Finite Group Databasebeta

← #27404826

Subgroups — #27404826

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×#16810742C211yesmaximal, characteristic, complemented
3#20283442C211yesmaximal, characteristic, complemented
4C22×#13133145C211yesmaximal, characteristic, complemented
5#20283165C211yesmaximal, characteristic, complemented
6#20275605C211yesmaximal, characteristic, complemented
7#20275427C211yesmaximal, characteristic, complemented
8#20275361C211yesmaximal, characteristic, complemented
9#20275040C211yesmaximal, characteristic, complemented
10#20275039C211yesmaximal, characteristic, complemented
11#20274991C211yesmaximal, characteristic, complemented
12#20274919C211yesmaximal, characteristic, complemented
13#20274556C211yesmaximal, characteristic, complemented
14#20274477C211yesmaximal, characteristic, complemented
15C53×#1896C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133237C2211yescharacteristic
19C2×#13133225C2211yescharacteristic
20C2×#13133225C2211yescharacteristic
21C2×#13133224C2211yescharacteristic, complemented
22C22×#11719917C2211yescharacteristic
23#16810783C411yescharacteristic, complemented
24#16810783C411yescharacteristic, complemented
25#16810778C411yescharacteristic, complemented
26#16810773C411yescharacteristic, complemented
27#16810766C411yescharacteristic, complemented
28#16810766C411yescharacteristic, complemented
29#16810761C411yescharacteristic, complemented
30#16810756C411yescharacteristic, complemented
31#16810742—24no—
32#16810701—21no—
33#16810695—21no—
34#16810695—21no—
35D4×#88322—21no—
36C2×#13133152C2211yescharacteristic, complemented
37C2×#13133152C2211yescharacteristic, complemented
38#16810650C2211yescharacteristic, complemented
39C2×#13133145—24no—
40C2×#13133145C2211yescharacteristic
41C2×#13133145C2211yescharacteristic
42C2×#13133145C2211yescharacteristic
43C2×#13133145C2211yescharacteristic
44#16810617C2211yescharacteristic
45#16810617C2211yescharacteristic
46#16810591C2211yescharacteristic
47#16810591C2211yescharacteristic
48#16810590C2211yescharacteristic, complemented
49#16810588—21no—
50#16810588—21no—
51#16810585—21no—
52C2×C22⋊#88322C2211yescharacteristic
53C2×C22⋊#88322C2211yescharacteristic
54C22⋊C8×D53—21no—
55#16810579C2211yescharacteristic, complemented
56C2×#13133128C2211yescharacteristic, complemented
57C2×#13133128C2211yescharacteristic, complemented
58#16810387C2211yescharacteristic, complemented
59#16810387C2211yescharacteristic, complemented
60#16810378C2211yescharacteristic, complemented
61#16810378C2211yescharacteristic, complemented
62C53×#525C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C2×#104×C53C2211yescharacteristic, complemented
65C2×#104×C53C2211yescharacteristic, complemented
66C53×#407C2211yescharacteristic
67C53×#339C2211yescharacteristic, complemented
68C53×#339C2211yescharacteristic, 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—
82C22×C4×D53—21no—
83#13133237—22no—
84#13133237—22no—
85#13133237—41no—
86#13133237—41no—
87C2×#11719925C2×C411yescharacteristic, complemented
88C2×#11719925C2×C411yescharacteristic, complemented
89C2×#11719923C2×C411yescharacteristic, complemented
90C2×#11719923C2×C411yescharacteristic, complemented
91C2×#11719924C2×C411yescharacteristic, complemented
92C2×#11719924C2×C411yescharacteristic, complemented
93C2×#11719922C2×C411yescharacteristic, complemented
94C2×#11719922C2×C411yescharacteristic, complemented
95#13133225—22no—
96#13133225—22no—
97#13133225—41no—
98#13133225—41no—
99#13133224—22no—
100#13133224—41no—
101C2×#11719917—21no—
102C2×#11719917—22no—
103C2×#11719917—21no—
104C2×#11719917—41no—
105C2×#11719917C2311yescharacteristic
106C2×#11719917C2311yescharacteristic
107C2×#11719912—21no—
108C2×#11719912—21no—
109C22×#88322—21no—
110C22×#88322—21no—
111C22×#88322C2311yescharacteristic
112C22×#88322C2311yescharacteristic
113C22×#88322C2311yescharacteristic
114C22×#88322C2311yescharacteristic
115C2×C8×D53—21no—
116C2×C8×D53—21no—
117#13133152—22no—
118#13133152—41no—
119C4⋊#88322—21no—
120C4⋊#88322—21no—
121#13133145—22no—
122#13133145—22no—
123#13133145—22no—
124#13133145D414yescomplemented
125#13133140C2×C411yescharacteristic, complemented
126#13133140C2×C411yescharacteristic, complemented
127#13133140C2×C411yescharacteristic, complemented
128#13133140C2×C411yescharacteristic, complemented
129#13133137C2×C411yescharacteristic, complemented
130#13133137C2×C411yescharacteristic, complemented
131#13133137C2×C411yescharacteristic, complemented
132#13133137C2×C411yescharacteristic, complemented
133C22⋊#88322—21no—
134C22⋊#88322—21no—
135C22⋊#88322C2×C411yescharacteristic
136C22⋊#88322C2×C411yescharacteristic
137C22⋊#88322C2×C411yescharacteristic
138C22⋊#88322C2×C411yescharacteristic
139C22⋊#88322D411yescharacteristic
140C22⋊#88322D411yescharacteristic
141C22⋊#88322D411yescharacteristic
142C22⋊#88322D411yescharacteristic
143#13133129—21no—
144#13133129—21no—
145#13133129—21no—
146#13133129—21no—
147#13133128—22no—
148#13133128—21no—
149#13133128—41no—
150C4×#88322—21no—
151C2×#41×C53C2311yescharacteristic
152C23×C4×C53—21no—
153C23×C4×C53C2311yescharacteristic
154C2×M16×C53C2311yescharacteristic
155C2×M16×C53C2311yescharacteristic
156#123×C53—21no—
157C22⋊Q8×C53C2×C411yescharacteristic
158C22⋊Q8×C53C2×C411yescharacteristic
159#121×C53C2×C411yescharacteristic
160#121×C53C2×C411yescharacteristic
161#120×C53—21no—
162C4×D4×C53—21no—
163C4×D4×C53—21no—
164#117×C53C2311yescharacteristic
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—41no—
172C22⋊C8×C53—21no—
173C22⋊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×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—42no—
193C22×C4×C53—42no—
194C22×C4×C53—42no—
195C22×C4×C53C22×C411yescharacteristic
196C22×C4×C53C22×C411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53#4111yescharacteristic
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—21no—
202C2×C22⋊D53—21no—
203C2×C22⋊D53—21no—
204C2×C22⋊D53—21no—
205C2×C22⋊D53—42no—
206C2×C22⋊D53—42no—
207C22×Dic53—21no—
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—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53C22×C411yescharacteristic
249C4⋊C4×C53C22×C411yescharacteristic
250C22⋊C4×C53—21no—
251C22⋊C4×C53—21no—
252C22⋊C4×C53—21no—
253C22⋊C4×C53—21no—
254C22⋊C4×C53—21no—
255C42×C53—21no—
256C42×C53—21no—
257C42×C53—21no—
258C42×C53—21no—
259C42×C53—42no—
260C42×C53C2×D412yes—
261#11719925—22no—
262#11719925—41no—
263#11719924—22no—
264#11719924—41no—
265#11719923—22no—
266#11719923—41no—
267#11719922—22no—
268#11719922—41no—
269#11719917—21no—
270#11719917—21no—
271#11719917—21no—
272#11719917—42no—
273#11719917—42no—
274#11719917C2×D412yes—
275C2×#88322—21no—
276C2×#88322—21no—
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—42no—
286C2×#88322—42no—
287C2×#88322C22×C411yescharacteristic
288C2×#88322C22×C411yescharacteristic
289C2×#88322C22×C411yescharacteristic
290C2×#88322C22×C411yescharacteristic
291C2×#88322C2×D411yescharacteristic
292C2×#88322C2×D411yescharacteristic
293C2×#88322C2×D411yescharacteristic
294C2×#88322C2×D411yescharacteristic
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—22no—
331C2×C4×C53—21no—
332C2×C4×C53—21no—
333C2×C4×C53—21no—
334C2×C4×C53—22no—
335C2×C4×C53—41no—
336C2×C4×C53—41no—
337C2×C4×C53—41no—
338C2×C4×C53—48no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53C4×D411yescharacteristic
343C2×C4×C53C4×D411yescharacteristic
344C2×C4×C53C23×C411yescharacteristic
345C2×C4×C53C22×D411yescharacteristic
346C2×C4×C53C22×D411yescharacteristic
347C2×C4×C53C2×#4111yescharacteristic
348C2×C4×C53H(5,𝔽2)11yescharacteristic
349C2×C4×C53H(5,𝔽2)11yescharacteristic
350C22⋊D53—22no—
351C22⋊D53—22no—
352C22⋊D53—42no—
353C22⋊D53—42no—
354C22⋊D53—41no—
355C22⋊D53—41no—
356C2×Dic53—21no—
357C2×Dic53—21no—
358C2×Dic53—42no—
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—41no—
376C8×C53—41no—
377#88322—21no—
378#88322—21no—
379#88322—21no—
380#88322—21no—
381#88322—21no—
382#88322—21no—
383#88322—22no—
384#88322—21no—
385#88322—21no—
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—42no—
414C4×C53—42no—
415C4×C53—41no—
416C4×C53—41no—
417C4×C53—41no—
418C4×C53C2×C4×D411yescharacteristic
419C4×C53#51811yescharacteristic
420C4×C53D4211yescharacteristic
421C4×C53#54611yescharacteristic
422Dic53—22no—
423Dic53—41no—
424#3002—531no—
425C2×#444—531no—
426#2933—531no—
427C22×#104—531no—
428#2880—531no—
429#1975—531no—
430#1938—531no—
431#1929—531no—
432#1896D5311yescharacteristic, complemented
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×#131—531no—
455C22×M16—531no—
456#525C2×D5311yescharacteristic
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—531no—
475C2×#104—531no—
476C2×#104—531no—
477C2×#104—531no—
478C2×#104—1064no—
479C2×#104C2×D5311yescharacteristic, complemented
480C2×#104C2×D5311yescharacteristic, complemented
481#416—531no—
482#416—531no—
483#408—531no—
484#408—531no—
485#408—531no—
486#408—1061no—
487#408—1061no—
488#407—1061no—
489#407C2×D5311yescharacteristic
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#339C2×D5311yescharacteristic, complemented
499#339C2×D5311yescharacteristic, complemented
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—21no—
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—1062no—
533#131—1062no—
534#131—1062no—
535#131—2121no—
536#131—2121no—
537#131—2121no—
538C2×M16—531no—
539C2×M16—531no—
540C2×M16—1061no—
541C2×M16—1061no—
542C2×M16—1061no—
543C2×M16—1061no—
544C2×M16—1062no—
545C2×M16—2121no—
546C2×M16C22×D5311yescharacteristic
547C2×M16C22×D5311yescharacteristic
548C22×C8—531no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—531no—
552C22×C8—1061no—
553C22×C8—1061no—
554C22×C8—1061no—
555C22×C8—1061no—
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—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—41no—
576#104—534no—
577#104—1062no—
578#104—1062no—
579#104—1062no—
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—531no—
595C22⋊C8—531no—
596C22⋊C8—531no—
597C22⋊C8—531no—
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—1061no—
609C24#1171994711yescharacteristic
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—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—1061no—
662C22×C4—1061no—
663C22×C4—1061no—
664C22×C4—1061no—
665C22×C4—1061no—
666C22×C4—2122no—
667C22×C4—2122no—
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—21no—
686M16—532no—
687M16—1061no—
688M16—1061no—
689M16—1061no—
690M16—2122no—
691M16—2122no—
692M16—2122no—
693M16—2122no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—531no—
697C2×C8—531no—
698C2×C8—531no—
699C2×C8—531no—
700C2×C8—531no—
701C2×C8—531no—
702C2×C8—531no—
703C2×C8—531no—
704C2×C8—1061no—
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—2122no—
715C2×C8—2122no—
716C2×C8—2122no—
717C2×C8—2122no—
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—21no—
729C42—21no—
730C42—21no—
731C42—42no—
732C42D4×D5312yes—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—21no—
737C23—41no—
738C23—1061no—
739C23—1061no—
740C23—4241no—
741C23—2122no—
742C23—2122no—
743C23#1313317711yescharacteristic
744C23#1313317711yescharacteristic
745C23C2×#1171994711yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—532no—
749Q8—1061no—
750Q8—1061no—
751Q8—1061no—
752Q8—2122no—
753D4—21no—
754D4—21no—
755D4—41no—
756D4—42no—
757D4—41no—
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—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—48no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—1061no—
793C2×C4—1062no—
794C2×C4—1062no—
795C2×C4—1061no—
796C2×C4—2122no—
797C2×C4—2122no—
798C2×C4—2122no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4#1313317711yescharacteristic
802C2×C4#1313317711yescharacteristic
803C2×C4C22×C4×D5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C2×D4×D5311yescharacteristic
806C2×C4#41×D5311yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326311yescharacteristic
809C8—41no—
810C8—41no—
811C8—1061no—
812C8—1061no—
813C8—1061no—
814C8—1061no—
815C8—1061no—
816C8—1061no—
817C8—1062no—
818C8—1061no—
819C8—1061no—
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#1681074212yescomplemented
841C22C2×#1313317711yescharacteristic
842C22#1681126011yescharacteristic
843C22#1681129611yescharacteristic
844C4—21no—
845C4—21no—
846C4—42no—
847C4—42no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—1062no—
852C4—2121no—
853C4C4×D4×D5311yescharacteristic
854C4#1681109511yescharacteristic
855C4#1681125711yescharacteristic
856C4#1681126211yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—81no—
862C2—4241no—
863C2—2122no—
864C2#2027769511yescharacteristic
865C2C2×#1681074211yescharacteristic
866C2#2028362111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1896C2
socleC22×C53C2×C4×D4
prime radical#20283931C2
cosocleC22×C4×C53C24
hypercenter#1896D53
hypocenterC53#22886
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1896

Complements

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

NH ≅ G/Ntype
2. C2×#16810742C2semidirect
3. #20283442C2semidirect
4. C22×#13133145C2semidirect
5. #20283165C2semidirect
6. #20275605C2semidirect
7. #20275427C2semidirect
8. #20275361C2semidirect
9. #20275040C2semidirect
10. #20275039C2semidirect
11. #20274991C2semidirect
12. #20274919C2semidirect
13. #20274556C2semidirect
14. #20274477C2semidirect
15. C53×#1896C2semidirect
21. C2×#13133224C22semidirect
23. #16810783C4semidirect
24. #16810783C4semidirect
25. #16810778C4semidirect
26. #16810773C4semidirect
27. #16810766C4semidirect
28. #16810766C4semidirect
29. #16810761C4semidirect
30. #16810756C4semidirect
36. C2×#13133152C22semidirect
37. C2×#13133152C22semidirect
38. #16810650C22semidirect
48. #16810590C22semidirect
55. #16810579C22semidirect
56. C2×#13133128C22semidirect
57. C2×#13133128C22semidirect
58. #16810387C22semidirect
59. #16810387C22semidirect
60. #16810378C22semidirect
61. #16810378C22semidirect
64. C2×#104×C53C22semidirect
65. C2×#104×C53C22semidirect
67. C53×#339C22semidirect
68. C53×#339C22semidirect
87. C2×#11719925C2×C4semidirect
88. C2×#11719925C2×C4semidirect
89. C2×#11719923C2×C4semidirect
90. C2×#11719923C2×C4semidirect
91. C2×#11719924C2×C4semidirect
92. C2×#11719924C2×C4semidirect
93. C2×#11719922C2×C4semidirect
94. C2×#11719922C2×C4semidirect
124. #13133145D4semidirect
125. #13133140C2×C4semidirect
126. #13133140C2×C4semidirect
127. #13133140C2×C4semidirect
128. #13133140C2×C4semidirect
129. #13133137C2×C4semidirect
130. #13133137C2×C4semidirect
131. #13133137C2×C4semidirect
132. #13133137C2×C4semidirect
400. C22×C53#444semidirect
432. #1896D53semidirect
479. C2×#104C2×D53semidirect
480. C2×#104C2×D53semidirect
498. #339C2×D53semidirect
499. #339C2×D53semidirect
502. C53#22886semidirect
840. C22#16810742semidirect

Maximal subgroups

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

subgroupindex
#202839312
C2×#168107422
#202834422
C22×#131331452
#202831652
#202756052
#202754272
#202753612
#202750402
#202750392
#202749912
#202749192
#202745562
#202744772
C53×#18962
#2288653