Finite Group Databasebeta

← #15790040

Subgroups — #15790040

Order 3328.

1290 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718336C211yesmaximal, characteristic
2#13113098C211yesmaximal, characteristic, complemented
3#13113097C211yesmaximal, characteristic, complemented
4#13113094C211yesmaximal, characteristic, complemented
5#13113087C211yesmaximal, characteristic, complemented
6#13113084C211yesmaximal, characteristic
7#13113080C211yesmaximal, characteristic
8#13113080C211yesmaximal, characteristic
9#13113074C211yesmaximal, characteristic
10#13113074C211yesmaximal, characteristic
11#13113074C211yesmaximal, characteristic
12#13113069C211yesmaximal, characteristic, complemented
13#13113069C211yesmaximal, characteristic, complemented
14#13113069C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C22×C42×C13C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51#11718336C418yescomplemented
52C24×D13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13—22no—
70C2×C42×C13—41no—
71C2×C42×C13—41no—
72C2×C42×C13—41no—
73C2×C42×C13—41no—
74C2×C42×C13—41no—
75C2×C42×C13—41no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—41no—
83C2×#6103—41no—
84C2×#6103—41no—
85C2×#6103—41no—
86C2×#6103—41no—
87C2×#6103—41no—
88C2×#6103—41no—
89C2×#6103—41no—
90C2×#6103—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103C2×C414yes—
95C2×#6103C2×C414yes—
96C2×#6103C2×C414yes—
97C2×#6101—22no—
98C2×#6101—22no—
99C2×#6101—41no—
100C2×#6101—41no—
101C2×#6101—41no—
102C2×#6101—41no—
103C2×#6101—41no—
104C2×#6101—41no—
105C2×#6101C2×C414yes—
106C13×#95—22no—
107C13×#95—22no—
108C13×#95—22no—
109C13×#95C2×C414yes—
110#88071—22no—
111#88071—22no—
112#88071—22no—
113#88071—22no—
114#88071—41no—
115#88071—41no—
116#88071—41no—
117#88071—41no—
118#88071—41no—
119#88071—41no—
120#88071—41no—
121#88071—41no—
122#88071—41no—
123#88071—41no—
124#88071—41no—
125#88071—41no—
126#88071C2×C414yes—
127#88071C2×C414yes—
128#14332—131nomaximal, Sylow
129C24×C13C2411yescharacteristic
130C23×D13—21no—
131C23×D13—21no—
132C23×D13—21no—
133C23×D13—21no—
134C23×D13—21no—
135C23×D13—21no—
136C23×D13—21no—
137C23×D13—21no—
138C23×D13—21no—
139C23×D13—21no—
140C23×D13—21no—
141C23×D13—21no—
142C23×D13—21no—
143C23×D13—21no—
144C23×D13C22×C412yes—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13C22×C412yes—
186C22×C4×C13C22×C412yes—
187C22×C4×C13C22×C412yes—
188C22×C4×C13#4112yes—
189C22×C4×C13#4112yes—
190C22×C4×C13#4112yes—
191C22×C4×C13#4112yes—
192C22×C4×C13#4112yes—
193C22×C4×C13#4112yes—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
240C22×Dic13C22×C412yes—
241C22×Dic13C22×C412yes—
242C22×Dic13C22×C412yes—
243C42×C13—44no—
244C42×C13—44no—
245C42×C13—44no—
246#6103—44no—
247#6103—44no—
248#6103—44no—
249#6103—44no—
250#6103—44no—
251#6103—44no—
252#6103—44no—
253#6101—44no—
254#6101—44no—
255#6101—44no—
256C2×#397—131no—
257#1443—131no—
258#1443—131no—
259#1442—131no—
260#1441—131no—
261#1440—131no—
262#1439—131no—
263#1439—131no—
264#1437—131no—
265#1437—131no—
266#1437—131no—
267#1436—131no—
268#1436—131no—
269#1436—131no—
270C4×#95D1311yescharacteristic, complemented
271C23×C13C23×C411yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C23×C13C2×#4111yescharacteristic
275C23×C13C2×#4111yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13C2×#4111yescharacteristic
278C23×C13H(5,𝔽2)11yescharacteristic
279C23×C13H(5,𝔽2)11yescharacteristic
280C23×C13H(5,𝔽2)11yescharacteristic
281C23×C13H(5,𝔽2)11yescharacteristic
282C23×C13H(5,𝔽2)11yescharacteristic
283C23×C13H(5,𝔽2)11yescharacteristic
284C23×C132−1+411yescharacteristic
285C23×C132−1+411yescharacteristic
286C22×D13—22no—
287C22×D13—22no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—22no—
291C22×D13—22no—
292C22×D13—22no—
293C22×D13—41no—
294C22×D13—41no—
295C22×D13—41no—
296C22×D13—41no—
297C22×D13—41no—
298C22×D13—41no—
299C22×D13—41no—
300C22×D13—41no—
301C22×D13—41no—
302C22×D13—41no—
303C22×D13—41no—
304C22×D13—41no—
305C22×D13—41no—
306C22×D13—41no—
307C22×D13—41no—
308C22×D13—41no—
309C22×D13—41no—
310C22×D13—41no—
311C22×D13—41no—
312C22×D13—41no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
316C22×D13—41no—
317C22×D13—41no—
318C22×D13—41no—
319C22×D13—41no—
320C22×D13—41no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—41no—
346C2×C4×C13—41no—
347C2×C4×C13—41no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13#12614yes—
370C2×Dic13—22no—
371C2×Dic13—22no—
372C2×Dic13—22no—
373C2×Dic13—22no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—22no—
377C2×Dic13—22no—
378C2×Dic13—22no—
379C2×Dic13—41no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—41no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387C2×Dic13—41no—
388C2×Dic13—41no—
389C2×Dic13—41no—
390C2×Dic13—41no—
391C2×Dic13—41no—
392C2×Dic13—41no—
393C2×Dic13—41no—
394C2×Dic13—41no—
395C2×Dic13—41no—
396C2×Dic13—41no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—41no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—41no—
403C2×Dic13—41no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C22×C4⋊C4—131no—
420C22×C4⋊C4—131no—
421C22×C4⋊C4—131no—
422C22×C22⋊C4—131no—
423C22×C22⋊C4—131no—
424C22×C22⋊C4—131no—
425C22×C22⋊C4—131no—
426C22×C22⋊C4—131no—
427C22×C22⋊C4—131no—
428C22×C22⋊C4—131no—
429C22×C42C2×D1311yescharacteristic
430C22×C42C2×D1311yescharacteristic
431C22×C42C2×D1311yescharacteristic
432#397—138no—
433C2×#95—131no—
434C2×#95—131no—
435C2×#95—131no—
436C2×#95—131no—
437C2×#95—131no—
438C2×#95—131no—
439C2×#95—131no—
440C2×#95—131no—
441C2×#95—131no—
442C2×#95—131no—
443C2×#95—131no—
444C2×#95—131no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95C2×D1311yescharacteristic
452C2×#95C2×D1311yescharacteristic
453C2×#95C2×D1311yescharacteristic
454C2×#95C2×D1311yescharacteristic
455C22×C13C4×#4111yescharacteristic
456C22×C13C4×#4111yescharacteristic
457C22×C13C4×#4111yescharacteristic
458C22×C13#51811yescharacteristic
459C22×C13#51811yescharacteristic
460C22×C13#52011yescharacteristic
461C22×C13#52011yescharacteristic
462C22×C13C2×#12611yescharacteristic
463C22×C13#52911yescharacteristic
464C22×C13#52911yescharacteristic
465C22×C13#52911yescharacteristic
466C22×C13#53811yescharacteristic
467C22×C13#53811yescharacteristic
468C22×C13#53811yescharacteristic
469C22×C13#53811yescharacteristic
470C22×C13#53811yescharacteristic
471C22×C13#53811yescharacteristic
472C22×C13#53811yescharacteristic
473C22×C13#53811yescharacteristic
474C22×C13#53911yescharacteristic
475C22×C13#53911yescharacteristic
476C22×C13#53911yescharacteristic
477C22×C13#53911yescharacteristic
478C22×C13#54011yescharacteristic
479C22×C13#54011yescharacteristic
480C22×C13#54011yescharacteristic
481C22×C13#54011yescharacteristic
482C22×C13#54011yescharacteristic
483C22×C13#54111yescharacteristic
484C22×C13#54211yescharacteristic
485C22×C13#54211yescharacteristic
486C22×C13#54211yescharacteristic
487C22×C13#54211yescharacteristic
488C22×C13#54211yescharacteristic
489C22×C13#54211yescharacteristic
490C2×D13—42no—
491C2×D13—42no—
492C2×D13—42no—
493C2×D13—42no—
494C2×D13—42no—
495C2×D13—42no—
496C2×D13—42no—
497C2×D13—81no—
498C2×D13—81no—
499C2×D13—81no—
500C2×D13—81no—
501C2×D13—81no—
502C2×D13—81no—
503C2×D13—81no—
504C2×D13—81no—
505C4×C13—24no—
506C4×C13—42no—
507C4×C13—42no—
508C4×C13—42no—
509C4×C13—42no—
510C4×C13—42no—
511C4×C13—42no—
512Dic13—42no—
513Dic13—42no—
514Dic13—42no—
515Dic13—81no—
516Dic13—81no—
517Dic13—81no—
518Dic13—81no—
519C25—131no—
520C23×C4—131no—
521C23×C4—131no—
522C23×C4—131no—
523C23×C4—131no—
524C23×C4—131no—
525C23×C4—131no—
526C23×C4—131no—
527C23×C4C22×D1311yescharacteristic
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C23×C4C22×D1311yescharacteristic
531C23×C4C22×D1311yescharacteristic
532C23×C4C22×D1311yescharacteristic
533C23×C4C22×D1311yescharacteristic
534C2×C4⋊C4—134no—
535C2×C4⋊C4—262no—
536C2×C4⋊C4—262no—
537C2×C4⋊C4—521no—
538C2×C4⋊C4—521no—
539C2×C4⋊C4—521no—
540C2×C4⋊C4—521no—
541C2×C4⋊C4—521no—
542C2×C4⋊C4—521no—
543C2×C22⋊C4—134no—
544C2×C22⋊C4—134no—
545C2×C22⋊C4—134no—
546C2×C22⋊C4—262no—
547C2×C22⋊C4—262no—
548C2×C22⋊C4—262no—
549C2×C22⋊C4—262no—
550C2×C22⋊C4—262no—
551C2×C22⋊C4—262no—
552C2×C22⋊C4—521no—
553C2×C22⋊C4—521no—
554C2×C22⋊C4—521no—
555C2×C22⋊C4—521no—
556C2×C22⋊C4—521no—
557C2×C22⋊C4—521no—
558C2×C22⋊C4—521no—
559C2×C22⋊C4—521no—
560C2×C22⋊C4—521no—
561C2×C22⋊C4—521no—
562C2×C22⋊C4—521no—
563C2×C22⋊C4—521no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—41no—
568C2×C42—41no—
569C2×C42—41no—
570C2×C42—41no—
571C2×C42—41no—
572C2×C42—41no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—134no—
577#95—134no—
578#95—262no—
579#95—262no—
580#95—262no—
581#95—262no—
582#95—521no—
583#95—521no—
584#95—521no—
585#95—521no—
586#95—521no—
587#95—521no—
588#95—521no—
589#95—521no—
590#95—521no—
591#95—521no—
592#95—521no—
593#95—521no—
594#95C4×D1314yes—
595C2×C13C4×#12611yescharacteristic
596C2×C13#233311yescharacteristic
597C2×C13#233411yescharacteristic
598C2×C13#233511yescharacteristic
599C2×C13#233511yescharacteristic
600C2×C13#233511yescharacteristic
601C2×C13#233711yescharacteristic
602C2×C13#264311yescharacteristic
603C2×C13#264411yescharacteristic
604C2×C13#264811yescharacteristic
605C2×C13#264811yescharacteristic
606C2×C13#265011yescharacteristic
607C2×C13#265111yescharacteristic
608C2×C13#265311yescharacteristic
609C2×C13#265411yescharacteristic
610D13—82no—
611C24—132no—
612C24—261no—
613C24—261no—
614C24—261no—
615C24—261no—
616C24—261no—
617C24—261no—
618C24—261no—
619C24—261no—
620C24—261no—
621C24—261no—
622C24—261no—
623C24—261no—
624C24—261no—
625C24—261no—
626C24C23×D1311yescharacteristic
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—132no—
668C22×C4—132no—
669C22×C4—132no—
670C22×C4—261no—
671C22×C4—261no—
672C22×C4—261no—
673C22×C4—261no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—261no—
677C22×C4—261no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—261no—
681C22×C4—261no—
682C22×C4—261no—
683C22×C4—261no—
684C22×C4—261no—
685C22×C4—261no—
686C22×C4—261no—
687C22×C4—261no—
688C22×C4—261no—
689C22×C4—261no—
690C22×C4—261no—
691C22×C4—261no—
692C22×C4—261no—
693C22×C4—261no—
694C22×C4—261no—
695C22×C4—261no—
696C22×C4—261no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—261no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—261no—
710C22×C4—261no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4C2×C4×D1312yes—
717C22×C4C2×C4×D1312yes—
718C22×C4C2×C4×D1312yes—
719C22×C4#612712yes—
720C22×C4#612712yes—
721C22×C4#612712yes—
722C22×C4#612712yes—
723C22×C4#612712yes—
724C22×C4#612712yes—
725C4⋊C4—524no—
726C4⋊C4—524no—
727C4⋊C4—524no—
728C22⋊C4—524no—
729C22⋊C4—524no—
730C22⋊C4—524no—
731C22⋊C4—524no—
732C22⋊C4—524no—
733C22⋊C4—524no—
734C22⋊C4—524no—
735C42—44no—
736C42—44no—
737C42—44no—
738C13#1433211yescharacteristic, complemented, Sylow
739C23—262no—
740C23—262no—
741C23—262no—
742C23—262no—
743C23—262no—
744C23—262no—
745C23—262no—
746C23—521no—
747C23—521no—
748C23—521no—
749C23—521no—
750C23—521no—
751C23—521no—
752C23—521no—
753C23—521no—
754C23—521no—
755C23—521no—
756C23—521no—
757C23—521no—
758C23—521no—
759C23—521no—
760C23—521no—
761C23—521no—
762C23—521no—
763C23—521no—
764C23—521no—
765C23—521no—
766C23—521no—
767C23—521no—
768C23—521no—
769C23—521no—
770C23—521no—
771C23—521no—
772C23—521no—
773C23—521no—
774C23C22×C4×D1311yescharacteristic
775C23C2×#612711yescharacteristic
776C23C2×#612711yescharacteristic
777C23C2×#612711yescharacteristic
778C23C2×#612711yescharacteristic
779C23C2×#612711yescharacteristic
780C23C2×#612711yescharacteristic
781C23#8825111yescharacteristic
782C23#8825111yescharacteristic
783C23#8825111yescharacteristic
784C23#8825411yescharacteristic
785C23#8825611yescharacteristic
786C23#8825611yescharacteristic
787C23#8825611yescharacteristic
788C23#8825711yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—262no—
838C2×C4—262no—
839C2×C4—262no—
840C2×C4—262no—
841C2×C4—262no—
842C2×C4—262no—
843C2×C4—262no—
844C2×C4—262no—
845C2×C4—262no—
846C2×C4—521no—
847C2×C4—521no—
848C2×C4—521no—
849C2×C4—521no—
850C2×C4—521no—
851C2×C4—521no—
852C2×C4—521no—
853C2×C4—521no—
854C2×C4—521no—
855C2×C4—521no—
856C2×C4—521no—
857C2×C4—521no—
858C2×C4—521no—
859C2×C4—521no—
860C2×C4—521no—
861C2×C4—521no—
862C2×C4—521no—
863C2×C4—521no—
864C2×C4—521no—
865C2×C4—521no—
866C2×C4—521no—
867C2×C4—521no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—521no—
872C2×C4—521no—
873C2×C4—521no—
874C2×C4—521no—
875C2×C4—521no—
876C2×C4—521no—
877C2×C4—521no—
878C2×C4—521no—
879C2×C4—521no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4#8813014yes—
887C22—522no—
888C22—522no—
889C22—522no—
890C22—522no—
891C22—522no—
892C22—522no—
893C22—522no—
894C22—1041no—
895C22—1041no—
896C22—1041no—
897C22—1041no—
898C22—1041no—
899C22—1041no—
900C22—1041no—
901C22—1041no—
902C22C4×#612711yescharacteristic
903C22C4×#612711yescharacteristic
904C22C4×#612711yescharacteristic
905C22C2×#8813011yescharacteristic
906C22#1171918411yescharacteristic
907C22#1171918411yescharacteristic
908C22#1171918411yescharacteristic
909C22#1171919911yescharacteristic
910C22#1171919911yescharacteristic
911C22#1171919911yescharacteristic
912C22#1171922011yescharacteristic
913C22#1171922011yescharacteristic
914C22#1171922011yescharacteristic
915C22#1171923911yescharacteristic
916C22#1171923911yescharacteristic
917C22#1171923911yescharacteristic
918C22#1171924011yescharacteristic
919C22#1171924011yescharacteristic
920C22#1171924011yescharacteristic
921C22#1171925011yescharacteristic
922C22#1171925011yescharacteristic
923C22#1171925111yescharacteristic
924C22#1171926511yescharacteristic
925C22#1171926511yescharacteristic
926C22#1171926511yescharacteristic
927C22#1171926511yescharacteristic
928C22#1171926511yescharacteristic
929C22#1171926611yescharacteristic
930C22#1171926711yescharacteristic
931C22#1171926711yescharacteristic
932C22#1171926911yescharacteristic
933C22#1171927911yescharacteristic
934C22#1171928711yescharacteristic
935C22#1171928711yescharacteristic
936C22#1171928811yescharacteristic
937C4—24no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—522no—
945C4—522no—
946C4—522no—
947C4—1041no—
948C4—1041no—
949C4—1041no—
950C4—1041no—
951C2—1042no—
952C2C4×#8813011yescharacteristic
953C2#1311759611yescharacteristic
954C2#1311760511yescharacteristic
955C2#1311762011yescharacteristic
956C2#1311762011yescharacteristic
957C2#1311762811yescharacteristic
958C2#1311764411yescharacteristic
959C2#1312078911yescharacteristic
960C2#1312079611yescharacteristic
961C2#1312081811yescharacteristic
962C2#1312081811yescharacteristic
963C2#1312084811yescharacteristic
964C2#1312086311yescharacteristic
965C2#1312089311yescharacteristic
966C2#1312090811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC4×C13×#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4×#95D13
hypocenterC13#14332
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #13113098C2semidirect
3. #13113097C2semidirect
4. #13113094C2semidirect
5. #13113087C2semidirect
12. #13113069C2semidirect
13. #13113069C2semidirect
14. #13113069C2semidirect
15. C4×C13×#95C2semidirect
51. #11718336C4semidirect
270. C4×#95D13semidirect
738. C13#14332semidirect

Maximal subgroups

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

subgroupindex
C2×#117183362
#131130982
#131130972
#131130942
#131130872
#131130842
#131130802
#131130742
#131130692
C4×C13×#952
#1433213