Finite Group Databasebeta

← #27393737

Subgroups — #27393737

Order 13568.

1128 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×#16811157C211yesmaximal, characteristic
2C2×#16810683C211yesmaximal, characteristic, complemented
3C2×#16810648C211yesmaximal, 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#20274696C211yesmaximal, characteristic, complemented
13#20274696C211yesmaximal, characteristic, complemented
14#20274695C211yesmaximal, characteristic, complemented
15C53×#1797C211yesmaximal, characteristic, complemented
16C22×#11719912C2211yescharacteristic
17C22×C8×D53C2211yescharacteristic
18#16811157—24no—
19#16811157—24no—
20C2×#13133211C411yescharacteristic
21C2×#13133211C411yescharacteristic
22C2×#13133209C411yescharacteristic
23C2×#13133205C411yescharacteristic
24C2×#13133200C411yescharacteristic
25C2×#13133200C411yescharacteristic
26C2×#13133196C411yescharacteristic
27C2×#13133191C411yescharacteristic
28C2×C4×Dic106C2211yescharacteristic
29C2×C4×D212C2211yescharacteristic
30C2×C4×C22⋊D53C2211yescharacteristic
31C2×C4×C22⋊D53C2211yescharacteristic
32C2×#13133174C2211yescharacteristic
33C2×#13133174C2211yescharacteristic
34#16810683—24no—
35#16810648—24no—
36C2×C4⋊#88322C2211yescharacteristic
37C2×C4⋊#88322C2211yescharacteristic
38C2×#13133146C2211yescharacteristic
39C2×#13133146C2211yescharacteristic
40C2×C22⋊#88322C2211yescharacteristic
41C2×C22⋊#88322C2211yescharacteristic
42C2×#13133129C2211yescharacteristic
43C2×#13133129C2211yescharacteristic
44C2×#13133129C2211yescharacteristic
45C2×#13133129C2211yescharacteristic
46C2×#13133129C2211yescharacteristic
47C2×#13133129C2211yescharacteristic
48C2×#13133127C2211yescharacteristic
49C2×C8×Dic53C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810378C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C22×C42×C53C2211yescharacteristic
57C2×C4⋊C8×C53C2211yescharacteristic
58C2×C4⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C53×#336C2211yescharacteristic
63C22×Dic106C2×C411yescharacteristic
64C22×D212C2×C411yescharacteristic
65C22×C22⋊D53C2×C411yescharacteristic
66C22×C22⋊D53C2×C411yescharacteristic
67C22×C4×D53C2311yescharacteristic
68C22×C4×D53C2311yescharacteristic
69C2×#11719912—22no—
70C2×#11719912—41no—
71C2×#11719912—41no—
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76C2×C8×D53—22no—
77C2×C8×D53—41no—
78C2×C8×D53—41no—
79#13133211—24no—
80#13133211—24no—
81#13133209—24no—
82#13133205—24no—
83#13133200—24no—
84#13133200—24no—
85#13133196—24no—
86#13133191—24no—
87C4×Dic106—22no—
88C4×Dic106—22no—
89C4×D212—22no—
90C4×D212—22no—
91C4×C22⋊D53—22no—
92C4×C22⋊D53—22no—
93C4×C22⋊D53—22no—
94C4×C22⋊D53—22no—
95#13133174—22no—
96#13133174—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×#11719919C2×C411yescharacteristic
108C2×#11719919C2×C411yescharacteristic
109C2×C22⋊Dic53C2×C411yescharacteristic
110C2×C22⋊Dic53C2×C411yescharacteristic
111C2×#11719921C2×C411yescharacteristic
112C2×#11719921C2×C411yescharacteristic
113C2×#11719921C2×C411yescharacteristic
114C2×#11719921C2×C411yescharacteristic
115C2×#11719921C2×C411yescharacteristic
116C2×#11719921C2×C411yescharacteristic
117C2×#11719921C2×C411yescharacteristic
118C2×#11719921C2×C411yescharacteristic
119C2×C4×Dic53C2311yescharacteristic
120C2×C4×Dic53C2311yescharacteristic
121C4⋊#88322—22no—
122C4⋊#88322—22no—
123#13133146—22no—
124#13133146—22no—
125C22⋊#88322—41no—
126C22⋊#88322—41no—
127#13133129—22no—
128#13133129—22no—
129#13133129—41no—
130#13133129—41no—
131#13133129—41no—
132#13133129—41no—
133#13133127—22no—
134C8×Dic53—22no—
135C23×C4×C53C2×C411yescharacteristic
136C23×C4×C53C2×C411yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139C22×C8×C53C2311yescharacteristic
140C22×C8×C53C2311yescharacteristic
141C22×C8×C53C2311yescharacteristic
142C2×C42×C53—22no—
143C2×C42×C53—22no—
144C2×C42×C53C2×C411yescharacteristic
145C2×C42×C53C2×C411yescharacteristic
146C2×C42×C53C2311yescharacteristic
147C2×C42×C53C2311yescharacteristic
148C4⋊C8×C53—22no—
149C4⋊C8×C53—22no—
150C22⋊C8×C53—41no—
151C22⋊C8×C53—41no—
152C24×C53C22×C411yescharacteristic
153C23×D53C22×C411yescharacteristic
154C23×D53C22×C411yescharacteristic
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
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—41no—
166C22×C4×C53—41no—
167C22×C4×C53C22×C411yescharacteristic
168C22×C4×C53C22×C411yescharacteristic
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C2411yescharacteristic
173C2×C22⋊D53—22no—
174C2×C22⋊D53—22no—
175C2×C22⋊D53—22no—
176C2×C22⋊D53—22no—
177C2×C22⋊D53—41no—
178C2×C22⋊D53—41no—
179C22×Dic53C22×C411yescharacteristic
180C22×Dic53C22×C411yescharacteristic
181C22×Dic53C22×C411yescharacteristic
182C22×Dic53C22×C411yescharacteristic
183C22×Dic53C22×C411yescharacteristic
184C22×Dic53C22×C411yescharacteristic
185C2×D212—22no—
186C2×D212—22no—
187C2×D212—41no—
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×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—21no—
214C2×C8×C53—21no—
215C42×C53—22no—
216C42×C53—22no—
217C42×C53—21no—
218C42×C53—21no—
219C42×C53C2×D412yes—
220C42×C53C2×D412yes—
221C22⋊Dic53—22no—
222C22⋊Dic53—22no—
223#11719921—22no—
224#11719921—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#11719919—22no—
238#11719919—22no—
239#11719919C22⋊C414yes—
240#11719919C22⋊C414yes—
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—21no—
256C2×#88322—21no—
257#11719912—44no—
258C8×D53—44no—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53#13112yes—
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×D53C2×C22⋊C412yes—
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—44no—
294C2×C4×C53—44no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53C2×C22⋊C412yes—
300C2×C4×C53C2×C22⋊C412yes—
301C2×C4×C53#13112yes—
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53H(5,𝔽2)11yescharacteristic
305C2×C4×C53H(5,𝔽2)11yescharacteristic
306C2×C4×C532−1+411yescharacteristic
307C2×C4×C532−1+411yescharacteristic
308C22⋊D53—44no—
309C22⋊D53—44no—
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×Dic53C2×C22⋊C412yes—
326C2×Dic53C2×C22⋊C412yes—
327C2×Dic53C2×C22⋊C412yes—
328D212—44no—
329C4×D53—22no—
330C4×D53—22no—
331C4×D53—22no—
332C4×D53—22no—
333C4×D53—41no—
334C4×D53—41no—
335C4×D53—41no—
336C4×D53—41no—
337Dic106—44no—
338C8×C53—41no—
339C8×C53—41no—
340C8×C53—41no—
341C8×C53—41no—
342#88322—41no—
343#88322—41no—
344#88322—41no—
345#88322—41no—
346#21855—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×C53#52011yescharacteristic
356C22×C53#52011yescharacteristic
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—41no—
379C4×C53—41no—
380C4×C53#53511yescharacteristic
381C4×C53#53611yescharacteristic
382C4×C53#53711yescharacteristic
383C4×C53#53711yescharacteristic
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—41no—
388Dic53—41no—
389Dic53—41no—
390C2×#529—531no—
391C2×#433—531no—
392C2×#424—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#1798—531no—
402#1798—531no—
403#1797—531no—
404#1797D5311yescharacteristic, complemented
405C2×C53—42no—
406C2×C53#231111yescharacteristic
407C2×C53#288011yescharacteristic
408C2×C53#288011yescharacteristic
409C2×C53#299211yescharacteristic
410C2×C53#299311yescharacteristic
411C2×C53#299411yescharacteristic
412C2×C53#299511yescharacteristic
413D53—42no—
414D53—81no—
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×#117—531no—
433C22×C42C2×D5311yescharacteristic
434#433—1064no—
435#424—1064no—
436C2×C4⋊C8—531no—
437C2×C4⋊C8—531no—
438C2×C4⋊C8—531no—
439C2×C4⋊C8—531no—
440C2×C4⋊C8C2×D5311yescharacteristic
441C2×C4⋊C8C2×D5311yescharacteristic
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×C22⋊C8C2×D5311yescharacteristic
451C2×C22⋊C8C2×D5311yescharacteristic
452C2×#97—531no—
453C2×C4×C8—531no—
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#2185511yescharacteristic, complemented, Sylow
463C22×Q8—531no—
464C22×D4—531no—
465C22×D4—531no—
466C22×D4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4C4×D5311yescharacteristic
470C23×C4C4×D5311yescharacteristic
471C23×C4C22×D5311yescharacteristic
472C2×M16—1062no—
473C2×M16—2121no—
474C2×M16—2121no—
475C22×C8—531no—
476C22×C8—531no—
477C22×C8—531no—
478C22×C8—531no—
479C22×C8—1062no—
480C22×C8—2121no—
481C22×C8—2121no—
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—534no—
503#117—534no—
504#117—1062no—
505#117—1062no—
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⋊C4—531no—
515C2×C4⋊C4—531no—
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⋊C4—531no—
525C2×C22⋊C4—531no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—531no—
529C2×C42—531no—
530C2×C42C4×D5311yescharacteristic
531C2×C42C4×D5311yescharacteristic
532C2×C42C22×D5311yescharacteristic
533C2×C42C22×D5311yescharacteristic
534C4⋊C8—22no—
535C4⋊C8—22no—
536C4⋊C8—1062no—
537C4⋊C8—1062no—
538C4⋊C8—1062no—
539C4⋊C8—1062no—
540C22⋊C8—41no—
541C22⋊C8—41no—
542C22⋊C8—1062no—
543C22⋊C8—1062no—
544C22⋊C8—2121no—
545C22⋊C8—2121no—
546C22⋊C8—2121no—
547C22⋊C8—2121no—
548C22⋊C8—2121no—
549C22⋊C8—2121no—
550#97—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—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—531no—
585C22×C4—531no—
586C22×C4—531no—
587C22×C4—1061no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1061no—
596C22×C4—1061no—
597C22×C4C2×C4×D5311yescharacteristic
598C22×C4C2×C4×D5311yescharacteristic
599C22×C4C2×C4×D5311yescharacteristic
600C22×C4C2×C4×D5311yescharacteristic
601C22×C4C2×C4×D5311yescharacteristic
602C22×C4C23×D5311yescharacteristic
603M16—2124no—
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—21no—
615C2×C8—21no—
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—1061no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—2124no—
629C4⋊C4—534no—
630C4⋊C4—534no—
631C4⋊C4—1062no—
632C4⋊C4—1062no—
633C4⋊C4—1062no—
634C4⋊C4—1062no—
635C4⋊C4—1062no—
636C4⋊C4—1062no—
637C4⋊C4—1062no—
638C4⋊C4—1062no—
639C22⋊C4—534no—
640C22⋊C4—534no—
641C22⋊C4—1062no—
642C22⋊C4—1062no—
643C22⋊C4—1062no—
644C22⋊C4—1062no—
645C22⋊C4—1062no—
646C22⋊C4—1062no—
647C22⋊C4—1062no—
648C22⋊C4—1062no—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—532no—
654C42—532no—
655C42—1061no—
656C42—1061no—
657C42D4×D5312yes—
658C42D4×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—
679C23#1313322512yes—
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—44no—
698C2×C4—44no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
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—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1061no—
717C2×C4—1061no—
718C2×C4—1061no—
719C2×C4—1061no—
720C2×C4—1061no—
721C2×C4—1061no—
722C2×C4—1061no—
723C2×C4—1061no—
724C2×C4—1061no—
725C2×C4—2121no—
726C2×C4—2121no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4C22⋊C4×D5312yes—
730C2×C4C22⋊C4×D5312yes—
731C2×C4#1313322312yes—
732C2×C4C2×D4×D5311yescharacteristic
733C2×C4C2×D4×D5311yescharacteristic
734C2×C4#1313326211yescharacteristic
735C2×C4#1313326311yescharacteristic
736C2×C4#1313326411yescharacteristic
737C2×C4#1313326511yescharacteristic
738C8—41no—
739C8—41no—
740C8—41no—
741C8—41no—
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—
767C22C2×C22⋊C4×D5311yescharacteristic
768C22#1681110311yescharacteristic
769C22#1681110411yescharacteristic
770C22C2×#1313322311yescharacteristic
771C22C2×#1313322511yescharacteristic
772C22#1681138911yescharacteristic
773C22#1681138911yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—1062no—
780C4—1062no—
781C4—1062no—
782C4—2121no—
783C4—2121no—
784C4—2121no—
785C4#1681118911yescharacteristic
786C4#1681119611yescharacteristic
787C4#1681120211yescharacteristic
788C4#1681120311yescharacteristic
789C2—42no—
790C2—4241no—
791C2—2122no—
792C2#2027730411yescharacteristic
793C2#2028316111yescharacteristic
794C2#2028316511yescharacteristic
795C2#2028385611yescharacteristic
796C2#2028386611yescharacteristic
797C2#2028387111yescharacteristic
798C2#2028388211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1797C2
prime radicalC2×#13133191C4
cosocleC22×C4×C53C24
hypercenter#1797D53
hypocenterC53#21855
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#16810683C2semidirect
3. C2×#16810648C2semidirect
4. #20275653C2semidirect
5. #20275649C2semidirect
6. #20275511C2semidirect
7. #20275507C2semidirect
8. #20275011C2semidirect
9. #20275009C2semidirect
10. #20275006C2semidirect
11. #20275004C2semidirect
12. #20274696C2semidirect
13. #20274696C2semidirect
14. #20274695C2semidirect
15. C53×#1797C2semidirect
404. #1797D53semidirect
462. C53#21855semidirect

Maximal subgroups

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

subgroupindex
C2×#168111572
C2×#168106832
C2×#168106482
#202756532
#202756492
#202755112
#202755072
#202750112
#202750092
#202750062
#202750042
#202746962
#202746952
C53×#17972
#2185553