Finite Group Databasebeta

← #15786723

Subgroups — #15786723

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C2×#11718307C211yesmaximal, characteristic, complemented
3C2×#11718329C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5C2×D13×#95C211yesmaximal, characteristic
6#13113106C211yesmaximal, characteristic, complemented
7#13113103C211yesmaximal, characteristic, complemented
8#13113089C211yesmaximal, characteristic, complemented
9#13113088C211yesmaximal, characteristic, complemented
10#13113070C211yesmaximal, characteristic, complemented
11#13113066C211yesmaximal, characteristic, complemented
12#13113057C211yesmaximal, characteristic
13#13113057C211yesmaximal, characteristic
14#13113057C211yesmaximal, characteristic
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C23×Dic26C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×#88151—24no—
32C2×#88151—24no—
33C2×#88151C418yescomplemented
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C4×#6103—24no—
55#11718329—24no—
56D13×#95—24no—
57#11718307—24no—
58C24×D13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C22×C4×D13—22no—
74C22×C4×D13—22no—
75C22×C4×D13—22no—
76C22×C4×D13—22no—
77C22×C4×D13—22no—
78C22×C4×D13—22no—
79C22×C4×D13—22no—
80C22×C4×D13—22no—
81C22×C4×D13—22no—
82C22×C4×D13—22no—
83C22×C4×D13—22no—
84C22×C4×D13—22no—
85C22×C4×D13—22no—
86C22×C4×D13—41no—
87C22×C4×D13—41no—
88C22×C4×D13—41no—
89C22×C4×D13—41no—
90C22×C4×D13—41no—
91C22×C4×D13—41no—
92C22×C4×D13C2×C414yes—
93C22×C4×D13Q814yescomplemented
94C22×Dic26—22no—
95C22×Dic26—22no—
96C22×Dic26—22no—
97C22×Dic26—22no—
98C22×Dic26—41no—
99C22×Dic26—41no—
100C22×Dic26C2×C414yescomplemented
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4C2×C414yescomplemented
104C2×C42×C13—22no—
105C2×C42×C13—22no—
106C2×C42×C13—41no—
107C2×#6103—22no—
108C2×#6103—22no—
109C2×#6103—22no—
110C2×#6103—22no—
111C2×#6103—22no—
112C2×#6103—22no—
113C2×#6103—22no—
114C2×#6103C2×C414yes—
115C2×#6103C2×C414yes—
116C2×#6103D414yes—
117C2×#6103D414yes—
118C2×#6103Q814yescomplemented
119C2×C4⋊Dic13—22no—
120C2×C4⋊Dic13—22no—
121C2×C4⋊Dic13—22no—
122C2×C4⋊Dic13—22no—
123C2×C4⋊Dic13—22no—
124C2×C4⋊Dic13—22no—
125C2×C4⋊Dic13—41no—
126C2×C4⋊Dic13C2×C414yescomplemented
127C2×C4⋊Dic13C2×C414yescomplemented
128C2×#6101—22no—
129C2×#6101—22no—
130C2×#6101—41no—
131C2×C4×Dic13—22no—
132C2×C4×Dic13—22no—
133C2×C4×Dic13—41no—
134#88151—232no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—41no—
139C13×#95D414yes—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071—22no—
150#88071—41no—
151#88071—41no—
152#88071—41no—
153#88071—41no—
154#88071—41no—
155#14052—131nomaximal, Sylow
156C24×C13C2411yescharacteristic
157C23×D13—21no—
158C23×D13—21no—
159C23×D13—21no—
160C23×D13—21no—
161C23×D13—21no—
162C23×D13—21no—
163C23×D13—21no—
164C23×D13—21no—
165C23×D13C22×C412yes—
166C23×D13C2×D412yes—
167C23×D13C2×D412yes—
168C23×D13C2×Q812yes—
169C23×D13C2×Q812yes—
170C23×D13#4112yes—
171C23×D13#4112yes—
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×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13C22×C412yes—
210C22×C4×C13C22×C412yes—
211C22×C4×C13C22×C412yes—
212C22×C4×C13C2×D412yes—
213C22×C4×C13C2×D412yes—
214C22×C4×C13C2×D412yes—
215C22×C4×C13C2×D412yes—
216C22×C4×C13C2×D412yes—
217C22×C4×C13C2×Q812yes—
218C22×C4×C13C2×Q812yes—
219C22×C4×C13#4112yes—
220C22×C4×C13#4112yes—
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×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13C22×C412yes—
263C22×Dic13C22×C412yes—
264C22×Dic13C22×C412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13C2×Q812yes—
268C22×Dic13C2×Q812yes—
269C22×Dic13#4112yes—
270C2×C4×D13—28no—
271C2×C4×D13—28no—
272C2×C4×D13—28no—
273C2×C4×D13—28no—
274C2×C4×D13—28no—
275C2×C4×D13—44no—
276C2×C4×D13—44no—
277C2×C4×D13—44no—
278C2×C4×D13—44no—
279C2×C4×D13—44no—
280C2×C4×D13—44no—
281C2×C4×D13—44no—
282C2×C4×D13—44no—
283C2×C4×D13—44no—
284C2×C4×D13—44no—
285C2×C4×D13—44no—
286C2×C4×D13—44no—
287C2×C4×D13—44no—
288C2×C4×D13—44no—
289C2×C4×D13—44no—
290C2×C4×D13—44no—
291C2×Dic26—28no—
292C2×Dic26—28no—
293C2×Dic26—44no—
294C2×Dic26—44no—
295C2×Dic26—44no—
296C2×Dic26—44no—
297C2×Dic26—44no—
298C13×C4⋊C4—28no—
299C42×C13—44no—
300#6103—28no—
301#6103—28no—
302#6103—44no—
303#6103C22⋊C4116yes—
304C4⋊Dic13—28no—
305C4⋊Dic13—28no—
306C4⋊Dic13—44no—
307#6101—44no—
308C4×Dic13—44no—
309C22×C22⋊Q8—131no—
310C2×#391—131no—
311C2×#385—131no—
312C2×C4×C22⋊C4—131no—
313C22×#95—131no—
314#1446—131no—
315#1445—131no—
316#1441—131no—
317#1441—131no—
318#1436—131no—
319#1436D1311yescharacteristic, complemented
320C4⋊#95—131no—
321C22⋊#95—131no—
322C22⋊#95—131no—
323C22⋊#95—131no—
324C23×C13C23×C411yescharacteristic
325C23×C13C22×D411yescharacteristic
326C23×C13C22×D411yescharacteristic
327C23×C13C22×D411yescharacteristic
328C23×C13C22×Q811yescharacteristic
329C23×C13C22×Q811yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C13H(5,𝔽2)11yescharacteristic
338C23×C132−1+411yescharacteristic
339C22×D13—22no—
340C22×D13—22no—
341C22×D13—22no—
342C22×D13—22no—
343C22×D13—22no—
344C22×D13—22no—
345C22×D13—22no—
346C22×D13—22no—
347C22×D13—22no—
348C22×D13—22no—
349C22×D13—22no—
350C22×D13—22no—
351C22×D13—22no—
352C22×D13—22no—
353C22×D13—22no—
354C22×D13—22no—
355C22×D13—22no—
356C22×D13—22no—
357C22×D13—22no—
358C22×D13—22no—
359C22×D13—22no—
360C22×D13—22no—
361C22×D13—22no—
362C22×D13—22no—
363C22×D13—22no—
364C22×D13—22no—
365C22×D13—22no—
366C22×D13—22no—
367C22×D13C2×C22⋊C414yes—
368C22×D13C4×Q814yes—
369C22×D13C4×Q814yes—
370C22×D13C22⋊Q814yes—
371C22×D13C22⋊Q814yes—
372C22×D13#12414yes—
373C22×D13C4⋊Q814yes—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13C2×C22⋊C414yes—
421C2×C4×C13C4×D414yes—
422C2×C4×C13C22⋊Q814yescomplemented
423C2×Dic13—22no—
424C2×Dic13—22no—
425C2×Dic13—22no—
426C2×Dic13—22no—
427C2×Dic13—22no—
428C2×Dic13—22no—
429C2×Dic13—22no—
430C2×Dic13—22no—
431C2×Dic13—22no—
432C2×Dic13—22no—
433C2×Dic13—22no—
434C2×Dic13—22no—
435C2×Dic13—22no—
436C2×Dic13—22no—
437C2×Dic13—22no—
438C2×Dic13—22no—
439C2×Dic13—22no—
440C2×Dic13—22no—
441C2×Dic13—22no—
442C2×Dic13—22no—
443C2×Dic13—22no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C2×Dic13—41no—
455C2×Dic13—41no—
456C2×Dic13—41no—
457C2×Dic13—41no—
458C2×Dic13—41no—
459C2×Dic13—41no—
460C2×Dic13—41no—
461C2×Dic13—41no—
462C2×Dic13—41no—
463C2×Dic13—41no—
464C2×Dic13—41no—
465C2×Dic13—41no—
466C2×Dic13—41no—
467C2×Dic13—41no—
468C2×Dic13—41no—
469C2×Dic13—41no—
470C2×Dic13—41no—
471C2×Dic13C2×C22⋊C414yes—
472C4×D13—416no—
473C4×D13—416no—
474C4×D13—416no—
475Dic26—416no—
476C23×Q8—131no—
477C24×C4—131no—
478C24×C4—131no—
479C24×C4—131no—
480C2×C22⋊Q8—138no—
481C2×C22⋊Q8—264no—
482C2×C22⋊Q8—264no—
483C22×C4⋊C4—131no—
484C22×C4⋊C4—131no—
485C22×C4⋊C4—131no—
486C22×C4⋊C4—131no—
487C22×C4⋊C4C2×D1311yescharacteristic
488C22×C22⋊C4—131no—
489C22×C22⋊C4—131no—
490C22×C22⋊C4—131no—
491C22×C22⋊C4—131no—
492C22×C42—131no—
493C22×C42C2×D1311yescharacteristic
494#391—264no—
495#385—264no—
496C4×C22⋊C4—264no—
497C2×#95—131no—
498C2×#95—131no—
499C2×#95—131no—
500C2×#95—131no—
501C2×#95—131no—
502C2×#95—131no—
503C2×#95—131no—
504C2×#95—131no—
505C2×#95—131no—
506C2×#95—131no—
507C2×#95—131no—
508C2×#95—131no—
509C2×#95—131no—
510C2×#95—131no—
511C2×#95—131no—
512C2×#95—264no—
513C2×#95C2×D1311yescharacteristic
514C2×#95C2×D1311yescharacteristic
515C2×#95C2×D1311yescharacteristic
516C2×#95C2×D1311yescharacteristic
517C2×#95C2×D1311yescharacteristic
518C22×C13C22×C22⋊C411yescharacteristic
519C22×C13C2×C4×D411yescharacteristic
520C22×C13C2×C4×Q811yescharacteristic
521C22×C13C2×C4×Q811yescharacteristic
522C22×C13C4×#4111yescharacteristic
523C22×C13#51811yescharacteristic
524C22×C13#52011yescharacteristic
525C22×C13C2×C22⋊Q811yescharacteristic
526C22×C13C2×C22⋊Q811yescharacteristic
527C22×C13C2×C22⋊Q811yescharacteristic
528C22×C13#52511yescharacteristic
529C22×C13C2×#12411yescharacteristic
530C22×C13#52911yescharacteristic
531C22×C13C2×C4⋊Q811yescharacteristic
532C22×C13#53311yescharacteristic
533C22×C13#53811yescharacteristic
534C22×C13#53911yescharacteristic
535C22×C13#54311yescharacteristic
536C22×C13#54411yescharacteristic
537C22×C13D4211yescharacteristic
538C22×C13D4211yescharacteristic
539C22×C13#54611yescharacteristic
540C22×C13#54611yescharacteristic
541C22×C13#54611yescharacteristic
542C22×C13#54611yescharacteristic
543C22×C13#54611yescharacteristic
544C22×C13#54711yescharacteristic
545C22×C13#54711yescharacteristic
546C22×C13D4×Q811yescharacteristic
547C22×C13#55111yescharacteristic
548C22×C13#55111yescharacteristic
549C22×C13#55211yescharacteristic
550C22×C13#55411yescharacteristic
551C22×C13#55411yescharacteristic
552C22×C13#55411yescharacteristic
553C2×D13—24no—
554C2×D13—24no—
555C2×D13—24no—
556C2×D13—24no—
557C2×D13—24no—
558C2×D13—24no—
559C2×D13—24no—
560C2×D13—24no—
561C2×D13—24no—
562C2×D13—24no—
563C2×D13—24no—
564C2×D13—24no—
565C2×D13—24no—
566C2×D13—24no—
567C2×D13#39118yescomplemented
568C4×C13—24no—
569C4×C13—24no—
570C4×C13—24no—
571C4×C13—42no—
572C4×C13—42no—
573C4×C13—42no—
574C4×C13—81no—
575Dic13—24no—
576Dic13—42no—
577Dic13—42no—
578Dic13—42no—
579Dic13—42no—
580Dic13—42no—
581Dic13—81no—
582C25—131no—
583C22×Q8—134no—
584C22×Q8—262no—
585C22×Q8—262no—
586C22×Q8—262no—
587C22×Q8—262no—
588C22×Q8—521no—
589C22×Q8—521no—
590C23×C4—131no—
591C23×C4—131no—
592C23×C4—131no—
593C23×C4—131no—
594C23×C4—131no—
595C23×C4—131no—
596C23×C4—134no—
597C23×C4—134no—
598C23×C4—131no—
599C23×C4—262no—
600C23×C4—262no—
601C23×C4—262no—
602C23×C4—262no—
603C23×C4—262no—
604C23×C4—262no—
605C23×C4—262no—
606C23×C4—262no—
607C23×C4—262no—
608C23×C4—262no—
609C23×C4—262no—
610C23×C4—262no—
611C23×C4—262no—
612C23×C4—521no—
613C23×C4—521no—
614C23×C4—521no—
615C23×C4—521no—
616C23×C4—521no—
617C23×C4—521no—
618C23×C4C22×D1311yescharacteristic
619C23×C4C22×D1311yescharacteristic
620C23×C4C22×D1311yescharacteristic
621C23×C4C22×D1311yescharacteristic
622C23×C4C22×D1311yescharacteristic
623C23×C4C22×D1311yescharacteristic
624C23×C4C22×D1311yescharacteristic
625C22⋊Q8—2632no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—134no—
629C2×C4⋊C4—134no—
630C2×C4⋊C4—262no—
631C2×C4⋊C4—262no—
632C2×C4⋊C4—262no—
633C2×C4⋊C4—262no—
634C2×C4⋊C4—262no—
635C2×C4⋊C4—262no—
636C2×C4⋊C4—262no—
637C2×C4⋊C4—262no—
638C2×C4⋊C4—521no—
639C2×C4⋊C4—521no—
640C2×C4⋊C4C4×D1314yescomplemented
641C2×C22⋊C4—134no—
642C2×C22⋊C4—134no—
643C2×C22⋊C4—134no—
644C2×C22⋊C4—134no—
645C2×C22⋊C4—134no—
646C2×C22⋊C4—262no—
647C2×C22⋊C4—262no—
648C2×C22⋊C4—262no—
649C2×C22⋊C4—262no—
650C2×C22⋊C4—262no—
651C2×C22⋊C4—262no—
652C2×C22⋊C4—262no—
653C2×C42—22no—
654C2×C42—22no—
655C2×C42—41no—
656C2×C42—262no—
657C2×C42—262no—
658C2×C42—521no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—41no—
663#95—262no—
664#95—262no—
665#95—262no—
666#95—262no—
667#95—262no—
668#95—262no—
669#95—262no—
670#95—262no—
671#95—262no—
672#95—262no—
673#95—521no—
674#95—521no—
675#95—521no—
676#95—521no—
677#95—521no—
678#95D5214yes—
679C2×C13C2×#39111yescharacteristic
680C2×C13C4×C22⋊Q811yescharacteristic
681C2×C13#232911yescharacteristic
682C2×C13D4×C22⋊C411yescharacteristic
683C2×C13#233911yescharacteristic
684C2×C13#236011yescharacteristic
685C2×C13#236811yescharacteristic
686C2×C13#243711yescharacteristic
687C2×C13#243811yescharacteristic
688C2×C13#244011yescharacteristic
689C2×C13#244911yescharacteristic
690C2×C13#245011yescharacteristic
691C2×C13#247211yescharacteristic
692C2×C13#248811yescharacteristic
693C2×C13#254911yescharacteristic
694D13—28no—
695C24—132no—
696C24—132no—
697C24—132no—
698C24—132no—
699C24—132no—
700C24—132no—
701C24—132no—
702C24—261no—
703C24—261no—
704C24—261no—
705C24—261no—
706C24—261no—
707C24—261no—
708C24—261no—
709C24—261no—
710C24C23×D1311yescharacteristic
711C2×Q8—268no—
712C2×Q8—268no—
713C2×Q8—524no—
714C2×Q8—524no—
715C2×Q8—524no—
716C2×Q8—524no—
717C2×Q8—524no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—132no—
756C22×C4—132no—
757C22×C4—132no—
758C22×C4—132no—
759C22×C4—132no—
760C22×C4—132no—
761C22×C4—132no—
762C22×C4—132no—
763C22×C4—268no—
764C22×C4—268no—
765C22×C4—268no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—261no—
770C22×C4—261no—
771C22×C4—261no—
772C22×C4—261no—
773C22×C4—261no—
774C22×C4—261no—
775C22×C4—261no—
776C22×C4—261no—
777C22×C4—261no—
778C22×C4—261no—
779C22×C4—261no—
780C22×C4—261no—
781C22×C4—261no—
782C22×C4—261no—
783C22×C4—261no—
784C22×C4—261no—
785C22×C4—261no—
786C22×C4—261no—
787C22×C4—261no—
788C22×C4—261no—
789C22×C4—261no—
790C22×C4—261no—
791C22×C4—261no—
792C22×C4—261no—
793C22×C4—261no—
794C22×C4—261no—
795C22×C4—261no—
796C22×C4—261no—
797C22×C4—261no—
798C22×C4—261no—
799C22×C4—261no—
800C22×C4—268no—
801C22×C4—268no—
802C22×C4—261no—
803C22×C4—261no—
804C22×C4—261no—
805C22×C4—261no—
806C22×C4—261no—
807C22×C4—261no—
808C22×C4—261no—
809C22×C4—524no—
810C22×C4—524no—
811C22×C4—524no—
812C22×C4—524no—
813C22×C4—524no—
814C22×C4—524no—
815C22×C4—524no—
816C22×C4—524no—
817C22×C4—524no—
818C22×C4—524no—
819C22×C4—524no—
820C22×C4—524no—
821C22×C4—524no—
822C22×C4—524no—
823C22×C4—524no—
824C22×C4—524no—
825C22×C4C2×C4×D1312yes—
826C22×C4C2×C4×D1312yes—
827C22×C4C2×C4×D1312yes—
828C22×C4C2×D5212yes—
829C22×C4C2×D5212yes—
830C22×C4C2×D5212yes—
831C22×C4#612712yes—
832C22×C4D4×D1312yes—
833C22×C4D4×D1312yes—
834C22×C4#612912yes—
835C22×C4Q8×D1312yes—
836C22×C4Q8×D1312yes—
837C4⋊C4—28no—
838C4⋊C4—268no—
839C4⋊C4—268no—
840C4⋊C4—524no—
841C4⋊C4—524no—
842C22⋊C4—1316no—
843C22⋊C4—268no—
844C22⋊C4—268no—
845C22⋊C4—524no—
846C42—44no—
847C42—524no—
848C13#1405211yescharacteristic, complemented, Sylow
849C23—134no—
850C23—134no—
851C23—134no—
852C23—134no—
853C23—134no—
854C23—134no—
855C23—134no—
856C23—262no—
857C23—262no—
858C23—262no—
859C23—262no—
860C23—262no—
861C23—262no—
862C23—262no—
863C23—262no—
864C23—262no—
865C23—262no—
866C23—262no—
867C23—262no—
868C23—262no—
869C23—262no—
870C23—262no—
871C23—262no—
872C23—262no—
873C23—262no—
874C23—262no—
875C23—262no—
876C23—262no—
877C23—262no—
878C23—262no—
879C23—262no—
880C23—262no—
881C23—262no—
882C23—262no—
883C23—262no—
884C23C22×C4×D1311yescharacteristic
885C23C22×D5211yescharacteristic
886C23C2×#612711yescharacteristic
887C23C2×D4×D1311yescharacteristic
888C23C2×D4×D1311yescharacteristic
889C23C2×#612911yescharacteristic
890C23#8825111yescharacteristic
891C23C2×Q8×D1311yescharacteristic
892C23C2×Q8×D1311yescharacteristic
893C23#41×D1311yescharacteristic
894C23#41×D1311yescharacteristic
895C23#41×D1311yescharacteristic
896C23#8825611yescharacteristic
897C23#8825611yescharacteristic
898C23#8825711yescharacteristic
899Q8—5216no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—134no—
947C2×C4—262no—
948C2×C4—262no—
949C2×C4—262no—
950C2×C4—262no—
951C2×C4—262no—
952C2×C4—262no—
953C2×C4—262no—
954C2×C4—262no—
955C2×C4—262no—
956C2×C4—262no—
957C2×C4—262no—
958C2×C4—262no—
959C2×C4—262no—
960C2×C4—262no—
961C2×C4—262no—
962C2×C4—262no—
963C2×C4—262no—
964C2×C4—262no—
965C2×C4—262no—
966C2×C4—262no—
967C2×C4—262no—
968C2×C4—5216no—
969C2×C4—5216no—
970C2×C4—5216no—
971C2×C4—521no—
972C2×C4—521no—
973C2×C4—521no—
974C2×C4—521no—
975C2×C4—521no—
976C2×C4—521no—
977C2×C4—521no—
978C2×C4—521no—
979C2×C4—521no—
980C2×C4—521no—
981C2×C4—521no—
982C2×C4—521no—
983C2×C4—521no—
984C2×C4—521no—
985C2×C4—521no—
986C2×C4—521no—
987C2×C4—521no—
988C2×C4—521no—
989C2×C4—521no—
990C2×C4—521no—
991C2×C4—521no—
992C2×C4—521no—
993C2×C4—521no—
994C2×C4—521no—
995C2×C4—521no—
996C2×C4—521no—
997C2×C4—521no—
998C2×C4C4×D5214yes—
999C2×C4C22⋊C4×D1314yes—
1000C2×C4#8815114yescomplemented
1001C22—138no—
1002C22—264no—
1003C22—264no—
1004C22—264no—
1005C22—264no—
1006C22—264no—
1007C22—264no—
1008C22—264no—
1009C22—264no—
1010C22—264no—
1011C22—264no—
1012C22—264no—
1013C22—264no—
1014C22—264no—
1015C22—264no—
1016C22C2×C4×D5211yescharacteristic
1017C22C2×C22⋊C4×D1311yescharacteristic
1018C22C2×#8815111yescharacteristic
1019C22#1171921611yescharacteristic
1020C22#1171922611yescharacteristic
1021C22#1171922911yescharacteristic
1022C22#1171923411yescharacteristic
1023C22C4×#612911yescharacteristic
1024C22#1171925111yescharacteristic
1025C22D4×D5211yescharacteristic
1026C22D4×D5211yescharacteristic
1027C22#1171925511yescharacteristic
1028C22#1171925511yescharacteristic
1029C22#1171925911yescharacteristic
1030C22#1171926211yescharacteristic
1031C22C4×Q8×D1311yescharacteristic
1032C22C4×Q8×D1311yescharacteristic
1033C22Q8×D5211yescharacteristic
1034C22#1171928311yescharacteristic
1035C22#1171929611yescharacteristic
1036C22#1171931511yescharacteristic
1037C22#1171931611yescharacteristic
1038C22D13×C22⋊Q811yescharacteristic
1039C22D13×C22⋊Q811yescharacteristic
1040C22#1171933911yescharacteristic
1041C22#1171934011yescharacteristic
1042C22#1171936011yescharacteristic
1043C22#1171936211yescharacteristic
1044C22#1171936311yescharacteristic
1045C22D13×#12411yescharacteristic
1046C22#1171939411yescharacteristic
1047C22#1171939511yescharacteristic
1048C22#1171941011yescharacteristic
1049C22#1171941211yescharacteristic
1050C22D13×C4⋊Q811yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—24no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—81no—
1058C4—264no—
1059C4—522no—
1060C4—522no—
1061C4—522no—
1062C4—522no—
1063C4—522no—
1064C4—1041no—
1065C2—268no—
1066C2D13×#39111yescharacteristic
1067C2C4×#8815111yescharacteristic
1068C2#1311756511yescharacteristic
1069C2C22⋊C4×D5211yescharacteristic
1070C2#1311766211yescharacteristic
1071C2#1311784311yescharacteristic
1072C2#1311791811yescharacteristic
1073C2#1311850011yescharacteristic
1074C2#1311851711yescharacteristic
1075C2#1311853611yescharacteristic
1076C2#1311865011yescharacteristic
1077C2#1311866511yescharacteristic
1078C2#1311896011yescharacteristic
1079C2#1311916111yescharacteristic
1080C2#1311984611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1436D13
hypocenterC13#14052
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#11718307C2semidirect
6. #13113106C2semidirect
7. #13113103C2semidirect
8. #13113089C2semidirect
9. #13113088C2semidirect
10. #13113070C2semidirect
11. #13113066C2semidirect
15. C13×#1436C2semidirect
33. C2×#88151C4semidirect
93. C22×C4×D13Q8semidirect
100. C22×Dic26C2×C4semidirect
103. C2×C13×C4⋊C4C2×C4semidirect
118. C2×#6103Q8semidirect
126. C2×C4⋊Dic13C2×C4semidirect
127. C2×C4⋊Dic13C2×C4semidirect
319. #1436D13semidirect
422. C2×C4×C13C22⋊Q8semidirect
567. C2×D13#391semidirect
640. C2×C4⋊C4C4×D13semidirect
848. C13#14052semidirect
1000. C2×C4#88151semidirect

Maximal subgroups

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

subgroupindex
C22×#881512
C2×#117183072
C2×#117183292
C2×C4×#61032
C2×D13×#952
#131131062
#131131032
#131130892
#131130882
#131130702
#131130662
#131130572
C13×#14362
#1405213