Finite Group Databasebeta

← #15786252

Subgroups — #15786252

Order 3328.

1462 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718331C211yesmaximal, characteristic
2C2×#11718651C211yesmaximal, characteristic
3C2×#11718312C211yesmaximal, characteristic, complemented
4#13113097C211yesmaximal, characteristic, complemented
5#13113089C211yesmaximal, characteristic, complemented
6#13113084C211yesmaximal, characteristic
7#13113078C211yesmaximal, characteristic
8#13113074C211yesmaximal, characteristic
9#13113072C211yesmaximal, characteristic
10#13113072C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13C4×#88071C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C13×C4⋊#95C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C42×C13C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
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#11718651C418yescomplemented
52#11718331—24no—
53#11718312—24no—
54C24×D13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×Dic13C2311yescharacteristic
63C23×Dic13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—41no—
72C2×C13×C4⋊C4—41no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4C2×C414yes—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13—41no—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×#6103—22no—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×#6103—22no—
88C2×#6103—22no—
89C2×#6103—22no—
90C2×#6103—41no—
91C2×#6103—41no—
92C2×#6103—41no—
93C2×#6103—41no—
94C2×#6103—41no—
95C2×#6103—41no—
96C2×#6103C2×C414yes—
97C2×#6103C2×C414yes—
98C2×#6103C2×C414yes—
99C2×C4⋊Dic13—22no—
100C2×C4⋊Dic13—22no—
101C2×C4⋊Dic13—41no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C2×C4×Dic13—22no—
106C2×C4×Dic13—22no—
107C2×C4×Dic13—22no—
108C2×C4×Dic13—22no—
109C2×C4×Dic13—41no—
110C2×C4×Dic13—41no—
111C2×C4×Dic13—41no—
112C2×C4×Dic13—41no—
113C2×C4×Dic13C2×C414yes—
114C13×#95—22no—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118#88071—22no—
119#88071—22no—
120#88071—22no—
121#88071—22no—
122#88071—22no—
123#88071—22no—
124#88071—22no—
125#88071—22no—
126#88071—22no—
127#88071—22no—
128#88071—41no—
129#88071—41no—
130#88071—41no—
131#88071C2×C414yes—
132#88071C2×C414yes—
133#88071D414yes—
134#14013—131nomaximal, Sylow
135C24×C13C2411yescharacteristic
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×D13—21no—
145C23×D13—21no—
146C23×D13—21no—
147C23×D13—21no—
148C23×D13—21no—
149C23×D13—21no—
150C23×D13C22×C412yes—
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×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13C22×C412yes—
191C22×C4×C13C22×C412yes—
192C22×C4×C13C22×C412yes—
193C22×C4×C13C2×D412yes—
194C22×C4×C13#4112yes—
195C22×C4×C13#4112yes—
196C22×C4×C13#4112yes—
197C22×C4×C13#4112yes—
198C22×C4×C13#4112yes—
199C22×C4×C13#4112yes—
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×Dic13—21no—
241C22×Dic13C22×C412yes—
242C22×Dic13C22×C412yes—
243C22×Dic13C22×C412yes—
244C22×Dic13C2×D412yes—
245C22×Dic13C2×D412yes—
246C22×Dic13#4112yes—
247C22×Dic13#4112yes—
248C22×Dic13#4112yes—
249C13×C4⋊C4—44no—
250C13×C4⋊C4—44no—
251C42×C13—44no—
252#6103—28no—
253#6103—28no—
254#6103—44no—
255#6103—44no—
256#6103—44no—
257#6103—44no—
258#6103—44no—
259C4⋊Dic13—44no—
260C4×Dic13—28no—
261C4×Dic13—44no—
262C4×Dic13—44no—
263C4×Dic13—44no—
264C2×#388—131no—
265C2×#388—131no—
266C2×#383—131no—
267#1443—131no—
268#1441—131no—
269#1440—131no—
270#1439—131no—
271#1437—131no—
272#1437—131no—
273#1437—131no—
274#1436—131no—
275#1436—131no—
276C4⋊#95D1311yescharacteristic, complemented
277C4×#95—131no—
278C4×#95—131no—
279C23×C13C23×C411yescharacteristic
280C23×C13C22×D411yescharacteristic
281C23×C13C2×#4111yescharacteristic
282C23×C13C2×#4111yescharacteristic
283C23×C13C2×#4111yescharacteristic
284C23×C13C2×#4111yescharacteristic
285C23×C13C2×#4111yescharacteristic
286C23×C13C2×#4111yescharacteristic
287C23×C13C2×#4111yescharacteristic
288C23×C13C2×#4111yescharacteristic
289C23×C13C2×#4111yescharacteristic
290C23×C13H(5,𝔽2)11yescharacteristic
291C23×C13H(5,𝔽2)11yescharacteristic
292C23×C13H(5,𝔽2)11yescharacteristic
293C23×C132−1+411yescharacteristic
294C22×D13—22no—
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
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—
321C22×D13—41no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
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—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
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—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
376C2×C4×C13#11714yes—
377C2×C4×C13#12614yes—
378C2×Dic13—22no—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—22no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
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—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13C4×D414yes—
427C22×C4⋊C4—131no—
428C22×C4⋊C4C2×D1311yescharacteristic
429C22×C4⋊C4C2×D1311yescharacteristic
430C22×C22⋊C4—131no—
431C22×C22⋊C4—131no—
432C22×C22⋊C4—131no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—131no—
435C22×C22⋊C4—131no—
436C22×C22⋊C4—131no—
437C22×C42—131no—
438C22×C42—131no—
439C22×C42—131no—
440C22×C42—131no—
441C22×C42C2×D1311yescharacteristic
442#388—138no—
443#388—264no—
444#383—264no—
445C2×#95—131no—
446C2×#95—131no—
447C2×#95—131no—
448C2×#95—131no—
449C2×#95—131no—
450C2×#95—131no—
451C2×#95—131no—
452C2×#95—131no—
453C2×#95—131no—
454C2×#95—131no—
455C2×#95—131no—
456C2×#95—131no—
457C2×#95—131no—
458C2×#95—131no—
459C2×#95—131no—
460C2×#95—131no—
461C2×#95C2×D1311yescharacteristic
462C2×#95C2×D1311yescharacteristic
463C2×#95C2×D1311yescharacteristic
464C2×#95C2×D1311yescharacteristic
465C22×C13C2×#11711yescharacteristic
466C22×C13C2×C4×D411yescharacteristic
467C22×C13C4×#4111yescharacteristic
468C22×C13C4×#4111yescharacteristic
469C22×C13C4×#4111yescharacteristic
470C22×C13#51811yescharacteristic
471C22×C13#52011yescharacteristic
472C22×C13C2×#12611yescharacteristic
473C22×C13#52911yescharacteristic
474C22×C13#52911yescharacteristic
475C22×C13#52911yescharacteristic
476C22×C13#52911yescharacteristic
477C22×C13#52911yescharacteristic
478C22×C13#53211yescharacteristic
479C22×C13#53211yescharacteristic
480C22×C13#53811yescharacteristic
481C22×C13#53811yescharacteristic
482C22×C13#54211yescharacteristic
483C22×C13#54211yescharacteristic
484C22×C13#54611yescharacteristic
485C22×C13#54611yescharacteristic
486C22×C13#54711yescharacteristic
487C22×C13#55011yescharacteristic
488C22×C13#55111yescharacteristic
489C22×C13#55111yescharacteristic
490C22×C13#55111yescharacteristic
491C22×C13#55211yescharacteristic
492C22×C13#55311yescharacteristic
493C22×C13#55311yescharacteristic
494C22×C13#55311yescharacteristic
495C22×C13#55311yescharacteristic
496C22×C13#55311yescharacteristic
497C22×C13#55511yescharacteristic
498C22×C13#55611yescharacteristic
499C22×C13#55611yescharacteristic
500C2×D13—42no—
501C2×D13—42no—
502C2×D13—42no—
503C2×D13—42no—
504C2×D13—42no—
505C2×D13—42no—
506C2×D13—42no—
507C2×D13—81no—
508C2×D13—81no—
509C2×D13—81no—
510C2×D13—81no—
511C2×D13—81no—
512C2×D13—81no—
513C2×D13—81no—
514C2×D13—81no—
515C4×C13—24no—
516C4×C13—24no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—42no—
521C4×C13—81no—
522Dic13—24no—
523Dic13—42no—
524Dic13—42no—
525Dic13—42no—
526Dic13—42no—
527Dic13—42no—
528Dic13—81no—
529C25—131no—
530C23×C4—131no—
531C23×C4—131no—
532C23×C4—131no—
533C23×C4—131no—
534C23×C4—131no—
535C23×C4—131no—
536C23×C4—131no—
537C23×C4C22×D1311yescharacteristic
538C23×C4C22×D1311yescharacteristic
539C23×C4C22×D1311yescharacteristic
540C23×C4C22×D1311yescharacteristic
541C23×C4C22×D1311yescharacteristic
542C23×C4C22×D1311yescharacteristic
543C23×C4C22×D1311yescharacteristic
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—262no—
550C2×C4⋊C4—262no—
551C2×C4⋊C4—521no—
552C2×C4⋊C4C4×D1314yes—
553C2×C22⋊C4—134no—
554C2×C22⋊C4—134no—
555C2×C22⋊C4—134no—
556C2×C22⋊C4—262no—
557C2×C22⋊C4—262no—
558C2×C22⋊C4—262no—
559C2×C22⋊C4—262no—
560C2×C22⋊C4—262no—
561C2×C22⋊C4—262no—
562C2×C22⋊C4—262no—
563C2×C22⋊C4—262no—
564C2×C22⋊C4—262no—
565C2×C22⋊C4—262no—
566C2×C22⋊C4—262no—
567C2×C22⋊C4—262no—
568C2×C22⋊C4—521no—
569C2×C22⋊C4—521no—
570C2×C22⋊C4—521no—
571C2×C22⋊C4—521no—
572C2×C22⋊C4—521no—
573C2×C22⋊C4—521no—
574C2×C42—22no—
575C2×C42—22no—
576C2×C42—41no—
577C2×C42—134no—
578C2×C42—262no—
579C2×C42—262no—
580C2×C42—262no—
581C2×C42—262no—
582C2×C42—262no—
583C2×C42—262no—
584C2×C42—262no—
585C2×C42—521no—
586C2×C42—521no—
587C2×C42—521no—
588C2×C42—521no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—134no—
594#95—134no—
595#95—134no—
596#95—262no—
597#95—262no—
598#95—262no—
599#95—262no—
600#95—262no—
601#95—262no—
602#95—262no—
603#95—262no—
604#95—262no—
605#95—262no—
606#95—521no—
607#95—521no—
608#95—521no—
609C2×C13#229311yescharacteristic
610C2×C13C4×#12611yescharacteristic
611C2×C13#233711yescharacteristic
612C2×C13#234711yescharacteristic
613C2×C13#235311yescharacteristic
614C2×C13#235911yescharacteristic
615C2×C13#236311yescharacteristic
616C2×C13#251011yescharacteristic
617C2×C13#251211yescharacteristic
618C2×C13#251811yescharacteristic
619C2×C13#252111yescharacteristic
620C2×C13#252511yescharacteristic
621C2×C13#253211yescharacteristic
622C2×C13#255411yescharacteristic
623C2×C13#255911yescharacteristic
624D13—82no—
625C24—132no—
626C24—261no—
627C24—261no—
628C24—261no—
629C24—261no—
630C24—261no—
631C24—261no—
632C24—261no—
633C24—261no—
634C24—261no—
635C24—261no—
636C24—261no—
637C24—261no—
638C24—261no—
639C24—261no—
640C24C23×D1311yescharacteristic
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—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—132no—
681C22×C4—132no—
682C22×C4—132no—
683C22×C4—132no—
684C22×C4—132no—
685C22×C4—132no—
686C22×C4—132no—
687C22×C4—132no—
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×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4C2×C4×D1312yes—
730C22×C4C2×C4×D1312yes—
731C22×C4C2×C4×D1312yes—
732C22×C4#612712yes—
733C22×C4#612712yes—
734C22×C4D4×D1312yes—
735C22×C4#612912yes—
736C22×C4#612912yes—
737C22×C4#613112yes—
738C22×C4#613112yes—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—524no—
742C22⋊C4—268no—
743C22⋊C4—268no—
744C22⋊C4—524no—
745C22⋊C4—524no—
746C22⋊C4—524no—
747C22⋊C4—524no—
748C22⋊C4—524no—
749C42—44no—
750C42—268no—
751C42—524no—
752C42—524no—
753C42—524no—
754C13#1401311yescharacteristic, complemented, Sylow
755C23—262no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—521no—
763C23—521no—
764C23—521no—
765C23—521no—
766C23—521no—
767C23—521no—
768C23—521no—
769C23—521no—
770C23—521no—
771C23—521no—
772C23—521no—
773C23—521no—
774C23—521no—
775C23—521no—
776C23—521no—
777C23—521no—
778C23—521no—
779C23—521no—
780C23—521no—
781C23—521no—
782C23—521no—
783C23—521no—
784C23—521no—
785C23—521no—
786C23—521no—
787C23—521no—
788C23—521no—
789C23—521no—
790C23C22×C4×D1311yescharacteristic
791C23C2×#612711yescharacteristic
792C23C2×#612711yescharacteristic
793C23C2×D4×D1311yescharacteristic
794C23C2×#612911yescharacteristic
795C23C2×#612911yescharacteristic
796C23#8825111yescharacteristic
797C23#8825111yescharacteristic
798C23C2×#613111yescharacteristic
799C23C2×#613111yescharacteristic
800C23#8825411yescharacteristic
801C23#41×D1311yescharacteristic
802C23#41×D1311yescharacteristic
803C23#41×D1311yescharacteristic
804C23#8825611yescharacteristic
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—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
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—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—134no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—262no—
856C2×C4—262no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—262no—
860C2×C4—262no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—262no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
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—521no—
887C2×C4—521no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—521no—
895C2×C4—521no—
896C2×C4—521no—
897C2×C4—521no—
898C2×C4—521no—
899C2×C4—521no—
900C2×C4—521no—
901C2×C4#8814614yes—
902C2×C4#8815214yes—
903C22—522no—
904C22—522no—
905C22—522no—
906C22—522no—
907C22—522no—
908C22—522no—
909C22—522no—
910C22—1041no—
911C22—1041no—
912C22—1041no—
913C22—1041no—
914C22—1041no—
915C22—1041no—
916C22—1041no—
917C22—1041no—
918C22C4×#612711yescharacteristic
919C22#1171919111yescharacteristic
920C22#1171920011yescharacteristic
921C22#1171920011yescharacteristic
922C22C2×#8814611yescharacteristic
923C22#1171921211yescharacteristic
924C22C2×#8815211yescharacteristic
925C22#1171921911yescharacteristic
926C22#1171921911yescharacteristic
927C22#1171923211yescharacteristic
928C22#1171923311yescharacteristic
929C22C4×#612911yescharacteristic
930C22#1171924311yescharacteristic
931C22C4×D4×D1311yescharacteristic
932C22#1171925511yescharacteristic
933C22C4×#613111yescharacteristic
934C22#1171927911yescharacteristic
935C22#1171928511yescharacteristic
936C22#1171928611yescharacteristic
937C22#1171930111yescharacteristic
938C22#1171930611yescharacteristic
939C22#1171931511yescharacteristic
940C22#1171932311yescharacteristic
941C22#1171932911yescharacteristic
942C22#1171934511yescharacteristic
943C22#1171934611yescharacteristic
944C22#1171934911yescharacteristic
945C22#1171937511yescharacteristic
946C22#1171938311yescharacteristic
947C22#1171939611yescharacteristic
948C22#1171940011yescharacteristic
949C22#1171942311yescharacteristic
950C22#1171943011yescharacteristic
951C22#1171943711yescharacteristic
952C22#1171943811yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—81no—
960C4—264no—
961C4—522no—
962C4—522no—
963C4—522no—
964C4—522no—
965C4—522no—
966C4—1041no—
967C2—1042no—
968C2#1311729411yescharacteristic
969C2C4×#8815211yescharacteristic
970C2#1311764811yescharacteristic
971C2#1311772811yescharacteristic
972C2#1311777211yescharacteristic
973C2#1311783311yescharacteristic
974C2#1311787111yescharacteristic
975C2#1311939211yescharacteristic
976C2#1311941811yescharacteristic
977C2#1311949011yescharacteristic
978C2#1311953511yescharacteristic
979C2#1311959211yescharacteristic
980C2#1311970511yescharacteristic
981C2#1311989311yescharacteristic
982C2#1311997211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#14013
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#11718312C2semidirect
4. #13113097C2semidirect
5. #13113089C2semidirect
11. #13113070C2semidirect
12. #13113068C2semidirect
13. C4×#88071C2semidirect
14. #95×Dic13C2semidirect
15. C13×C4⋊#95C2semidirect
51. #11718651C4semidirect
276. C4⋊#95D13semidirect
754. C13#14013semidirect

Maximal subgroups

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

subgroupindex
C2×#117183312
C2×#117186512
C2×#117183122
#131130972
#131130892
#131130842
#131130782
#131130742
#131130722
#131130702
#131130682
C4×#880712
#95×Dic132
C13×C4⋊#952
#1401313