Finite Group Databasebeta

← #27427832

Subgroups — #27427832

Order 13568.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810757C211yesmaximal, characteristic
2C2×C4×#11719922C211yesmaximal, characteristic, complemented
3#20278229C211yesmaximal, characteristic, complemented
4#20276243C211yesmaximal, characteristic, complemented
5#20276141C211yesmaximal, characteristic, complemented
6#20276025C211yesmaximal, characteristic, complemented
7#20275897C211yesmaximal, characteristic, complemented
8#20275401C211yesmaximal, characteristic, complemented
9#20275323C211yesmaximal, characteristic, complemented
10#20275066C211yesmaximal, characteristic, complemented
11#20275063C211yesmaximal, characteristic, complemented
12#20274962C211yesmaximal, characteristic, complemented
13#20274715C211yesmaximal, characteristic, complemented
14#20274646C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719922C2211yescharacteristic
17C22×#11719922C2211yescharacteristic
18C2×#13133199—21no—
19C2×#13133191C2211yescharacteristic
20C2×C4×D212C2211yescharacteristic, complemented
21#16810757—24no—
22C4×#11719922—24no—
23C2×#13133150C2211yescharacteristic, complemented
24C2×#13133150C2211yescharacteristic, complemented
25C2×C4⋊#88322C2211yescharacteristic, complemented
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×#13133138C2211yescharacteristic
29C2×#13133138C2211yescharacteristic
30C2×#13133138C2211yescharacteristic
31C2×#13133138C2211yescharacteristic
32C2×#13133137C2211yescharacteristic, complemented
33C2×#13133137C2211yescharacteristic, complemented
34C2×C22⋊#88322C2211yescharacteristic
35C2×C22⋊#88322C2211yescharacteristic
36C2×C4×#88322C2211yescharacteristic, complemented
37#16810550—21no—
38#16810539—21no—
39#16810525C2211yescharacteristic, complemented
40#16810521C2211yescharacteristic, complemented
41#16810497—21no—
42#16810493C2211yescharacteristic, complemented
43#16810483C2211yescharacteristic
44#16810385C2211yescharacteristic, complemented
45#16810385C2211yescharacteristic, complemented
46#16810385C2211yescharacteristic, complemented
47#16810385C2211yescharacteristic, complemented
48#16810378C2211yescharacteristic, complemented
49#16810378C2211yescharacteristic, complemented
50C23×D4×C53C2211yescharacteristic
51C2×C4×D4×C53C2211yescharacteristic
52C2×C4×D4×C53C2211yescharacteristic
53C22×C22⋊C4×C53—21no—
54C53×#390C2211yescharacteristic
55C53×#390C2211yescharacteristic
56C53×#386—21no—
57C53×#386—21no—
58C53×#380C2211yescharacteristic
59C53×#379—21no—
60C4×C22⋊C4×C53C2211yescharacteristic
61C22×D212C2311yescharacteristic
62C22×C22⋊D53—21no—
63C22×C4×D53—21no—
64C2×#11719922—22no—
65C2×#11719922—22no—
66C2×#11719922—22no—
67C2×#11719922—22no—
68C2×#11719922—41no—
69C2×#11719922D414yes—
70C22×#88322C2311yescharacteristic
71C22×#88322C2311yescharacteristic
72C22×#88322C2311yescharacteristic
73C22×#88322C2311yescharacteristic
74#13133199—44no—
75#13133191—22no—
76#13133191—41no—
77C4×D212—22no—
78C4×D212—41no—
79C2×C4⋊Dic53—21no—
80C2×C4⋊Dic53—21no—
81C2×C4⋊Dic53C2311yescharacteristic
82C2×C4⋊Dic53C2311yescharacteristic
83C2×C4⋊Dic53C2311yescharacteristic
84C2×#11719919—21no—
85C2×C22⋊Dic53—21no—
86C2×#11719921—21no—
87C2×#11719921—21no—
88C2×#11719921—21no—
89C2×#11719921—21no—
90#13133150—22no—
91#13133150—41no—
92C4⋊#88322—41no—
93#13133138—22no—
94#13133138—22no—
95#13133138—22no—
96#13133138—22no—
97#13133138—22no—
98#13133138—41no—
99#13133137—22no—
100#13133137—41no—
101C22⋊#88322—22no—
102C22⋊#88322—41no—
103C4×#88322—22no—
104#13133124—21no—
105#13133124—21no—
106C25×C53—21no—
107C22×D4×C53—22no—
108C22×D4×C53—22no—
109C22×D4×C53—22no—
110C22×D4×C53—22no—
111C22×D4×C53—21no—
112C22×D4×C53—41no—
113C22×D4×C53—41no—
114C22×D4×C53C2311yescharacteristic
115C22×D4×C53C2311yescharacteristic
116C23×C4×C53—21no—
117C23×C4×C53—21no—
118C23×C4×C53C2311yescharacteristic
119C4×D4×C53—22no—
120C4×D4×C53—22no—
121C4×D4×C53—41no—
122C4×D4×C53—41no—
123C2×C4⋊C4×C53C2311yescharacteristic
124C2×C4⋊C4×C53C2311yescharacteristic
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53—21no—
127C2×C22⋊C4×C53—21no—
128C2×C22⋊C4×C53—21no—
129C2×C22⋊C4×C53—21no—
130C2×C22⋊C4×C53—21no—
131C2×C22⋊C4×C53—21no—
132C2×C22⋊C4×C53—44no—
133C2×C22⋊C4×C53D411yescharacteristic
134C2×C22⋊C4×C53D411yescharacteristic
135C2×C42×C53C2311yescharacteristic
136C2×C42×C53C2311yescharacteristic
137#95×C53—21no—
138#95×C53D411yescharacteristic
139#95×C53D411yescharacteristic
140C24×C53—21no—
141C24×C53—24no—
142C24×C53—21no—
143C24×C53—42no—
144C24×C53—42no—
145C24×C53—42no—
146C24×C53—42no—
147C24×C53—81no—
148C24×C53—81no—
149C24×C53C2×D411yescharacteristic
150C23×D53—21no—
151C2×D4×C53—24no—
152C2×D4×C53—21no—
153C2×D4×C53—21no—
154C2×D4×C53—21no—
155C2×D4×C53—21no—
156C2×D4×C53—21no—
157C2×D4×C53—21no—
158C2×D4×C53—21no—
159C2×D4×C53—21no—
160C2×D4×C53—42no—
161C2×D4×C53—42no—
162C2×D4×C53—44no—
163C2×D4×C53—44no—
164C2×D4×C53—44no—
165C2×D4×C53—44no—
166C2×D4×C53C2×D412yes—
167C2×D4×C53#4112yes—
168C2×D4×C53#4112yes—
169C2×D4×C53#4112yes—
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—42no—
179C22×C4×C53—42no—
180C22×C4×C53—42no—
181C22×C4×C53—42no—
182C22×C4×C53—81no—
183C22×C4×C53—81no—
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D411yescharacteristic
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2411yescharacteristic
190C2×C22⋊D53—42no—
191C2×C22⋊D53—42no—
192C2×C22⋊D53—81no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C2×D212—21no—
197C2×D212—21no—
198C2×D212—21no—
199C2×D212—21no—
200C2×D212—21no—
201C2×D212C2×D412yes—
202C2×C4×D53—42no—
203C2×C4×D53—42no—
204C2×C4×D53—81no—
205C4⋊C4×C53—21no—
206C4⋊C4×C53—21no—
207C4⋊C4×C53—21no—
208C4⋊C4×C53—21no—
209C22⋊C4×C53—41no—
210C22⋊C4×C53—42no—
211C22⋊C4×C53—42no—
212C22⋊C4×C53—42no—
213C22⋊C4×C53—42no—
214C22⋊C4×C53—42no—
215C22⋊C4×C53—81no—
216C22⋊C4×C53—81no—
217C22⋊C4×C53D814yescomplemented
218C42×C53—21no—
219C42×C53—21no—
220C42×C53—21no—
221C42×C53—21no—
222C22⋊Dic53—42no—
223#11719922—28no—
224#11719922—44no—
225#11719921—42no—
226#11719921—42no—
227#11719921—42no—
228#11719921—42no—
229C4⋊Dic53—21no—
230C4⋊Dic53—21no—
231C4⋊Dic53—21no—
232C4⋊Dic53—21no—
233C4⋊Dic53—21no—
234C4⋊Dic53—21no—
235C4⋊Dic53—42no—
236C4⋊Dic53—81no—
237#11719919—42no—
238C2×#88322—21no—
239C2×#88322—21no—
240C2×#88322—21no—
241C2×#88322—21no—
242C2×#88322—21no—
243C2×#88322—21no—
244C2×#88322—21no—
245C2×#88322—21no—
246C2×#88322—21no—
247C2×#88322—21no—
248C2×#88322—21no—
249C2×#88322C2×D412yes—
250C23×C53—21no—
251C23×C53—22no—
252C23×C53—21no—
253C23×C53—22no—
254C23×C53—21no—
255C23×C53—22no—
256C23×C53—21no—
257C23×C53—21no—
258C23×C53—21no—
259C23×C53—22no—
260C23×C53—48no—
261C23×C53—48no—
262C23×C53—41no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53—41no—
268C23×C53—41no—
269C23×C53—41no—
270C23×C53—41no—
271C23×C53—41no—
272C23×C53—84no—
273C23×C53—84no—
274C23×C53—84no—
275C23×C53—84no—
276C23×C53—84no—
277C23×C53C2×D812yes—
278C23×C53C22×D411yescharacteristic
279C22×D53—22no—
280C22×D53—41no—
281C22×D53—41no—
282C22×D53—41no—
283C22×D53—41no—
284C22×D53—41no—
285C22×D53—41no—
286D4×C53—22no—
287D4×C53—22no—
288D4×C53—22no—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—48no—
292D4×C53—41no—
293D4×C53—41no—
294D4×C53#12314yescomplemented
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—21no—
301C2×C4×C53—21no—
302C2×C4×C53—21no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—41no—
318C2×C4×C53—84no—
319C2×C4×C53—84no—
320C2×C4×C53C2×D812yes—
321C2×C4×C53C2×D812yes—
322C2×C4×C53C22×D411yescharacteristic
323C2×C4×C53C2×#4111yescharacteristic
324C2×C4×C53C2×#4111yescharacteristic
325C2×C4×C53C2×#4111yescharacteristic
326C2×C4×C53H(5,𝔽2)11yescharacteristic
327C2×C4×C53H(5,𝔽2)11yescharacteristic
328C22⋊D53—84no—
329C2×Dic53—41no—
330C2×Dic53—41no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—41no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338D212—22no—
339D212—22no—
340D212—41no—
341D212—41no—
342C4×D53—84no—
343#88322—22no—
344#88322—41no—
345#88322—41no—
346#88322—41no—
347#24893—531nomaximal, Sylow
348C22×C53—22no—
349C22×C53—24no—
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—42no—
353C22×C53—41no—
354C22×C53—42no—
355C22×C53—41no—
356C22×C53—41no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—41no—
361C22×C53—42no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—816no—
366C22×C53—81no—
367C22×C53—81no—
368C22×C53—81no—
369C22×C53—81no—
370C22×C53#52511yescharacteristic
371C22×C53D4211yescharacteristic
372C22×C53#54611yescharacteristic
373C22×C53C22×D811yescharacteristic
374C22×C53#57511yescharacteristic
375C22×C53#57611yescharacteristic
376C22×C53#57711yescharacteristic
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—81no—
381C2×D53—81no—
382C2×D53—81no—
383C2×D53—81no—
384C4×C53—22no—
385C4×C53—22no—
386C4×C53—41no—
387C4×C53—41no—
388C4×C53—41no—
389C4×C53—81no—
390C4×C53—81no—
391C4×C53C2×#12311yescharacteristic
392C4×C53#53811yescharacteristic
393C4×C53#54611yescharacteristic
394C4×C53#55111yescharacteristic
395Dic53—81no—
396Dic53—81no—
397Dic53—81no—
398C2×#447—531no—
399C2×C4×D8—531no—
400#2422—531no—
401D4×C22⋊C4D5311yescharacteristic, complemented
402#2093—531no—
403#2075—531no—
404#2054—531no—
405#2033—531no—
406#1934—531no—
407#1923—531no—
408#1879—531no—
409#1879—531no—
410#1862—531no—
411#1802—531no—
412#1786—531no—
413C2×C53—42no—
414C2×C53—44no—
415C2×C53—82no—
416C2×C53#241811yescharacteristic
417C2×C53#310011yescharacteristic
418C2×C53#311811yescharacteristic
419C2×C53#326711yescharacteristic
420C2×C53D4×D811yescharacteristic
421C2×C53#329411yescharacteristic
422C2×C53#332211yescharacteristic
423D53—82no—
424C23×D4C2×D5311yescharacteristic
425C22×D8—531no—
426C22×D8—531no—
427C2×#123—1061no—
428C2×#121—531no—
429C2×C4×D4—531no—
430C2×C4×D4C2×D5311yescharacteristic
431C2×C4×D4C2×D5311yescharacteristic
432C22×C22⋊C4—21no—
433#447—1064no—
434C4×D8—1064no—
435C2×#107—531no—
436C2×#107—531no—
437C2×C4⋊C8—531no—
438C2×#102—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×#102—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—531no—
445C2×#102—531no—
446C2×C22⋊C8—531no—
447C2×C22⋊C8—531no—
448C2×C4×C8—531no—
449#397—1061no—
450#394—1061no—
451#390—531no—
452#390C2×D5311yescharacteristic
453#390C2×D5311yescharacteristic
454#389—531no—
455#386—21no—
456#386—21no—
457#385—1061no—
458#384—531no—
459#380—531no—
460#380C2×D5311yescharacteristic
461#379—21no—
462C4×C22⋊C4C2×D5311yescharacteristic
463#340—531no—
464#340—531no—
465#340—531no—
466#340—531no—
467#336—531no—
468#336—531no—
469C53#2489311yescharacteristic, complemented, Sylow
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—41no—
477C22×D4—41no—
478C22×D4—531no—
479C22×D4—1061no—
480C22×D4C22×D5311yescharacteristic
481C22×D4C22×D5311yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—1061no—
485C23×C4C22×D5311yescharacteristic
486C2×D8—534no—
487C2×D8—1062no—
488C2×D8—1062no—
489C2×D8—1062no—
490C2×D8—1062no—
491C2×D8—2121no—
492C22×C8—531no—
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—531no—
496#123—2124no—
497#121—1062no—
498#121—2121no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—41no—
502C4×D4—41no—
503C4×D4—1062no—
504C4×D4—2121no—
505C2×C4⋊C4—531no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—531no—
508C2×C4⋊C4—1061no—
509C2×C4⋊C4—1061no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—44no—
521C2×C22⋊C4—1061no—
522C2×C22⋊C4—1061no—
523C2×C22⋊C4—1061no—
524C2×C22⋊C4—1061no—
525C2×C22⋊C4—1061no—
526C2×C22⋊C4C22⋊D5311yescharacteristic
527C2×C22⋊C4C22⋊D5311yescharacteristic
528C2×C42C22×D5311yescharacteristic
529C2×C42C22×D5311yescharacteristic
530#107—1062no—
531#107—2121no—
532C4⋊C8—2121no—
533#102—1062no—
534#102—1062no—
535#102—1062no—
536#102—1062no—
537#102—1062no—
538#102—1062no—
539#102—2121no—
540#102—2121no—
541C22⋊C8—1062no—
542C22⋊C8—2121no—
543C4×C8—1062no—
544#95—21no—
545#95—1061no—
546#95—1061no—
547#95C22⋊D5311yescharacteristic
548#95C22⋊D5311yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—42no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—81no—
557C24—81no—
558C24—1061no—
559C24C2×C22⋊D5311yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—532no—
576C2×D4—1061no—
577C2×D4—1061no—
578C2×D4—1061no—
579C2×D4—1061no—
580C2×D4—1061no—
581C2×D4—4241no—
582C2×D4—2122no—
583C2×D4—2122no—
584C2×D4#1171994512yes—
585C2×D4#1171994512yes—
586C2×D4D4×D5312yes—
587C2×D4#1171994712yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—81no—
601C22×C4—81no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—4241no—
606C22×C4—2122no—
607C22×C4—2122no—
608C22×C4C2×C22⋊D5311yescharacteristic
609C22×C4C2×C22⋊D5311yescharacteristic
610C22×C4C2×C22⋊D5311yescharacteristic
611C22×C4C2×C22⋊D5311yescharacteristic
612C22×C4C2×C22⋊D5311yescharacteristic
613C22×C4C23×D5311yescharacteristic
614D8—1068no—
615D8—2124no—
616C2×C8—532no—
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—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—1061no—
633C4⋊C4—1061no—
634C4⋊C4—1061no—
635C4⋊C4—1061no—
636C4⋊C4—1061no—
637C4⋊C4—1061no—
638C4⋊C4—4241no—
639C4⋊C4—2122no—
640C4⋊C4—2122no—
641C22⋊C4—41no—
642C22⋊C4—42no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—81no—
648C22⋊C4—81no—
649C22⋊C4—2122no—
650C22⋊C4—2122no—
651C22⋊C4—2122no—
652C22⋊C4—2122no—
653C22⋊C4—2122no—
654C22⋊C4#1171992214yescomplemented
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—22no—
660C23—21no—
661C23—21no—
662C23—22no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—22no—
667C23—21no—
668C23—22no—
669C23—48no—
670C23—48no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23—84no—
685C23—84no—
686C23—1062no—
687C23—2121no—
688C23—2121no—
689C23—2121no—
690C23—2121no—
691C23—2121no—
692C23—2121no—
693C23C2×#1171992212yes—
694C23C22×C22⋊D5311yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—48no—
701D4—41no—
702D4—41no—
703D4—1062no—
704D4—1062no—
705D4—4244no—
706D4—2121no—
707D4—2121no—
708D4#1313319914yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—4244no—
735C2×C4—2121no—
736C2×C4—2121no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4C2×#1171992212yes—
745C2×C4C2×#1171992212yes—
746C2×C4C2×D4×D5311yescharacteristic
747C2×C4C2×#1171994711yescharacteristic
748C2×C4C2×#1171994511yescharacteristic
749C2×C4C2×#1171994511yescharacteristic
750C2×C4#1313326211yescharacteristic
751C2×C4#1313326211yescharacteristic
752C8—1062no—
753C8—2121no—
754C8—2121no—
755C8—2121no—
756C22—22no—
757C22—22no—
758C22—24no—
759C22—22no—
760C22—41no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—41no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—816no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—4241no—
779C22—4241no—
780C22—4241no—
781C22—4241no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22#1681113411yescharacteristic
786C22D4×C22⋊D5311yescharacteristic
787C22#1681126711yescharacteristic
788C22C22×#1171992211yescharacteristic
789C22#1681142111yescharacteristic
790C22#1681142611yescharacteristic
791C22#1681143411yescharacteristic
792C4—22no—
793C4—22no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—4241no—
800C4—4241no—
801C4—4241no—
802C4C2×#1313319911yescharacteristic
803C4#1681121111yescharacteristic
804C4#1681126311yescharacteristic
805C4#1681129911yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—4242no—
810C2#2027817711yescharacteristic
811C2#2028471511yescharacteristic
812C2#2028489911yescharacteristic
813C2#2028623611yescharacteristic
814C2D4×#1171992211yescharacteristic
815C2#2028652811yescharacteristic
816C2#2028691611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
FittingD4×C22⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC2×#16810757C2
hypercenterD4×C22⋊C4D53
hypocenterC53#24893
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719922C2semidirect
3. #20278229C2semidirect
4. #20276243C2semidirect
5. #20276141C2semidirect
6. #20276025C2semidirect
7. #20275897C2semidirect
8. #20275401C2semidirect
9. #20275323C2semidirect
10. #20275066C2semidirect
11. #20275063C2semidirect
12. #20274962C2semidirect
13. #20274715C2semidirect
14. #20274646C2semidirect
15. D4×C22⋊C4×C53C2semidirect
20. C2×C4×D212C22semidirect
23. C2×#13133150C22semidirect
24. C2×#13133150C22semidirect
25. C2×C4⋊#88322C22semidirect
32. C2×#13133137C22semidirect
33. C2×#13133137C22semidirect
36. C2×C4×#88322C22semidirect
39. #16810525C22semidirect
40. #16810521C22semidirect
42. #16810493C22semidirect
44. #16810385C22semidirect
45. #16810385C22semidirect
46. #16810385C22semidirect
47. #16810385C22semidirect
48. #16810378C22semidirect
49. #16810378C22semidirect
217. C22⋊C4×C53D8semidirect
294. D4×C53#123semidirect
401. D4×C22⋊C4D53semidirect
469. C53#24893semidirect
654. C22⋊C4#11719922semidirect
708. D4#13133199semidirect

Maximal subgroups

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

subgroupindex
C2×#168107572
C2×C4×#117199222
#202782292
#202762432
#202761412
#202760252
#202758972
#202754012
#202753232
#202750662
#202750632
#202749622
#202747152
#202746462
D4×C22⋊C4×C532
#2489353