Finite Group Databasebeta

← #27290319

Subgroups — #27290319

Order 13568.

1246 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810498C211yesmaximal, characteristic
2#20277068C211yesmaximal, characteristic
3C2×#16810389C211yesmaximal, characteristic
4C2×#16810389C211yesmaximal, characteristic
5#20272937C211yesmaximal, characteristic
6#20272937C211yesmaximal, characteristic
7C2×C53×#342C211yesmaximal, characteristic
8C24×Dic53C2211yescharacteristic
9C22×C4⋊Dic53—21no—
10C22×C22⋊Dic53C2211yescharacteristic
11C22×C22⋊Dic53C2211yescharacteristic
12C22×C22⋊Dic53C2211yescharacteristic
13#16810498—22no—
14#16810498C414yescomplemented
15C22⋊C4×Dic53—21no—
16C22⋊C4×Dic53—21no—
17C22⋊C4×Dic53—22no—
18C4×C22⋊Dic53—22no—
19C2×#13133124—21no—
20C2×#13133124—22no—
21C2×#13133124—22no—
22#16810389—22no—
23#16810389C414yescomplemented
24C22×C22⋊C4×C53C2211yescharacteristic
25C22×C22⋊C4×C53C2211yescharacteristic
26C22×C22⋊C4×C53C2211yescharacteristic
27C53×#342C414yescomplemented
28C23×Dic53—21no—
29C23×Dic53—21no—
30C23×Dic53—21no—
31C23×Dic53—21no—
32C23×Dic53—21no—
33C23×Dic53—21no—
34C23×Dic53—21no—
35C23×Dic53—44no—
36C23×Dic53C2×C412yes—
37C23×Dic53D411yescharacteristic
38C23×Dic53D411yescharacteristic
39C23×Dic53D412yes—
40C2×C4⋊Dic53—24no—
41C2×C4⋊Dic53—44no—
42C2×C22⋊Dic53—21no—
43C2×C22⋊Dic53—21no—
44C2×C22⋊Dic53—21no—
45C2×C22⋊Dic53—21no—
46C2×C22⋊Dic53—21no—
47C2×C22⋊Dic53—21no—
48C2×C22⋊Dic53—21no—
49C2×C22⋊Dic53—21no—
50C2×C22⋊Dic53—21no—
51C2×C22⋊Dic53—21no—
52C2×C22⋊Dic53—21no—
53C2×C22⋊Dic53—21no—
54C2×C22⋊Dic53—21no—
55C2×C22⋊Dic53C2×C412yes—
56C2×C22⋊Dic53C2×C412yes—
57C2×C22⋊Dic53C2×C412yes—
58C2×C22⋊Dic53D412yes—
59C2×C22⋊Dic53Q812yes—
60C2×C4×Dic53—22no—
61C2×C4×Dic53—22no—
62#13133124—22no—
63#13133124—22no—
64#13133124—24no—
65#13133124—44no—
66#13133124—44no—
67C25×C53C2311yescharacteristic
68C23×C4×C53—21no—
69C23×C4×C53—21no—
70C23×C4×C53D412yes—
71C2×C22⋊C4×C53—21no—
72C2×C22⋊C4×C53—21no—
73C2×C22⋊C4×C53—21no—
74C2×C22⋊C4×C53—21no—
75C2×C22⋊C4×C53—21no—
76C2×C22⋊C4×C53—21no—
77C2×C22⋊C4×C53—21no—
78C2×C22⋊C4×C53—21no—
79C2×C22⋊C4×C53—21no—
80C2×C22⋊C4×C53—21no—
81C2×C22⋊C4×C53—21no—
82C2×C22⋊C4×C53—21no—
83C2×C22⋊C4×C53C2×C412yes—
84C2×C22⋊C4×C53C2×C412yes—
85C2×C22⋊C4×C53C2×C412yes—
86C2×C22⋊C4×C53C2×C412yes—
87C2×C22⋊C4×C53C2×C412yes—
88C2×C22⋊C4×C53Q812yes—
89C24×C53—42no—
90C24×C53—42no—
91C24×C53C22×C411yescharacteristic
92C24×C53C22×C411yescharacteristic
93C24×C53C22×C411yescharacteristic
94C24×C53C2×D411yescharacteristic
95C24×C53C2×D411yescharacteristic
96C24×C53C2×D411yescharacteristic
97C24×C53C2×D411yescharacteristic
98C24×C53C2×Q811yescharacteristic
99C24×C53C2×Q811yescharacteristic
100C24×C53#4111yescharacteristic
101C24×C53#4111yescharacteristic
102C24×C53#4111yescharacteristic
103C24×C53#4111yescharacteristic
104C24×C53#4111yescharacteristic
105C24×C53#4111yescharacteristic
106C22×C4×C53—22no—
107C22×C4×C53—22no—
108C22×C4×C53—22no—
109C22×C4×C53—22no—
110C22×C4×C53—22no—
111C22×C4×C53—22no—
112C22×C4×C53—42no—
113C22×C4×C53—42no—
114C22×C4×C53—42no—
115C22×C4×C53—42no—
116C22×C4×C53—42no—
117C22×C4×C53—42no—
118C22×C4×C53—41no—
119C22×C4×C53—41no—
120C22×C4×C53C4⋊C414yescomplemented
121C22×Dic53—24no—
122C22×Dic53—24no—
123C22×Dic53—24no—
124C22×Dic53—22no—
125C22×Dic53—22no—
126C22×Dic53—22no—
127C22×Dic53—22no—
128C22×Dic53—21no—
129C22×Dic53—21no—
130C22×Dic53—22no—
131C22×Dic53—21no—
132C22×Dic53—21no—
133C22×Dic53—22no—
134C22×Dic53—44no—
135C22×Dic53—44no—
136C22×Dic53—44no—
137C22×Dic53—44no—
138C22×Dic53—42no—
139C22×Dic53—42no—
140C22×Dic53—42no—
141C22×Dic53—41no—
142C22×Dic53—41no—
143C22×Dic53—41no—
144C22×Dic53—41no—
145C22×Dic53—42no—
146C22×Dic53—42no—
147C22×Dic53—42no—
148C22×Dic53—42no—
149C22×Dic53—42no—
150C22×Dic53—42no—
151C22×Dic53—41no—
152C22×Dic53—41no—
153C22×Dic53C22⋊C412yes—
154C22×Dic53C22⋊C412yes—
155C22×Dic53C4⋊C414yescomplemented
156C22⋊C4×C53—22no—
157C22⋊C4×C53—22no—
158C22⋊C4×C53—22no—
159C22⋊C4×C53—22no—
160C22⋊C4×C53—22no—
161C22⋊C4×C53—22no—
162C22⋊C4×C53—22no—
163C22⋊C4×C53—22no—
164C22⋊C4×C53—22no—
165C22⋊C4×C53—41no—
166C22⋊C4×C53—41no—
167C22⋊C4×C53C4214yescomplemented
168C22⋊Dic53—22no—
169C22⋊Dic53—22no—
170C22⋊Dic53—22no—
171C22⋊Dic53—22no—
172C22⋊Dic53—22no—
173C22⋊Dic53—22no—
174C22⋊Dic53—22no—
175C22⋊Dic53—22no—
176C22⋊Dic53—22no—
177C22⋊Dic53—22no—
178C22⋊Dic53—41no—
179C22⋊Dic53—41no—
180C4⋊Dic53—48no—
181C4×Dic53—82no—
182C4×Dic53—82no—
183C23×C53—22no—
184C23×C53—22no—
185C23×C53—22no—
186C23×C53—22no—
187C23×C53—22no—
188C23×C53—22no—
189C23×C53—41no—
190C23×C53—41no—
191C23×C53—41no—
192C23×C53—41no—
193C23×C53—42no—
194C23×C53—41no—
195C23×C53—42no—
196C23×C53—41no—
197C23×C53—42no—
198C23×C53—42no—
199C23×C53—42no—
200C23×C53—41no—
201C23×C53—42no—
202C23×C53—42no—
203C23×C53—42no—
204C23×C53—41no—
205C23×C53C2×C4211yescharacteristic
206C23×C53C2×C22⋊C411yescharacteristic
207C23×C53C2×C4⋊C411yescharacteristic
208C23×C53C2×C4⋊C411yescharacteristic
209C23×C53#11711yescharacteristic
210C23×C53#11711yescharacteristic
211C23×C53#11711yescharacteristic
212C23×C53C4×D411yescharacteristic
213C23×C53C4×D411yescharacteristic
214C23×C53C4×D411yescharacteristic
215C23×C53C4×D411yescharacteristic
216C23×C53C4×D411yescharacteristic
217C23×C53C4×D411yescharacteristic
218C23×C53C4×D411yescharacteristic
219C23×C53C4×D411yescharacteristic
220C23×C53C4×Q811yescharacteristic
221C23×C53C4×Q811yescharacteristic
222C23×C53C4×Q811yescharacteristic
223C23×C53C4×Q811yescharacteristic
224C23×C53#12011yescharacteristic
225C23×C53#12111yescharacteristic
226C23×C53#12111yescharacteristic
227C23×C53C22⋊Q811yescharacteristic
228C23×C53C22⋊Q811yescharacteristic
229C23×C53C22⋊Q811yescharacteristic
230C23×C53C22⋊Q811yescharacteristic
231C23×C53#12311yescharacteristic
232C23×C53#12311yescharacteristic
233C23×C53#12311yescharacteristic
234C23×C53#12411yescharacteristic
235C23×C53#12511yescharacteristic
236C23×C53#12511yescharacteristic
237C23×C53#12611yescharacteristic
238C23×C53#12611yescharacteristic
239C23×C53C4⋊Q811yescharacteristic
240C2×C4×C53—24no—
241C2×C4×C53—24no—
242C2×C4×C53—44no—
243C2×C4×C53—44no—
244C2×C4×C53—42no—
245C2×C4×C53—42no—
246C2×C4×C53—42no—
247C2×C4×C53—42no—
248C2×C4×C53—44no—
249C2×C4×C53—44no—
250C2×C4×C53—42no—
251C2×C4×C53—82no—
252C2×C4×C53—82no—
253C2×C4×C53—81no—
254C2×C4×C53—81no—
255C2×Dic53—24no—
256C2×Dic53—24no—
257C2×Dic53—24no—
258C2×Dic53—24no—
259C2×Dic53—22no—
260C2×Dic53—22no—
261C2×Dic53—42no—
262C2×Dic53—42no—
263C2×Dic53—42no—
264C2×Dic53—44no—
265C2×Dic53—44no—
266C2×Dic53—44no—
267C2×Dic53—42no—
268C2×Dic53—44no—
269C2×Dic53—42no—
270C2×Dic53—42no—
271C2×Dic53—42no—
272C2×Dic53—42no—
273C2×Dic53—42no—
274C2×Dic53—42no—
275C2×Dic53—44no—
276C2×Dic53—44no—
277C2×Dic53—42no—
278C2×Dic53—82no—
279C2×Dic53—81no—
280C2×Dic53—81no—
281C2×Dic53—82no—
282C2×Dic53—81no—
283C2×Dic53—81no—
284#10918—531nomaximal, Sylow
285C22×C53—22no—
286C22×C53—22no—
287C22×C53—22no—
288C22×C53—22no—
289C22×C53—22no—
290C22×C53—22no—
291C22×C53—22no—
292C22×C53—22no—
293C22×C53—22no—
294C22×C53—22no—
295C22×C53—22no—
296C22×C53—22no—
297C22×C53—21no—
298C22×C53—21no—
299C22×C53—21no—
300C22×C53—21no—
301C22×C53—21no—
302C22×C53—21no—
303C22×C53—21no—
304C22×C53—21no—
305C22×C53—21no—
306C22×C53—21no—
307C22×C53—21no—
308C22×C53—21no—
309C22×C53—41no—
310C22×C53—41no—
311C22×C53—41no—
312C22×C53—41no—
313C22×C53—41no—
314C22×C53—41no—
315C22×C53—41no—
316C22×C53—41no—
317C22×C53—41no—
318C22×C53—41no—
319C22×C53—41no—
320C22×C53—41no—
321C22×C53—41no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—41no—
325C22×C53C4×C22⋊C411yescharacteristic
326C22×C53C4×C4⋊C411yescharacteristic
327C22×C53C4×C4⋊C411yescharacteristic
328C22×C53#38511yescharacteristic
329C22×C53#38511yescharacteristic
330C22×C53#38611yescharacteristic
331C22×C53#38711yescharacteristic
332C22×C53#38711yescharacteristic
333C22×C53#38711yescharacteristic
334C22×C53#38711yescharacteristic
335C22×C53#38811yescharacteristic
336C22×C53#38811yescharacteristic
337C22×C53#38911yescharacteristic
338C22×C53#38911yescharacteristic
339C22×C53#39111yescharacteristic
340C22×C53B(4,𝔽2)12yes—
341C22×C53#45812yes—
342C4×C53—44no—
343C4×C53—44no—
344C4×C53—82no—
345Dic53—44no—
346Dic53—44no—
347Dic53—42no—
348Dic53—42no—
349Dic53—82no—
350C2×#385—531no—
351#2273—531no—
352C2×#342—531no—
353C2×#342—531no—
354C2×#342D5311yescharacteristic
355C22⋊#95—531no—
356C22⋊#95—531no—
357C2×C53—21no—
358C2×C53—21no—
359C2×C53—21no—
360C2×C53—21no—
361C2×C53—21no—
362C2×C53—21no—
363C2×C53—21no—
364C2×C53—21no—
365C2×C53—21no—
366C2×C53—21no—
367C2×C53—21no—
368C2×C53—21no—
369C2×C53#143611yescharacteristic
370C2×C53#186712yes—
371C2×C53#186712yes—
372C2×C53#188911yescharacteristic
373C2×C53#189011yescharacteristic
374C24×C4—531no—
375C22×C4⋊C4—1061no—
376C22×C22⋊C4—531no—
377C22×C22⋊C4—531no—
378C22×C22⋊C4—531no—
379C22×C22⋊C4C2×D5311yescharacteristic
380C22×C22⋊C4C2×D5311yescharacteristic
381C22×C22⋊C4C2×D5311yescharacteristic
382#385—534no—
383#385—1062no—
384C4×C22⋊C4—1061no—
385C4×C22⋊C4—1061no—
386C4×C22⋊C4—1062no—
387C4×C22⋊C4—1062no—
388C2×#95—1061no—
389C2×#95—1062no—
390C2×#95—1062no—
391#342—534no—
392#342—1062no—
393#342Dic5314yescomplemented
394C53#1091811yescharacteristic, complemented, Sylow
395C25C22×D5311yescharacteristic
396C23×C4—21no—
397C23×C4—21no—
398C23×C4—531no—
399C23×C4—531no—
400C23×C4—532no—
401C23×C4—532no—
402C23×C4—1061no—
403C23×C4—1061no—
404C23×C4—1061no—
405C23×C4—1061no—
406C23×C4—1061no—
407C23×C4—1061no—
408C23×C4—1061no—
409C23×C4—2124no—
410C23×C4D21212yes—
411C2×C4⋊C4—1064no—
412C2×C4⋊C4—2124no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—532no—
426C2×C22⋊C4—532no—
427C2×C22⋊C4—532no—
428C2×C22⋊C4—532no—
429C2×C22⋊C4—532no—
430C2×C22⋊C4—1061no—
431C2×C22⋊C4—1061no—
432C2×C22⋊C4—1061no—
433C2×C22⋊C4—1061no—
434C2×C22⋊C4—1061no—
435C2×C22⋊C4—1061no—
436C2×C22⋊C4—1061no—
437C2×C22⋊C4—1061no—
438C2×C22⋊C4—1061no—
439C2×C22⋊C4—1061no—
440C2×C22⋊C4—1061no—
441C2×C22⋊C4—1061no—
442C2×C22⋊C4—1061no—
443C2×C22⋊C4Dic10612yes—
444C2×C22⋊C4C4×D5312yes—
445C2×C22⋊C4C4×D5312yes—
446C2×C22⋊C4C2×Dic5312yes—
447C2×C22⋊C4C2×Dic5312yes—
448C2×C22⋊C4C2×Dic5312yes—
449C2×C42—1062no—
450C2×C42—1062no—
451#95—1064no—
452#95—1062no—
453#95—1062no—
454#95—2124no—
455#95—2124no—
456C24—42no—
457C24—42no—
458C24C2×Dic10611yescharacteristic
459C24C2×C4×D5311yescharacteristic
460C24C2×C4×D5311yescharacteristic
461C24C2×D21211yescharacteristic
462C24#1171994511yescharacteristic
463C24#1171994511yescharacteristic
464C24D4×D5311yescharacteristic
465C24D4×D5311yescharacteristic
466C24D4×D5311yescharacteristic
467C24#1171994711yescharacteristic
468C24#1171994711yescharacteristic
469C24#1171994711yescharacteristic
470C24Q8×D5311yescharacteristic
471C24#1171994911yescharacteristic
472C24C22×Dic5311yescharacteristic
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—532no—
488C22×C4—532no—
489C22×C4—534no—
490C22×C4—1062no—
491C22×C4—1061no—
492C22×C4—1061no—
493C22×C4—1064no—
494C22×C4—1064no—
495C22×C4—1064no—
496C22×C4—1062no—
497C22×C4—1062no—
498C22×C4—1062no—
499C22×C4—1062no—
500C22×C4—1061no—
501C22×C4—1061no—
502C22×C4—1062no—
503C22×C4—2124no—
504C22×C4—2124no—
505C22×C4—2124no—
506C22×C4—2124no—
507C22×C4—2122no—
508C22×C4—2122no—
509C22×C4—2121no—
510C22×C4—2121no—
511C22×C4—2122no—
512C22×C4—2122no—
513C22×C4—2122no—
514C22×C4—2122no—
515C22×C4—2122no—
516C22×C4—2122no—
517C22×C4—2122no—
518C22×C4—2121no—
519C22×C4—2121no—
520C22×C4—2121no—
521C22×C4—2121no—
522C22×C4C4⋊Dic5314yescomplemented
523C4⋊C4—2128no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—41no—
534C22⋊C4—41no—
535C22⋊C4—1062no—
536C22⋊C4—1062no—
537C22⋊C4—1062no—
538C22⋊C4—1062no—
539C22⋊C4—1062no—
540C22⋊C4—1062no—
541C22⋊C4—1062no—
542C22⋊C4—1062no—
543C22⋊C4—1062no—
544C22⋊C4—1062no—
545C22⋊C4—2121no—
546C22⋊C4—2121no—
547C22⋊C4C4×Dic5314yescomplemented
548C42—4242no—
549C42—4242no—
550C23—22no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—42no—
561C23—42no—
562C23—41no—
563C23—42no—
564C23—41no—
565C23—41no—
566C23—42no—
567C23—42no—
568C23—42no—
569C23—42no—
570C23—41no—
571C23—42no—
572C23C2×C4×Dic5311yescharacteristic
573C23C22⋊C4×D5311yescharacteristic
574C23C4⋊C4×D5311yescharacteristic
575C23C2×C4⋊Dic5311yescharacteristic
576C23#1313317311yescharacteristic
577C23#1313317511yescharacteristic
578C23#1313317611yescharacteristic
579C23#1313317711yescharacteristic
580C23#1313317711yescharacteristic
581C23#1313317911yescharacteristic
582C23D4×Dic5311yescharacteristic
583C23D4×Dic5311yescharacteristic
584C23D4×Dic5311yescharacteristic
585C23C4×D21211yescharacteristic
586C23C4×D21211yescharacteristic
587C23#1313318211yescharacteristic
588C23C4×Dic10611yescharacteristic
589C23C4×Dic10611yescharacteristic
590C23Q8×Dic5311yescharacteristic
591C23#1313318711yescharacteristic
592C23#1313319011yescharacteristic
593C23#1313319211yescharacteristic
594C23#1313319411yescharacteristic
595C23#1313319411yescharacteristic
596C23#1313319511yescharacteristic
597C23#1313319711yescharacteristic
598C23#1313319911yescharacteristic
599C23#1313320111yescharacteristic
600C23#1313320211yescharacteristic
601C23#1313320311yescharacteristic
602C23#1313320711yescharacteristic
603C23#1313320811yescharacteristic
604C23#1313321011yescharacteristic
605C23#1313321211yescharacteristic
606C23#1313321611yescharacteristic
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—42no—
610C2×C4—44no—
611C2×C4—44no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—44no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—1064no—
623C2×C4—1064no—
624C2×C4—1064no—
625C2×C4—1064no—
626C2×C4—1062no—
627C2×C4—1062no—
628C2×C4—4242no—
629C2×C4—4241no—
630C2×C4—4241no—
631C2×C4—4242no—
632C2×C4—4241no—
633C2×C4—4241no—
634C2×C4—2124no—
635C2×C4—2122no—
636C2×C4—2122no—
637C2×C4—2124no—
638C2×C4—2122no—
639C2×C4—2122no—
640C2×C4—2124no—
641C2×C4—2124no—
642C2×C4—2122no—
643C2×C4—2122no—
644C2×C4—2122no—
645C2×C4—2124no—
646C2×C4—2122no—
647C2×C4—2122no—
648C2×C4—2122no—
649C2×C4—2124no—
650C2×C4—2122no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—22no—
657C22—22no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—21no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C22⋊C4×Dic5311yescharacteristic
692C22C4×C4⋊Dic5311yescharacteristic
693C22C4⋊C4×Dic5311yescharacteristic
694C22#1681049711yescharacteristic
695C22#1681049811yescharacteristic
696C22#1681050111yescharacteristic
697C22#1681050611yescharacteristic
698C22#1681050811yescharacteristic
699C22#1681050911yescharacteristic
700C22#1681051011yescharacteristic
701C22#1681051511yescharacteristic
702C22#1681051611yescharacteristic
703C22#1681052011yescharacteristic
704C22#1681052211yescharacteristic
705C22#1681052711yescharacteristic
706C22#1681081112yes—
707C22#1681081412yes—
708C4—44no—
709C4—44no—
710C4—82no—
711C4—4242no—
712C4—2124no—
713C4—2124no—
714C4—2122no—
715C4—2122no—
716C2—21no—
717C2—21no—
718C2—21no—
719C2—21no—
720C2—21no—
721C2—21no—
722C2—21no—
723C2—21no—
724C2—21no—
725C2—21no—
726C2—21no—
727C2—21no—
728C2#2027294911yescharacteristic
729C2#2027499712yes—
730C2#2027499812yes—
731C2#2027512211yescharacteristic
732C2#2027512711yescharacteristic
subgroupG/H
centerC23#13133187
commutatorC23×C53C2×C42
FrattiniC25C22×D53
FittingC2×C53×#342C2
socleC23×C53#120
prime radical, cosocleC25×C53C23
hypercenterC2×#342D53
hypocenterC53#10918
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
14. #16810498C4semidirect
23. #16810389C4semidirect
27. C53×#342C4semidirect
120. C22×C4×C53C4⋊C4semidirect
155. C22×Dic53C4⋊C4semidirect
167. C22⋊C4×C53C42semidirect
393. #342Dic53semidirect
394. C53#10918semidirect
522. C22×C4C4⋊Dic53semidirect
547. C22⋊C4C4×Dic53semidirect

Maximal subgroups

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

subgroupindex
C2×#168104982
#202770682
C2×#168103892
#202729372
C2×C53×#3422
#1091853