Finite Group Databasebeta

← #27400302

Subgroups — #27400302

Order 13568.

1474 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811274C211yesmaximal, characteristic
2C2×C8×C22⋊D53C211yesmaximal, characteristic, complemented
3C4⋊C4×C22⋊D53C211yesmaximal, characteristic, complemented
4#20275674C211yesmaximal, characteristic, complemented
5#20275665C211yesmaximal, characteristic, complemented
6#20275143C211yesmaximal, characteristic, complemented
7#20275142C211yesmaximal, characteristic, complemented
8#20275032C211yesmaximal, characteristic, complemented
9#20275031C211yesmaximal, characteristic, complemented
10#20274801C211yesmaximal, characteristic, complemented
11#20274800C211yesmaximal, characteristic, complemented
12#20274714C211yesmaximal, characteristic, complemented
13#20274529C211yesmaximal, characteristic, complemented
14#340×D53C211yesmaximal, characteristic, complemented
15C2×C53×#340C211yesmaximal, characteristic, complemented
16C22×#11719945—21no—
17C22×C8×D53C2211yescharacteristic
18#16811274—24no—
19#16811274C418yescomplemented
20C2×#13133216C2211yescharacteristic
21C2×#13133202—21no—
22C2×#13133200—21no—
23C2×#13133195—21no—
24C2×#13133192C2211yescharacteristic
25C2×#13133191C2211yescharacteristic
26C2×#13133179C2211yescharacteristic
27C2×C4×C22⋊D53—21no—
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×C4⋊C4×D53C2211yescharacteristic
30C2×C4⋊C4×D53C2211yescharacteristic
31C8×C22⋊D53—24no—
32C2×#13133146C2211yescharacteristic
33C2×#13133139C2211yescharacteristic
34C2×#13133139C2211yescharacteristic
35C2×#13133137C2211yescharacteristic
36C2×#13133137C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39C2×C8×Dic53C2211yescharacteristic
40#16810518—21no—
41#16810496—21no—
42#16810494—21no—
43#16810492C2211yescharacteristic
44#16810483C2211yescharacteristic
45#16810480C2211yescharacteristic
46C4⋊C4×Dic53C2211yescharacteristic
47#16810386C2211yescharacteristic
48#16810386C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53#16810385C2211yescharacteristic
54#16810385C2211yescharacteristic
55C23×C8×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C22×C4⋊C4×C53C2211yescharacteristic
58C53×#340C2211yescharacteristic
59C53×#340C2211yescharacteristic
60C53×#340C2211yescharacteristic
61C53×#340C2211yescharacteristic
62C2×#11719945—28no—
63C2×#11719945—44no—
64C2×#11719945—44no—
65C22×Dic106—21no—
66C22×D212—21no—
67C22×D212C2311yescharacteristic
68C22×C22⋊D53—21no—
69C22×C22⋊D53D411yescharacteristic
70C22×C4×D53—21no—
71C22×C4×D53—21no—
72C22×C4×D53—21no—
73C22×C4×D53C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C2×C8×D53—22no—
77C2×C8×D53—22no—
78C2×C8×D53—41no—
79#13133216—22no—
80#13133216C2×C414yescomplemented
81#13133202—28no—
82#13133200—28no—
83#13133195—28no—
84#13133192—22no—
85#13133192C2×C414yescomplemented
86#13133191—22no—
87#13133191C2×C414yescomplemented
88#13133179—22no—
89#13133179C2×C414yescomplemented
90C4×C22⋊D53—44no—
91C4×C22⋊D53C2×C414yes—
92C4×C22⋊D53D414yes—
93C2×C4⋊Dic53C2311yescharacteristic
94C2×C4⋊Dic53C2311yescharacteristic
95C2×C4⋊Dic53C2311yescharacteristic
96C2×#11719919—21no—
97C2×#11719919—21no—
98C2×#11719919—21no—
99C2×#11719919—21no—
100C2×#11719919—21no—
101C2×#11719919D411yescharacteristic
102C4⋊C4×D53—22no—
103C4⋊C4×D53—22no—
104C4⋊C4×D53—41no—
105C4⋊C4×D53C2×C414yescomplemented
106C2×C22⋊Dic53—21no—
107C2×C22⋊Dic53D411yescharacteristic
108C2×#11719921—21no—
109C2×#11719921—21no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921D411yescharacteristic
113C2×C4×Dic53—21no—
114C2×C4×Dic53C2311yescharacteristic
115#13133146—22no—
116#13133139—22no—
117#13133139—41no—
118#13133137—22no—
119#13133137—41no—
120C22⋊#88322—22no—
121#13133129—22no—
122C8×Dic53—22no—
123#13133124—21no—
124#13133124—21no—
125#13133124—21no—
126C23×C4×C53—21no—
127C23×C4×C53—21no—
128C23×C4×C53C2311yescharacteristic
129C22×C8×C53—22no—
130C22×C8×C53—22no—
131C22×C8×C53—41no—
132C22×C8×C53C2311yescharacteristic
133C22×C8×C53C2311yescharacteristic
134C2×C4⋊C4×C53—22no—
135C2×C4⋊C4×C53—21no—
136C2×C4⋊C4×C53—21no—
137C2×C4⋊C4×C53—22no—
138C2×C4⋊C4×C53—41no—
139C2×C4⋊C4×C53C2×C414yescomplemented
140C2×C4⋊C4×C53C2311yescharacteristic
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C24×C53C2×D411yescharacteristic
145C23×D53—21no—
146C23×D53C2×D411yescharacteristic
147C22×C4×C53—21no—
148C22×C4×C53—21no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—24no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—42no—
157C22×C4×C53—42no—
158C22×C4×C53—42no—
159C22×C4×C53—42no—
160C22×C4×C53—81no—
161C22×C4×C53C22×C412yes—
162C22×C4×C53C2×D411yescharacteristic
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2411yescharacteristic
165C2×C22⋊D53—24no—
166C2×C22⋊D53—42no—
167C2×C22⋊D53—42no—
168C2×C22⋊D53C22⋊C414yes—
169C2×C22⋊D53D814yes—
170C2×C22⋊D53SD1614yes—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53C2×D411yescharacteristic
175C22×Dic53C2×D411yescharacteristic
176C22×Dic53C2×D411yescharacteristic
177#11719945—432no—
178C2×D212—21no—
179C2×D212—21no—
180C2×D212—21no—
181C2×D212—21no—
182C2×D212—24no—
183C2×D212—21no—
184C2×D212—42no—
185C2×D212—42no—
186C2×D212C22×C412yes—
187C2×C4×D53—21no—
188C2×C4×D53—21no—
189C2×C4×D53—21no—
190C2×C4×D53—21no—
191C2×C4×D53—24no—
192C2×C4×D53—24no—
193C2×C4×D53—42no—
194C2×C4×D53—42no—
195C2×C4×D53—42no—
196C2×C4×D53—42no—
197C2×C4×D53—42no—
198C2×C4×D53—42no—
199C2×C4×D53—81no—
200C2×C4×D53C22×C412yes—
201C2×C4×D53C2×D412yes—
202C2×Dic106—24no—
203C2×Dic106—42no—
204C2×Dic106—42no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—44no—
211C2×C8×C53#4112yescomplemented
212C4⋊C4×C53—24no—
213C4⋊C4×C53—21no—
214C4⋊C4×C53—21no—
215C4⋊C4×C53—21no—
216C4⋊C4×C53—21no—
217C4⋊C4×C53—21no—
218C4⋊C4×C53—42no—
219C4⋊C4×C53C22×C412yes—
220C4⋊C4×C53C22×C412yes—
221C4⋊C4×C53#4112yescomplemented
222C22⋊Dic53—42no—
223C22⋊Dic53C22⋊C414yes—
224#11719921—24no—
225#11719921—24no—
226#11719921—24no—
227#11719921—42no—
228#11719921C22⋊C414yes—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53C22×C412yes—
235#11719919—24no—
236#11719919—24no—
237#11719919—42no—
238#11719919—42no—
239#11719919—81no—
240#11719919C22⋊C414yes—
241C4×Dic53—42no—
242C4×Dic53C22×C412yes—
243C4×Dic53C2×D412yes—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C8×D53—44no—
251C23×C53—21no—
252C23×C53—21no—
253C23×C53—21no—
254C23×C53—21no—
255C23×C53C2×C22⋊C412yes—
256C23×C53C2×D812yes—
257C23×C53C2×SD1612yes—
258C23×C53C22×D411yescharacteristic
259C22×D53—21no—
260C22×D53—21no—
261C22×D53—21no—
262C22×D53—21no—
263C22×D53—22no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53C2×C22⋊C412yes—
271C22×D53C2×D812yes—
272C22×D53C2×SD1612yes—
273C2×C4×C53—21no—
274C2×C4×C53—21no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—48no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—84no—
293C2×C4×C53C2×C22⋊C412yes—
294C2×C4×C53C23×C411yescharacteristic
295C2×C4×C53C22×D411yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53C2×#4111yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C2×C4×C532−1+411yescharacteristic
300C22⋊D53—48no—
301C22⋊D53#102116yescomplemented
302C2×Dic53—21no—
303C2×Dic53—21no—
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—22no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313C2×Dic53—41no—
314C2×Dic53—41no—
315C2×Dic53C2×C22⋊C412yes—
316C2×Dic53C2×C22⋊C412yes—
317C2×Dic53C2×C22⋊C412yes—
318C2×Dic53C2×D812yes—
319C2×Dic53C2×SD1612yes—
320D212—22no—
321D212—22no—
322D212—48no—
323D212—41no—
324D212—41no—
325C4×D53—22no—
326C4×D53—22no—
327C4×D53—22no—
328C4×D53—22no—
329C4×D53—48no—
330C4×D53—48no—
331C4×D53—84no—
332Dic106—48no—
333C8×C53—22no—
334C8×C53—41no—
335#88322—41no—
336#88322—41no—
337#22485—531nomaximal, Sylow
338C22×C53—22no—
339C22×C53—22no—
340C22×C53—22no—
341C22×C53—22no—
342C22×C53—22no—
343C22×C53—22no—
344C22×C53C2×#10214yes—
345C22×C53C22×C22⋊C411yescharacteristic
346C22×C53#54611yescharacteristic
347C22×C53#54711yescharacteristic
348C22×C53C22×D811yescharacteristic
349C22×C53C22×SD1611yescharacteristic
350C22×C53#57711yescharacteristic
351C22×C53#57811yescharacteristic
352C2×D53—22no—
353C2×D53—22no—
354C2×D53—22no—
355C2×D53—22no—
356C2×D53—22no—
357C2×D53—22no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—81no—
362C2×D53—81no—
363C2×D53—81no—
364C2×D53—81no—
365C2×D53C2×#10214yes—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53—81no—
371C4×C53C4×#4111yescharacteristic
372C4×C53#52011yescharacteristic
373C4×C53#54611yescharacteristic
374C4×C53#54711yescharacteristic
375Dic53—22no—
376Dic53—22no—
377Dic53—42no—
378Dic53—81no—
379Dic53—81no—
380Dic53C2×#10214yes—
381C2×#547—531no—
382C2×C8×D4—531no—
383D4×C4⋊C4—531no—
384#1990—531no—
385#1988—531no—
386#1893—531no—
387#1893—531no—
388#1874—531no—
389#1874—531no—
390#1823—531no—
391#1823—531no—
392#1802—531no—
393C4×#102—531no—
394C2×#340—531no—
395C2×#340D5311yescharacteristic, complemented
396C2×C53—24no—
397C2×C53#233911yescharacteristic
398C2×C53C22×#10211yescharacteristic
399C2×C53#289811yescharacteristic
400C2×C53#329411yescharacteristic
401C2×C53#329811yescharacteristic
402C2×C53#333411yescharacteristic
403C2×C53#333511yescharacteristic
404D53—24no—
405D53—82no—
406C22×#41—1061no—
407C23×C8—531no—
408C23×C8C2×D5311yescharacteristic
409#547—538no—
410#547—1064no—
411C2×C4⋊Q8—531no—
412C2×#123—1061no—
413C2×#123—1061no—
414C2×C22⋊Q8—1061no—
415C2×#121—531no—
416C2×#121—531no—
417C2×C4×D4—531no—
418C2×C4×D4—531no—
419C2×C4×D4—1061no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4—531no—
422C22×C4⋊C4C2×D5311yescharacteristic
423C22×C4⋊C4C2×D5311yescharacteristic
424C8×D4—1064no—
425C2×C4⋊C8—531no—
426C2×#102—531no—
427C2×#102—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×C22⋊C8—531no—
431C2×C22⋊C8—531no—
432C2×C4×C8—531no—
433#389—1061no—
434#385—1061no—
435#385—1061no—
436#384—531no—
437#380—531no—
438#380—531no—
439C4×C4⋊C4—531no—
440#340—531no—
441#340—531no—
442#340—531no—
443#340—531no—
444#340—531no—
445#340—531no—
446#340—531no—
447#340—531no—
448#340C2×D5311yescharacteristic
449#340C2×D5311yescharacteristic
450#340C2×D5311yescharacteristic
451#340C2×D5311yescharacteristic
452C53#2248511yescharacteristic, complemented, Sylow
453C2×#41—1068no—
454C2×#41—2124no—
455C2×#41—2124no—
456C22×Q8—1061no—
457C22×D4—531no—
458C22×D4—531no—
459C22×D4—1061no—
460C22×D4—1061no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—531no—
464C23×C4—1061no—
465C23×C4—1061no—
466C23×C4—1061no—
467C23×C4C22×D5311yescharacteristic
468C22×C8—22no—
469C22×C8—22no—
470C22×C8—41no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—1062no—
474C22×C8—1062no—
475C22×C8—2121no—
476C22×C8C22×D5311yescharacteristic
477C22×C8C22×D5311yescharacteristic
478C4⋊Q8—534no—
479C4⋊Q8—1062no—
480#123—1068no—
481#123—1068no—
482C22⋊Q8—1068no—
483#121—534no—
484#121—534no—
485#121—1062no—
486#121—1062no—
487C4×D4—534no—
488C4×D4—534no—
489C4×D4—534no—
490C4×D4—1062no—
491C4×D4—2124no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—41no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—1062no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1062no—
506C2×C4⋊C4—1061no—
507C2×C4⋊C4—1061no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—2121no—
510C2×C4⋊C4C4×D5314yescomplemented
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C4⋊C4C22×D5311yescharacteristic
514C2×C4⋊C4C22×D5311yescharacteristic
515C2×C22⋊C4—531no—
516C2×C22⋊C4—531no—
517C2×C22⋊C4—1061no—
518C2×C22⋊C4—1061no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C22⋊C4—1061no—
522C2×C42—531no—
523C2×C42—1061no—
524C4⋊C8—1062no—
525#102—1062no—
526#102—1062no—
527#102—2121no—
528#102—2121no—
529C22⋊C8—1062no—
530C22⋊C8—1062no—
531C4×C8—1062no—
532#95—1061no—
533#95—1061no—
534#95—1061no—
535C24—531no—
536C24—1061no—
537C24D4×D5311yescharacteristic
538#41—21232no—
539C2×Q8—1064no—
540C2×Q8—2122no—
541C2×Q8—2122no—
542C2×D4—534no—
543C2×D4—534no—
544C2×D4—534no—
545C2×D4—532no—
546C2×D4—1064no—
547C2×D4—1064no—
548C2×D4—1061no—
549C2×D4—1061no—
550C2×D4—1061no—
551C2×D4—1061no—
552C2×D4—1061no—
553C2×D4—2122no—
554C2×D4—2122no—
555C2×D4—2122no—
556C2×D4—2122no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—81no—
571C22×C4—531no—
572C22×C4—531no—
573C22×C4—531no—
574C22×C4—532no—
575C22×C4—532no—
576C22×C4—1064no—
577C22×C4—1064no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—4241no—
586C22×C4—2122no—
587C22×C4—2122no—
588C22×C4—2122no—
589C22×C4—2122no—
590C22×C4—2122no—
591C22×C4—2122no—
592C22×C4C2×C4×D5312yes—
593C22×C4D4×D5311yescharacteristic
594C22×C4D4×D5312yes—
595C22×C4C23×D5311yescharacteristic
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—44no—
602C2×C8—1061no—
603C2×C8—1061no—
604C2×C8—1061no—
605C2×C8—1061no—
606C2×C8—1061no—
607C2×C8—1061no—
608C2×C8—2124no—
609C2×C8#1171994512yescomplemented
610C4⋊C4—24no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—42no—
617C4⋊C4—534no—
618C4⋊C4—532no—
619C4⋊C4—1064no—
620C4⋊C4—1064no—
621C4⋊C4—1061no—
622C4⋊C4—1061no—
623C4⋊C4—1061no—
624C4⋊C4—1061no—
625C4⋊C4—1061no—
626C4⋊C4—4241no—
627C4⋊C4—2122no—
628C4⋊C4—2122no—
629C4⋊C4C2×C4×D5312yes—
630C4⋊C4C2×C4×D5312yes—
631C4⋊C4#1171994512yescomplemented
632C22⋊C4—534no—
633C22⋊C4—534no—
634C22⋊C4—1064no—
635C22⋊C4—1064no—
636C22⋊C4—1064no—
637C22⋊C4—2122no—
638C22⋊C4—2122no—
639C42—532no—
640C42—532no—
641C42—2122no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—532no—
647C23—532no—
648C23—532no—
649C23—1061no—
650C23—1061no—
651C23—1061no—
652C23—1061no—
653C23—1062no—
654C23—2121no—
655C23—2121no—
656C23—2121no—
657C23—2121no—
658C23—2121no—
659C23—2121no—
660C23C22⋊C4×D5312yes—
661C23D8×D5312yes—
662C23SD16×D5312yes—
663C23C2×D4×D5311yescharacteristic
664Q8—2128no—
665D4—5316no—
666D4—1062no—
667D4—1062no—
668D4—2128no—
669D4—2128no—
670D4—2121no—
671D4—2121no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—48no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—84no—
692C2×C4—532no—
693C2×C4—532no—
694C2×C4—532no—
695C2×C4—532no—
696C2×C4—532no—
697C2×C4—1061no—
698C2×C4—1061no—
699C2×C4—1061no—
700C2×C4—1061no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—4244no—
707C2×C4—2128no—
708C2×C4—2128no—
709C2×C4—2121no—
710C2×C4—2121no—
711C2×C4—2121no—
712C2×C4—2121no—
713C2×C4—2121no—
714C2×C4—2121no—
715C2×C4—2121no—
716C2×C4—2121no—
717C2×C4C22⋊C4×D5312yes—
718C2×C4C22×C4×D5311yescharacteristic
719C2×C4C2×D4×D5311yescharacteristic
720C2×C4C2×#1171994511yescharacteristic
721C2×C4C2×#1171994511yescharacteristic
722C2×C4#1313326211yescharacteristic
723C2×C4#1313326511yescharacteristic
724C8—22no—
725C8—41no—
726C8—2121no—
727C8—2121no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—534no—
735C22—1062no—
736C22—1062no—
737C22—1062no—
738C22—1062no—
739C22—1062no—
740C22—1062no—
741C22—4241no—
742C22—4241no—
743C22—4241no—
744C22—4241no—
745C22—2122no—
746C22—2122no—
747C22—2122no—
748C22#102×D5314yes—
749C22C2×C22⋊C4×D5311yescharacteristic
750C22#1681126311yescharacteristic
751C22#1681127411yescharacteristic
752C22C2×D8×D5311yescharacteristic
753C22C2×SD16×D5311yescharacteristic
754C22#1681142911yescharacteristic
755C22#1681143611yescharacteristic
756C4—22no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—81no—
761C4—534no—
762C4—1062no—
763C4—1062no—
764C4—4241no—
765C4—4241no—
766C4—2122no—
767C4C4×#1171994511yescharacteristic
768C4#1681110411yescharacteristic
769C4#1681126311yescharacteristic
770C4#1681127411yescharacteristic
771C2—24no—
772C2—1064no—
773C2—4242no—
774C2#2027754211yescharacteristic
775C2C2×#102×D5311yescharacteristic
776C2#2028324311yescharacteristic
777C2#2028652411yescharacteristic
778C2#2028657611yescharacteristic
779C2#2028706011yescharacteristic
780C2#2028706811yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#340C2
socleC23×C53C22×D4
prime radicalC2×#16811274C2
cosocleC22×C4×C53C24
hypercenterC2×#340D53
hypocenterC53#22485
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C2×C8×C22⋊D53C2semidirect
3. C4⋊C4×C22⋊D53C2semidirect
4. #20275674C2semidirect
5. #20275665C2semidirect
6. #20275143C2semidirect
7. #20275142C2semidirect
8. #20275032C2semidirect
9. #20275031C2semidirect
10. #20274801C2semidirect
11. #20274800C2semidirect
12. #20274714C2semidirect
13. #20274529C2semidirect
14. #340×D53C2semidirect
15. C2×C53×#340C2semidirect
19. #16811274C4semidirect
80. #13133216C2×C4semidirect
85. #13133192C2×C4semidirect
87. #13133191C2×C4semidirect
89. #13133179C2×C4semidirect
105. C4⋊C4×D53C2×C4semidirect
139. C2×C4⋊C4×C53C2×C4semidirect
211. C2×C8×C53#41semidirect
221. C4⋊C4×C53#41semidirect
301. C22⋊D53#102semidirect
395. C2×#340D53semidirect
452. C53#22485semidirect
510. C2×C4⋊C4C4×D53semidirect
609. C2×C8#11719945semidirect
631. C4⋊C4#11719945semidirect

Maximal subgroups

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

subgroupindex
C2×#168112742
C2×C8×C22⋊D532
C4⋊C4×C22⋊D532
#202756742
#202756652
#202751432
#202751422
#202750322
#202750312
#202748012
#202748002
#202747142
#202745292
#340×D532
C2×C53×#3402
#2248553