8C4×D5311yescharacteristic
559#121C4×D5311yescharacteristic
560#121C4×D5311yescharacteristic
561#120—21no—
562C4×D4—21no—
563C4×D4—21no—
564#117C22×D5311yescharacteristic
565C2×C42—531no—
566C2×C42—531no—
567C2×C42—1062no—
568C2×C42—1061no—
569C2×C42—2121no—
570#108—1062no—
571#108—2121no—
572C4⋊C8—21no—
573C4⋊C8—21no—
574#104—534no—
575#104—1062no—
576#104—1062no—
577#104—1062no—
578#104—1062no—
579#104—2121no—
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—21no—
589C22⋊C8—21no—
590C22⋊C8—531no—
591C22⋊C8—531no—
592C22⋊C8—531no—
593C22⋊C8—531no—
594C22⋊C8—1061no—
595C22⋊C8—1061no—
596C22⋊C8—1061no—
597C22⋊C8—1061no—
598C22⋊C8—1061no—
599C22⋊C8—1061no—
600C22⋊C8C22⋊D5311yescharacteristic
601C22⋊C8C22⋊D5311yescharacteristic
602C22⋊C8C22⋊D5311yescharacteristic
603C22⋊C8C22⋊D5311yescharacteristic
604#97—21no—
605#97—1062no—
606#97—2121no—
607C4×C8—21no—
608C24—1061no—
609C24#1171994511yescharacteristic
610#41—21no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—532no—
615#41—532no—
616#41—1062no—
617#41—1062no—
618#41—1061no—
619#41—1061no—
620#41—1061no—
621#41—1061no—
622#41—1061no—
623#41—1061no—
624#41—2122no—
625#41—2122no—
626#41—2121no—
627#41—2121no—
628#41—2122no—
629#41—2122no—
630C2×Q8—531no—
631C2×Q8—531no—
632C2×Q8—1062no—
633C2×Q8—1061no—
634C2×Q8—2121no—
635C2×Q8C2×C4×D5311yescharacteristic
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—531no—
640C2×D4—531no—
641C2×D4—1062no—
642C2×D4—1061no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1061no—
647C2×D4—2121no—
648C2×D4—2122no—
649C2×D4—2122no—
650C2×D4C2×C4×D5311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—2122no—
664C22×C4—2122no—
665C22×C4—2122no—
666C22×C4—2122no—
667C22×C4—2122no—
668C22×C4C2×C4×D5311yescharacteristic
669C22×C4C2×C4×D5311yescharacteristic
670C22×C4#1171994511yescharacteristic
671C22×C4C2×C22⋊D5311yescharacteristic
672C22×C4C2×C22⋊D5311yescharacteristic
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—42no—
687M16—1061no—
688M16—1061no—
689M16—1061no—
690M16—1061no—
691M16—2122no—
692M16—2122no—
693M16D4×D5312yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—42no—
701C2×C8—42no—
702C2×C8—531no—
703C2×C8—531no—
704C2×C8—531no—
705C2×C8—531no—
706C2×C8—1061no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—1061no—
712C2×C8—2122no—
713C2×C8—2122no—
714C2×C8C2×C22⋊D5311yescharacteristic
715C2×C8C2×C22⋊D5311yescharacteristic
716C2×C8C2×C22⋊D5311yescharacteristic
717C2×C8C2×C22⋊D5311yescharacteristic
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4C2×C4×D5311yescharacteristic
721C4⋊C4C2×C4×D5311yescharacteristic
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C42—21no—
728C42—532no—
729C42—1061no—
730C42—1061no—
731C42—1061no—
732C42—2122no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—21no—
737C23—41no—
738C23—1061no—
739C23—1061no—
740C23—4241no—
741C23—2122no—
742C23—2122no—
743C23C4×C22⋊D5311yescharacteristic
744C23C4×C22⋊D5311yescharacteristic
745C23C2×#1171994511yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—532no—
749Q8—1061no—
750Q8—1061no—
751Q8—1061no—
752Q8—2122no—
753D4—21no—
754D4—21no—
755D4—41no—
756D4—41no—
757D4—42no—
758D4—81no—
759D4—532no—
760D4—1062no—
761D4—1062no—
762D4—1061no—
763D4—1061no—
764D4—1061no—
765D4—2122no—
766D4—2122no—
767D4—2122no—
768D4—2121no—
769D4—2121no—
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—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—1061no—
786C2×C4—1062no—
787C2×C4—1062no—
788C2×C4—1062no—
789C2×C4—1062no—
790C2×C4—1061no—
791C2×C4—2122no—
792C2×C4—2122no—
793C2×C4—2122no—
794C2×C4—2121no—
795C2×C4—2121no—
796C2×C4—2121no—
797C2×C4—2128no—
798C2×C4—2121no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4C4×C22⋊D5311yescharacteristic
802C2×C4C4×C22⋊D5311yescharacteristic
803C2×C4C22×C4×D5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C22×C22⋊D5311yescharacteristic
806C2×C4#41×D5311yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326311yescharacteristic
809C8—21no—
810C8—21no—
811C8—22no—
812C8—21no—
813C8—21no—
814C8—41no—
815C8—1061no—
816C8—1061no—
817C8—1061no—
818C8—1061no—
819C8—2121no—
820C8—2121no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—1062no—
834C22—4244no—
835C22—2121no—
836C22—2121no—
837C22—2121no—
838C22—2121no—
839C22—2121no—
840C22#1681074312yescomplemented
841C22C2×C4×C22⋊D5311yescharacteristic
842C22#1681126911yescharacteristic
843C22#1681130211yescharacteristic
844C4—21no—
845C4—21no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—1062no—
850C4—2122no—
851C4—2122no—
852C4—2121no—
853C4C4×D4×D5311yescharacteristic
854C4#1681109511yescharacteristic
855C4D4×C22⋊D5311yescharacteristic
856C4#1681126111yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—4241no—
863C2—2122no—
864C2#2027769211yescharacteristic
865C2C2×#1681074311yescharacteristic
866C2#2028362211yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2933C2
socleC22×C53C2×C4×D4
prime radical#20283931C2
cosocleC22×C4×C53C24
hypercenter#2933D53
hypocenterC53#22886
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2933

Complements

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

NH ≅ G/Ntype
2. C2×#16810743C2semidirect
3. C22×#13133143C2semidirect
4. #20283161C2semidirect
5. #20275607C2semidirect
6. #20275425C2semidirect
7. #20275363C2semidirect
8. #20275159C2semidirect
9. #20275045C2semidirect
10. #20275042C2semidirect
11. #20274989C2semidirect
12. #20274920C2semidirect
13. #20274561C2semidirect
14. #20274479C2semidirect
15. C53×#2933C2semidirect
22. #16810783C4semidirect
23. #16810783C4semidirect
24. #16810778C4semidirect
25. #16810773C4semidirect
26. #16810766C4semidirect
27. #16810766C4semidirect
28. #16810761C4semidirect
29. #16810756C4semidirect
31. C2×#13133152C22semidirect
32. C2×#13133152C22semidirect
33. C2×#13133144C22semidirect
34. C2×#13133144C22semidirect
50. C2×#13133127C22semidirect
51. C2×#13133127C22semidirect
52. #16810387C22semidirect
53. #16810387C22semidirect
54. #16810382C22semidirect
55. #16810382C22semidirect
56. #16810377C22semidirect
57. #16810377C22semidirect
58. C2×#131×C53C22semidirect
65. C53×#424C22semidirect
66. C53×#408C22semidirect
68. C53×#405C22semidirect
88. C2×#11719925C2×C4semidirect
89. C2×#11719925C2×C4semidirect
90. C2×#11719923C2×C4semidirect
91. C2×#11719923C2×C4semidirect
92. C2×#11719924C2×C4semidirect
93. C2×#11719924C2×C4semidirect
94. C2×#11719922C2×C4semidirect
95. C2×#11719922C2×C4semidirect
120. #13133143D4semidirect
121. #13133140C2×C4semidirect
122. #13133140C2×C4semidirect
123. #13133140C2×C4semidirect
124. #13133140C2×C4semidirect
125. #13133137C2×C4semidirect
126. #13133137C2×C4semidirect
127. #13133137C2×C4semidirect
128. #13133137C2×C4semidirect
400. C22×C53#444semidirect
426. #2933D53semidirect
454. C2×#131C2×D53semidirect
473. #424C2×D53semidirect
487. #408C2×D53semidirect
493. #405C2×D53semidirect
502. C53#22886semidirect
840. C22#16810743semidirect

Maximal subgroups

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

subgroupindex
#202839312
C2×#168107432
C22×#131331432
#202831612
#202756072
#202754252
#202753632
#202751592
#202750452
#202750422
#202749892
#202749202
#202745612
#202744792
C53×#29332
#2288653