Finite Group Databasebeta

← #27389112

Subgroups — #27389112

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×#16811153C211yesmaximal, characteristic
2C2×#16810681C211yesmaximal, characteristic, complemented
3C2×#16810581C211yesmaximal, characteristic, complemented
4#20275653C211yesmaximal, characteristic, complemented
5#20275649C211yesmaximal, characteristic, complemented
6#20275511C211yesmaximal, characteristic, complemented
7#20275507C211yesmaximal, characteristic, complemented
8#20275012C211yesmaximal, characteristic, complemented
9#20275008C211yesmaximal, characteristic, complemented
10#20275005C211yesmaximal, characteristic, complemented
11#20274480C211yesmaximal, characteristic, complemented
12#20274480C211yesmaximal, characteristic, complemented
13#20274479C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic53C211yesmaximal, characteristic, complemented
15C53×#1870C211yesmaximal, characteristic, complemented
16C23×#88322C2211yescharacteristic
17#16811153—24no—
18#16811153—24no—
19C2×#13133212C411yescharacteristic
20C2×#13133210C411yescharacteristic
21C2×#13133207C411yescharacteristic
22C2×#13133203C411yescharacteristic
23C2×#13133201C411yescharacteristic
24C2×#13133198C411yescharacteristic
25C2×#13133194C411yescharacteristic
26C2×#13133189C411yescharacteristic
27C2×C4×Dic106C2211yescharacteristic
28C2×C4×C22⋊D53C2211yescharacteristic
29C2×C4×C22⋊D53C2211yescharacteristic
30C2×#13133176C2211yescharacteristic
31C2×#13133174C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810681—24no—
34C2×#13133146C2211yescharacteristic
35C2×#13133146C2211yescharacteristic
36C2×C22⋊#88322C2211yescharacteristic
37C2×C22⋊#88322C2211yescharacteristic
38C2×C22⋊#88322C2211yescharacteristic
39C2×#13133129C2211yescharacteristic
40C2×#13133129C2211yescharacteristic
41C2×#13133129C2211yescharacteristic
42C2×#13133129C2211yescharacteristic
43#16810581—24no—
44C2×#13133127C2211yescharacteristic
45C2×#13133127C2211yescharacteristic
46C2×#13133127C2211yescharacteristic
47C2×C8×Dic53C2211yescharacteristic
48C2×C8×Dic53C2211yescharacteristic
49C2×C8×Dic53C2211yescharacteristic
50#16810378C2211yescharacteristic
51#16810378C2211yescharacteristic
52#16810377C2211yescharacteristic
53#16810377C2211yescharacteristic
54#16810377C2211yescharacteristic
55#16810377C2211yescharacteristic
56C22×M16×C53C2211yescharacteristic
57C2×C4×D4×C53C2211yescharacteristic
58C2×C22⋊C8×C53C2211yescharacteristic
59C2×C22⋊C8×C53C2211yescharacteristic
60C2×C22⋊C8×C53C2211yescharacteristic
61C53×#336C2211yescharacteristic
62C53×#336C2211yescharacteristic
63C22×Dic106C2×C411yescharacteristic
64C22×C22⋊D53C2×C411yescharacteristic
65C22×C22⋊D53C2×C411yescharacteristic
66C23×Dic53C2×C411yescharacteristic
67C23×Dic53C2×C411yescharacteristic
68C22×C4×D53C2311yescharacteristic
69C22×#88322—22no—
70C22×#88322—22no—
71C22×#88322—22no—
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74C22×#88322C2311yescharacteristic
75C22×#88322C2311yescharacteristic
76#13133212—24no—
77#13133210—24no—
78#13133207—24no—
79#13133203—24no—
80#13133201—24no—
81#13133198—24no—
82#13133194—24no—
83#13133189—24no—
84C4×Dic106—22no—
85C4×Dic106—22no—
86C4×C22⋊D53—22no—
87C4×C22⋊D53—22no—
88C4×C22⋊D53—22no—
89C4×C22⋊D53—22no—
90#13133176D414yes—
91#13133176D414yes—
92#13133174—22no—
93#13133174—22no—
94C2×C4⋊Dic53C2×C411yescharacteristic
95C2×C4⋊Dic53C2×C411yescharacteristic
96C2×C4⋊Dic53C2×C411yescharacteristic
97C2×#11719919C2×C411yescharacteristic
98C2×#11719919C2×C411yescharacteristic
99C2×#11719919C2×C411yescharacteristic
100C2×#11719919C2×C411yescharacteristic
101C2×#11719919C2×C411yescharacteristic
102C2×#11719919C2×C411yescharacteristic
103C2×C22⋊Dic53C2×C411yescharacteristic
104C2×C22⋊Dic53C2×C411yescharacteristic
105C2×C22⋊Dic53C2×C411yescharacteristic
106C2×C22⋊Dic53C2×C411yescharacteristic
107C2×#11719921C2×C411yescharacteristic
108C2×#11719921C2×C411yescharacteristic
109C2×#11719921C2×C411yescharacteristic
110C2×#11719921C2×C411yescharacteristic
111C2×C4×Dic53—22no—
112C2×C4×Dic53—22no—
113C2×C4×Dic53C2×C411yescharacteristic
114C2×C4×Dic53C2×C411yescharacteristic
115C2×C4×Dic53C2311yescharacteristic
116C2×C4×Dic53C2311yescharacteristic
117C2×C4×Dic53C2311yescharacteristic
118#13133146—22no—
119#13133146—22no—
120C22⋊#88322—22no—
121C22⋊#88322—22no—
122C22⋊#88322—22no—
123#13133129—22no—
124#13133129—22no—
125#13133129—22no—
126#13133129—22no—
127#13133127—22no—
128#13133127—22no—
129#13133127—22no—
130C8×Dic53—22no—
131C8×Dic53—22no—
132C8×Dic53—22no—
133C22×D4×C53C2×C411yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C2×M16×C53—22no—
137C2×M16×C53—22no—
138C2×M16×C53—22no—
139C22×C8×C53C2311yescharacteristic
140C22×C8×C53C2311yescharacteristic
141C22×C8×C53C2311yescharacteristic
142C22×C8×C53C2311yescharacteristic
143C4×D4×C53—22no—
144C4×D4×C53—22no—
145C2×C4⋊C4×C53C2×C411yescharacteristic
146C2×C22⋊C4×C53C2×C411yescharacteristic
147C2×C22⋊C4×C53C2×C411yescharacteristic
148C2×C42×C53C2311yescharacteristic
149C22⋊C8×C53—22no—
150C22⋊C8×C53—22no—
151C22⋊C8×C53—22no—
152C24×C53C22×C411yescharacteristic
153C24×C53C22×C411yescharacteristic
154C23×D53C22×C411yescharacteristic
155C2×D4×C53—22no—
156C2×D4×C53—22no—
157C2×D4×C53—41no—
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×C53C22×C411yescharacteristic
169C22×C4×C53C22×C411yescharacteristic
170C22×C4×C53C22×C411yescharacteristic
171C22×C4×C53C22×C411yescharacteristic
172C22×C4×C53C2×D412yes—
173C22×C4×C53C2×D412yes—
174C22×C4×C53C2411yescharacteristic
175C2×C22⋊D53—22no—
176C2×C22⋊D53—22no—
177C2×C22⋊D53—22no—
178C2×C22⋊D53—22no—
179C2×C22⋊D53—41no—
180C2×C22⋊D53—41no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—41no—
186C22×Dic53—41no—
187C22×Dic53C22×C411yescharacteristic
188C22×Dic53C22×C411yescharacteristic
189C22×Dic53C22×C411yescharacteristic
190C22×Dic53C22×C411yescharacteristic
191C22×Dic53C22×C411yescharacteristic
192C22×Dic53C22×C411yescharacteristic
193C22×Dic53C22×C411yescharacteristic
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×Dic106—22no—
201C2×Dic106—22no—
202C2×Dic106—41no—
203M16×C53—28no—
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—
215C2×C8×C53#4112yes—
216C4⋊C4×C53—22no—
217C22⋊C4×C53—22no—
218C22⋊C4×C53—22no—
219C42×C53—21no—
220C42×C53—21no—
221C22⋊Dic53—22no—
222C22⋊Dic53—22no—
223C22⋊Dic53C22⋊C414yes—
224C22⋊Dic53C22⋊C414yes—
225#11719921—22no—
226#11719921—22no—
227#11719921—22no—
228#11719921—22no—
229C4⋊Dic53—22no—
230C4⋊Dic53C22⋊C414yes—
231C4⋊Dic53C22⋊C414yes—
232#11719919—22no—
233#11719919—22no—
234#11719919—22no—
235#11719919—22no—
236#11719919—22no—
237#11719919—22no—
238C4×Dic53—21no—
239C4×Dic53—21no—
240C4×Dic53—22no—
241C4×Dic53—22no—
242C4×Dic53C2×D412yes—
243C4×Dic53C2×D412yes—
244C4×Dic53C2×D412yes—
245C4×Dic53C2×D412yes—
246C2×#88322—28no—
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#4112yes—
258C2×#88322#4112yes—
259C23×C53—21no—
260C23×C53—21no—
261C23×C53—21no—
262C23×C53—21no—
263C23×C53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53C2×C22⋊C412yes—
272C23×C53#13112yes—
273C23×C53C23×C411yescharacteristic
274C22×D53—21no—
275C22×D53—21no—
276C22×D53—21no—
277C22×D53—21no—
278C22×D53—21no—
279C22×D53—21no—
280C22×D53—21no—
281D4×C53—44no—
282C2×C4×C53—21no—
283C2×C4×C53—21no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
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—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—41no—
298C2×C4×C53—41no—
299C2×C4×C53—41no—
300C2×C4×C53—41no—
301C2×C4×C53C2×C22⋊C412yes—
302C2×C4×C53C22×D411yescharacteristic
303C2×C4×C53C22×D411yescharacteristic
304C2×C4×C53C2×#4111yescharacteristic
305C2×C4×C53C2×#4111yescharacteristic
306C2×C4×C53C2×#4111yescharacteristic
307C2×C4×C53C2×#4111yescharacteristic
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×Dic53—21no—
326C2×Dic53—44no—
327C2×Dic53—44no—
328C2×Dic53C2×C22⋊C412yes—
329C2×Dic53C2×C22⋊C412yes—
330C2×Dic53C2×C22⋊C412yes—
331C2×Dic53C2×C22⋊C412yes—
332C2×Dic53#13112yes—
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—22no—
348C22×C53—22no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—41no—
354C22×C53—41no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—41no—
358C22×C53—41no—
359C22×C53—41no—
360C22×C53—41no—
361C22×C53C22×C22⋊C411yescharacteristic
362C22×C53C4×#4111yescharacteristic
363C22×C53C4×#4111yescharacteristic
364C22×C53C2×#13111yescharacteristic
365C22×C53C2×#13111yescharacteristic
366C22×C53#56811yescharacteristic
367C22×C53#56811yescharacteristic
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—41no—
377C4×C53—41no—
378C4×C53—41no—
379C4×C53#52511yescharacteristic
380C4×C53#52511yescharacteristic
381C4×C53#53211yescharacteristic
382C4×C53#53211yescharacteristic
383Dic53—22no—
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#1870D5311yescharacteristic, complemented
399#1869—531no—
400#1869—531no—
401#1750—531no—
402#1750—531no—
403#1749—531no—
404C4×C22⋊C8—531no—
405C2×C53—42no—
406C2×C53—42no—
407C2×C53#229711yescharacteristic
408C2×C53#288011yescharacteristic
409C2×C53#288011yescharacteristic
410C2×C53#296611yescharacteristic
411C2×C53#296711yescharacteristic
412C2×C53#296811yescharacteristic
413C2×C53#296911yescharacteristic
414D53—81no—
415C22×M16C2×D5311yescharacteristic
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×D4C2×D5311yescharacteristic
431C2×#117—531no—
432C2×#117—531no—
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⋊C8C2×D5311yescharacteristic
445C2×C22⋊C8C2×D5311yescharacteristic
446C2×C22⋊C8C2×D5311yescharacteristic
447#405—1064no—
448C2×#97—531no—
449C2×#97—531no—
450C2×#97—531no—
451C2×C4×C8—531no—
452C2×C4×C8—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#2138111yescharacteristic, complemented, Sylow
463C22×Q8—531no—
464C22×D4—531no—
465C22×D4—531no—
466C22×D4C4×D5311yescharacteristic
467C23×C4—531no—
468C23×C4—531no—
469C23×C4—531no—
470C23×C4C22×D5311yescharacteristic
471C23×C4C22×D5311yescharacteristic
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
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—22no—
497C4×D4—22no—
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⋊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—531no—
531C2×C42—1062no—
532C2×C42—1062no—
533C2×C42C22×D5311yescharacteristic
534C4⋊C8—1062no—
535C4⋊C8—1062no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C22⋊C8—22no—
539C22⋊C8—1062no—
540C22⋊C8—1062no—
541C22⋊C8—1062no—
542C22⋊C8—1062no—
543C22⋊C8—1062no—
544C22⋊C8—1062no—
545C22⋊C8—1062no—
546#97—1062no—
547#97—1062no—
548#97—1062no—
549C4×C8—1062no—
550C4×C8—1062no—
551C4×C8—1062no—
552C24—531no—
553C24C2×C4×D5311yescharacteristic
554C24C2×C4×D5311yescharacteristic
555C2×Q8—1062no—
556C2×Q8—1062no—
557C2×Q8—2121no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—41no—
561C2×D4—1062no—
562C2×D4—1062no—
563C2×D4—1062no—
564C2×D4—1062no—
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—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—531no—
578C22×C4—531no—
579C22×C4—531no—
580C22×C4—531no—
581C22×C4—531no—
582C22×C4—531no—
583C22×C4—531no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1061no—
591C22×C4—1061no—
592C22×C4—1061no—
593C22×C4—1061no—
594C22×C4—2121no—
595C22×C4—2121no—
596C22×C4C2×C4×D5311yescharacteristic
597C22×C4C2×C4×D5311yescharacteristic
598C22×C4C2×C4×D5311yescharacteristic
599C22×C4C2×C4×D5311yescharacteristic
600C22×C4D4×D5312yes—
601C22×C4D4×D5312yes—
602C22×C4C23×D5311yescharacteristic
603M16—28no—
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#1171994712yes—
628C2×C8#1171994712yes—
629C4⋊C4—22no—
630C4⋊C4—534no—
631C4⋊C4—534no—
632C4⋊C4—1062no—
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—532no—
654C42—532no—
655C42—1062no—
656C42—1062no—
657C42—1061no—
658C42—1061no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—1061no—
672C23—1061no—
673C23—1061no—
674C23—1061no—
675C23—1061no—
676C23—1061no—
677C23—1061no—
678C23C22⋊C4×D5312yes—
679C23#1313322512yes—
680C23C22×C4×D5311yescharacteristic
681Q8—2124no—
682D4—44no—
683D4—2124no—
684D4—2124no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—532no—
705C2×C4—532no—
706C2×C4—532no—
707C2×C4—532no—
708C2×C4—532no—
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—1061no—
718C2×C4—1061no—
719C2×C4—1061no—
720C2×C4—1061no—
721C2×C4—1061no—
722C2×C4—1061no—
723C2×C4—1061no—
724C2×C4—1061no—
725C2×C4—2124no—
726C2×C4—2124no—
727C2×C4—2121no—
728C2×C4—2121no—
729C2×C4—2121no—
730C2×C4—2121no—
731C2×C4C22⋊C4×D5312yes—
732C2×C4C2×D4×D5311yescharacteristic
733C2×C4C2×D4×D5311yescharacteristic
734C2×C4#41×D5311yescharacteristic
735C2×C4#41×D5311yescharacteristic
736C2×C4C2×#1171994711yescharacteristic
737C2×C4C2×#1171994711yescharacteristic
738C8—22no—
739C8—22no—
740C8—41no—
741C8—41no—
742C8—1062no—
743C8—1062no—
744C8—2121no—
745C8—2121no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—2121no—
761C22—2121no—
762C22—2121no—
763C22—2121no—
764C22—2121no—
765C22—2121no—
766C22—2121no—
767C22C2×C22⋊C4×D5311yescharacteristic
768C22C4×#1171994711yescharacteristic
769C22C4×#1171994711yescharacteristic
770C22#131×D5311yescharacteristic
771C22C2×#1313322511yescharacteristic
772C22#1681138811yescharacteristic
773C22#1681138911yescharacteristic
774C4—22no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—1062no—
779C4—1062no—
780C4—1062no—
781C4—1062no—
782C4—1062no—
783C4—2121no—
784C4—2121no—
785C4#1681112911yescharacteristic
786C4#1681113111yescharacteristic
787C4#1681116811yescharacteristic
788C4#1681116811yescharacteristic
789C2—42no—
790C2—42no—
791C2—4241no—
792C2#2027720011yescharacteristic
793C2#2028316311yescharacteristic
794C2#2028316511yescharacteristic
795C2#2028368511yescharacteristic
796C2#2028370111yescharacteristic
797C2#2028371011yescharacteristic
798C2#2028371411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D53
commutator, socleC23×C53C23×C4
FittingC53×#1870C2
prime radicalC2×#13133189C4
cosocleC22×C4×C53C24
hypercenter#1870D53
hypocenterC53#21381
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#16810681C2semidirect
3. C2×#16810581C2semidirect
4. #20275653C2semidirect
5. #20275649C2semidirect
6. #20275511C2semidirect
7. #20275507C2semidirect
8. #20275012C2semidirect
9. #20275008C2semidirect
10. #20275005C2semidirect
11. #20274480C2semidirect
12. #20274480C2semidirect
13. #20274479C2semidirect
14. C22⋊C8×Dic53C2semidirect
15. C53×#1870C2semidirect
398. #1870D53semidirect
462. C53#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168111532
C2×#168106812
C2×#168105812
#202756532
#202756492
#202755112
#202755072
#202750122
#202750082
#202750052
#202744802
#202744792
C22⋊C8×Dic532
C53×#18702
#2138153