Finite Group Databasebeta

← #15791237

Subgroups — #15791237

Order 3328.

1266 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718307C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic
3C2×#11718639C211yesmaximal, characteristic
4#13113106C211yesmaximal, characteristic
5#13113102C211yesmaximal, characteristic
6#13113098C211yesmaximal, characteristic
7#13113097C211yesmaximal, characteristic
8#13113091C211yesmaximal, characteristic
9#13113068C211yesmaximal, characteristic
10#13113067C211yesmaximal, characteristic
11#13113062C211yesmaximal, characteristic
12#13113061C211yesmaximal, characteristic
13#13113060C211yesmaximal, characteristic
14#13113060C211yesmaximal, characteristic
15C13×#1442C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×#6101C2211yescharacteristic
19C22×#6101C2211yescharacteristic
20C22×C4×Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23C2×C13×#95C2211yescharacteristic
24C2×C13×#95C2211yescharacteristic
25C2×C13×#95C2211yescharacteristic
26C2×C13×#95C2211yescharacteristic
27C2×C13×#95C2211yescharacteristic
28C2×C13×#95C2211yescharacteristic
29C2×#88071C2211yescharacteristic
30C2×#88071C2211yescharacteristic
31C2×#88071C2211yescharacteristic
32C2×#88071C2211yescharacteristic
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#11718639—24no—
52#11718307—24no—
53#11718307C418yescomplemented
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C22×Dic26—22no—
70C22×Dic26—22no—
71C22×Dic26—22no—
72C22×Dic26—22no—
73C22×Dic26—41no—
74C22×Dic26—41no—
75C22×Dic26C2×C414yes—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—41no—
79C2×#6101—22no—
80C2×#6101—22no—
81C2×#6101—22no—
82C2×#6101—22no—
83C2×#6101—41no—
84C2×#6101C2×C414yes—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—41no—
90C2×C4×Dic13—41no—
91C2×C4×Dic13—41no—
92C2×C4×Dic13—41no—
93C2×C4×Dic13C2×C414yes—
94C13×#95—22no—
95C13×#95—22no—
96C13×#95—41no—
97C13×#95—41no—
98C13×#95—41no—
99C13×#95C2×C414yes—
100#88071—22no—
101#88071—22no—
102#88071—22no—
103#88071—22no—
104#88071—22no—
105#88071—22no—
106#88071—22no—
107#88071—22no—
108#88071—22no—
109#88071—22no—
110#88071—22no—
111#88071—41no—
112#88071—41no—
113#88071—41no—
114#88071—41no—
115#88071—41no—
116#88071—41no—
117#88071—41no—
118#88071C2×C414yes—
119#88071C2×C414yes—
120#88071C2×C414yes—
121#88071D414yes—
122#14432—131nomaximal, Sylow
123C24×C13C2411yescharacteristic
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
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×C13C22×C412yes—
169C22×C4×C13C22×C412yes—
170C22×C4×C13C22×C412yes—
171C22×C4×C13C2×D412yes—
172C22×C4×C13#4112yes—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
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×Dic13C22×C412yes—
220C22×Dic13C22×C412yes—
221C22×Dic13C22×C412yes—
222C22×Dic13C22×C412yes—
223C22×Dic13C2×D412yes—
224C22×Dic13C2×D412yes—
225C22×Dic13#4112yes—
226C22×Dic13#4112yes—
227C22×Dic13#4112yes—
228C22×Dic13#4112yes—
229C2×Dic26—28no—
230C2×Dic26—28no—
231C2×Dic26—44no—
232C2×Dic26—44no—
233C2×Dic26—44no—
234C2×Dic26—44no—
235C2×Dic26—44no—
236C13×C4⋊C4—44no—
237#6101—28no—
238#6101—44no—
239C4×Dic13—44no—
240C4×Dic13—44no—
241C4×Dic13—44no—
242C2×#391—131no—
243C2×#391—131no—
244C2×#387—131no—
245#1446—131no—
246#1445—131no—
247#1443—131no—
248#1443—131no—
249#1442—131no—
250#1442D1311yescharacteristic
251#1436—131no—
252#1436—131no—
253#1434—131no—
254#1434—131no—
255#1434—131no—
256#1434—131no—
257C23×C13C23×C411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C2×#4111yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13H(5,𝔽2)11yescharacteristic
265C23×C13H(5,𝔽2)11yescharacteristic
266C23×C13H(5,𝔽2)11yescharacteristic
267C23×C132−1+411yescharacteristic
268C23×C132−1+411yescharacteristic
269C23×C132−1+411yescharacteristic
270C23×C132−1+411yescharacteristic
271C23×C132−1+411yescharacteristic
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13—41no—
359C2×Dic13—41no—
360C2×Dic13—41no—
361C2×Dic13—41no—
362C2×Dic13—41no—
363C2×Dic13—41no—
364C2×Dic13—41no—
365C2×Dic13—41no—
366C2×Dic13—41no—
367C2×Dic13—41no—
368C2×Dic13—41no—
369C2×Dic13—41no—
370C2×Dic13—41no—
371C2×Dic13—41no—
372C2×Dic13—41no—
373C2×Dic13—41no—
374C2×Dic13—41no—
375C2×Dic13#11714yes—
376C2×Dic13C4×D414yes—
377Dic26—416no—
378C23×Q8—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4C2×D1311yescharacteristic
382C22×C42—131no—
383C22×C42—131no—
384C22×C42—131no—
385#391—138no—
386#391—264no—
387#387—264no—
388C2×#95—131no—
389C2×#95—131no—
390C2×#95—131no—
391C2×#95—131no—
392C2×#95—131no—
393C2×#95—131no—
394C2×#95—131no—
395C2×#95—131no—
396C2×#95—131no—
397C2×#95—131no—
398C2×#95—131no—
399C2×#95—131no—
400C2×#95—131no—
401C2×#95—131no—
402C2×#95—131no—
403C2×#95—131no—
404C2×#95—131no—
405C2×#95—131no—
406C2×#95—131no—
407C2×#95—131no—
408C2×#95—131no—
409C2×#95—131no—
410C2×#95C2×D1311yescharacteristic
411C2×#95C2×D1311yescharacteristic
412C2×#95C2×D1311yescharacteristic
413C2×#95C2×D1311yescharacteristic
414C2×#95C2×D1311yescharacteristic
415C2×#95C2×D1311yescharacteristic
416C22×C13C2×#11711yescharacteristic
417C22×C13C2×C4×D411yescharacteristic
418C22×C13C4×#4111yescharacteristic
419C22×C13#51811yescharacteristic
420C22×C13#51911yescharacteristic
421C22×C13#51911yescharacteristic
422C22×C13#52011yescharacteristic
423C22×C13#53611yescharacteristic
424C22×C13#53611yescharacteristic
425C22×C13#53911yescharacteristic
426C22×C13#53911yescharacteristic
427C22×C13#54111yescharacteristic
428C22×C13#54111yescharacteristic
429C22×C13#54111yescharacteristic
430C22×C13#54111yescharacteristic
431C22×C13#54211yescharacteristic
432C22×C13#54211yescharacteristic
433C22×C13#54211yescharacteristic
434C22×C13#54211yescharacteristic
435C22×C13#54611yescharacteristic
436C22×C13#54611yescharacteristic
437C22×C13#54611yescharacteristic
438C22×C13#54811yescharacteristic
439C22×C13#55111yescharacteristic
440C22×C13#55111yescharacteristic
441C22×C13#55211yescharacteristic
442C22×C13#55211yescharacteristic
443C22×C13#55611yescharacteristic
444C22×C13#55611yescharacteristic
445C22×C13#55611yescharacteristic
446C22×C13#55911yescharacteristic
447C22×C13#56211yescharacteristic
448C22×C13#56211yescharacteristic
449C22×C13#56311yescharacteristic
450C22×C13#56311yescharacteristic
451C4×C13—42no—
452C4×C13—42no—
453C4×C13—42no—
454C4×C13—42no—
455C4×C13—42no—
456C4×C13—81no—
457C4×C13—81no—
458Dic13—24no—
459Dic13—24no—
460Dic13—42no—
461Dic13—42no—
462Dic13—42no—
463Dic13—42no—
464Dic13—81no—
465Dic13—81no—
466C22×Q8—134no—
467C22×Q8—262no—
468C22×Q8—262no—
469C22×Q8—262no—
470C22×Q8—262no—
471C22×Q8—521no—
472C22×Q8—521no—
473C23×C4—131no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—131no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4C22×D1311yescharacteristic
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C23×C4C22×D1311yescharacteristic
485C23×C4C22×D1311yescharacteristic
486C23×C4C22×D1311yescharacteristic
487C23×C4C22×D1311yescharacteristic
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—134no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—262no—
495C2×C4⋊C4—262no—
496C2×C4⋊C4—521no—
497C2×C42—134no—
498C2×C42—262no—
499C2×C42—262no—
500C2×C42—262no—
501C2×C42—262no—
502C2×C42—521no—
503C2×C42—521no—
504C2×C42—521no—
505C2×C42—521no—
506#95—22no—
507#95—22no—
508#95—41no—
509#95—41no—
510#95—41no—
511#95—134no—
512#95—134no—
513#95—134no—
514#95—134no—
515#95—262no—
516#95—262no—
517#95—262no—
518#95—262no—
519#95—262no—
520#95—262no—
521#95—262no—
522#95—262no—
523#95—262no—
524#95—262no—
525#95—262no—
526#95—521no—
527#95—521no—
528#95—521no—
529#95—521no—
530#95—521no—
531#95—521no—
532#95—521no—
533#95C4×D1314yes—
534C2×C13#232011yescharacteristic
535C2×C13#232711yescharacteristic
536C2×C13#233211yescharacteristic
537C2×C13#234211yescharacteristic
538C2×C13#235611yescharacteristic
539C2×C13#236711yescharacteristic
540C2×C13#237811yescharacteristic
541C2×C13#268711yescharacteristic
542C2×C13#269011yescharacteristic
543C2×C13#270011yescharacteristic
544C2×C13#271611yescharacteristic
545C2×C13#275411yescharacteristic
546C2×C13#275811yescharacteristic
547C2×C13#278911yescharacteristic
548C2×C13#279811yescharacteristic
549C24C23×D1311yescharacteristic
550C2×Q8—268no—
551C2×Q8—268no—
552C2×Q8—524no—
553C2×Q8—524no—
554C2×Q8—524no—
555C2×Q8—524no—
556C2×Q8—524no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
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—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
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—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—132no—
602C22×C4—132no—
603C22×C4—132no—
604C22×C4—132no—
605C22×C4—132no—
606C22×C4—132no—
607C22×C4—132no—
608C22×C4—132no—
609C22×C4—132no—
610C22×C4—132no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—261no—
615C22×C4—261no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—261no—
624C22×C4—261no—
625C22×C4—261no—
626C22×C4—261no—
627C22×C4—261no—
628C22×C4—261no—
629C22×C4—261no—
630C22×C4—261no—
631C22×C4—261no—
632C22×C4—261no—
633C22×C4—261no—
634C22×C4—261no—
635C22×C4—261no—
636C22×C4—261no—
637C22×C4—261no—
638C22×C4—261no—
639C22×C4—261no—
640C22×C4—261no—
641C22×C4—261no—
642C22×C4—261no—
643C22×C4—261no—
644C22×C4—261no—
645C22×C4—261no—
646C22×C4—261no—
647C22×C4—261no—
648C22×C4—261no—
649C22×C4—261no—
650C22×C4—261no—
651C22×C4—261no—
652C22×C4—261no—
653C22×C4—261no—
654C22×C4—261no—
655C22×C4—261no—
656C22×C4—261no—
657C22×C4C2×C4×D1312yes—
658C22×C4C2×C4×D1312yes—
659C22×C4C2×C4×D1312yes—
660C22×C4D4×D1312yes—
661C22×C4#612912yes—
662C4⋊C4—44no—
663C4⋊C4—268no—
664C4⋊C4—524no—
665C42—524no—
666C42—524no—
667C42—524no—
668C13#1443211yescharacteristic, complemented, Sylow
669C23C22×C4×D1311yescharacteristic
670C23C2×D4×D1311yescharacteristic
671C23C2×#612911yescharacteristic
672C23#8825111yescharacteristic
673C23#8825111yescharacteristic
674C23#8825411yescharacteristic
675C23#8825411yescharacteristic
676C23#41×D1311yescharacteristic
677C23#41×D1311yescharacteristic
678C23#41×D1311yescharacteristic
679C23#41×D1311yescharacteristic
680C23#8825611yescharacteristic
681C23#8825711yescharacteristic
682C23#8825711yescharacteristic
683C23#8825711yescharacteristic
684Q8—5216no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
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—41no—
733C2×C4—41no—
734C2×C4—134no—
735C2×C4—134no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—262no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—262no—
752C2×C4—262no—
753C2×C4—262no—
754C2×C4—262no—
755C2×C4—262no—
756C2×C4—262no—
757C2×C4—262no—
758C2×C4—262no—
759C2×C4—262no—
760C2×C4—521no—
761C2×C4—521no—
762C2×C4—521no—
763C2×C4—521no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—521no—
767C2×C4—521no—
768C2×C4—521no—
769C2×C4—521no—
770C2×C4—521no—
771C2×C4—521no—
772C2×C4—521no—
773C2×C4—521no—
774C2×C4—521no—
775C2×C4—521no—
776C2×C4—521no—
777C2×C4—521no—
778C2×C4—521no—
779C2×C4—521no—
780C2×C4—521no—
781C2×C4—521no—
782C2×C4—521no—
783C2×C4—521no—
784C2×C4—521no—
785C2×C4—521no—
786C2×C4—521no—
787C2×C4—521no—
788C2×C4—521no—
789C2×C4—521no—
790C22#1171920911yescharacteristic
791C22#1171922111yescharacteristic
792C22D13×#11711yescharacteristic
793C22C4×#612911yescharacteristic
794C22C4×D4×D1311yescharacteristic
795C22#1171925011yescharacteristic
796C22#1171927711yescharacteristic
797C22#1171929611yescharacteristic
798C22#1171930711yescharacteristic
799C22#1171931511yescharacteristic
800C22#1171932611yescharacteristic
801C22#1171933311yescharacteristic
802C22#1171933811yescharacteristic
803C22#1171934611yescharacteristic
804C22#1171934611yescharacteristic
805C22#1171935211yescharacteristic
806C22#1171935311yescharacteristic
807C22#1171935511yescharacteristic
808C22#1171936411yescharacteristic
809C22#1171936511yescharacteristic
810C22#1171936911yescharacteristic
811C22#1171937411yescharacteristic
812C22#1171937411yescharacteristic
813C22#1171938111yescharacteristic
814C22#1171938711yescharacteristic
815C22#1171939811yescharacteristic
816C22#1171940111yescharacteristic
817C22#1171940111yescharacteristic
818C22#1171940111yescharacteristic
819C22#1171940411yescharacteristic
820C22#1171940611yescharacteristic
821C22#1171940711yescharacteristic
822C22#1171941011yescharacteristic
823C22#1171941511yescharacteristic
824C22#1171944011yescharacteristic
825C4—42no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—42no—
830C4—81no—
831C4—81no—
832C4—264no—
833C4—264no—
834C4—522no—
835C4—522no—
836C4—522no—
837C4—522no—
838C4—1041no—
839C4—1041no—
840C2#1311748411yescharacteristic
841C2#1311755111yescharacteristic
842C2#1311758611yescharacteristic
843C2#1311768411yescharacteristic
844C2#1311779811yescharacteristic
845C2#1311790411yescharacteristic
846C2#1311799811yescharacteristic
847C2#1312126311yescharacteristic
848C2#1312130811yescharacteristic
849C2#1312144111yescharacteristic
850C2#1312166711yescharacteristic
851C2#1312213511yescharacteristic
852C2#1312219511yescharacteristic
853C2#1312259711yescharacteristic
854C2#1312271511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1442C2
socle, prime radical, cosocleC24×C13C24
hypercenter#1442D13
hypocenterC13#14432
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
53. #11718307C4semidirect
668. C13#14432semidirect

Maximal subgroups

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

subgroupindex
C2×#117183072
C2×#117186392
#131131062
#131131022
#131130982
#131130972
#131130912
#131130682
#131130672
#131130622
#131130612
#131130602
C13×#14422
#1443213