Finite Group Databasebeta

← #27404822

Subgroups — #27404822

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#20283937C211yesmaximal, characteristic
2C2×#16810744C211yesmaximal, characteristic, complemented
3#20283440C211yesmaximal, characteristic, complemented
4C22×#13133143C211yesmaximal, characteristic, complemented
5#20283165C211yesmaximal, characteristic, complemented
6#20275606C211yesmaximal, characteristic, complemented
7#20275424C211yesmaximal, characteristic, complemented
8#20275362C211yesmaximal, characteristic, complemented
9#20275156C211yesmaximal, characteristic, complemented
10#20275043C211yesmaximal, characteristic, complemented
11#20275043C211yesmaximal, characteristic, complemented
12#20274987C211yesmaximal, characteristic, complemented
13#20274558C211yesmaximal, characteristic, complemented
14#20274479C211yesmaximal, characteristic, complemented
15C53×#1855C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C2×#13133239C2211yescharacteristic
18C2×#13133239C2211yescharacteristic
19C2×#13133225C2211yescharacteristic
20C2×#13133225C2211yescharacteristic
21C2×#13133225C2211yescharacteristic, complemented
22#16811134C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24#16810787C411yescharacteristic, complemented
25#16810787C411yescharacteristic, complemented
26#16810781C411yescharacteristic, complemented
27#16810776C411yescharacteristic, complemented
28#16810770C411yescharacteristic, complemented
29#16810770C411yescharacteristic, complemented
30#16810764C411yescharacteristic, complemented
31#16810759C411yescharacteristic, complemented
32#16810744—24no—
33#16810699—21no—
34#16810694—21no—
35#16810692—21no—
36C8×C22⋊D53—21no—
37#16810651C2211yescharacteristic, complemented
38C2×#13133143—24no—
39C2×#13133143C2211yescharacteristic
40C2×#13133143C2211yescharacteristic
41C2×#13133143C2211yescharacteristic
42C2×#13133143C2211yescharacteristic
43C2×#13133143C2211yescharacteristic, complemented
44C2×#13133143C2211yescharacteristic, complemented
45#16810620C2211yescharacteristic
46#16810620C2211yescharacteristic
47#16810591C2211yescharacteristic
48#16810591C2211yescharacteristic
49#16810591C2211yescharacteristic, complemented
50#16810588—21no—
51#16810588—21no—
52#16810585—21no—
53C2×C22⋊#88322C2211yescharacteristic
54C22⋊C8×D53—21no—
55#16810581C2211yescharacteristic, complemented
56C2×#13133127C2211yescharacteristic, complemented
57C2×#13133127C2211yescharacteristic, complemented
58#16810384C2211yescharacteristic, complemented
59#16810384C2211yescharacteristic, complemented
60#16810377C2211yescharacteristic, complemented
61#16810377C2211yescharacteristic, complemented
62C22×M16×C53C2211yescharacteristic
63C2×#108×C53C2211yescharacteristic, complemented
64C2×#108×C53C2211yescharacteristic, complemented
65C53×#407C2211yescharacteristic
66C2×C22⋊C8×C53C2211yescharacteristic
67C53×#341C2211yescharacteristic, complemented
68C53×#341C2211yescharacteristic, 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
79C2×#11719945C2311yescharacteristic
80C22×Dic106C2×C411yescharacteristic
81C22×D212C2×C411yescharacteristic
82C22×C22⋊D53—21no—
83C23×Dic53—21no—
84C22×C4×D53—21no—
85#13133239—22no—
86#13133239—22no—
87#13133239—41no—
88#13133239—41no—
89C2×Dic212C2×C411yescharacteristic, complemented
90C2×Dic212C2×C411yescharacteristic, complemented
91C2×#11719913C2×C411yescharacteristic, complemented
92C2×#11719913C2×C411yescharacteristic, complemented
93C2×#11719913C2×C411yescharacteristic, complemented
94C2×#11719913C2×C411yescharacteristic, complemented
95C2×D424C2×C411yescharacteristic, complemented
96C2×D424C2×C411yescharacteristic, complemented
97#13133225—22no—
98#13133225—22no—
99#13133225—22no—
100#13133225—41no—
101#13133225—41no—
102#13133225—41no—
103C2×#11719912—21no—
104C2×#11719912—21no—
105C2×#11719912—21no—
106C22×#88322C2311yescharacteristic
107C22×#88322C2311yescharacteristic
108C2×C8×D53—21no—
109C2×C8×D53—21no—
110C2×C8×D53—21no—
111#13133200—21no—
112#13133196C2×C411yescharacteristic
113#13133196C2×C411yescharacteristic
114#13133191C2×C411yescharacteristic
115#13133191C2×C411yescharacteristic
116#13133186—21no—
117C4×C22⋊D53—21no—
118C4×C22⋊D53—21no—
119#13133176C2311yescharacteristic
120C2×C4×Dic53—21no—
121C2×C4×Dic53—22no—
122C2×C4×Dic53—41no—
123C2×C4×Dic53C2311yescharacteristic
124C2×C4×Dic53C2311yescharacteristic
125#13133146—21no—
126#13133146—21no—
127#13133143—22no—
128#13133143—22no—
129#13133143—22no—
130#13133143—22no—
131#13133143—41no—
132#13133143D414yescomplemented
133#13133142C2×C411yescharacteristic, complemented
134#13133142C2×C411yescharacteristic, complemented
135#13133142C2×C411yescharacteristic, complemented
136#13133142C2×C411yescharacteristic, complemented
137#13133139C2×C411yescharacteristic, complemented
138#13133139C2×C411yescharacteristic, complemented
139#13133139C2×C411yescharacteristic, complemented
140#13133139C2×C411yescharacteristic, complemented
141C22⋊#88322D411yescharacteristic
142C22⋊#88322D411yescharacteristic
143C22⋊#88322D411yescharacteristic
144C22⋊#88322D411yescharacteristic
145#13133129—21no—
146#13133129—21no—
147#13133129—21no—
148#13133129—21no—
149#13133129—21no—
150#13133129—21no—
151#13133127—22no—
152#13133127—21no—
153#13133127—41no—
154C8×Dic53—21no—
155C23×C4×C53C2311yescharacteristic
156C2×M16×C53—22no—
157C2×M16×C53—21no—
158C2×M16×C53—41no—
159C2×M16×C53C2311yescharacteristic
160C2×M16×C53C2311yescharacteristic
161C2×M16×C53C2311yescharacteristic
162C2×M16×C53C2311yescharacteristic
163C22×C8×C53—21no—
164C22×C8×C53C2311yescharacteristic
165C22×C8×C53C2311yescharacteristic
166#108×C53—22no—
167#108×C53—41no—
168C22⋊C8×C53—21no—
169C22⋊C8×C53—21no—
170C22⋊C8×C53C2×C411yescharacteristic
171C22⋊C8×C53C2×C411yescharacteristic
172C22⋊C8×C53C2×C411yescharacteristic
173C22⋊C8×C53C2×C411yescharacteristic
174C24×C53#4111yescharacteristic
175C23×D53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
179C22×C4×C53—21no—
180C22×C4×C53C22×C411yescharacteristic
181C22×C4×C53C22×C411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53#4111yescharacteristic
185C22×C4×C53C2411yescharacteristic
186C2×C22⋊D53—21no—
187C2×C22⋊D53—21no—
188C2×C22⋊D53—21no—
189C2×C22⋊D53—21no—
190C2×C22⋊D53—21no—
191C2×C22⋊D53—21no—
192C2×C22⋊D53—21no—
193C2×C22⋊D53—42no—
194C2×C22⋊D53—42no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53—42no—
199C22×Dic53—42no—
200C22×Dic53—42no—
201#11719945—21no—
202#11719945—21no—
203#11719945—21no—
204#11719945—21no—
205#11719945—21no—
206#11719945—21no—
207#11719945—21no—
208#11719945—21no—
209#11719945—21no—
210#11719945—21no—
211#11719945—22no—
212#11719945—22no—
213#11719945—41no—
214#11719945—41no—
215#11719945—42no—
216#11719945—42no—
217#11719945—42no—
218#11719945—42no—
219#11719945C2×D412yes—
220#11719945#4112yes—
221C2×D212—22no—
222C2×D212—21no—
223C2×D212—41no—
224C2×D212C22×C411yescharacteristic
225C2×D212C22×C411yescharacteristic
226C2×D212C22×C411yescharacteristic
227C2×C4×D53—21no—
228C2×C4×D53—21no—
229C2×C4×D53—21no—
230C2×C4×D53—21no—
231C2×C4×D53—21no—
232C2×C4×D53—42no—
233C2×C4×D53—42no—
234C2×Dic106—22no—
235C2×Dic106—21no—
236C2×Dic106—41no—
237C2×Dic106C22×C411yescharacteristic
238C2×Dic106C22×C411yescharacteristic
239C2×Dic106C22×C411yescharacteristic
240M16×C53—21no—
241M16×C53—21no—
242M16×C53—21no—
243M16×C53—21no—
244M16×C53—21no—
245M16×C53—21no—
246M16×C53—21no—
247M16×C53—42no—
248M16×C53C2×D412yes—
249C2×C8×C53—21no—
250C2×C8×C53—21no—
251C2×C8×C53—21no—
252C2×C8×C53—21no—
253C2×C8×C53—21no—
254C2×C8×C53—21no—
255C2×C8×C53—21no—
256C2×C8×C53—21no—
257C2×C8×C53—42no—
258C2×C8×C53C22×C411yescharacteristic
259C2×C8×C53C22×C411yescharacteristic
260C2×C8×C53C22×C411yescharacteristic
261C2×C8×C53C22×C411yescharacteristic
262C22⋊Dic53—21no—
263C22⋊Dic53—21no—
264C22⋊Dic53—21no—
265#11719921—21no—
266#11719921—21no—
267C4⋊Dic53C22×C411yescharacteristic
268C4⋊Dic53C22×C411yescharacteristic
269#11719919—21no—
270#11719919—21no—
271C4×Dic53—21no—
272C4×Dic53—21no—
273C4×Dic53—21no—
274C4×Dic53—21no—
275C4×Dic53—42no—
276C4×Dic53C2×D412yes—
277C2×#88322—21no—
278C2×#88322—21no—
279C2×#88322—21no—
280C2×#88322—21no—
281C2×#88322C2×D411yescharacteristic
282C2×#88322C2×D411yescharacteristic
283C2×#88322C2×D411yescharacteristic
284C2×#88322C2×D411yescharacteristic
285Dic212—22no—
286Dic212—41no—
287D424—22no—
288D424—41no—
289#11719913—22no—
290#11719913—22no—
291#11719913—41no—
292#11719913—41no—
293#11719912—42no—
294#11719912—42no—
295#11719912—42no—
296C8×D53—42no—
297C8×D53—42no—
298C8×D53—42no—
299C23×C53—21no—
300C23×C53—21no—
301C23×C53—22no—
302C23×C53—41no—
303C23×C53C4×D411yescharacteristic
304C23×C53C4×D411yescharacteristic
305C23×C53C2×#4111yescharacteristic
306C22×D53—21no—
307C22×D53—21no—
308C22×D53—21no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53—81no—
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—21no—
322C2×C4×C53C4×D411yescharacteristic
323C2×C4×C53C4×D411yescharacteristic
324C2×C4×C53C23×C411yescharacteristic
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C22×D411yescharacteristic
327C2×C4×C53C2×#4111yescharacteristic
328C2×C4×C53H(5,𝔽2)11yescharacteristic
329C2×C4×C53H(5,𝔽2)11yescharacteristic
330C22⋊D53—22no—
331C22⋊D53—22no—
332C22⋊D53—42no—
333C22⋊D53—42no—
334C22⋊D53—41no—
335C22⋊D53—41no—
336C22⋊D53—41no—
337C22⋊D53—41no—
338C22⋊D53—42no—
339C22⋊D53—81no—
340C2×Dic53—21no—
341C2×Dic53—22no—
342C2×Dic53—21no—
343C2×Dic53—21no—
344C2×Dic53—21no—
345C2×Dic53—21no—
346C2×Dic53—22no—
347C2×Dic53—42no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351C2×Dic53—48no—
352C2×Dic53—41no—
353D212—21no—
354D212—21no—
355D212—21no—
356D212—21no—
357D212—21no—
358D212—42no—
359D212C4×D412yes—
360C4×D53—22no—
361C4×D53—22no—
362C4×D53—42no—
363C4×D53—42no—
364C4×D53—41no—
365C4×D53—41no—
366C4×D53—41no—
367C4×D53—41no—
368Dic106—21no—
369Dic106—21no—
370Dic106—21no—
371Dic106—21no—
372Dic106—21no—
373Dic106—42no—
374Dic106C4×D412yes—
375C8×C53—21no—
376C8×C53—21no—
377C8×C53—21no—
378C8×C53—21no—
379C8×C53—22no—
380C8×C53—41no—
381C8×C53—41no—
382C8×C53—41no—
383#88322—21no—
384#88322—21no—
385#88322—21no—
386#88322—21no—
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#44412yescomplemented
398C22×C53C2×C4×D411yescharacteristic
399C22×C53#54611yescharacteristic
400C22×C53#55111yescharacteristic
401C2×D53—22no—
402C2×D53—41no—
403C2×D53—41no—
404C2×D53—41no—
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×C53C2×C4×D411yescharacteristic
414C4×C53#51811yescharacteristic
415C4×C53D4211yescharacteristic
416C4×C53#54611yescharacteristic
417Dic53—22no—
418Dic53—42no—
419Dic53—42no—
420Dic53—41no—
421Dic53—41no—
422Dic53—41no—
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#1896—531no—
433#1876—531no—
434#1876—531no—
435#1866—531no—
436#1855D5311yescharacteristic, complemented
437#1765—531no—
438#1749—531no—
439C2×C53—21no—
440C2×C53—22no—
441C2×C53—21no—
442C2×C53—41no—
443C2×C53#235811yescharacteristic
444C2×C53C2×#44411yescharacteristic
445C2×C53#295611yescharacteristic
446D53—42no—
447D53—81no—
448D53—81no—
449C22×#41—531no—
450C2×#135—531no—
451C2×#135—531no—
452C2×#131—531no—
453C2×#131—531no—
454C2×#131—531no—
455C22×M16C2×D5311yescharacteristic
456#525—531no—
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—1061no—
468#435—1061no—
469#435—1061no—
470C8×D4—1061no—
471C2×#108C2×D5311yescharacteristic, complemented
472C2×#108C2×D5311yescharacteristic, complemented
473#424—531no—
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—531no—
486#408—1061no—
487#408—1061no—
488#407—1061no—
489#407C2×D5311yescharacteristic
490C2×C22⋊C8—531no—
491C2×C22⋊C8—1061no—
492C2×C22⋊C8C2×D5311yescharacteristic
493#405—531no—
494C2×#97—531no—
495C2×#97—531no—
496#341C2×D5311yescharacteristic, complemented
497#341C2×D5311yescharacteristic, complemented
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—531no—
508C2×#41—1062no—
509C2×#41—1062no—
510C2×#41—1061no—
511C2×#41—1061no—
512C2×#41—2121no—
513C2×#41—2121no—
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—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—1061no—
542C2×M16—1061no—
543C2×M16—1061no—
544C2×M16C22×D5311yescharacteristic
545C2×M16C22×D5311yescharacteristic
546C2×M16C22×D5311yescharacteristic
547C2×M16C22×D5311yescharacteristic
548C22×C8—21no—
549C22×C8—531no—
550C22×C8—531no—
551C22×C8—1061no—
552C22×C8—1061no—
553C22×C8—1061no—
554C22×C8C22×D5311yescharacteristic
555C22×C8C22×D5311yescharacteristic
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—531no—
566C2×C42—531no—
567C2×C42—1062no—
568C2×C42—1061no—
569C2×C42—2121no—
570#108—22no—
571#108—41no—
572C4⋊C8—1061no—
573C4⋊C8—1061no—
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⋊C8C4×D5311yescharacteristic
601C22⋊C8C4×D5311yescharacteristic
602C22⋊C8C4×D5311yescharacteristic
603C22⋊C8C4×D5311yescharacteristic
604#97—1062no—
605#97—1061no—
606#97—2121no—
607C4×C8—1061no—
608C24—1061no—
609C24#1171994911yescharacteristic
610#41—532no—
611#41—532no—
612#41—1062no—
613#41—1062no—
614#41—1061no—
615#41—1061no—
616#41—1061no—
617#41—1061no—
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—531no—
633C2×Q8—1062no—
634C2×Q8—1061no—
635C2×Q8—2121no—
636C2×D4—531no—
637C2×D4—531no—
638C2×D4—531no—
639C2×D4—1062no—
640C2×D4—1061no—
641C2×D4—1061no—
642C2×D4—1061no—
643C2×D4—1061no—
644C2×D4—1061no—
645C2×D4—1061no—
646C2×D4—1061no—
647C2×D4—1061no—
648C2×D4—2121no—
649C2×D4—2122no—
650C2×D4—2122no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—1061no—
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×C4D4×D5311yescharacteristic
671C22×C4D4×D5311yescharacteristic
672C22×C4#1171994911yescharacteristic
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—21no—
687M16—21no—
688M16—21no—
689M16—42no—
690M16—2122no—
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—21no—
701C2×C8—21no—
702C2×C8—42no—
703C2×C8—531no—
704C2×C8—531no—
705C2×C8—531no—
706C2×C8—531no—
707C2×C8—1061no—
708C2×C8—1061no—
709C2×C8—1061no—
710C2×C8—1061no—
711C2×C8—2122no—
712C2×C8—2122no—
713C2×C8—2122no—
714C2×C8C2×C4×D5311yescharacteristic
715C2×C8C2×C4×D5311yescharacteristic
716C2×C8C2×C4×D5311yescharacteristic
717C2×C8C2×C4×D5311yescharacteristic
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—532no—
728C42—1061no—
729C42—1061no—
730C42—1061no—
731C42—1061no—
732C42—2122no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—1061no—
738C23—1061no—
739C23—1061no—
740C23—4241no—
741C23—2122no—
742C23—2122no—
743C23#1313317911yescharacteristic
744C23#1313317911yescharacteristic
745C23C2×#1171994911yescharacteristic
746Q8—532no—
747Q8—1061no—
748Q8—1061no—
749Q8—1061no—
750Q8—1061no—
751Q8—1061no—
752Q8—2122no—
753D4—532no—
754D4—1062no—
755D4—1062no—
756D4—1061no—
757D4—1061no—
758D4—1061no—
759D4—1061no—
760D4—1061no—
761D4—4241no—
762D4—2122no—
763D4—2122no—
764D4—2122no—
765D4—2121no—
766D4—2121no—
767D4—2121no—
768D4—2121no—
769D4—2122no—
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—1061no—
781C2×C4—1062no—
782C2×C4—1062no—
783C2×C4—1062no—
784C2×C4—1062no—
785C2×C4—1061no—
786C2×C4—1061no—
787C2×C4—1061no—
788C2×C4—1061no—
789C2×C4—2122no—
790C2×C4—2122no—
791C2×C4—2122no—
792C2×C4—2121no—
793C2×C4—2121no—
794C2×C4—2121no—
795C2×C4—2128no—
796C2×C4—2121no—
797C2×C4—2121no—
798C2×C4—2121no—
799C2×C4—2121no—
800C2×C4—2121no—
801C2×C4#1313317911yescharacteristic
802C2×C4#1313317911yescharacteristic
803C2×C4C22×C4×D5311yescharacteristic
804C2×C4C2×D4×D5311yescharacteristic
805C2×C4C2×D4×D5311yescharacteristic
806C2×C4#41×D5311yescharacteristic
807C2×C4#1313326211yescharacteristic
808C2×C4#1313326311yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—22no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—1061no—
818C8—1061no—
819C8—1061no—
820C8—1061no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—1062no—
831C22—4244no—
832C22—2121no—
833C22—2121no—
834C22—2121no—
835C22—2121no—
836C22—2121no—
837C22—2121no—
838C22—2121no—
839C22—2121no—
840C22#1681074412yescomplemented
841C22C2×#1313317911yescharacteristic
842C22#1681126411yescharacteristic
843C22#1681130011yescharacteristic
844C4—21no—
845C4—21no—
846C4—1062no—
847C4—2122no—
848C4—2122no—
849C4—2121no—
850C4—2121no—
851C4—2121no—
852C4—2121no—
853C4C4×D4×D5311yescharacteristic
854C4#1681109511yescharacteristic
855C4#1681125511yescharacteristic
856C4#1681126511yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—4241no—
862C2—4241no—
863C2—2122no—
864C2#2027769111yescharacteristic
865C2C2×#1681074411yescharacteristic
866C2#2028362411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#1855C2
socleC22×C53C2×C4×D4
prime radical#20283937C2
cosocleC22×C4×C53C24
hypercenter#1855D53
hypocenterC53#22886
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1855

Complements

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

NH ≅ G/Ntype
2. C2×#16810744C2semidirect
3. #20283440C2semidirect
4. C22×#13133143C2semidirect
5. #20283165C2semidirect
6. #20275606C2semidirect
7. #20275424C2semidirect
8. #20275362C2semidirect
9. #20275156C2semidirect
10. #20275043C2semidirect
11. #20275043C2semidirect
12. #20274987C2semidirect
13. #20274558C2semidirect
14. #20274479C2semidirect
15. C53×#1855C2semidirect
21. C2×#13133225C22semidirect
24. #16810787C4semidirect
25. #16810787C4semidirect
26. #16810781C4semidirect
27. #16810776C4semidirect
28. #16810770C4semidirect
29. #16810770C4semidirect
30. #16810764C4semidirect
31. #16810759C4semidirect
37. #16810651C22semidirect
43. C2×#13133143C22semidirect
44. C2×#13133143C22semidirect
49. #16810591C22semidirect
55. #16810581C22semidirect
56. C2×#13133127C22semidirect
57. C2×#13133127C22semidirect
58. #16810384C22semidirect
59. #16810384C22semidirect
60. #16810377C22semidirect
61. #16810377C22semidirect
63. C2×#108×C53C22semidirect
64. C2×#108×C53C22semidirect
67. C53×#341C22semidirect
68. C53×#341C22semidirect
89. C2×Dic212C2×C4semidirect
90. C2×Dic212C2×C4semidirect
91. C2×#11719913C2×C4semidirect
92. C2×#11719913C2×C4semidirect
93. C2×#11719913C2×C4semidirect
94. C2×#11719913C2×C4semidirect
95. C2×D424C2×C4semidirect
96. C2×D424C2×C4semidirect
132. #13133143D4semidirect
133. #13133142C2×C4semidirect
134. #13133142C2×C4semidirect
135. #13133142C2×C4semidirect
136. #13133142C2×C4semidirect
137. #13133139C2×C4semidirect
138. #13133139C2×C4semidirect
139. #13133139C2×C4semidirect
140. #13133139C2×C4semidirect
397. C22×C53#444semidirect
436. #1855D53semidirect
471. C2×#108C2×D53semidirect
472. C2×#108C2×D53semidirect
496. #341C2×D53semidirect
497. #341C2×D53semidirect
502. C53#22886semidirect
840. C22#16810744semidirect

Maximal subgroups

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

subgroupindex
#202839372
C2×#168107442
#202834402
C22×#131331432
#202831652
#202756062
#202754242
#202753622
#202751562
#202750432
#202749872
#202745582
#202744792
C53×#18552
#2288653