Finite Group Databasebeta

← #27400829

Subgroups — #27400829

Order 13568.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811160C211yesmaximal, characteristic
2C2×#16810754C211yesmaximal, characteristic, complemented
3#20275513C211yesmaximal, characteristic, complemented
4#20275513C211yesmaximal, characteristic, complemented
5#20275512C211yesmaximal, characteristic, complemented
6#20275512C211yesmaximal, characteristic, complemented
7#20275509C211yesmaximal, characteristic, complemented
8#20275508C211yesmaximal, characteristic, complemented
9#20274696C211yesmaximal, characteristic, complemented
10#20274696C211yesmaximal, characteristic, complemented
11#20274692C211yesmaximal, characteristic, complemented
12#20274484C211yesmaximal, characteristic, complemented
13#20274482C211yesmaximal, characteristic, complemented
14#20274478C211yesmaximal, characteristic, complemented
15C2×C53×#446C211yesmaximal, characteristic, complemented
16#16811160—24no—
17#16811160—24no—
18C2×#13133212C411yescharacteristic
19C2×#13133212C411yescharacteristic
20C2×#13133208C411yescharacteristic
21C2×#13133206C411yescharacteristic
22C2×#13133202C411yescharacteristic
23C2×#13133202C411yescharacteristic
24C2×#13133193C411yescharacteristic
25C2×#13133192C411yescharacteristic
26C2×C4×D212C2211yescharacteristic
27C2×C4×D212C2211yescharacteristic
28C2×C4×D212C2211yescharacteristic
29C2×#13133174C2211yescharacteristic
30C2×#13133174C2211yescharacteristic
31C2×C42×D53C2211yescharacteristic
32#16810754—24no—
33C2×C4⋊#88322C2211yescharacteristic
34C2×C4⋊#88322C2211yescharacteristic
35C2×C4⋊#88322C2211yescharacteristic
36C2×#13133129C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39C2×#13133129C2211yescharacteristic
40C2×#13133129C2211yescharacteristic
41C2×#13133129C2211yescharacteristic
42C2×#13133129C2211yescharacteristic
43C2×#13133129C2211yescharacteristic
44C2×#13133129C2211yescharacteristic
45C2×#13133129C2211yescharacteristic
46C2×#13133129C2211yescharacteristic
47C2×#13133129C2211yescharacteristic
48C2×#13133128C2211yescharacteristic
49C2×#13133128C2211yescharacteristic
50C2×C4×#88322C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55C2×C4×Q8×C53C2211yescharacteristic
56C53×#446—24no—
57C2×C4⋊C8×C53C2211yescharacteristic
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×C4⋊C8×C53C2211yescharacteristic
60C2×#97×C53C2211yescharacteristic
61C2×#97×C53C2211yescharacteristic
62C2×C4×C8×C53C2211yescharacteristic
63C22×D212C2×C411yescharacteristic
64C22×D212C2×C411yescharacteristic
65C22×D212C2×C411yescharacteristic
66C22×C4×D53C2×C411yescharacteristic
67C22×C4×D53C2×C411yescharacteristic
68C22×C4×D53C2311yescharacteristic
69C22×C4×D53C2311yescharacteristic
70C22×C4×D53C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133212—24no—
76#13133212—24no—
77#13133208—24no—
78#13133206—24no—
79#13133202—24no—
80#13133202—24no—
81#13133193—24no—
82#13133192—24no—
83C4×D212—22no—
84C4×D212—22no—
85C4×D212—22no—
86C4×D212—22no—
87C4×D212—22no—
88C4×D212—22no—
89#13133174—22no—
90#13133174—22no—
91#13133174—22no—
92#13133174—22no—
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×C4⋊Dic53C2×C411yescharacteristic
96C2×#11719919C2×C411yescharacteristic
97C2×#11719919C2×C411yescharacteristic
98C2×#11719919C2×C411yescharacteristic
99C2×#11719919C2×C411yescharacteristic
100C2×#11719921C2×C411yescharacteristic
101C2×#11719921C2×C411yescharacteristic
102C2×#11719921C2×C411yescharacteristic
103C2×#11719921C2×C411yescharacteristic
104C2×#11719921C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×#11719921C2×C411yescharacteristic
110C2×C4×Dic53C2×C411yescharacteristic
111C2×C4×Dic53C2×C411yescharacteristic
112C2×C4×Dic53C2311yescharacteristic
113C42×D53—22no—
114C42×D53—22no—
115C4⋊#88322—22no—
116C4⋊#88322—22no—
117C4⋊#88322—22no—
118#13133129—22no—
119#13133129—22no—
120#13133129—22no—
121#13133129—22no—
122#13133129—22no—
123#13133129—22no—
124#13133129—41no—
125#13133129—41no—
126#13133129—41no—
127#13133129—41no—
128#13133129—41no—
129#13133129—41no—
130#13133128—22no—
131#13133128—22no—
132C4×#88322—22no—
133C22×Q8×C53C2×C411yescharacteristic
134C22×C8×C53C2311yescharacteristic
135C22×C8×C53C2311yescharacteristic
136C22×C8×C53C2311yescharacteristic
137C22×C8×C53C2311yescharacteristic
138C4×Q8×C53D414yes—
139C4×Q8×C53D414yes—
140C2×C4⋊C4×C53C2×C411yescharacteristic
141C2×C4⋊C4×C53C2×C411yescharacteristic
142C2×C4⋊C4×C53C2×C411yescharacteristic
143C2×C42×C53C2311yescharacteristic
144C2×C42×C53C2311yescharacteristic
145C2×C42×C53C2311yescharacteristic
146C4⋊C8×C53—22no—
147C4⋊C8×C53—22no—
148C4⋊C8×C53—22no—
149#97×C53—22no—
150#97×C53—22no—
151C4×C8×C53—22no—
152C23×D53C22×C411yescharacteristic
153C23×D53C22×C411yescharacteristic
154C23×D53C22×C411yescharacteristic
155C2×Q8×C53—41no—
156C2×Q8×C53—41no—
157C2×Q8×C53C22⋊C414yes—
158C22×C4×C53C22×C411yescharacteristic
159C22×C4×C53C22×C411yescharacteristic
160C22×C4×C53C22×C411yescharacteristic
161C22×C4×C53C22×C411yescharacteristic
162C22×C4×C53C22×C411yescharacteristic
163C22×C4×C53C22×C411yescharacteristic
164C22×C4×C53C2411yescharacteristic
165C22×Dic53C22×C411yescharacteristic
166C22×Dic53C22×C411yescharacteristic
167C22×Dic53C22×C411yescharacteristic
168C22×Dic53C22×C411yescharacteristic
169C22×Dic53C22×C411yescharacteristic
170C2×D212—22no—
171C2×D212—22no—
172C2×D212—22no—
173C2×D212—22no—
174C2×D212—22no—
175C2×D212—41no—
176C2×D212—41no—
177C2×D212—41no—
178C2×D212—41no—
179C2×C4×D53—22no—
180C2×C4×D53—22no—
181C2×C4×D53—22no—
182C2×C4×D53—21no—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—21no—
187C2×C4×D53—21no—
188C2×C4×D53—21no—
189C2×C4×D53—21no—
190C2×C4×D53—21no—
191C2×C4×D53—21no—
192C2×C4×D53—21no—
193C2×C4×D53—21no—
194C2×C4×D53—21no—
195C2×C4×D53—21no—
196C2×C4×D53—21no—
197C2×C4×D53—21no—
198C2×C4×D53—21no—
199C2×C4×D53—21no—
200C2×C4×D53—41no—
201C2×C4×D53—41no—
202C2×C4×D53—41no—
203C2×C8×C53—21no—
204C2×C8×C53—21no—
205C2×C8×C53—21no—
206C2×C8×C53—21no—
207C2×C8×C53—21no—
208C2×C8×C53—21no—
209C2×C8×C53—21no—
210C2×C8×C53—21no—
211C2×C8×C53—21no—
212C2×C8×C53—21no—
213C2×C8×C53—21no—
214C2×C8×C53#4112yes—
215C4⋊C4×C53C22⋊C414yes—
216C4⋊C4×C53C22⋊C414yes—
217C4⋊C4×C53C22⋊C414yes—
218C42×C53C2×D412yes—
219C42×C53C2×D412yes—
220C42×C53C2×D412yes—
221C42×C53C2×D412yes—
222C42×C53C2×D412yes—
223C42×C53C2×D412yes—
224#11719921—22no—
225#11719921—22no—
226#11719921—22no—
227#11719921—22no—
228#11719921—22no—
229#11719921—22no—
230#11719921—22no—
231#11719921—22no—
232#11719921—22no—
233#11719921—22no—
234C4⋊Dic53—22no—
235C4⋊Dic53—22no—
236C4⋊Dic53—22no—
237#11719919—22no—
238#11719919—22no—
239#11719919—22no—
240#11719919—22no—
241C4×Dic53—22no—
242C4×Dic53—22no—
243C4×Dic53—21no—
244C4×Dic53—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322—21no—
250C2×#88322—21no—
251C2×#88322—21no—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322#4112yes—
257C23×C53C23×C411yescharacteristic
258C22×D53—21no—
259C22×D53—21no—
260C22×D53—21no—
261C22×D53—21no—
262C22×D53—21no—
263C22×D53—21no—
264C22×D53—21no—
265C22×D53—21no—
266C22×D53—21no—
267C22×D53—21no—
268C22×D53—21no—
269C22×D53—21no—
270C22×D53—21no—
271C22×D53—21no—
272C22×D53—21no—
273C22×D53—21no—
274C22×D53—21no—
275C22×D53—21no—
276C22×D53—21no—
277C22×D53—21no—
278C22×D53#13112yes—
279Q8×C53—44no—
280C2×C4×C53—21no—
281C2×C4×C53—21no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—21no—
285C2×C4×C53—21no—
286C2×C4×C53—21no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53C2×C22⋊C412yes—
293C2×C4×C53C2×C22⋊C412yes—
294C2×C4×C53C2×C22⋊C412yes—
295C2×C4×C53C2×C22⋊C412yes—
296C2×C4×C53C2×C22⋊C412yes—
297C2×C4×C53C2×C22⋊C412yes—
298C2×C4×C53C22×D411yescharacteristic
299C2×C4×C53C22×D411yescharacteristic
300C2×C4×C53C2×#4111yescharacteristic
301C2×C4×C53C2×#4111yescharacteristic
302C2×C4×C53H(5,𝔽2)11yescharacteristic
303C2×C4×C532−1+411yescharacteristic
304C2×Dic53—21no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—21no—
310C2×Dic53—21no—
311C2×Dic53—21no—
312C2×Dic53—21no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319D212—44no—
320D212—44no—
321D212—44no—
322C4×D53—44no—
323C4×D53—44no—
324C4×D53—41no—
325C4×D53—41no—
326C4×D53—41no—
327C4×D53—41no—
328C4×D53—41no—
329C4×D53—41no—
330C4×D53—41no—
331C4×D53—41no—
332C4×D53—41no—
333C4×D53—41no—
334C4×D53—41no—
335C4×D53—41no—
336C8×C53—22no—
337C8×C53—41no—
338C8×C53—41no—
339C8×C53—41no—
340#88322—22no—
341#88322—41no—
342#88322—41no—
343#88322—41no—
344#22533—531nomaximal, Sylow
345C22×C53C22×C22⋊C411yescharacteristic
346C22×C53C4×#4111yescharacteristic
347C22×C53#52011yescharacteristic
348C22×C53C2×#13111yescharacteristic
349C22×C53#56811yescharacteristic
350C22×C53#56811yescharacteristic
351C22×C53#56811yescharacteristic
352C2×D53—22no—
353C2×D53—22no—
354C2×D53—22no—
355C2×D53—41no—
356C2×D53—41no—
357C2×D53—41no—
358C2×D53—41no—
359C2×D53—41no—
360C2×D53—41no—
361C2×D53—41no—
362C2×D53—41no—
363C2×D53—41no—
364C2×D53—41no—
365C2×D53—41no—
366C2×D53—41no—
367C2×D53—41no—
368C2×D53—41no—
369C2×D53—41no—
370C2×D53—41no—
371C2×D53—41no—
372C2×D53—41no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—22no—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53#54811yescharacteristic
380C4×C53#54811yescharacteristic
381C4×C53#55011yescharacteristic
382C4×C53#55011yescharacteristic
383Dic53—41no—
384Dic53—41no—
385Dic53—41no—
386Dic53—41no—
387Dic53—41no—
388C2×#529—531no—
389C2×#446—531no—
390C2×#446D5311yescharacteristic, complemented
391#1955—531no—
392#1955—531no—
393#1955—531no—
394#1955—531no—
395#1954—531no—
396#1954—531no—
397#1798—531no—
398#1798—531no—
399#1797—531no—
400#1750—531no—
401#1750—531no—
402#1749—531no—
403C2×C53#234111yescharacteristic
404C2×C53#287911yescharacteristic
405C2×C53#288011yescharacteristic
406C2×C53#296711yescharacteristic
407C2×C53#296811yescharacteristic
408C2×C53#299211yescharacteristic
409C2×C53#299511yescharacteristic
410D53—42no—
411D53—81no—
412D53—81no—
413#529—1064no—
414#529—1064no—
415C2×#126—531no—
416C2×#126—531no—
417C2×#125—531no—
418C2×#124—531no—
419C2×#123—531no—
420C2×#123—531no—
421C2×C22⋊Q8—531no—
422C2×#121—531no—
423C2×C4×Q8C2×D5311yescharacteristic
424C2×C4×D4—531no—
425C2×C4×D4—531no—
426C2×C4×D4—531no—
427C2×#117—531no—
428C2×#117—531no—
429C22×C42—531no—
430#446—24no—
431#446—1064no—
432C2×C4⋊C8—531no—
433C2×C4⋊C8—531no—
434C2×C4⋊C8—531no—
435C2×C4⋊C8C2×D5311yescharacteristic
436C2×C4⋊C8C2×D5311yescharacteristic
437C2×C4⋊C8C2×D5311yescharacteristic
438C2×C22⋊C8—531no—
439C2×C22⋊C8—531no—
440C2×C22⋊C8—531no—
441C2×C22⋊C8—531no—
442C2×C22⋊C8—531no—
443C2×C22⋊C8—531no—
444C2×C22⋊C8—531no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447C2×C22⋊C8—531no—
448C2×C22⋊C8—531no—
449C2×C22⋊C8—531no—
450C2×#97—531no—
451C2×#97—531no—
452C2×#97C2×D5311yescharacteristic
453C2×#97C2×D5311yescharacteristic
454C2×C4×C8—531no—
455C2×C4×C8C2×D5311yescharacteristic
456#336—531no—
457#336—531no—
458#336—531no—
459#336—531no—
460C53#2253311yescharacteristic, complemented, Sylow
461C22×Q8C4×D5311yescharacteristic
462C22×D4—531no—
463C22×D4—531no—
464C22×D4—531no—
465C23×C4—531no—
466C23×C4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C22×C8—531no—
471C22×C8—531no—
472C22×C8—531no—
473C22×C8—531no—
474C22×C8C22×D5311yescharacteristic
475C22×C8C22×D5311yescharacteristic
476C22×C8C22×D5311yescharacteristic
477C22×C8C22×D5311yescharacteristic
478#126—1064no—
479#126—1064no—
480#125—1064no—
481#124—1064no—
482#123—1064no—
483#123—1064no—
484C22⋊Q8—1064no—
485#121—1064no—
486C4×Q8D21214yes—
487C4×Q8C22⋊D5314yes—
488C4×D4—1062no—
489C4×D4—1062no—
490C4×D4—1062no—
491C4×D4—1062no—
492C4×D4—1062no—
493C4×D4—1062no—
494#117—1062no—
495#117—1062no—
496#117—1062no—
497#117—1062no—
498C2×C4⋊C4—531no—
499C2×C4⋊C4—531no—
500C2×C4⋊C4—531no—
501C2×C4⋊C4—531no—
502C2×C4⋊C4—531no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—531no—
505C2×C4⋊C4C4×D5311yescharacteristic
506C2×C4⋊C4C4×D5311yescharacteristic
507C2×C4⋊C4C4×D5311yescharacteristic
508C2×C22⋊C4—531no—
509C2×C22⋊C4—531no—
510C2×C22⋊C4—531no—
511C2×C22⋊C4—531no—
512C2×C22⋊C4—531no—
513C2×C22⋊C4—531no—
514C2×C22⋊C4—531no—
515C2×C22⋊C4—531no—
516C2×C22⋊C4—531no—
517C2×C22⋊C4—531no—
518C2×C42—531no—
519C2×C42—531no—
520C2×C42—531no—
521C2×C42—1062no—
522C2×C42—1062no—
523C2×C42C22×D5311yescharacteristic
524C2×C42C22×D5311yescharacteristic
525C2×C42C22×D5311yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—1062no—
530C4⋊C8—1062no—
531C4⋊C8—1062no—
532C22⋊C8—1062no—
533C22⋊C8—1062no—
534C22⋊C8—1062no—
535C22⋊C8—1062no—
536C22⋊C8—1062no—
537C22⋊C8—1062no—
538C22⋊C8—2121no—
539C22⋊C8—2121no—
540C22⋊C8—2121no—
541C22⋊C8—2121no—
542C22⋊C8—2121no—
543C22⋊C8—2121no—
544#97—22no—
545#97—22no—
546#97—1062no—
547#97—1062no—
548C4×C8—22no—
549C4×C8—1062no—
550C24—531no—
551C24—531no—
552C24—531no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8#1171992114yes—
556C2×D4—1062no—
557C2×D4—1062no—
558C2×D4—1062no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—2121no—
562C2×D4—2121no—
563C2×D4—2121no—
564C2×D4—2121no—
565C22×C4—531no—
566C22×C4—531no—
567C22×C4—531no—
568C22×C4—531no—
569C22×C4—531no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—1061no—
582C22×C4—1061no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—2121no—
592C22×C4—2121no—
593C22×C4—2121no—
594C22×C4C2×C4×D5311yescharacteristic
595C22×C4C2×C4×D5311yescharacteristic
596C22×C4C2×C4×D5311yescharacteristic
597C22×C4C2×C4×D5311yescharacteristic
598C22×C4C2×C4×D5311yescharacteristic
599C22×C4C2×C4×D5311yescharacteristic
600C22×C4C23×D5311yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—532no—
613C2×C8—1061no—
614C2×C8—1061no—
615C2×C8—1061no—
616C2×C8—1061no—
617C2×C8—1061no—
618C2×C8—1061no—
619C2×C8—1061no—
620C2×C8—1061no—
621C2×C8—1061no—
622C2×C8—1061no—
623C2×C8—1061no—
624C2×C8#1171994912yes—
625C4⋊C4—1062no—
626C4⋊C4—1062no—
627C4⋊C4—1062no—
628C4⋊C4—1062no—
629C4⋊C4—1062no—
630C4⋊C4—1062no—
631C4⋊C4—1062no—
632C4⋊C4#1171992114yes—
633C4⋊C4#1171992114yes—
634C4⋊C4#1171992114yes—
635C22⋊C4—1062no—
636C22⋊C4—1062no—
637C22⋊C4—1062no—
638C22⋊C4—1062no—
639C22⋊C4—1062no—
640C22⋊C4—1062no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C42—1062no—
646C42—1062no—
647C42—1061no—
648C42—1061no—
649C42C2×D21212yes—
650C42C2×D21212yes—
651C42C2×D21212yes—
652C42C2×C22⋊D5312yes—
653C42C2×C22⋊D5312yes—
654C42C2×C22⋊D5312yes—
655C23—532no—
656C23—1061no—
657C23—1061no—
658C23—1061no—
659C23—1061no—
660C23—1061no—
661C23—1061no—
662C23—1061no—
663C23—1061no—
664C23—1061no—
665C23—1061no—
666C23—1061no—
667C23—1061no—
668C23—1061no—
669C23—1061no—
670C23—1061no—
671C23—1061no—
672C23—1061no—
673C23—1061no—
674C23—1061no—
675C23—1061no—
676C23C22×C4×D5311yescharacteristic
677Q8—44no—
678D4—2124no—
679D4—2124no—
680D4—2124no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—1061no—
694C2×C4—1061no—
695C2×C4—1061no—
696C2×C4—1061no—
697C2×C4—1061no—
698C2×C4—1061no—
699C2×C4—1061no—
700C2×C4—1061no—
701C2×C4—1061no—
702C2×C4—1061no—
703C2×C4—1061no—
704C2×C4—1061no—
705C2×C4—1061no—
706C2×C4—1061no—
707C2×C4—1061no—
708C2×C4—2124no—
709C2×C4—2124no—
710C2×C4—2121no—
711C2×C4—2121no—
712C2×C4—2121no—
713C2×C4—2121no—
714C2×C4—2121no—
715C2×C4—2121no—
716C2×C4—2121no—
717C2×C4—2121no—
718C2×C4—2121no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4C2×#1171992112yes—
723C2×C4C2×#1171992112yes—
724C2×C4C2×#1171992112yes—
725C2×C4C2×#1171992112yes—
726C2×C4C2×#1171992112yes—
727C2×C4C2×#1171992112yes—
728C2×C4C22×C22⋊D5311yescharacteristic
729C2×C4C22×D21211yescharacteristic
730C2×C4#41×D5311yescharacteristic
731C2×C4C2×#1171994911yescharacteristic
732C2×C4#1313326311yescharacteristic
733C2×C4#1313326511yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—1062no—
739C8—2121no—
740C8—2121no—
741C8—2121no—
742C22—1062no—
743C22—1062no—
744C22—1062no—
745C22—2121no—
746C22—2121no—
747C22—2121no—
748C22—2121no—
749C22—2121no—
750C22—2121no—
751C22—2121no—
752C22—2121no—
753C22—2121no—
754C22—2121no—
755C22—2121no—
756C22—2121no—
757C22—2121no—
758C22—2121no—
759C22—2121no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22C22×#1171992111yescharacteristic
764C22C4×#1171994911yescharacteristic
765C22#1681110511yescharacteristic
766C22#131×D5311yescharacteristic
767C22#1681138811yescharacteristic
768C22#1681138911yescharacteristic
769C22#1681138911yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—2121no—
777C4—2121no—
778C4—2121no—
779C4—2121no—
780C4—2121no—
781C4#1681128411yescharacteristic
782C4#1681128511yescharacteristic
783C4#1681129211yescharacteristic
784C4#1681129511yescharacteristic
785C2—4241no—
786C2—4241no—
787C2—2122no—
788C2#2027755311yescharacteristic
789C2#2028315911yescharacteristic
790C2#2028316211yescharacteristic
791C2#2028369911yescharacteristic
792C2#2028370811yescharacteristic
793C2#2028385311yescharacteristic
794C2#2028388411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC2×C53×#446C2
prime radicalC2×#13133192C4
cosocleC22×C4×C53C24
hypercenterC2×#446D53
hypocenterC53#22533
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#16810754C2semidirect
3. #20275513C2semidirect
4. #20275513C2semidirect
5. #20275512C2semidirect
6. #20275512C2semidirect
7. #20275509C2semidirect
8. #20275508C2semidirect
9. #20274696C2semidirect
10. #20274696C2semidirect
11. #20274692C2semidirect
12. #20274484C2semidirect
13. #20274482C2semidirect
14. #20274478C2semidirect
15. C2×C53×#446C2semidirect
390. C2×#446D53semidirect
460. C53#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#168111602
C2×#168107542
#202755132
#202755122
#202755092
#202755082
#202746962
#202746922
#202744842
#202744822
#202744782
C2×C53×#4462
#2253353