Finite Group Databasebeta

← #27389107

Subgroups — #27389107

Order 13568.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811151C211yesmaximal, characteristic
2C2×#16810684C211yesmaximal, characteristic, complemented
3#20275655C211yesmaximal, characteristic, complemented
4#20275651C211yesmaximal, characteristic, complemented
5#20275513C211yesmaximal, characteristic, complemented
6#20275509C211yesmaximal, characteristic, complemented
7#20275012C211yesmaximal, characteristic, complemented
8#20275012C211yesmaximal, characteristic, complemented
9#20275007C211yesmaximal, characteristic, complemented
10#20275007C211yesmaximal, characteristic, complemented
11#20274484C211yesmaximal, characteristic, complemented
12#20274482C211yesmaximal, characteristic, complemented
13#20274478C211yesmaximal, characteristic, complemented
14C4×#13133129C211yesmaximal, characteristic, complemented
15C2×C53×#405C211yesmaximal, characteristic, complemented
16#16811151—24no—
17#16811151—24no—
18C2×#13133212C411yescharacteristic
19C2×#13133210C411yescharacteristic
20C2×#13133207C411yescharacteristic
21C2×#13133203C411yescharacteristic
22C2×#13133202C411yescharacteristic
23C2×#13133199C411yescharacteristic
24C2×#13133195C411yescharacteristic
25C2×#13133190C411yescharacteristic
26C2×C4×Dic106C2211yescharacteristic
27C2×C4×D212C2211yescharacteristic
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×C4×C22⋊D53C2211yescharacteristic
30C2×#13133174C2211yescharacteristic
31C2×C42×D53C2211yescharacteristic
32#16810684—24no—
33C2×C4⋊#88322C2211yescharacteristic
34C2×C4⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×#13133129C2211yescharacteristic
38C2×#13133129C2211yescharacteristic
39C2×#13133129C2211yescharacteristic
40C2×#13133129C2211yescharacteristic
41C2×#13133129C2211yescharacteristic
42C2×#13133129C2211yescharacteristic
43C2×#13133129C2211yescharacteristic
44C2×#13133129C2211yescharacteristic
45C2×#13133128C2211yescharacteristic
46C2×C4×#88322C2211yescharacteristic
47#16810377C2211yescharacteristic
48#16810377C2211yescharacteristic
49#16810377C2211yescharacteristic
50#16810377C2211yescharacteristic
51#16810377C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55C22×M16×C53C2211yescharacteristic
56C23×C8×C53C2211yescharacteristic
57C2×#117×C53C2211yescharacteristic
58C53×#405—24no—
59C2×#97×C53C2211yescharacteristic
60C2×#97×C53C2211yescharacteristic
61C2×C4×C8×C53C2211yescharacteristic
62C2×C4×C8×C53C2211yescharacteristic
63C22×Dic106C2×C411yescharacteristic
64C22×D212C2×C411yescharacteristic
65C22×C22⋊D53C2×C411yescharacteristic
66C22×C22⋊D53C2×C411yescharacteristic
67C22×C4×D53C2×C411yescharacteristic
68C22×C4×D53C2×C411yescharacteristic
69C22×C4×D53C2311yescharacteristic
70C22×C4×D53C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75#13133212—24no—
76#13133210—24no—
77#13133207—24no—
78#13133203—24no—
79#13133202—24no—
80#13133199—24no—
81#13133195—24no—
82#13133190—24no—
83C4×Dic106—22no—
84C4×Dic106—22no—
85C4×D212—22no—
86C4×D212—22no—
87C4×C22⋊D53—22no—
88C4×C22⋊D53—22no—
89C4×C22⋊D53—22no—
90C4×C22⋊D53—22no—
91#13133174—22no—
92#13133174—22no—
93C2×C4⋊Dic53C2×C411yescharacteristic
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×#11719919C2×C411yescharacteristic
96C2×#11719919C2×C411yescharacteristic
97C2×#11719919C2×C411yescharacteristic
98C2×#11719919C2×C411yescharacteristic
99C2×#11719919C2×C411yescharacteristic
100C2×#11719919C2×C411yescharacteristic
101C2×C22⋊Dic53C2×C411yescharacteristic
102C2×C22⋊Dic53C2×C411yescharacteristic
103C2×#11719921C2×C411yescharacteristic
104C2×#11719921C2×C411yescharacteristic
105C2×#11719921C2×C411yescharacteristic
106C2×#11719921C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×C4×Dic53C2×C411yescharacteristic
110C2×C4×Dic53C2×C411yescharacteristic
111C2×C4×Dic53C2311yescharacteristic
112C2×C4×Dic53C2311yescharacteristic
113C42×D53—22no—
114C42×D53—22no—
115C4⋊#88322—22no—
116C4⋊#88322—22no—
117C22⋊#88322—22no—
118C22⋊#88322—22no—
119#13133129—22no—
120#13133129—22no—
121#13133129—22no—
122#13133129—22no—
123#13133129—22no—
124#13133129—22no—
125#13133129—22no—
126#13133129—22no—
127#13133128—22no—
128C4×#88322—22no—
129C23×C4×C53C2311yescharacteristic
130C2×M16×C53—22no—
131C2×M16×C53—22no—
132C2×M16×C53—22no—
133C22×C8×C53—22no—
134C22×C8×C53—22no—
135C22×C8×C53—22no—
136C22×C8×C53C2311yescharacteristic
137C22×C8×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139C22×C8×C53C2311yescharacteristic
140#117×C53D414yes—
141#117×C53D414yes—
142C2×C4⋊C4×C53C2×C411yescharacteristic
143C2×C4⋊C4×C53C2×C411yescharacteristic
144C2×C22⋊C4×C53C2×C411yescharacteristic
145C2×C22⋊C4×C53C2×C411yescharacteristic
146C2×C42×C53C2311yescharacteristic
147C2×C42×C53C2311yescharacteristic
148#97×C53—22no—
149#97×C53—22no—
150C4×C8×C53—22no—
151C4×C8×C53—22no—
152C24×C53C22×C411yescharacteristic
153C23×D53C22×C411yescharacteristic
154C23×D53C22×C411yescharacteristic
155C22×C4×C53—21no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53C22×C411yescharacteristic
160C22×C4×C53C22×C411yescharacteristic
161C22×C4×C53C22×C411yescharacteristic
162C22×C4×C53C22×C411yescharacteristic
163C22×C4×C53C22×C411yescharacteristic
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2×D412yes—
166C22×C4×C53C2411yescharacteristic
167C2×C22⋊D53—22no—
168C2×C22⋊D53—22no—
169C2×C22⋊D53—22no—
170C2×C22⋊D53—22no—
171C2×C22⋊D53—41no—
172C2×C22⋊D53—41no—
173C22×Dic53C22×C411yescharacteristic
174C22×Dic53C22×C411yescharacteristic
175C22×Dic53C22×C411yescharacteristic
176C22×Dic53C22×C411yescharacteristic
177C22×Dic53C22×C411yescharacteristic
178C22×Dic53C22×C411yescharacteristic
179C2×D212—22no—
180C2×D212—22no—
181C2×D212—41no—
182C2×C4×D53—22no—
183C2×C4×D53—22no—
184C2×C4×D53—22no—
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—22no—
198C2×C4×D53—41no—
199C2×C4×D53—41no—
200C2×Dic106—22no—
201C2×Dic106—22no—
202C2×Dic106—41no—
203M16×C53—28no—
204C2×C8×C53—28no—
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#4112yes—
214C2×C8×C53#4112yes—
215C2×C8×C53#4112yes—
216C2×C8×C53#4112yes—
217C4⋊C4×C53C22⋊C414yes—
218C4⋊C4×C53C22⋊C414yes—
219C22⋊C4×C53C22⋊C414yes—
220C22⋊C4×C53C22⋊C414yes—
221C42×C53C2×D412yes—
222C42×C53C2×D412yes—
223C42×C53C2×D412yes—
224C42×C53C2×D412yes—
225C22⋊Dic53—22no—
226C22⋊Dic53—22no—
227#11719921—22no—
228#11719921—22no—
229#11719921—22no—
230#11719921—22no—
231#11719921—22no—
232#11719921—22no—
233C4⋊Dic53—22no—
234C4⋊Dic53—22no—
235#11719919—22no—
236#11719919—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—
245C4×Dic53—21no—
246C4×Dic53—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—21no—
257C2×#88322—21no—
258C2×#88322—21no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53C2×C22⋊C412yes—
266C23×C53C23×C411yescharacteristic
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—21no—
279C22×D53—21no—
280C22×D53#13112yes—
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—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53C2×C22⋊C412yes—
296C2×C4×C53C2×C22⋊C412yes—
297C2×C4×C53C2×C22⋊C412yes—
298C2×C4×C53C2×C22⋊C412yes—
299C2×C4×C53C2×C22⋊C412yes—
300C2×C4×C53C22×D411yescharacteristic
301C2×C4×C53C22×D411yescharacteristic
302C2×C4×C53C2×#4111yescharacteristic
303C2×C4×C53C2×#4111yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C22⋊D53—44no—
307C22⋊D53—44no—
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—
319C2×Dic53—21no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—21no—
323C2×Dic53—21no—
324C2×Dic53—21no—
325C2×Dic53#13112yes—
326D212—44no—
327C4×D53—44no—
328C4×D53—44no—
329C4×D53—41no—
330C4×D53—41no—
331C4×D53—41no—
332C4×D53—41no—
333C4×D53—41no—
334C4×D53—41no—
335C4×D53—41no—
336C4×D53—41no—
337Dic106—44no—
338C8×C53—22no—
339C8×C53—22no—
340C8×C53—22no—
341C8×C53—22no—
342#88322—41no—
343#88322—41no—
344#88322—41no—
345#88322—41no—
346#21381—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—41no—
351C22×C53—41no—
352C22×C53—41no—
353C22×C53—41no—
354C22×C53C22×C22⋊C411yescharacteristic
355C22×C53C4×#4111yescharacteristic
356C22×C53C4×#4111yescharacteristic
357C22×C53C2×#13111yescharacteristic
358C22×C53C2×#13111yescharacteristic
359C22×C53#56811yescharacteristic
360C22×C53#56811yescharacteristic
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—22no—
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—
373C2×D53—41no—
374C2×D53—41no—
375C4×C53—22no—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—22no—
379C4×C53—22no—
380C4×C53#52511yescharacteristic
381C4×C53#52511yescharacteristic
382C4×C53#53211yescharacteristic
383C4×C53#53211yescharacteristic
384Dic53—22no—
385Dic53—41no—
386Dic53—41no—
387Dic53—41no—
388Dic53—41no—
389Dic53—41no—
390C2×#529—531no—
391C2×#433—531no—
392C2×#405D5311yescharacteristic, complemented
393#1985—531no—
394#1984—531no—
395#1955—531no—
396#1954—531no—
397#1870—531no—
398#1870—531no—
399#1869—531no—
400#1869—531no—
401#1750—531no—
402#1750—531no—
403#1749—531no—
404C4×C22⋊C8—531no—
405C2×C53—42no—
406C2×C53#229711yescharacteristic
407C2×C53#288011yescharacteristic
408C2×C53#288011yescharacteristic
409C2×C53#296611yescharacteristic
410C2×C53#296711yescharacteristic
411C2×C53#296811yescharacteristic
412C2×C53#296911yescharacteristic
413D53—42no—
414D53—81no—
415C22×M16C2×D5311yescharacteristic
416C23×C8C2×D5311yescharacteristic
417#529—1064no—
418#529—1064no—
419C2×#126—531no—
420C2×#126—531no—
421C2×#125—531no—
422C2×#124—531no—
423C2×#123—531no—
424C2×#123—531no—
425C2×C22⋊Q8—531no—
426C2×#121—531no—
427C2×C4×Q8—531no—
428C2×C4×D4—531no—
429C2×C4×D4—531no—
430C2×C4×D4—531no—
431C2×#117—531no—
432C2×#117C2×D5311yescharacteristic
433C22×C42—531no—
434#433—1064no—
435C2×C4⋊C8—531no—
436C2×C4⋊C8—531no—
437C2×C22⋊C8—531no—
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—
447#405—24no—
448C2×#97—531no—
449C2×#97C2×D5311yescharacteristic
450C2×#97C2×D5311yescharacteristic
451C2×C4×C8—531no—
452C2×C4×C8C2×D5311yescharacteristic
453C2×C4×C8C2×D5311yescharacteristic
454#336—531no—
455#336—531no—
456#336—531no—
457#336—531no—
458#336—531no—
459#336—531no—
460#336—531no—
461#336—531no—
462C53#2138111yescharacteristic, complemented, Sylow
463C22×Q8—531no—
464C22×D4—531no—
465C22×D4—531no—
466C22×D4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4—531no—
471C23×C4C22×D5311yescharacteristic
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
475C22×C8—22no—
476C22×C8—22no—
477C22×C8—22no—
478C22×C8—531no—
479C22×C8—531no—
480C22×C8—531no—
481C22×C8—531no—
482C22×C8C22×D5311yescharacteristic
483C22×C8C22×D5311yescharacteristic
484C22×C8C22×D5311yescharacteristic
485C22×C8C22×D5311yescharacteristic
486#126—1064no—
487#126—1064no—
488#125—1064no—
489#124—1064no—
490#123—1064no—
491#123—1064no—
492C22⋊Q8—1064no—
493#121—1064no—
494C4×Q8—1062no—
495C4×Q8—1062no—
496C4×D4—1062no—
497C4×D4—1062no—
498C4×D4—1062no—
499C4×D4—1062no—
500C4×D4—1062no—
501C4×D4—1062no—
502#117—1062no—
503#117—1062no—
504#117D21214yes—
505#117C22⋊D5314yes—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—531no—
509C2×C4⋊C4—531no—
510C2×C4⋊C4—531no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4C4×D5311yescharacteristic
515C2×C4⋊C4C4×D5311yescharacteristic
516C2×C22⋊C4—531no—
517C2×C22⋊C4—531no—
518C2×C22⋊C4—531no—
519C2×C22⋊C4—531no—
520C2×C22⋊C4—531no—
521C2×C22⋊C4—531no—
522C2×C22⋊C4—531no—
523C2×C22⋊C4—531no—
524C2×C22⋊C4C4×D5311yescharacteristic
525C2×C22⋊C4C4×D5311yescharacteristic
526C2×C42—531no—
527C2×C42—531no—
528C2×C42—531no—
529C2×C42—531no—
530C2×C42—1062no—
531C2×C42—1062no—
532C2×C42C22×D5311yescharacteristic
533C2×C42C22×D5311yescharacteristic
534C4⋊C8—1062no—
535C4⋊C8—1062no—
536C22⋊C8—1062no—
537C22⋊C8—1062no—
538C22⋊C8—1062no—
539C22⋊C8—1062no—
540C22⋊C8—1062no—
541C22⋊C8—1062no—
542C22⋊C8—1062no—
543C22⋊C8—1062no—
544C22⋊C8—1062no—
545C22⋊C8—1062no—
546#97—22no—
547#97—22no—
548#97—1062no—
549C4×C8—22no—
550C4×C8—22no—
551C4×C8—1062no—
552C24—531no—
553C24—531no—
554C24C2×C4×D5311yescharacteristic
555C2×Q8—1062no—
556C2×Q8—1062no—
557C2×Q8—2121no—
558C2×D4—1062no—
559C2×D4—1062no—
560C2×D4—1062no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—1062no—
564C2×D4—2121no—
565C2×D4—2121no—
566C2×D4—2121no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—531no—
572C22×C4—531no—
573C22×C4—531no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—531no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
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—1061no—
592C22×C4—1061no—
593C22×C4—2121no—
594C22×C4—2121no—
595C22×C4C2×C4×D5311yescharacteristic
596C22×C4C2×C4×D5311yescharacteristic
597C22×C4C2×C4×D5311yescharacteristic
598C22×C4C2×C4×D5311yescharacteristic
599C22×C4C2×C4×D5311yescharacteristic
600C22×C4C2×D21212yes—
601C22×C4C2×C22⋊D5312yes—
602C22×C4C23×D5311yescharacteristic
603M16—28no—
604C2×C8—28no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
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—1061no—
625C2×C8#1171994512yes—
626C2×C8#1171994512yes—
627C2×C8#1171994512yes—
628C2×C8#1171994512yes—
629C4⋊C4—1062no—
630C4⋊C4—1062no—
631C4⋊C4—1062no—
632C4⋊C4—1062no—
633C4⋊C4—1062no—
634C4⋊C4—1062no—
635C4⋊C4—1062no—
636C4⋊C4—1062no—
637C4⋊C4#1171992114yes—
638C4⋊C4#1171992114yes—
639C22⋊C4—1062no—
640C22⋊C4—1062no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C22⋊C4—1062no—
646C22⋊C4—1062no—
647C22⋊C4#1171992114yes—
648C22⋊C4#1171992114yes—
649C42—1062no—
650C42—1062no—
651C42—1061no—
652C42—1061no—
653C42—1061no—
654C42—1061no—
655C42C2×D21212yes—
656C42C2×D21212yes—
657C42C2×C22⋊D5312yes—
658C42C2×C22⋊D5312yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—532no—
666C23—1061no—
667C23—1061no—
668C23—1061no—
669C23—1061no—
670C23—1061no—
671C23—1061no—
672C23—1061no—
673C23—1061no—
674C23—1061no—
675C23—1061no—
676C23—1061no—
677C23—1061no—
678C23—1061no—
679C23C2×#1171992112yes—
680C23C22×C4×D5311yescharacteristic
681Q8—2124no—
682D4—2124no—
683D4—2124no—
684D4—2124no—
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—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—532no—
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—1061no—
709C2×C4—1061no—
710C2×C4—1061no—
711C2×C4—1061no—
712C2×C4—1061no—
713C2×C4—1061no—
714C2×C4—1061no—
715C2×C4—1061no—
716C2×C4—1061no—
717C2×C4—2124no—
718C2×C4—2124no—
719C2×C4—2121no—
720C2×C4—2121no—
721C2×C4—2121no—
722C2×C4—2121no—
723C2×C4—2121no—
724C2×C4—2121no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4C2×#1171992112yes—
728C2×C4C2×#1171992112yes—
729C2×C4C2×#1171992112yes—
730C2×C4C2×#1171992112yes—
731C2×C4C2×#1171992112yes—
732C2×C4C22×C22⋊D5311yescharacteristic
733C2×C4C22×D21211yescharacteristic
734C2×C4C2×#1171994511yescharacteristic
735C2×C4C2×#1171994511yescharacteristic
736C2×C4C2×#1171994511yescharacteristic
737C2×C4C2×#1171994511yescharacteristic
738C8—22no—
739C8—22no—
740C8—22no—
741C8—22no—
742C8—2121no—
743C8—2121no—
744C8—2121no—
745C8—2121no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—1062no—
754C22—1062no—
755C22—1062no—
756C22—2121no—
757C22—2121no—
758C22—2121no—
759C22—2121no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22—2121no—
764C22—2121no—
765C22—2121no—
766C22—2121no—
767C22C22×#1171992111yescharacteristic
768C22C4×#1171994511yescharacteristic
769C22C4×#1171994511yescharacteristic
770C22#131×D5311yescharacteristic
771C22#131×D5311yescharacteristic
772C22#1681138811yescharacteristic
773C22#1681138811yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—1062no—
780C4—2121no—
781C4—2121no—
782C4—2121no—
783C4—2121no—
784C4—2121no—
785C4#1681113411yescharacteristic
786C4#1681113411yescharacteristic
787C4#1681117311yescharacteristic
788C4#1681117311yescharacteristic
789C2—42no—
790C2—4241no—
791C2—2122no—
792C2#2027720511yescharacteristic
793C2#2028316211yescharacteristic
794C2#2028316211yescharacteristic
795C2#2028368611yescharacteristic
796C2#2028369611yescharacteristic
797C2#2028370511yescharacteristic
798C2#2028371511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC2×C53×#405C2
prime radicalC2×#13133190C4
cosocleC22×C4×C53C24
hypercenterC2×#405D53
hypocenterC53#21381
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. C2×#16810684C2semidirect
3. #20275655C2semidirect
4. #20275651C2semidirect
5. #20275513C2semidirect
6. #20275509C2semidirect
7. #20275012C2semidirect
8. #20275012C2semidirect
9. #20275007C2semidirect
10. #20275007C2semidirect
11. #20274484C2semidirect
12. #20274482C2semidirect
13. #20274478C2semidirect
14. C4×#13133129C2semidirect
15. C2×C53×#405C2semidirect
392. C2×#405D53semidirect
462. C53#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168111512
C2×#168106842
#202756552
#202756512
#202755132
#202755092
#202750122
#202750072
#202744842
#202744822
#202744782
C4×#131331292
C2×C53×#4052
#2138153