Finite Group Databasebeta

← #27389105

Subgroups — #27389105

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×#16810682C211yesmaximal, characteristic, complemented
3C2×#16810580C211yesmaximal, characteristic, complemented
4#20275653C211yesmaximal, characteristic, complemented
5#20275649C211yesmaximal, characteristic, complemented
6#20275511C211yesmaximal, characteristic, complemented
7#20275507C211yesmaximal, characteristic, complemented
8#20275011C211yesmaximal, characteristic, complemented
9#20275009C211yesmaximal, characteristic, complemented
10#20275006C211yesmaximal, characteristic, complemented
11#20275004C211yesmaximal, characteristic, complemented
12#20274481C211yesmaximal, characteristic, complemented
13#20274478C211yesmaximal, characteristic, complemented
14C4×#13133129C211yesmaximal, characteristic, complemented
15C53×#1750C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18#16811151—24no—
19#16811151—24no—
20C2×#13133212C411yescharacteristic
21C2×#13133210C411yescharacteristic
22C2×#13133207C411yescharacteristic
23C2×#13133203C411yescharacteristic
24C2×#13133202C411yescharacteristic
25C2×#13133199C411yescharacteristic
26C2×#13133195C411yescharacteristic
27C2×#13133190C411yescharacteristic
28C2×C4×Dic106C2211yescharacteristic
29C2×C4×D212C2211yescharacteristic
30C2×C4×C22⋊D53C2211yescharacteristic
31C2×C4×C22⋊D53C2211yescharacteristic
32C2×#13133174C2211yescharacteristic
33C2×C42×D53C2211yescharacteristic
34#16810682—24no—
35C2×#13133146C2211yescharacteristic
36C2×#13133146C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38C2×C22⋊#88322C2211yescharacteristic
39C2×#13133129C2211yescharacteristic
40C2×#13133129C2211yescharacteristic
41C2×#13133129C2211yescharacteristic
42C2×#13133129C2211yescharacteristic
43C2×#13133129C2211yescharacteristic
44C2×#13133129C2211yescharacteristic
45#16810580—24no—
46C2×#13133128C2211yescharacteristic
47C2×#13133127C2211yescharacteristic
48C2×C4×#88322C2211yescharacteristic
49C2×C8×Dic53C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810378C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C2×#117×C53C2211yescharacteristic
57C2×C22⋊C8×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×#97×C53C2211yescharacteristic
60C2×C4×C8×C53C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C53×#336C2211yescharacteristic
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
71C2×#11719912—22no—
72C2×#11719912—22no—
73C2×#11719912—22no—
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C22×#88322C2311yescharacteristic
77C22×#88322C2311yescharacteristic
78C2×C8×D53—22no—
79C2×C8×D53—22no—
80C2×C8×D53—22no—
81#13133212—24no—
82#13133210—24no—
83#13133207—24no—
84#13133203—24no—
85#13133202—24no—
86#13133199—24no—
87#13133195—24no—
88#13133190—24no—
89C4×Dic106—22no—
90C4×Dic106—22no—
91C4×D212—22no—
92C4×D212—22no—
93C4×C22⋊D53—22no—
94C4×C22⋊D53—22no—
95C4×C22⋊D53—22no—
96C4×C22⋊D53—22no—
97#13133174D414yes—
98#13133174D414yes—
99C2×C4⋊Dic53C2×C411yescharacteristic
100C2×C4⋊Dic53C2×C411yescharacteristic
101C2×#11719919C2×C411yescharacteristic
102C2×#11719919C2×C411yescharacteristic
103C2×#11719919C2×C411yescharacteristic
104C2×#11719919C2×C411yescharacteristic
105C2×#11719919C2×C411yescharacteristic
106C2×#11719919C2×C411yescharacteristic
107C2×C22⋊Dic53C2×C411yescharacteristic
108C2×C22⋊Dic53C2×C411yescharacteristic
109C2×#11719921C2×C411yescharacteristic
110C2×#11719921C2×C411yescharacteristic
111C2×#11719921C2×C411yescharacteristic
112C2×#11719921C2×C411yescharacteristic
113C2×#11719921C2×C411yescharacteristic
114C2×#11719921C2×C411yescharacteristic
115C2×C4×Dic53C2×C411yescharacteristic
116C2×C4×Dic53C2×C411yescharacteristic
117C2×C4×Dic53C2311yescharacteristic
118C2×C4×Dic53C2311yescharacteristic
119C42×D53—22no—
120C42×D53—22no—
121#13133146—22no—
122#13133146—22no—
123C22⋊#88322—22no—
124C22⋊#88322—22no—
125#13133129—22no—
126#13133129—22no—
127#13133129—22no—
128#13133129—22no—
129#13133129—22no—
130#13133129—22no—
131#13133128—22no—
132#13133127—22no—
133C4×#88322—22no—
134C8×Dic53—22no—
135C23×C4×C53C2311yescharacteristic
136C22×C8×C53C2311yescharacteristic
137C22×C8×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139C22×C8×C53C2311yescharacteristic
140#117×C53—22no—
141#117×C53—22no—
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
148C22⋊C8×C53—22no—
149C22⋊C8×C53—22no—
150#97×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×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53C22×C411yescharacteristic
162C22×C4×C53C22×C411yescharacteristic
163C22×C4×C53C22×C411yescharacteristic
164C22×C4×C53C22×C411yescharacteristic
165C22×C4×C53C22×C411yescharacteristic
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—21no—
183C2×C4×D53—21no—
184C2×C4×D53—21no—
185C2×C4×D53—21no—
186C2×C4×D53—22no—
187C2×C4×D53—22no—
188C2×C4×D53—22no—
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—22no—
196C2×C4×D53—41no—
197C2×C4×D53—41no—
198C2×C4×D53C2×D412yes—
199C2×C4×D53C2×D412yes—
200C2×Dic106—22no—
201C2×Dic106—22no—
202C2×Dic106—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#4112yes—
214C2×C8×C53#4112yes—
215C4⋊C4×C53—22no—
216C4⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C42×C53—21no—
220C42×C53—21no—
221C42×C53C2×D412yes—
222C42×C53C2×D412yes—
223C22⋊Dic53—22no—
224C22⋊Dic53—22no—
225#11719921—22no—
226#11719921—22no—
227#11719921—22no—
228#11719921—22no—
229#11719921C22⋊C414yes—
230#11719921C22⋊C414yes—
231C4⋊Dic53—22no—
232C4⋊Dic53—22no—
233#11719919—22no—
234#11719919—22no—
235#11719919—22no—
236#11719919—22no—
237#11719919C22⋊C414yes—
238#11719919C22⋊C414yes—
239C4×Dic53—22no—
240C4×Dic53—22no—
241C4×Dic53—21no—
242C4×Dic53—21no—
243C4×Dic53C2×D412yes—
244C4×Dic53C2×D412yes—
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#4112yes—
256C2×#88322#4112yes—
257#11719912—28no—
258C8×D53—28no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
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×D53C2×C22⋊C412yes—
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—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
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×Dic53C2×C22⋊C412yes—
323C2×Dic53C2×C22⋊C412yes—
324C2×Dic53C2×C22⋊C412yes—
325C2×Dic53#13112yes—
326D212—44no—
327C4×D53—22no—
328C4×D53—22no—
329C4×D53—22no—
330C4×D53—22no—
331C4×D53—44no—
332C4×D53—44no—
333C4×D53—41no—
334C4×D53—41no—
335C4×D53—41no—
336C4×D53—41no—
337Dic106—44no—
338C8×C53—22no—
339C8×C53—22no—
340C8×C53—41no—
341C8×C53—41no—
342#88322—22no—
343#88322—22no—
344#88322—41no—
345#88322—41no—
346#21381—531nomaximal, Sylow
347C22×C53—41no—
348C22×C53—41no—
349C22×C53—41no—
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—22no—
365C2×D53—22no—
366C2×D53—22no—
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—41no—
378C4×C53—41no—
379C4×C53—41no—
380C4×C53#52511yescharacteristic
381C4×C53#52511yescharacteristic
382C4×C53#53211yescharacteristic
383C4×C53#53211yescharacteristic
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—22no—
388Dic53—41no—
389Dic53—41no—
390C2×#529—531no—
391C2×#433—531no—
392C2×#405—531no—
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#1750D5311yescharacteristic, complemented
403#1749—531no—
404C4×C22⋊C8—531no—
405C2×C53—81no—
406C2×C53#229711yescharacteristic
407C2×C53#288011yescharacteristic
408C2×C53#288011yescharacteristic
409C2×C53#296611yescharacteristic
410C2×C53#296711yescharacteristic
411C2×C53#296811yescharacteristic
412C2×C53#296911yescharacteristic
413D53—42no—
414D53—42no—
415C22×M16—531no—
416C23×C8—531no—
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⋊C8C2×D5311yescharacteristic
446C2×C22⋊C8C2×D5311yescharacteristic
447#405—1064no—
448C2×#97—531no—
449C2×#97—531no—
450C2×#97C2×D5311yescharacteristic
451C2×C4×C8—531no—
452C2×C4×C8—531no—
453C2×C4×C8C2×D5311yescharacteristic
454#336—531no—
455#336—531no—
456#336—531no—
457#336—531no—
458#336—531no—
459#336—531no—
460#336C2×D5311yescharacteristic
461#336C2×D5311yescharacteristic
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—1062no—
473C2×M16—1062no—
474C2×M16—1062no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—1062no—
480C22×C8—1062no—
481C22×C8—1062no—
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—22no—
503#117—22no—
504#117—534no—
505#117—534no—
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—22no—
537C22⋊C8—22no—
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—1062no—
548#97—1062no—
549C4×C8—22no—
550C4×C8—1062no—
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—21no—
572C22×C4—21no—
573C22×C4—531no—
574C22×C4—531no—
575C22×C4—531no—
576C22×C4—531no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1061no—
584C22×C4—1061no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—2121no—
596C22×C4—2121no—
597C22×C4C2×C4×D5311yescharacteristic
598C22×C4C2×C4×D5311yescharacteristic
599C22×C4C2×C4×D5311yescharacteristic
600C22×C4C2×C4×D5311yescharacteristic
601C22×C4C2×C4×D5311yescharacteristic
602C22×C4C23×D5311yescharacteristic
603M16—1068no—
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—21no—
613C2×C8—21no—
614C2×C8—532no—
615C2×C8—532no—
616C2×C8—1068no—
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—1061no—
626C2×C8—1061no—
627C2×C8#1171994512yes—
628C2×C8#1171994512yes—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—534no—
632C4⋊C4—534no—
633C4⋊C4—1062no—
634C4⋊C4—1062no—
635C4⋊C4—1062no—
636C4⋊C4—1062no—
637C4⋊C4—1062no—
638C4⋊C4—1062no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—534no—
642C22⋊C4—534no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C22⋊C4—1062no—
646C22⋊C4—1062no—
647C22⋊C4—1062no—
648C22⋊C4—1062no—
649C42—21no—
650C42—21no—
651C42—532no—
652C42—532no—
653C42—1062no—
654C42—1062no—
655C42—1061no—
656C42—1061no—
657C42D4×D5312yes—
658C42D4×D5312yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—532no—
667C23—532no—
668C23—1061no—
669C23—1061no—
670C23—1061no—
671C23—1061no—
672C23—1061no—
673C23—1061no—
674C23—1061no—
675C23—1061no—
676C23—1061no—
677C23—1061no—
678C23—1061no—
679C23—1061no—
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—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—532no—
703C2×C4—532no—
704C2×C4—532no—
705C2×C4—532no—
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—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1061no—
719C2×C4—1061no—
720C2×C4—1061no—
721C2×C4—1061no—
722C2×C4—1061no—
723C2×C4—1061no—
724C2×C4—2124no—
725C2×C4—2124no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4C22⋊C4×D5312yes—
731C2×C4C22⋊C4×D5312yes—
732C2×C4C2×D4×D5311yescharacteristic
733C2×C4C2×D4×D5311yescharacteristic
734C2×C4#41×D5311yescharacteristic
735C2×C4#41×D5311yescharacteristic
736C2×C4C2×#1171994511yescharacteristic
737C2×C4C2×#1171994511yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—1062no—
743C8—1062no—
744C8—2121no—
745C8—2121no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—1062no—
754C22—1062no—
755C22—1062no—
756C22—1062no—
757C22—1062no—
758C22—1062no—
759C22—2121no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22—2121no—
764C22—2121no—
765C22—2121no—
766C22—2121no—
767C22C2×C22⋊C4×D5311yescharacteristic
768C22#1681109111yescharacteristic
769C22C4×#1171994511yescharacteristic
770C22#131×D5311yescharacteristic
771C22#131×D5311yescharacteristic
772C22#1681138811yescharacteristic
773C22#1681138811yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—1062no—
780C4—1062no—
781C4—1062no—
782C4—1062no—
783C4—2121no—
784C4—2121no—
785C4#1681113211yescharacteristic
786C4#1681113211yescharacteristic
787C4#1681117011yescharacteristic
788C4#1681117011yescharacteristic
789C2—81no—
790C2—2122no—
791C2—2122no—
792C2#2027720111yescharacteristic
793C2#2028316311yescharacteristic
794C2#2028316311yescharacteristic
795C2#2028368811yescharacteristic
796C2#2028369811yescharacteristic
797C2#2028370511yescharacteristic
798C2#2028371511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1750C2
prime radicalC2×#13133190C4
cosocleC22×C4×C53C24
hypercenter#1750D53
hypocenterC53#21381
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#16810682C2semidirect
3. C2×#16810580C2semidirect
4. #20275653C2semidirect
5. #20275649C2semidirect
6. #20275511C2semidirect
7. #20275507C2semidirect
8. #20275011C2semidirect
9. #20275009C2semidirect
10. #20275006C2semidirect
11. #20275004C2semidirect
12. #20274481C2semidirect
13. #20274478C2semidirect
14. C4×#13133129C2semidirect
15. C53×#1750C2semidirect
402. #1750D53semidirect
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×#168106822
C2×#168105802
#202756532
#202756492
#202755112
#202755072
#202750112
#202750092
#202750062
#202750042
#202744812
#202744782
C4×#131331292
C53×#17502
#2138153