Finite Group Databasebeta

← #27311560

Subgroups — #27311560

Order 13568.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810485C211yesmaximal, characteristic
2C2×#16810480C211yesmaximal, characteristic
3#20272983C211yesmaximal, characteristic, complemented
4#20272976C211yesmaximal, characteristic, complemented
5#20272970C211yesmaximal, characteristic, complemented
6#20272967C211yesmaximal, characteristic, complemented
7#20272959C211yesmaximal, characteristic
8#20272957C211yesmaximal, characteristic
9#20272953C211yesmaximal, characteristic
10#20272951C211yesmaximal, characteristic
11#20272949C211yesmaximal, characteristic, complemented
12#20272947C211yesmaximal, characteristic, complemented
13#20272942C211yesmaximal, characteristic, complemented
14#20272936C211yesmaximal, characteristic
15C2×C53×#387C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719921C2211yescharacteristic
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26#16810485—24no—
27#16810480C418yescomplemented
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2211yescharacteristic
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2211yescharacteristic
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C22×C4⋊C4×C53C2211yescharacteristic
47C22×C4⋊C4×C53C2211yescharacteristic
48C22×C42×C53C2211yescharacteristic
49C53×#387—24no—
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C24×D53C2311yescharacteristic
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C22×C4×D53—22no—
63C22×C4×D53—22no—
64C22×C4×D53—22no—
65C22×C4×D53—22no—
66C22×C4×D53—41no—
67C22×C4×D53—41no—
68C22×C4×D53C2×C414yes—
69C2×C4⋊Dic53—41no—
70C2×C4⋊Dic53—41no—
71C2×C4⋊Dic53C2×C414yes—
72C2×#11719919—41no—
73C2×#11719919—41no—
74C2×#11719919—41no—
75C2×#11719921—22no—
76C2×#11719921—22no—
77C2×#11719921—22no—
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—22no—
81C2×#11719921—22no—
82C2×#11719921—22no—
83C2×#11719921—41no—
84C2×#11719921—41no—
85C2×#11719921—41no—
86C2×#11719921—41no—
87C2×#11719921—41no—
88C2×#11719921—41no—
89C2×#11719921—41no—
90C2×#11719921—41no—
91C2×#11719921C2×C414yes—
92C2×#11719921C2×C414yes—
93C2×C4×Dic53—41no—
94C2×C4×Dic53—41no—
95C2×C4×Dic53—41no—
96#13133124—22no—
97#13133124—22no—
98#13133124—22no—
99#13133124—22no—
100#13133124—22no—
101#13133124—22no—
102#13133124—41no—
103#13133124—41no—
104#13133124—41no—
105#13133124—41no—
106#13133124—41no—
107#13133124—41no—
108#13133124—41no—
109#13133124—41no—
110#13133124—41no—
111#13133124—41no—
112#13133124C2×C414yes—
113#13133124C2×C414yes—
114C23×C4×C53C2311yescharacteristic
115C23×C4×C53C2311yescharacteristic
116C23×C4×C53C2311yescharacteristic
117C23×C4×C53C2311yescharacteristic
118C23×C4×C53C2311yescharacteristic
119C23×C4×C53C2311yescharacteristic
120C23×C4×C53C2311yescharacteristic
121C2×C4⋊C4×C53—22no—
122C2×C4⋊C4×C53—22no—
123C2×C4⋊C4×C53—22no—
124C2×C4⋊C4×C53—22no—
125C2×C4⋊C4×C53—41no—
126C2×C4⋊C4×C53C2×C414yes—
127C2×C42×C53—22no—
128C2×C42×C53—22no—
129C2×C42×C53—41no—
130#95×C53—22no—
131#95×C53—22no—
132#95×C53—22no—
133#95×C53D414yes—
134C24×C53C2411yescharacteristic
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—21no—
138C23×D53—21no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—21no—
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—21no—
147C23×D53C22×C412yes—
148C23×D53#4112yes—
149C23×D53#4112yes—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—21no—
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—21no—
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×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53C22×C412yes—
192C22×C4×C53C22×C412yes—
193C22×C4×C53C22×C412yes—
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2×D412yes—
196C22×C4×C53C2×D412yes—
197C22×C4×C53#4112yes—
198C22×C4×C53#4112yes—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53C22×C412yes—
245C22×Dic53C22×C412yes—
246C22×Dic53C22×C412yes—
247C22×Dic53#4112yes—
248C2×C4×D53—28no—
249C2×C4×D53—28no—
250C2×C4×D53—44no—
251C2×C4×D53—44no—
252C2×C4×D53—44no—
253C2×C4×D53—44no—
254C2×C4×D53—44no—
255C4⋊C4×C53—28no—
256C4⋊C4×C53—44no—
257C42×C53—44no—
258#11719921—44no—
259#11719921—44no—
260#11719921—44no—
261#11719921—44no—
262#11719921—44no—
263#11719921—44no—
264C4⋊Dic53—44no—
265#11719919—44no—
266C4×Dic53—44no—
267C23×C53C23×C411yescharacteristic
268C23×C53C22×D411yescharacteristic
269C23×C53C2×#4111yescharacteristic
270C23×C53C2×#4111yescharacteristic
271C23×C53C2×#4111yescharacteristic
272C23×C53C2×#4111yescharacteristic
273C23×C53C2×#4111yescharacteristic
274C23×C53H(5,𝔽2)11yescharacteristic
275C23×C53H(5,𝔽2)11yescharacteristic
276C23×C53H(5,𝔽2)11yescharacteristic
277C23×C53H(5,𝔽2)11yescharacteristic
278C23×C53H(5,𝔽2)11yescharacteristic
279C23×C532−1+411yescharacteristic
280C23×C532−1+411yescharacteristic
281C23×C532−1+411yescharacteristic
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—22no—
286C22×D53—22no—
287C22×D53—22no—
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—41no—
301C22×D53—41no—
302C22×D53—41no—
303C22×D53—41no—
304C22×D53—41no—
305C22×D53—41no—
306C22×D53—41no—
307C22×D53—41no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C22×D53—41no—
314C22×D53—41no—
315C22×D53—41no—
316C22×D53#11714yes—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—41no—
339C2×C4×C53—41no—
340C2×C4×C53—41no—
341C2×C4×C53—41no—
342C2×C4×C53—41no—
343C2×C4×C53—41no—
344C2×C4×C53—41no—
345C2×C4×C53—41no—
346C2×C4×C53—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53C4×D414yes—
366C2×Dic53—22no—
367C2×Dic53—22no—
368C2×Dic53—22no—
369C2×Dic53—22no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—22no—
373C2×Dic53—22no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—41no—
379C2×Dic53—41no—
380C2×Dic53—41no—
381C2×Dic53—41no—
382C2×Dic53—41no—
383C2×Dic53—41no—
384C2×Dic53—41no—
385C2×Dic53—41no—
386C2×Dic53—41no—
387C2×Dic53—41no—
388C2×Dic53—41no—
389C2×Dic53—41no—
390C2×Dic53—41no—
391C2×Dic53—41no—
392C2×Dic53—41no—
393C2×Dic53—41no—
394C2×Dic53—41no—
395C2×Dic53—41no—
396C2×Dic53—41no—
397C2×Dic53—41no—
398C2×Dic53—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C4×D53—416no—
416#14371—531nomaximal, Sylow
417C22×C53C2×#11711yescharacteristic
418C22×C53C2×C4×D411yescharacteristic
419C22×C53C4×#4111yescharacteristic
420C22×C53#51811yescharacteristic
421C22×C53#51811yescharacteristic
422C22×C53#51911yescharacteristic
423C22×C53#52011yescharacteristic
424C22×C53#53611yescharacteristic
425C22×C53#53711yescharacteristic
426C22×C53#53911yescharacteristic
427C22×C53#53911yescharacteristic
428C22×C53#53911yescharacteristic
429C22×C53#53911yescharacteristic
430C22×C53#53911yescharacteristic
431C22×C53#53911yescharacteristic
432C22×C53#54111yescharacteristic
433C22×C53#54211yescharacteristic
434C22×C53#54211yescharacteristic
435C22×C53#54211yescharacteristic
436C22×C53#54611yescharacteristic
437C22×C53#54611yescharacteristic
438C22×C53#54611yescharacteristic
439C22×C53#55011yescharacteristic
440C22×C53#55111yescharacteristic
441C22×C53#55111yescharacteristic
442C22×C53#55111yescharacteristic
443C22×C53#55111yescharacteristic
444C22×C53#55211yescharacteristic
445C22×C53#55211yescharacteristic
446C22×C53#55311yescharacteristic
447C22×C53#55511yescharacteristic
448C22×C53#56011yescharacteristic
449C22×C53#56011yescharacteristic
450C22×C53#56211yescharacteristic
451C22×C53#56211yescharacteristic
452C2×D53—24no—
453C2×D53—24no—
454C2×D53—24no—
455C2×D53—42no—
456C2×D53—42no—
457C2×D53—42no—
458C2×D53—42no—
459C2×D53—42no—
460C2×D53—42no—
461C2×D53—42no—
462C2×D53—42no—
463C2×D53—42no—
464C2×D53—42no—
465C2×D53—42no—
466C2×D53—42no—
467C4×C53—24no—
468C4×C53—42no—
469C4×C53—42no—
470C4×C53—42no—
471C4×C53—42no—
472C4×C53—42no—
473C4×C53—81no—
474Dic53—42no—
475Dic53—42no—
476Dic53—42no—
477Dic53—42no—
478Dic53—81no—
479Dic53—81no—
480Dic53—81no—
481C2×#387D5311yescharacteristic, complemented
482C2×#381—531no—
483C2×#380—531no—
484#1445—531no—
485#1443—531no—
486#1442—531no—
487#1441—531no—
488#1439—531no—
489#1439—531no—
490#1437—531no—
491#1437—531no—
492#1436—531no—
493#1436—531no—
494#1434—531no—
495C22⋊#95—531no—
496C2×C53#231311yescharacteristic
497C2×C53#232311yescharacteristic
498C2×C53#233211yescharacteristic
499C2×C53#234211yescharacteristic
500C2×C53#234311yescharacteristic
501C2×C53#236311yescharacteristic
502C2×C53#237711yescharacteristic
503C2×C53#268711yescharacteristic
504C2×C53#269311yescharacteristic
505C2×C53#269411yescharacteristic
506C2×C53#270511yescharacteristic
507C2×C53#273711yescharacteristic
508C2×C53#273911yescharacteristic
509C2×C53#274411yescharacteristic
510C2×C53#274611yescharacteristic
511D53—44no—
512C24×C4—531no—
513C22×C4⋊C4—531no—
514C22×C4⋊C4—531no—
515C22×C4⋊C4C2×D5311yescharacteristic
516C22×C4⋊C4C2×D5311yescharacteristic
517C22×C22⋊C4—531no—
518C22×C22⋊C4—531no—
519C22×C22⋊C4—531no—
520C22×C22⋊C4—531no—
521C22×C22⋊C4—531no—
522C22×C22⋊C4—531no—
523C22×C42—531no—
524C22×C42C2×D5311yescharacteristic
525#387—24no—
526#381—1064no—
527#380—538no—
528C2×#95—531no—
529C2×#95—531no—
530C2×#95—531no—
531C2×#95—531no—
532C2×#95—531no—
533C2×#95—531no—
534C2×#95—531no—
535C2×#95—531no—
536C2×#95—531no—
537C2×#95—531no—
538C2×#95—531no—
539C2×#95—531no—
540C2×#95—531no—
541C2×#95—531no—
542C2×#95—531no—
543C2×#95—531no—
544C2×#95—531no—
545C2×#95—531no—
546C2×#95C2×D5311yescharacteristic
547C2×#95C2×D5311yescharacteristic
548C2×#95C2×D5311yescharacteristic
549C2×#95C2×D5311yescharacteristic
550C53#1437111yescharacteristic, complemented, Sylow
551C25—531no—
552C23×C4—531no—
553C23×C4—531no—
554C23×C4—531no—
555C23×C4—531no—
556C23×C4—534no—
557C23×C4—531no—
558C23×C4—531no—
559C23×C4—531no—
560C23×C4—1062no—
561C23×C4—1062no—
562C23×C4—1062no—
563C23×C4—1062no—
564C23×C4—2121no—
565C23×C4—2121no—
566C23×C4C22×D5311yescharacteristic
567C23×C4C22×D5311yescharacteristic
568C23×C4C22×D5311yescharacteristic
569C23×C4C22×D5311yescharacteristic
570C23×C4C22×D5311yescharacteristic
571C23×C4C22×D5311yescharacteristic
572C23×C4C22×D5311yescharacteristic
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—534no—
579C2×C4⋊C4—2121no—
580C2×C4⋊C4—2121no—
581C2×C4⋊C4—2121no—
582C2×C4⋊C4—2121no—
583C2×C4⋊C4—2121no—
584C2×C4⋊C4C4×D5314yes—
585C2×C22⋊C4—534no—
586C2×C22⋊C4—534no—
587C2×C22⋊C4—1062no—
588C2×C22⋊C4—1062no—
589C2×C22⋊C4—1062no—
590C2×C22⋊C4—1062no—
591C2×C22⋊C4—1062no—
592C2×C22⋊C4—1062no—
593C2×C22⋊C4—1062no—
594C2×C22⋊C4—1062no—
595C2×C22⋊C4—2121no—
596C2×C22⋊C4—2121no—
597C2×C22⋊C4—2121no—
598C2×C22⋊C4—2121no—
599C2×C22⋊C4—2121no—
600C2×C22⋊C4—2121no—
601C2×C22⋊C4—2121no—
602C2×C22⋊C4—2121no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—41no—
606C2×C42—2121no—
607C2×C42—2121no—
608C2×C42—2121no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—534no—
613#95—534no—
614#95—1062no—
615#95—1062no—
616#95—1062no—
617#95—1062no—
618#95—1062no—
619#95—1062no—
620#95—2121no—
621#95—2121no—
622#95—2121no—
623#95—2121no—
624#95—2121no—
625#95—2121no—
626#95—2121no—
627#95—2121no—
628#95—2121no—
629#95—2121no—
630#95C22⋊D5314yes—
631C24—532no—
632C24—532no—
633C24—532no—
634C24—1061no—
635C24—1061no—
636C24—1061no—
637C24—1061no—
638C24—1061no—
639C24—1061no—
640C24—1061no—
641C24—1061no—
642C24—1061no—
643C24—1061no—
644C24—1061no—
645C24—1061no—
646C24C23×D5311yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—532no—
689C22×C4—532no—
690C22×C4—532no—
691C22×C4—532no—
692C22×C4—1068no—
693C22×C4—1061no—
694C22×C4—1061no—
695C22×C4—1061no—
696C22×C4—1061no—
697C22×C4—1061no—
698C22×C4—1061no—
699C22×C4—1061no—
700C22×C4—1061no—
701C22×C4—1061no—
702C22×C4—1061no—
703C22×C4—1061no—
704C22×C4—1061no—
705C22×C4—1061no—
706C22×C4—1061no—
707C22×C4—1061no—
708C22×C4—1061no—
709C22×C4—1061no—
710C22×C4—1061no—
711C22×C4—1061no—
712C22×C4—1061no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1068no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
736C22×C4—1061no—
737C22×C4—1061no—
738C22×C4—1061no—
739C22×C4—2124no—
740C22×C4—2124no—
741C22×C4—2124no—
742C22×C4—2124no—
743C22×C4—2124no—
744C22×C4C2×C4×D5312yes—
745C22×C4C2×C4×D5312yes—
746C22×C4C2×C4×D5312yes—
747C22×C4#1171994512yes—
748C22×C4#1171994712yes—
749C22×C4C2×C22⋊D5312yes—
750C22×C4C2×C22⋊D5312yes—
751C22×C4C2×C22⋊D5312yes—
752C4⋊C4—28no—
753C4⋊C4—44no—
754C4⋊C4—2124no—
755C4⋊C4—2124no—
756C22⋊C4—2124no—
757C22⋊C4—2124no—
758C22⋊C4—2124no—
759C22⋊C4—2124no—
760C22⋊C4—2124no—
761C22⋊C4—2124no—
762C42—44no—
763C42—2124no—
764C23—534no—
765C23—1062no—
766C23—1062no—
767C23—1062no—
768C23—1062no—
769C23—1062no—
770C23—1062no—
771C23—1062no—
772C23—1062no—
773C23—1062no—
774C23—1062no—
775C23—1062no—
776C23—1062no—
777C23—1062no—
778C23—1062no—
779C23—1062no—
780C23—1062no—
781C23—1062no—
782C23—1062no—
783C23—2121no—
784C23—2121no—
785C23—2121no—
786C23—2121no—
787C23—2121no—
788C23—2121no—
789C23—2121no—
790C23—2121no—
791C23—2121no—
792C23—2121no—
793C23—2121no—
794C23—2121no—
795C23—2121no—
796C23—2121no—
797C23—2121no—
798C23—2121no—
799C23C22×C4×D5311yescharacteristic
800C23C22×C22⋊D5311yescharacteristic
801C23#41×D5311yescharacteristic
802C23#41×D5311yescharacteristic
803C23#41×D5311yescharacteristic
804C23C2×#1171994711yescharacteristic
805C23C2×#1171994511yescharacteristic
806C23#1313326211yescharacteristic
807C23#1313326311yescharacteristic
808C23#1313326311yescharacteristic
809C23#1313326311yescharacteristic
810C23#1313326311yescharacteristic
811C23#1313326411yescharacteristic
812C23#1313326511yescharacteristic
813C23#1313326511yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—1062no—
863C2×C4—1062no—
864C2×C4—1062no—
865C2×C4—1062no—
866C2×C4—1062no—
867C2×C4—1062no—
868C2×C4—1062no—
869C2×C4—1062no—
870C2×C4—1062no—
871C2×C4—1062no—
872C2×C4—1062no—
873C2×C4—1062no—
874C2×C4—21216no—
875C2×C4—2121no—
876C2×C4—2121no—
877C2×C4—2121no—
878C2×C4—2121no—
879C2×C4—2121no—
880C2×C4—2121no—
881C2×C4—2121no—
882C2×C4—2121no—
883C2×C4—2121no—
884C2×C4—2121no—
885C2×C4—2121no—
886C2×C4—2121no—
887C2×C4—2121no—
888C2×C4—2121no—
889C2×C4—2121no—
890C2×C4—2121no—
891C2×C4—2121no—
892C2×C4—2121no—
893C2×C4—2121no—
894C2×C4—2121no—
895C2×C4—2121no—
896C2×C4—2121no—
897C2×C4—2121no—
898C2×C4—2121no—
899C2×C4—2121no—
900C2×C4—2121no—
901C2×C4—2121no—
902C2×C4—2121no—
903C2×C4—2121no—
904C2×C4—2121no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4C4×C22⋊D5314yes—
913C22—1064no—
914C22—1064no—
915C22—1064no—
916C22—2122no—
917C22—2122no—
918C22—2122no—
919C22—2122no—
920C22—2122no—
921C22—2122no—
922C22—2122no—
923C22—2122no—
924C22—2122no—
925C22—2122no—
926C22—2122no—
927C22—2122no—
928C22#117×D5311yescharacteristic
929C22C2×C4×C22⋊D5311yescharacteristic
930C22C4×#1171994711yescharacteristic
931C22#1681109511yescharacteristic
932C22#1681109711yescharacteristic
933C22#1681109911yescharacteristic
934C22#1681110511yescharacteristic
935C22#1681119711yescharacteristic
936C22#1681120111yescharacteristic
937C22#1681121411yescharacteristic
938C22#1681121611yescharacteristic
939C22#1681121711yescharacteristic
940C22#1681121911yescharacteristic
941C22#1681122111yescharacteristic
942C22#1681122111yescharacteristic
943C22#1681123111yescharacteristic
944C22#1681123911yescharacteristic
945C22#1681124511yescharacteristic
946C22#1681124611yescharacteristic
947C22#1681126111yescharacteristic
948C22#1681126111yescharacteristic
949C22#1681126711yescharacteristic
950C22#1681129211yescharacteristic
951C22#1681129611yescharacteristic
952C22#1681129711yescharacteristic
953C22#1681129711yescharacteristic
954C22#1681129811yescharacteristic
955C22#1681130511yescharacteristic
956C22#1681130711yescharacteristic
957C22#1681132311yescharacteristic
958C22#1681133811yescharacteristic
959C22#1681136311yescharacteristic
960C22#1681136411yescharacteristic
961C22#1681136911yescharacteristic
962C22#1681137111yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—81no—
970C4—4241no—
971C4—4241no—
972C4—4241no—
973C4—2122no—
974C4—2122no—
975C4—2122no—
976C4—2122no—
977C2—2124no—
978C2#2027731411yescharacteristic
979C2#2027739111yescharacteristic
980C2#2027746711yescharacteristic
981C2#2027756511yescharacteristic
982C2#2027757011yescharacteristic
983C2#2027774911yescharacteristic
984C2#2027787011yescharacteristic
985C2#2028113211yescharacteristic
986C2#2028122011yescharacteristic
987C2#2028122911yescharacteristic
988C2#2028138211yescharacteristic
989C2#2028176511yescharacteristic
990C2#2028179511yescharacteristic
991C2#2028187211yescharacteristic
992C2#2028190211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#387C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#387D53
hypocenterC53#14371
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
3. #20272983C2semidirect
4. #20272976C2semidirect
5. #20272970C2semidirect
6. #20272967C2semidirect
11. #20272949C2semidirect
12. #20272947C2semidirect
13. #20272942C2semidirect
15. C2×C53×#387C2semidirect
27. #16810480C4semidirect
481. C2×#387D53semidirect
550. C53#14371semidirect

Maximal subgroups

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

subgroupindex
C2×#168104852
C2×#168104802
#202729832
#202729762
#202729702
#202729672
#202729592
#202729572
#202729532
#202729512
#202729492
#202729472
#202729422
#202729362
C2×C53×#3872
#1437153