Finite Group Databasebeta

← #15784417

Subgroups — #15784417

Order 3328.

2882 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88135C211yesmaximal, characteristic
2C2×#11718874C211yesmaximal, characteristic
3C2×#11718619C211yesmaximal, characteristic
4C2×C22⋊C4×Dic13C211yesmaximal, characteristic, complemented
5C2×C4×#6103C211yesmaximal, characteristic, complemented
6C22×#88071C211yesmaximal, characteristic, complemented
7#13113074C211yesmaximal, characteristic, complemented
8#13113072C211yesmaximal, characteristic, complemented
9#13113071C211yesmaximal, characteristic, complemented
10#13113069C211yesmaximal, characteristic, complemented
11#13113060C211yesmaximal, characteristic, complemented
12#13113058C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic, complemented
14C4×#88071C211yesmaximal, characteristic, complemented
15C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C23×C22⋊D13C2211yescharacteristic
18C24×Dic13C2211yescharacteristic
19C24×Dic13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C42×C13C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C2×#88135—24no—
36C2×#88135—24no—
37C2×#88135C418yescomplemented
38C4×C13×C22⋊C4—24no—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41#11718874C418yescomplemented
42C2×#88071—24no—
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56C2×#88071C2211yescharacteristic
57#11718619C418yescomplemented
58C22⋊C4×Dic13—24no—
59C4×#6103—24no—
60C25×C13C2311yescharacteristic
61C24×D13C2311yescharacteristic
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—41no—
67C23×C4×C13—41no—
68C23×C4×C13C2×C414yescomplemented
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C22×C22⋊D13—22no—
76C22×C22⋊D13—22no—
77C22×C22⋊D13—22no—
78C22×C22⋊D13—22no—
79C22×C22⋊D13C2×C414yes—
80C22×C22⋊D13C2×C414yes—
81C22×C22⋊D13C2×C414yes—
82C23×Dic13—22no—
83C23×Dic13—22no—
84C23×Dic13—22no—
85C23×Dic13—22no—
86C23×Dic13—22no—
87C23×Dic13—22no—
88C23×Dic13—22no—
89C23×Dic13—22no—
90C23×Dic13—41no—
91C23×Dic13—41no—
92C23×Dic13—41no—
93C23×Dic13—41no—
94C23×Dic13C2×C414yes—
95C23×Dic13C2×C414yescomplemented
96C23×Dic13C2311yescharacteristic
97C23×Dic13C2311yescharacteristic
98C23×Dic13C2311yescharacteristic
99C23×Dic13C2311yescharacteristic
100C23×Dic13C2311yescharacteristic
101C23×Dic13C2311yescharacteristic
102C23×Dic13C2311yescharacteristic
103C22×C4×D13—22no—
104C22×C4×D13—22no—
105C22×C4×D13—22no—
106C22×C4×D13—22no—
107C22×C4×D13—41no—
108C22×C4×D13—41no—
109C22×C4×D13C2×C414yescomplemented
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4C2×C414yes—
113C2×C13×C22⋊C4C2×C414yescomplemented
114C2×C13×C22⋊C4D414yes—
115C2×C13×C22⋊C4D414yes—
116C2×C42×C13—22no—
117C2×C42×C13—22no—
118C2×C42×C13—22no—
119C2×C42×C13—22no—
120C2×C42×C13—41no—
121C2×C42×C13—41no—
122C2×C22⋊Dic13—22no—
123C2×C22⋊Dic13—22no—
124C2×C22⋊Dic13C2×C414yescomplemented
125C2×#6103—22no—
126C2×#6103—22no—
127C2×#6103—22no—
128C2×#6103—22no—
129C2×#6103—22no—
130C2×#6103—22no—
131C2×#6103—41no—
132C2×#6103—41no—
133C2×#6103—41no—
134C2×#6103—41no—
135C2×#6103C2×C414yescomplemented
136C2×#6103C2×C414yescomplemented
137C2×#6103C2×C414yescomplemented
138C2×#6103C2×C414yescomplemented
139C2×#6103C2×C414yescomplemented
140C2×#6101—22no—
141C2×#6101—22no—
142C2×#6101C2×C414yescomplemented
143C2×C4×Dic13—22no—
144C2×C4×Dic13—22no—
145C2×C4×Dic13—22no—
146C2×C4×Dic13—22no—
147C2×C4×Dic13—22no—
148C2×C4×Dic13—22no—
149C2×C4×Dic13—41no—
150C2×C4×Dic13—41no—
151C2×C4×Dic13C2×C414yescomplemented
152#88135—232no—
153C13×#95—22no—
154C13×#95—22no—
155#88071—22no—
156#88071—22no—
157#88071—22no—
158#88071—22no—
159#88071—22no—
160#88071—22no—
161#88071—22no—
162#88071—41no—
163#88071—41no—
164#88071C2×C414yescomplemented
165#88071C2×C414yescomplemented
166#88071C2×C414yescomplemented
167#88071C2×C414yescomplemented
168#88071D414yescomplemented
169#13813—131nomaximal, Sylow
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13C22×C412yes—
179C24×C13C22×C412yes—
180C24×C13C22×C412yes—
181C24×C13C2×D412yes—
182C24×C13C2×D412yes—
183C24×C13#4112yes—
184C24×C13#4112yes—
185C24×C13C2411yescharacteristic
186C23×D13—21no—
187C23×D13—21no—
188C23×D13—21no—
189C23×D13—21no—
190C23×D13—21no—
191C23×D13—21no—
192C23×D13—21no—
193C23×D13—21no—
194C23×D13—21no—
195C23×D13—21no—
196C23×D13—21no—
197C23×D13—21no—
198C23×D13C22×C412yes—
199C23×D13C22×C412yes—
200C23×D13C22×C412yes—
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×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—28no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—28no—
233C22×C4×C13—44no—
234C22×C4×C13—44no—
235C22×C4×C13—44no—
236C22×C4×C13—44no—
237C22×C4×C13—44no—
238C22×C4×C13C22×C412yes—
239C22×C4×C13C22×C412yes—
240C22×C4×C13C22×C412yes—
241C22×C4×C13C22×C412yes—
242C22×C4×C13C22×C412yes—
243C22×C4×C13C22×C412yes—
244C22×C4×C13C2×D412yes—
245C22×C4×C13C2×D412yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D412yes—
248C22×C4×C13C2×D412yes—
249C22×C4×C13#4112yes—
250C2×C22⋊D13—28no—
251C2×C22⋊D13—28no—
252C2×C22⋊D13—28no—
253C2×C22⋊D13—28no—
254C2×C22⋊D13—28no—
255C2×C22⋊D13—28no—
256C2×C22⋊D13C42116yescomplemented
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263C22×Dic13—21no—
264C22×Dic13—21no—
265C22×Dic13—21no—
266C22×Dic13—21no—
267C22×Dic13—21no—
268C22×Dic13—21no—
269C22×Dic13—28no—
270C22×Dic13—28no—
271C22×Dic13—21no—
272C22×Dic13—21no—
273C22×Dic13—21no—
274C22×Dic13—21no—
275C22×Dic13—21no—
276C22×Dic13—21no—
277C22×Dic13—21no—
278C22×Dic13—21no—
279C22×Dic13—21no—
280C22×Dic13—21no—
281C22×Dic13—21no—
282C22×Dic13—21no—
283C22×Dic13—21no—
284C22×Dic13—21no—
285C22×Dic13—21no—
286C22×Dic13—21no—
287C22×Dic13—21no—
288C22×Dic13—21no—
289C22×Dic13—21no—
290C22×Dic13—21no—
291C22×Dic13—21no—
292C22×Dic13—21no—
293C22×Dic13—21no—
294C22×Dic13—21no—
295C22×Dic13—28no—
296C22×Dic13—28no—
297C22×Dic13—44no—
298C22×Dic13—44no—
299C22×Dic13—44no—
300C22×Dic13—44no—
301C22×Dic13—44no—
302C22×Dic13—44no—
303C22×Dic13—44no—
304C22×Dic13—44no—
305C22×Dic13—44no—
306C22×Dic13—44no—
307C22×Dic13C22×C412yes—
308C22×Dic13C22×C412yes—
309C22×Dic13C22×C412yes—
310C22×Dic13C22×C412yes—
311C22×Dic13C22×C412yes—
312C22×Dic13C22×C412yes—
313C22×Dic13C22×C412yes—
314C22×Dic13C22×C412yes—
315C22×Dic13C22×C412yes—
316C22×Dic13C2×D412yes—
317C22×Dic13C2×D412yes—
318C22×Dic13#4112yes—
319C22×Dic13#4112yes—
320C2×C4×D13—28no—
321C2×C4×D13—28no—
322C2×C4×D13—44no—
323C2×C4×D13—44no—
324C2×C4×D13—44no—
325C2×C4×D13—44no—
326C2×C4×D13—44no—
327C13×C22⋊C4—28no—
328C13×C22⋊C4C22⋊C4116yescomplemented
329C42×C13—44no—
330C42×C13—44no—
331C22⋊Dic13—28no—
332#6103—28no—
333#6103—28no—
334#6103—28no—
335#6103—44no—
336#6103—44no—
337#6101—28no—
338C4×Dic13—28no—
339C4×Dic13—44no—
340C4×Dic13—44no—
341C22×C4×D4—131no—
342C2×#386—131no—
343C2×#386—131no—
344C2×C4×C22⋊C4—131no—
345C2×C4×C22⋊C4—131no—
346C2×C4×C22⋊C4D1311yescharacteristic, complemented
347C22×#95—131no—
348#1437—131no—
349#1437—131no—
350#1436—131no—
351#1436—131no—
352#1434—131no—
353C22⋊#95—131no—
354C22⋊#95—131no—
355C4×#95—131no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—22no—
378C23×C13—22no—
379C23×C13—22no—
380C23×C13—22no—
381C23×C13—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13C2×C4214yes—
385C23×C13C2×C22⋊C414yes—
386C23×C13#11714yes—
387C23×C13C4×D414yes—
388C23×C13C4×D414yes—
389C23×C13C4×D414yes—
390C23×C13C4×D414yes—
391C23×C13C23×C411yescharacteristic
392C23×C13C23×C411yescharacteristic
393C23×C13C23×C411yescharacteristic
394C23×C13C22×D411yescharacteristic
395C23×C13C22×D411yescharacteristic
396C23×C13C22×D411yescharacteristic
397C23×C13C2×#4111yescharacteristic
398C23×C13C2×#4111yescharacteristic
399C23×C13C2×#4111yescharacteristic
400C23×C13C2×#4111yescharacteristic
401C23×C13C2×#4111yescharacteristic
402C23×C13H(5,𝔽2)11yescharacteristic
403C23×C13H(5,𝔽2)11yescharacteristic
404C23×C13H(5,𝔽2)11yescharacteristic
405C23×C132−1+411yescharacteristic
406C22×D13—22no—
407C22×D13—22no—
408C22×D13—22no—
409C22×D13—22no—
410C22×D13—22no—
411C22×D13—22no—
412C22×D13—22no—
413C22×D13—22no—
414C22×D13—22no—
415C22×D13—22no—
416C22×D13—22no—
417C22×D13—22no—
418C22×D13—22no—
419C22×D13—22no—
420C22×D13—22no—
421C22×D13—22no—
422C22×D13—22no—
423C22×D13—22no—
424C22×D13—41no—
425C22×D13—41no—
426C22×D13—41no—
427C22×D13—41no—
428C22×D13—41no—
429C22×D13—41no—
430C22×D13—41no—
431C22×D13—41no—
432C22×D13—41no—
433C22×D13—41no—
434C22×D13—41no—
435C22×D13—41no—
436C22×D13—41no—
437C22×D13—41no—
438C22×D13—41no—
439C22×D13—41no—
440C22×D13C2×C4214yes—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—22no—
452C2×C4×C13—22no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—22no—
457C2×C4×C13—22no—
458C2×C4×C13—22no—
459C2×C4×C13—22no—
460C2×C4×C13—22no—
461C2×C4×C13—22no—
462C2×C4×C13—22no—
463C2×C4×C13—22no—
464C2×C4×C13—22no—
465C2×C4×C13—22no—
466C2×C4×C13—22no—
467C2×C4×C13—22no—
468C2×C4×C13—416no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13C2×C22⋊C414yes—
482C2×C4×C13C2×C22⋊C414yes—
483C2×C4×C13C4×D414yescomplemented
484C22⋊D13—232no—
485C2×Dic13—22no—
486C2×Dic13—22no—
487C2×Dic13—22no—
488C2×Dic13—22no—
489C2×Dic13—22no—
490C2×Dic13—22no—
491C2×Dic13—22no—
492C2×Dic13—22no—
493C2×Dic13—22no—
494C2×Dic13—22no—
495C2×Dic13—22no—
496C2×Dic13—22no—
497C2×Dic13—22no—
498C2×Dic13—22no—
499C2×Dic13—22no—
500C2×Dic13—22no—
501C2×Dic13—22no—
502C2×Dic13—22no—
503C2×Dic13—22no—
504C2×Dic13—22no—
505C2×Dic13—22no—
506C2×Dic13—22no—
507C2×Dic13—22no—
508C2×Dic13—22no—
509C2×Dic13—22no—
510C2×Dic13—22no—
511C2×Dic13—22no—
512C2×Dic13—22no—
513C2×Dic13—22no—
514C2×Dic13—22no—
515C2×Dic13—416no—
516C2×Dic13—416no—
517C2×Dic13—41no—
518C2×Dic13—41no—
519C2×Dic13—41no—
520C2×Dic13—41no—
521C2×Dic13—41no—
522C2×Dic13—41no—
523C2×Dic13—41no—
524C2×Dic13—41no—
525C2×Dic13—41no—
526C2×Dic13—41no—
527C2×Dic13—41no—
528C2×Dic13—41no—
529C2×Dic13—41no—
530C2×Dic13—41no—
531C2×Dic13—41no—
532C2×Dic13—41no—
533C2×Dic13C2×C4214yes—
534C2×Dic13C4×D414yes—
535C2×Dic13C4×D414yescomplemented
536C4×D13—416no—
537C23×D4—131no—
538C24×C4—131no—
539C24×C4—131no—
540C24×C4—131no—
541C24×C4C2×D1311yescharacteristic
542C2×C4×D4—138no—
543C2×C4×D4—264no—
544C2×C4×D4—264no—
545C22×C4⋊C4—131no—
546C22×C22⋊C4—131no—
547C22×C22⋊C4—131no—
548C22×C22⋊C4—131no—
549C22×C22⋊C4—131no—
550C22×C22⋊C4—131no—
551C22×C22⋊C4—131no—
552C22×C22⋊C4C2×D1311yescharacteristic
553C22×C22⋊C4C2×D1311yescharacteristic
554C22×C42—131no—
555C22×C42—131no—
556C22×C42—131no—
557C22×C42C2×D1311yescharacteristic
558C22×C42C2×D1311yescharacteristic
559#386—138no—
560#386—138no—
561C4×C22⋊C4—24no—
562C4×C22⋊C4—264no—
563C4×C22⋊C4—264no—
564C2×#95—131no—
565C2×#95—131no—
566C2×#95—131no—
567C2×#95—131no—
568C2×#95—131no—
569C2×#95—131no—
570C2×#95—131no—
571C2×#95—131no—
572C2×#95—131no—
573C2×#95—131no—
574C2×#95—131no—
575C2×#95—131no—
576C2×#95—131no—
577C2×#95—131no—
578C2×#95—264no—
579C2×#95C2×D1311yescharacteristic
580C2×#95C2×D1311yescharacteristic
581C22×C13—24no—
582C22×C13—24no—
583C22×C13—24no—
584C22×C13—24no—
585C22×C13—24no—
586C22×C13—24no—
587C22×C13—24no—
588C22×C13—24no—
589C22×C13—24no—
590C22×C13—24no—
591C22×C13—24no—
592C22×C13—24no—
593C22×C13—24no—
594C22×C13—24no—
595C22×C13C4×C22⋊C418yescomplemented
596C22×C13C22×C4211yescharacteristic
597C22×C13C22×C22⋊C411yescharacteristic
598C22×C13C2×#11711yescharacteristic
599C22×C13C2×C4×D411yescharacteristic
600C22×C13C2×C4×D411yescharacteristic
601C22×C13C2×C4×D411yescharacteristic
602C22×C13C2×C4×D411yescharacteristic
603C22×C13C2×C4×D411yescharacteristic
604C22×C13C2×C4×D411yescharacteristic
605C22×C13C2×C4×D411yescharacteristic
606C22×C13C4×#4111yescharacteristic
607C22×C13C4×#4111yescharacteristic
608C22×C13C4×#4111yescharacteristic
609C22×C13#51811yescharacteristic
610C22×C13#51811yescharacteristic
611C22×C13#51811yescharacteristic
612C22×C13#52011yescharacteristic
613C22×C13#52011yescharacteristic
614C22×C13#52011yescharacteristic
615C22×C13D4211yescharacteristic
616C22×C13D4211yescharacteristic
617C22×C13#54611yescharacteristic
618C22×C13#54611yescharacteristic
619C22×C13#54611yescharacteristic
620C22×C13#54611yescharacteristic
621C22×C13#54611yescharacteristic
622C22×C13#54711yescharacteristic
623C22×C13#54711yescharacteristic
624C22×C13#54811yescharacteristic
625C22×C13#55111yescharacteristic
626C22×C13#55111yescharacteristic
627C22×C13#55211yescharacteristic
628C22×C13#55311yescharacteristic
629C22×C13#55311yescharacteristic
630C22×C13#55311yescharacteristic
631C2×D13—24no—
632C2×D13—24no—
633C2×D13—24no—
634C2×D13—42no—
635C2×D13—42no—
636C2×D13—42no—
637C2×D13—42no—
638C2×D13—42no—
639C2×D13—42no—
640C2×D13—42no—
641C2×D13—42no—
642C2×D13—42no—
643C2×D13—42no—
644C2×D13—42no—
645C2×D13—42no—
646C4×C13—24no—
647C4×C13—24no—
648C4×C13—24no—
649C4×C13—42no—
650C4×C13—42no—
651C4×C13—42no—
652Dic13—24no—
653Dic13—24no—
654Dic13—24no—
655Dic13—42no—
656Dic13—42no—
657Dic13—42no—
658Dic13—42no—
659C25—131no—
660C25C22×D1311yescharacteristic
661C22×D4—134no—
662C22×D4—134no—
663C22×D4—134no—
664C22×D4—262no—
665C22×D4—262no—
666C22×D4—262no—
667C22×D4—262no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—131no—
675C23×C4—131no—
676C23×C4—131no—
677C23×C4—131no—
678C23×C4—131no—
679C23×C4—131no—
680C23×C4—131no—
681C23×C4—134no—
682C23×C4—134no—
683C23×C4—134no—
684C23×C4—262no—
685C23×C4—262no—
686C23×C4—262no—
687C23×C4—262no—
688C23×C4—262no—
689C23×C4—262no—
690C23×C4—262no—
691C23×C4—262no—
692C23×C4—262no—
693C23×C4—262no—
694C23×C4—262no—
695C23×C4—262no—
696C23×C4—521no—
697C23×C4—521no—
698C23×C4—521no—
699C23×C4—521no—
700C23×C4—521no—
701C23×C4—521no—
702C23×C4C4×D1314yescomplemented
703C23×C4C22×D1311yescharacteristic
704C23×C4C22×D1311yescharacteristic
705C23×C4C22×D1311yescharacteristic
706C23×C4C22×D1311yescharacteristic
707C23×C4C22×D1311yescharacteristic
708C23×C4C22×D1311yescharacteristic
709C4×D4—2632no—
710C2×C4⋊C4—134no—
711C2×C4⋊C4—262no—
712C2×C4⋊C4—262no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—134no—
716C2×C22⋊C4—134no—
717C2×C22⋊C4—134no—
718C2×C22⋊C4—134no—
719C2×C22⋊C4—134no—
720C2×C22⋊C4—134no—
721C2×C22⋊C4—262no—
722C2×C22⋊C4—262no—
723C2×C22⋊C4—262no—
724C2×C22⋊C4—262no—
725C2×C22⋊C4—262no—
726C2×C22⋊C4—262no—
727C2×C22⋊C4—262no—
728C2×C22⋊C4—262no—
729C2×C22⋊C4—521no—
730C2×C22⋊C4—521no—
731C2×C22⋊C4—521no—
732C2×C22⋊C4—521no—
733C2×C22⋊C4C4×D1314yes—
734C2×C22⋊C4C4×D1314yescomplemented
735C2×C22⋊C4D5214yes—
736C2×C22⋊C4C22⋊D1314yes—
737C2×C42—22no—
738C2×C42—22no—
739C2×C42—22no—
740C2×C42—22no—
741C2×C42—41no—
742C2×C42—41no—
743C2×C42—134no—
744C2×C42—262no—
745C2×C42—262no—
746C2×C42—262no—
747C2×C42—262no—
748C2×C42—262no—
749C2×C42—262no—
750C2×C42—521no—
751C2×C42—521no—
752#95—22no—
753#95—22no—
754#95—134no—
755#95—134no—
756#95—134no—
757#95—134no—
758#95—134no—
759#95—262no—
760#95—262no—
761#95—262no—
762#95—262no—
763#95—262no—
764#95—262no—
765#95—262no—
766#95—521no—
767#95—521no—
768C2×C13—28no—
769C2×C13C2×C4×C22⋊C411yescharacteristic
770C2×C13C42×D411yescharacteristic
771C2×C13#227511yescharacteristic
772C2×C13D4×C22⋊C411yescharacteristic
773C2×C13#233911yescharacteristic
774C2×C13#235211yescharacteristic
775C2×C13#235311yescharacteristic
776C2×C13#235811yescharacteristic
777C2×C13#235811yescharacteristic
778C2×C13#235911yescharacteristic
779C2×C13#235911yescharacteristic
780C2×C13#236111yescharacteristic
781C2×C13#236111yescharacteristic
782C2×C13#236411yescharacteristic
783C2×C13#236411yescharacteristic
784D13—44no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—132no—
794C24—132no—
795C24—132no—
796C24—261no—
797C24—261no—
798C24—261no—
799C24—261no—
800C24—261no—
801C24—261no—
802C24—261no—
803C24—261no—
804C24—261no—
805C24—261no—
806C24—261no—
807C24—261no—
808C24C2×C4×D1312yes—
809C24C2×C4×D1312yes—
810C24C2×C4×D1312yes—
811C24C2×D5212yes—
812C24#612712yes—
813C24#612712yes—
814C24C2×C22⋊D1312yes—
815C24C23×D1311yescharacteristic
816C2×D4—1316no—
817C2×D4—268no—
818C2×D4—268no—
819C2×D4—268no—
820C2×D4—268no—
821C2×D4—268no—
822C2×D4—268no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—28no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—28no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—132no—
861C22×C4—132no—
862C22×C4—132no—
863C22×C4—132no—
864C22×C4—132no—
865C22×C4—132no—
866C22×C4—132no—
867C22×C4—132no—
868C22×C4—132no—
869C22×C4—132no—
870C22×C4—132no—
871C22×C4—132no—
872C22×C4—132no—
873C22×C4—268no—
874C22×C4—268no—
875C22×C4—268no—
876C22×C4—261no—
877C22×C4—261no—
878C22×C4—261no—
879C22×C4—261no—
880C22×C4—261no—
881C22×C4—261no—
882C22×C4—261no—
883C22×C4—261no—
884C22×C4—261no—
885C22×C4—261no—
886C22×C4—261no—
887C22×C4—261no—
888C22×C4—268no—
889C22×C4—268no—
890C22×C4—261no—
891C22×C4—261no—
892C22×C4—261no—
893C22×C4—261no—
894C22×C4—261no—
895C22×C4—261no—
896C22×C4—261no—
897C22×C4—261no—
898C22×C4—261no—
899C22×C4—261no—
900C22×C4—261no—
901C22×C4—261no—
902C22×C4—261no—
903C22×C4—261no—
904C22×C4—261no—
905C22×C4—261no—
906C22×C4—261no—
907C22×C4—261no—
908C22×C4—261no—
909C22×C4—261no—
910C22×C4—261no—
911C22×C4—261no—
912C22×C4—261no—
913C22×C4—261no—
914C22×C4—268no—
915C22×C4—524no—
916C22×C4—524no—
917C22×C4—524no—
918C22×C4—524no—
919C22×C4—524no—
920C22×C4—524no—
921C22×C4—524no—
922C22×C4—524no—
923C22×C4—524no—
924C22×C4—524no—
925C22×C4—524no—
926C22×C4—524no—
927C22×C4—524no—
928C22×C4—524no—
929C22×C4—524no—
930C22×C4C2×C4×D1312yes—
931C22×C4C2×C4×D1312yes—
932C22×C4C2×C4×D1312yes—
933C22×C4C2×C4×D1312yes—
934C22×C4C2×C4×D1312yes—
935C22×C4C2×C4×D1312yes—
936C22×C4C2×D5212yes—
937C22×C4C2×D5212yes—
938C22×C4D4×D1312yes—
939C22×C4#612912yes—
940C22×C4C2×C22⋊D1312yes—
941C22×C4C2×C22⋊D1312yes—
942C4⋊C4—268no—
943C22⋊C4—28no—
944C22⋊C4—268no—
945C22⋊C4—268no—
946C22⋊C4—268no—
947C22⋊C4—268no—
948C22⋊C4—524no—
949C22⋊C4—524no—
950C22⋊C4#6103116yescomplemented
951C42—44no—
952C42—44no—
953C42—268no—
954C42—524no—
955C42—524no—
956C13#1381311yescharacteristic, complemented, Sylow
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—134no—
986C23—262no—
987C23—262no—
988C23—262no—
989C23—262no—
990C23—262no—
991C23—262no—
992C23—262no—
993C23—262no—
994C23—262no—
995C23—262no—
996C23—262no—
997C23—262no—
998C23—262no—
999C23—262no—
1000C23—262no—
1001C23—262no—
1002C23—262no—
1003C23—262no—
1004C23—521no—
1005C23—521no—
1006C23—521no—
1007C23—521no—
1008C23—521no—
1009C23—521no—
1010C23—521no—
1011C23—521no—
1012C23—521no—
1013C23—521no—
1014C23—521no—
1015C23—521no—
1016C23—521no—
1017C23—521no—
1018C23—521no—
1019C23—521no—
1020C23C42×D1314yes—
1021C23#8812614yes—
1022C23C4×D5214yes—
1023C23C4×D5214yes—
1024C23C2×#610314yes—
1025C23C4×C22⋊D1314yes—
1026C23C4×C22⋊D1314yes—
1027C23C22×C4×D1311yescharacteristic
1028C23C22×C4×D1311yescharacteristic
1029C23C22×C4×D1311yescharacteristic
1030C23C22×D5211yescharacteristic
1031C23C2×#612711yescharacteristic
1032C23C2×#612711yescharacteristic
1033C23C2×D4×D1311yescharacteristic
1034C23C2×#612911yescharacteristic
1035C23#8825111yescharacteristic
1036C23#8825111yescharacteristic
1037C23#41×D1311yescharacteristic
1038C23#41×D1311yescharacteristic
1039C23#8825611yescharacteristic
1040C23#8825711yescharacteristic
1041C23C22×C22⋊D1311yescharacteristic
1042D4—2632no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—134no—
1084C2×C4—134no—
1085C2×C4—134no—
1086C2×C4—262no—
1087C2×C4—262no—
1088C2×C4—262no—
1089C2×C4—262no—
1090C2×C4—262no—
1091C2×C4—262no—
1092C2×C4—262no—
1093C2×C4—262no—
1094C2×C4—262no—
1095C2×C4—262no—
1096C2×C4—262no—
1097C2×C4—262no—
1098C2×C4—262no—
1099C2×C4—262no—
1100C2×C4—262no—
1101C2×C4—262no—
1102C2×C4—262no—
1103C2×C4—262no—
1104C2×C4—262no—
1105C2×C4—262no—
1106C2×C4—262no—
1107C2×C4—262no—
1108C2×C4—262no—
1109C2×C4—262no—
1110C2×C4—262no—
1111C2×C4—262no—
1112C2×C4—262no—
1113C2×C4—262no—
1114C2×C4—262no—
1115C2×C4—262no—
1116C2×C4—5216no—
1117C2×C4—5216no—
1118C2×C4—5216no—
1119C2×C4—521no—
1120C2×C4—521no—
1121C2×C4—521no—
1122C2×C4—521no—
1123C2×C4—521no—
1124C2×C4—521no—
1125C2×C4—521no—
1126C2×C4—521no—
1127C2×C4—521no—
1128C2×C4—521no—
1129C2×C4—521no—
1130C2×C4—521no—
1131C2×C4—521no—
1132C2×C4—521no—
1133C2×C4—521no—
1134C2×C4—521no—
1135C2×C4#8813514yescomplemented
1136C2×C4C2×#610314yes—
1137C2×C4C2×#610314yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—264no—
1153C22—264no—
1154C22—264no—
1155C22—522no—
1156C22—522no—
1157C22—522no—
1158C22—522no—
1159C22—522no—
1160C22—522no—
1161C22—522no—
1162C22—522no—
1163C22—522no—
1164C22—522no—
1165C22—522no—
1166C22—522no—
1167C22C4×#610318yescomplemented
1168C22C2×C42×D1311yescharacteristic
1169C22C2×#8812611yescharacteristic
1170C22C2×C4×D5211yescharacteristic
1171C22C2×C4×D5211yescharacteristic
1172C22C2×#8813511yescharacteristic
1173C22#1171919111yescharacteristic
1174C22#1171919511yescharacteristic
1175C22#1171920011yescharacteristic
1176C22#1171922711yescharacteristic
1177C22#1171922811yescharacteristic
1178C22#1171923211yescharacteristic
1179C22#1171923611yescharacteristic
1180C22C4×#612911yescharacteristic
1181C22C4×#612911yescharacteristic
1182C22#1171924511yescharacteristic
1183C22#1171924511yescharacteristic
1184C22C4×D4×D1311yescharacteristic
1185C22C4×D4×D1311yescharacteristic
1186C22#1171925011yescharacteristic
1187C22#1171925011yescharacteristic
1188C22#1171925111yescharacteristic
1189C22#1171925111yescharacteristic
1190C22D4×D5211yescharacteristic
1191C22#1171925711yescharacteristic
1192C22#1171925911yescharacteristic
1193C22#1171925911yescharacteristic
1194C22#1171926011yescharacteristic
1195C22#1171927011yescharacteristic
1196C22C22×#610311yescharacteristic
1197C22C2×C4×C22⋊D1311yescharacteristic
1198C22C2×C4×C22⋊D1311yescharacteristic
1199C22D4×C22⋊D1311yescharacteristic
1200C22#1171951111yescharacteristic
1201C22#1171952911yescharacteristic
1202C22#1171953411yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—264no—
1210C4—264no—
1211C4—264no—
1212C4—522no—
1213C4—522no—
1214C4—522no—
1215C4—522no—
1216C2—28no—
1217C2—524no—
1218C2C2×C4×#610311yescharacteristic
1219C2C4×#8813511yescharacteristic
1220C2#1311719511yescharacteristic
1221C2D4×#610311yescharacteristic
1222C2#1311766111yescharacteristic
1223C2#1311775911yescharacteristic
1224C2#1311777011yescharacteristic
1225C2#1311781511yescharacteristic
1226C2#1311781811yescharacteristic
1227C2#1311782811yescharacteristic
1228C2#1311783011yescharacteristic
1229C2#1311785011yescharacteristic
1230C2#1311785311yescharacteristic
1231C2#1311788111yescharacteristic
1232C2#1311788611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13813
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C22⋊C4×Dic13C2semidirect
5. C2×C4×#6103C2semidirect
6. C22×#88071C2semidirect
7. #13113074C2semidirect
8. #13113072C2semidirect
9. #13113071C2semidirect
10. #13113069C2semidirect
11. #13113060C2semidirect
12. #13113058C2semidirect
13. #13113057C2semidirect
14. C4×#88071C2semidirect
15. C2×C4×C13×C22⋊C4C2semidirect
37. C2×#88135C4semidirect
41. #11718874C4semidirect
57. #11718619C4semidirect
68. C23×C4×C13C2×C4semidirect
95. C23×Dic13C2×C4semidirect
109. C22×C4×D13C2×C4semidirect
113. C2×C13×C22⋊C4C2×C4semidirect
124. C2×C22⋊Dic13C2×C4semidirect
135. C2×#6103C2×C4semidirect
136. C2×#6103C2×C4semidirect
137. C2×#6103C2×C4semidirect
138. C2×#6103C2×C4semidirect
139. C2×#6103C2×C4semidirect
142. C2×#6101C2×C4semidirect
151. C2×C4×Dic13C2×C4semidirect
164. #88071C2×C4semidirect
165. #88071C2×C4semidirect
166. #88071C2×C4semidirect
167. #88071C2×C4semidirect
168. #88071D4semidirect
256. C2×C22⋊D13C42semidirect
328. C13×C22⋊C4C22⋊C4semidirect
346. C2×C4×C22⋊C4D13semidirect
483. C2×C4×C13C4×D4semidirect
535. C2×Dic13C4×D4semidirect
595. C22×C13C4×C22⋊C4semidirect
702. C23×C4C4×D13semidirect
734. C2×C22⋊C4C4×D13semidirect
950. C22⋊C4#6103semidirect
956. C13#13813semidirect
1135. C2×C4#88135semidirect
1167. C22C4×#6103semidirect

Maximal subgroups

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

subgroupindex
C22×#881352
C2×#117188742
C2×#117186192
C2×C22⋊C4×Dic132
C2×C4×#61032
C22×#880712
#131130742
#131130722
#131130712
#131130692
#131130602
#131130582
#131130572
C4×#880712
C2×C4×C13×C22⋊C42
#1381313