Finite Group Databasebeta

← #27395521

Subgroups — #27395521

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#20283931C211yesmaximal, characteristic
2#20283419C211yesmaximal, characteristic, complemented
3#20283159C211yesmaximal, characteristic, complemented
4#20275605C211yesmaximal, characteristic, complemented
5#20275600C211yesmaximal, characteristic, complemented
6#20275427C211yesmaximal, characteristic, complemented
7#20275420C211yesmaximal, characteristic, complemented
8#20275361C211yesmaximal, characteristic, complemented
9#20275361C211yesmaximal, characteristic, complemented
10#20275040C211yesmaximal, characteristic, complemented
11#20275040C211yesmaximal, characteristic, complemented
12#20274920C211yesmaximal, characteristic, complemented
13#20274660C211yesmaximal, characteristic, complemented
14#20274499C211yesmaximal, characteristic, complemented
15C53×#1871C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133237C2211yescharacteristic
18C2×#13133237C2211yescharacteristic
19C2×#13133224C2211yescharacteristic, complemented
20C22×#11719917C2211yescharacteristic
21#16810783C411yescharacteristic, complemented
22#16810783C411yescharacteristic, complemented
23#16810778C411yescharacteristic, complemented
24#16810773C411yescharacteristic, complemented
25#16810766C411yescharacteristic, complemented
26#16810766C411yescharacteristic, complemented
27#16810761C411yescharacteristic, complemented
28#16810756C411yescharacteristic, complemented
29#16810701—21no—
30#16810701—21no—
31#16810695—21no—
32#16810695—21no—
33C2×#13133152C2211yescharacteristic, complemented
34C2×#13133152C2211yescharacteristic, complemented
35#16810650C2211yescharacteristic, complemented
36C2×#13133145C2211yescharacteristic
37C2×#13133145C2211yescharacteristic
38C2×#13133145C2211yescharacteristic
39C2×#13133145C2211yescharacteristic
40#16810617C2211yescharacteristic
41#16810617C2211yescharacteristic
42#16810591C2211yescharacteristic
43#16810591C2211yescharacteristic
44#16810591C2211yescharacteristic
45#16810591C2211yescharacteristic
46#16810590C2211yescharacteristic, complemented
47#16810589—21no—
48#16810589—21no—
49#16810587C2211yescharacteristic
50#16810586—21no—
51#16810586—21no—
52C2×C22⋊#88322C2211yescharacteristic
53#16810579C2211yescharacteristic, complemented
54C2×#13133128C2211yescharacteristic, complemented
55C2×C4×#88322C2211yescharacteristic, complemented
56#16810387C2211yescharacteristic, complemented
57#16810387C2211yescharacteristic, complemented
58#16810378C2211yescharacteristic, complemented
59#16810378C2211yescharacteristic, complemented
60C22×M16×C53C2211yescharacteristic
61C53×#525C2211yescharacteristic
62C2×#104×C53C2211yescharacteristic, complemented
63C2×#104×C53C2211yescharacteristic, complemented
64C4×C22⋊C4×C53C2211yescharacteristic
65C53×#339C2211yescharacteristic, complemented
66C53×#339C2211yescharacteristic, complemented
67C2×#11719945—21no—
68C2×#11719945—21no—
69C2×#11719945—41no—
70C2×#11719945—41no—
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#13133237—41no—
82#13133237—41no—
83#13133237—41no—
84#13133237—41no—
85C2×#11719925C2×C411yescharacteristic
86C2×#11719925C2×C411yescharacteristic
87C2×#11719923C2×C411yescharacteristic
88C2×#11719923C2×C411yescharacteristic
89C2×#11719924C2×C411yescharacteristic
90C2×#11719924C2×C411yescharacteristic
91C2×#11719922C2×C411yescharacteristic
92C2×#11719922C2×C411yescharacteristic
93#13133224—41no—
94#13133224—41no—
95C2×#11719917—21no—
96C2×#11719917—41no—
97C2×#11719917—41no—
98C2×#11719917D411yescharacteristic
99C2×#11719917D411yescharacteristic
100C2×#11719917D411yescharacteristic
101C2×#11719917D411yescharacteristic
102C2×#11719917C2311yescharacteristic
103C2×#11719917C2311yescharacteristic
104C22×#88322—21no—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107C22×#88322C2311yescharacteristic
108C22×#88322C2311yescharacteristic
109#13133152—41no—
110#13133152—41no—
111C4⋊#88322—21no—
112C4⋊#88322—21no—
113#13133145—41no—
114#13133145—41no—
115#13133145—41no—
116#13133145—41no—
117#13133140C2×C411yescharacteristic
118#13133140C2×C411yescharacteristic
119#13133140C2×C411yescharacteristic
120#13133140C2×C411yescharacteristic
121#13133137C2×C411yescharacteristic
122#13133137C2×C411yescharacteristic
123#13133137C2×C411yescharacteristic
124#13133137C2×C411yescharacteristic
125C22⋊#88322—21no—
126C22⋊#88322—21no—
127C22⋊#88322—21no—
128C22⋊#88322—21no—
129C22⋊#88322C2×C411yescharacteristic
130C22⋊#88322C2×C411yescharacteristic
131C22⋊#88322C2×C411yescharacteristic
132C22⋊#88322C2×C411yescharacteristic
133#13133129—21no—
134#13133129—21no—
135#13133129—21no—
136#13133129—21no—
137#13133129—21no—
138#13133129—21no—
139#13133129—21no—
140#13133129—21no—
141#13133128—21no—
142#13133128—41no—
143C4×#88322—21no—
144C4×#88322—41no—
145C2×#41×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C2×M16×C53—21no—
148C2×M16×C53—41no—
149C2×M16×C53—41no—
150C2×M16×C53C2311yescharacteristic
151C2×M16×C53C2311yescharacteristic
152C22×C8×C53—21no—
153#123×C53—21no—
154C22⋊Q8×C53C2×C411yescharacteristic
155C22⋊Q8×C53C2×C411yescharacteristic
156#121×C53C2×C411yescharacteristic
157#121×C53C2×C411yescharacteristic
158#120×C53—21no—
159C4×D4×C53—21no—
160C4×D4×C53—21no—
161#117×C53C2311yescharacteristic
162C2×C22⋊C4×C53—21no—
163C2×C42×C53C2311yescharacteristic
164C2×C42×C53C2311yescharacteristic
165#104×C53—41no—
166#104×C53—41no—
167#95×C53—21no—
168C24×C53#4111yescharacteristic
169C23×D53—21no—
170#41×C53—21no—
171#41×C53—21no—
172#41×C53—21no—
173#41×C53—21no—
174C2×Q8×C53C22×C411yescharacteristic
175C2×D4×C53—21no—
176C2×D4×C53—21no—
177C2×D4×C53—21no—
178C2×D4×C53C22×C411yescharacteristic
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53C22×C411yescharacteristic
187C22×C4×C53C22×C411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53#4111yescharacteristic
191C22×C4×C53C2411yescharacteristic
192C2×C22⋊D53—21no—
193C2×C22⋊D53—21no—
194C2×C22⋊D53—21no—
195C2×C22⋊D53—21no—
196C2×C22⋊D53—42no—
197C2×C22⋊D53—42no—
198C22×Dic53—21no—
199#11719945—21no—
200#11719945—21no—
201#11719945—21no—
202#11719945—21no—
203#11719945—21no—
204#11719945—21no—
205#11719945—21no—
206#11719945—21no—
207#11719945—41no—
208#11719945—41no—
209#11719945—41no—
210#11719945—41no—
211#11719945—42no—
212#11719945—42no—
213#11719945—42no—
214#11719945—42no—
215C2×D212—21no—
216C2×D212—41no—
217C2×D212—41no—
218C2×D212C22×C411yescharacteristic
219C2×D212C22×C411yescharacteristic
220C2×C4×D53—21no—
221C2×C4×D53—21no—
222C2×C4×D53—21no—
223C2×C4×D53—21no—
224C2×C4×D53—42no—
225C2×C4×D53—42no—
226C2×Dic106—21no—
227C2×Dic106—41no—
228C2×Dic106—41no—
229C2×Dic106C22×C411yescharacteristic
230C2×Dic106C22×C411yescharacteristic
231M16×C53—21no—
232M16×C53—21no—
233M16×C53—21no—
234M16×C53—21no—
235M16×C53—42no—
236C2×C8×C53—21no—
237C2×C8×C53—21no—
238C2×C8×C53—42no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53C22×C411yescharacteristic
242C4⋊C4×C53C22×C411yescharacteristic
243C22⋊C4×C53—21no—
244C22⋊C4×C53—21no—
245C22⋊C4×C53—21no—
246C22⋊C4×C53—21no—
247C22⋊C4×C53—21no—
248C22⋊C4×C53—42no—
249C42×C53—21no—
250C42×C53—21no—
251C42×C53—21no—
252C42×C53—21no—
253C42×C53—21no—
254#11719925—41no—
255#11719925—41no—
256#11719924—41no—
257#11719924—41no—
258#11719923—41no—
259#11719923—41no—
260#11719922—41no—
261#11719922—41no—
262#11719917—21no—
263#11719917—21no—
264#11719917—21no—
265#11719917—21no—
266#11719917—41no—
267#11719917—41no—
268#11719917—41no—
269#11719917—41no—
270#11719917—42no—
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—21no—
280C2×#88322—21no—
281C2×#88322—42no—
282C2×#88322C22×C411yescharacteristic
283C2×#88322C22×C411yescharacteristic
284C2×#88322C22×C411yescharacteristic
285C2×#88322C22×C411yescharacteristic
286C2×#88322C2×D411yescharacteristic
287C2×#88322C2×D411yescharacteristic
288C2×#88322C2×D411yescharacteristic
289C2×#88322C2×D411yescharacteristic
290C23×C53—21no—
291C23×C53—21no—
292C23×C53—21no—
293C23×C53—41no—
294C23×C53—41no—
295C23×C53C4×D411yescharacteristic
296C23×C53C4×D411yescharacteristic
297C23×C53C2×#4111yescharacteristic
298C22×D53—21no—
299C22×D53—21no—
300C22×D53—42no—
301C22×D53—81no—
302C22×D53—81no—
303Q8×C53—21no—
304Q8×C53—21no—
305D4×C53—21no—
306D4×C53—21no—
307D4×C53—41no—
308D4×C53—41no—
309D4×C53—81no—
310D4×C53—81no—
311C2×C4×C53—21no—
312C2×C4×C53—21no—
313C2×C4×C53—21no—
314C2×C4×C53—21no—
315C2×C4×C53—21no—
316C2×C4×C53—21no—
317C2×C4×C53—21no—
318C2×C4×C53—21no—
319C2×C4×C53—21no—
320C2×C4×C53—21no—
321C2×C4×C53—22no—
322C2×C4×C53—21no—
323C2×C4×C53—21no—
324C2×C4×C53—21no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53—41no—
328C2×C4×C53—41no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—41no—
332C2×C4×C53C4×D411yescharacteristic
333C2×C4×C53C4×D411yescharacteristic
334C2×C4×C53C23×C411yescharacteristic
335C2×C4×C53C22×D411yescharacteristic
336C2×C4×C53H(5,𝔽2)11yescharacteristic
337C2×C4×C53H(5,𝔽2)11yescharacteristic
338C2×C4×C53H(5,𝔽2)11yescharacteristic
339C2×C4×C53H(5,𝔽2)11yescharacteristic
340C22⋊D53—42no—
341C22⋊D53—42no—
342C22⋊D53—41no—
343C22⋊D53—41no—
344C22⋊D53—41no—
345C22⋊D53—41no—
346C2×Dic53—21no—
347C2×Dic53—21no—
348C2×Dic53—42no—
349D212—21no—
350D212—21no—
351D212—21no—
352D212—21no—
353D212—42no—
354C4×D53—42no—
355C4×D53—42no—
356C4×D53—41no—
357C4×D53—41no—
358C4×D53—41no—
359C4×D53—41no—
360Dic106—21no—
361Dic106—21no—
362Dic106—21no—
363Dic106—21no—
364Dic106—42no—
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—81no—
390C22×C53—81no—
391C22×C53C2×C4×D411yescharacteristic
392C22×C53#53811yescharacteristic
393C22×C53#53811yescharacteristic
394C2×D53—41no—
395C2×D53—41no—
396C2×D53—41no—
397C2×D53—41no—
398C2×D53—41no—
399C2×D53—41no—
400C2×D53—84no—
401C4×C53—21no—
402C4×C53—21no—
403C4×C53—42no—
404C4×C53—41no—
405C4×C53—41no—
406C4×C53—41no—
407C4×C53—81no—
408C4×C53#51811yescharacteristic
409C4×C53#51811yescharacteristic
410C4×C53#53411yescharacteristic
411C4×C53#53511yescharacteristic
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#1871D5311yescharacteristic, complemented
426#1855—531no—
427#1789—531no—
428#1753—531no—
429C2×C53—21no—
430C2×C53—21no—
431C2×C53—41no—
432C2×C53—41no—
433C2×C53—81no—
434C2×C53#232111yescharacteristic
435C2×C53#295611yescharacteristic
436C2×C53#295711yescharacteristic
437D53—81no—
438D53—81no—
439C22×#41—531no—
440C2×#135—531no—
441C2×#135—531no—
442C2×#131—531no—
443C22×M16—531no—
444C22×M16C2×D5311yescharacteristic
445#525C2×D5311yescharacteristic
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×#104—531no—
464C2×#104—531no—
465C2×#104C2×D5311yescharacteristic, complemented
466C2×#104C2×D5311yescharacteristic, complemented
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—531no—
477#407—1061no—
478#407—1061no—
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#339C2×D5311yescharacteristic, complemented
487#339C2×D5311yescharacteristic, complemented
488#336—531no—
489#336—531no—
490C53#2206211yescharacteristic, complemented, Sylow
491C2×#41—531no—
492C2×#41—531no—
493C2×#41—531no—
494C2×#41—531no—
495C2×#41—1061no—
496C2×#41—1061no—
497C2×#41—2121no—
498C2×#41—2121no—
499C2×#41—2121no—
500C2×#41—2121no—
501C2×#41C22×D5311yescharacteristic
502C22×Q8—531no—
503C22×D4—531no—
504C22×D4—1061no—
505C23×C4—1061no—
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—21no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—531no—
525C2×M16—531no—
526C2×M16—531no—
527C2×M16—531no—
528C2×M16—531no—
529C2×M16—531no—
530C2×M16—1061no—
531C2×M16—2121no—
532C2×M16—2121no—
533C2×M16C22×D5311yescharacteristic
534C2×M16C22×D5311yescharacteristic
535C22×C8—21no—
536C22×C8—531no—
537C22×C8—531no—
538C22×C8—531no—
539C22×C8—531no—
540C22×C8—1061no—
541#123—21no—
542C22⋊Q8C4×D5311yescharacteristic
543C22⋊Q8C4×D5311yescharacteristic
544#121C4×D5311yescharacteristic
545#121C4×D5311yescharacteristic
546#120—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117C22×D5311yescharacteristic
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—2121no—
560#104—2121no—
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—531no—
572C22⋊C8—531no—
573C22⋊C8—531no—
574C22⋊C8—531no—
575C22⋊C8—1061no—
576C22⋊C8—1061no—
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—1061no—
593C24#1171994711yescharacteristic
594#41—21no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—1061no—
599#41—1061no—
600#41—1061no—
601#41—1061no—
602#41—1061no—
603#41—1061no—
604#41—1061no—
605#41—1061no—
606#41—2121no—
607#41—2121no—
608#41—2121no—
609#41—2121no—
610#41—2122no—
611#41—2122no—
612#41—2122no—
613#41—2122no—
614C2×Q8—531no—
615C2×Q8—531no—
616C2×Q8—1061no—
617C2×Q8—2121no—
618C2×Q8—2121no—
619C2×Q8C2×C4×D5311yescharacteristic
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—531no—
624C2×D4—531no—
625C2×D4—1061no—
626C2×D4—1061no—
627C2×D4—1061no—
628C2×D4—1061no—
629C2×D4—1061no—
630C2×D4—2121no—
631C2×D4—2121no—
632C2×D4—2122no—
633C2×D4—2122no—
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—1061no—
643C22×C4—1061no—
644C22×C4—1061no—
645C22×C4—1061no—
646C22×C4—1061no—
647C22×C4—2122no—
648C22×C4—2122no—
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—42no—
668M16—1061no—
669M16—1061no—
670M16—1061no—
671M16—1061no—
672M16—2121no—
673M16—2121no—
674M16—2121no—
675M16—2121no—
676M16—2122no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—42no—
680C2×C8—531no—
681C2×C8—531no—
682C2×C8—531no—
683C2×C8—531no—
684C2×C8—531no—
685C2×C8—531no—
686C2×C8—531no—
687C2×C8—531no—
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—1061no—
698C2×C8—2122no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4C2×C4×D5311yescharacteristic
702C4⋊C4C2×C4×D5311yescharacteristic
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—42no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—41no—
718C23—41no—
719C23—1061no—
720C23—1061no—
721C23—4241no—
722C23—4241no—
723C23—2122no—
724C23#1313317711yescharacteristic
725C23#1313317711yescharacteristic
726C23C2×#1171994711yescharacteristic
727Q8—21no—
728Q8—21no—
729Q8—1061no—
730Q8—1061no—
731Q8—1061no—
732Q8—1061no—
733Q8—2122no—
734D4—21no—
735D4—21no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—1061no—
741D4—1061no—
742D4—1061no—
743D4—1061no—
744D4—2122no—
745D4—2122no—
746D4—2122no—
747D4—2121no—
748D4—2121no—
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—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—1061no—
773C2×C4—1061no—
774C2×C4—2122no—
775C2×C4—2122no—
776C2×C4—2122no—
777C2×C4—2121no—
778C2×C4—2121no—
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#1313326311yescharacteristic
788C2×C4#1313326311yescharacteristic
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—81no—
813C22—81no—
814C22—4244no—
815C22—2121no—
816C22—2121no—
817C22—2121no—
818C22—2121no—
819C22—2121no—
820C22—2121no—
821C22C2×#1313317711yescharacteristic
822C22#1681121011yescharacteristic
823C22#1681121011yescharacteristic
824C4—21no—
825C4—21no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—41no—
830C4—81no—
831C4—2121no—
832C4—2121no—
833C4#1681109511yescharacteristic
834C4#1681109511yescharacteristic
835C4#1681118411yescharacteristic
836C4#1681118811yescharacteristic
837C2—21no—
838C2—21no—
839C2—41no—
840C2—41no—
841C2—81no—
842C2—4241no—
843C2—4241no—
844C2#2027737811yescharacteristic
845C2#2028362111yescharacteristic
846C2#2028362811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1871C2
socleC22×C53C2×C4×D4
prime radical#20283931C2
cosocleC22×C4×C53C24
hypercenter#1871D53
hypocenterC53#22062
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
2. #20283419C2semidirect
3. #20283159C2semidirect
4. #20275605C2semidirect
5. #20275600C2semidirect
6. #20275427C2semidirect
7. #20275420C2semidirect
8. #20275361C2semidirect
9. #20275361C2semidirect
10. #20275040C2semidirect
11. #20275040C2semidirect
12. #20274920C2semidirect
13. #20274660C2semidirect
14. #20274499C2semidirect
15. C53×#1871C2semidirect
19. C2×#13133224C22semidirect
21. #16810783C4semidirect
22. #16810783C4semidirect
23. #16810778C4semidirect
24. #16810773C4semidirect
25. #16810766C4semidirect
26. #16810766C4semidirect
27. #16810761C4semidirect
28. #16810756C4semidirect
33. C2×#13133152C22semidirect
34. C2×#13133152C22semidirect
35. #16810650C22semidirect
46. #16810590C22semidirect
53. #16810579C22semidirect
54. C2×#13133128C22semidirect
55. C2×C4×#88322C22semidirect
56. #16810387C22semidirect
57. #16810387C22semidirect
58. #16810378C22semidirect
59. #16810378C22semidirect
62. C2×#104×C53C22semidirect
63. C2×#104×C53C22semidirect
65. C53×#339C22semidirect
66. C53×#339C22semidirect
425. #1871D53semidirect
465. C2×#104C2×D53semidirect
466. C2×#104C2×D53semidirect
486. #339C2×D53semidirect
487. #339C2×D53semidirect
490. C53#22062semidirect

Maximal subgroups

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

subgroupindex
#202839312
#202834192
#202831592
#202756052
#202756002
#202754272
#202754202
#202753612
#202750402
#202749202
#202746602
#202744992
C53×#18712
#2206253