Finite Group Databasebeta

← #15785178

Subgroups — #15785178

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718328C211yesmaximal, characteristic
2C2×#11718328C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5C2×D13×#95C211yesmaximal, characteristic
6#13113100C211yesmaximal, characteristic, complemented
7#13113099C211yesmaximal, characteristic, complemented
8#13113094C211yesmaximal, characteristic, complemented
9#13113091C211yesmaximal, characteristic, complemented
10#13113070C211yesmaximal, characteristic, complemented
11#13113069C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13#13113057C211yesmaximal, characteristic
14#13113057C211yesmaximal, characteristic
15C13×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D13C2211yescharacteristic
17C23×C4×D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C42×C13C2211yescharacteristic
21C22×#6103C2211yescharacteristic
22C22×#6103C2211yescharacteristic
23C22×#6103C2211yescharacteristic
24C22×#6103C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
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#11718648—24no—
52C4×#6103—24no—
53#11718328—24no—
54#11718328—24no—
55D13×#95C418yescomplemented
56C24×D13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×Dic13C2311yescharacteristic
65C23×Dic13C2311yescharacteristic
66C23×Dic13C2311yescharacteristic
67C23×Dic13C2311yescharacteristic
68C23×Dic13C2311yescharacteristic
69C23×Dic13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C22×C4×D13—22no—
72C22×C4×D13—22no—
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—41no—
80C22×C4×D13—41no—
81C22×C4×D13—41no—
82C22×C4×D13—41no—
83C22×C4×D13—41no—
84C22×C4×D13—41no—
85C22×C4×D13—41no—
86C22×C4×D13—41no—
87C22×C4×D13C2×C414yes—
88C22×C4×D13C2×C414yes—
89C22×C4×D13C2×C414yes—
90C22×C4×D13D414yes—
91C22×C4×D13Q814yes—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—41no—
95C2×C42×C13—22no—
96C2×C42×C13—41no—
97C2×C42×C13—41no—
98C2×#6103—22no—
99C2×#6103—22no—
100C2×#6103—22no—
101C2×#6103—22no—
102C2×#6103—22no—
103C2×#6103—22no—
104C2×#6103—22no—
105C2×#6103—22no—
106C2×#6103—22no—
107C2×#6103—22no—
108C2×#6103D414yes—
109C2×#6103Q814yes—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—41no—
113C2×#6101—22no—
114C2×#6101—22no—
115C2×#6101—22no—
116C2×#6101—22no—
117C2×#6101—22no—
118C2×#6101—22no—
119C2×#6101—41no—
120C2×#6101—41no—
121C2×#6101—41no—
122C2×#6101—41no—
123C2×#6101—41no—
124C2×#6101—41no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—41no—
127C2×C4×Dic13—41no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—41no—
132C13×#95C2×C414yes—
133#88071—22no—
134#88071—22no—
135#88071—22no—
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—41no—
143#88071—41no—
144#88071—41no—
145#88071C2×C414yes—
146#88071C2×C414yes—
147#88071C2×C414yes—
148#13908—131nomaximal, Sylow
149C24×C13C2411yescharacteristic
150C23×D13—21no—
151C23×D13—21no—
152C23×D13—21no—
153C23×D13—21no—
154C23×D13—21no—
155C23×D13—21no—
156C23×D13—21no—
157C23×D13—21no—
158C23×D13C22×C412yes—
159C23×D13C2×D412yes—
160C23×D13C2×D412yes—
161C23×D13C2×Q812yes—
162C23×D13C2×Q812yes—
163C23×D13#4112yes—
164C23×D13#4112yes—
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×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×C13C22×C412yes—
206C22×C4×C13C22×C412yes—
207C22×C4×C13C22×C412yes—
208C22×C4×C13C2×D412yes—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2×Q812yes—
211C22×C4×C13C2×Q812yes—
212C22×C4×C13#4112yes—
213C22×C4×C13#4112yes—
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×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×Dic13C22×C412yes—
255C22×Dic13C22×C412yes—
256C22×Dic13C22×C412yes—
257C22×Dic13C2×D412yes—
258C22×Dic13C2×D412yes—
259C22×Dic13C2×Q812yes—
260C22×Dic13C2×Q812yes—
261C22×Dic13#4112yes—
262C22×Dic13#4112yes—
263C2×C4×D13—28no—
264C2×C4×D13—28no—
265C2×C4×D13—28no—
266C2×C4×D13—28no—
267C2×C4×D13—44no—
268C2×C4×D13—44no—
269C2×C4×D13—44no—
270C2×C4×D13—44no—
271C2×C4×D13—44no—
272C2×C4×D13—44no—
273C2×C4×D13—44no—
274C2×C4×D13—44no—
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×D13C4⋊C4116yescomplemented
284C13×C4⋊C4—44no—
285C42×C13—44no—
286#6103—28no—
287#6103—28no—
288#6103—44no—
289#6103—44no—
290C4⋊Dic13—44no—
291#6101—44no—
292#6101—44no—
293#6101—44no—
294#6101—44no—
295C4×Dic13—44no—
296C2×#380—131no—
297C2×#380—131no—
298C2×#380—131no—
299C2×C4×C22⋊C4—131no—
300C22×#95—131no—
301#1444—131no—
302#1444—131no—
303#1442—131no—
304#1442—131no—
305#1436—131no—
306#1436—131no—
307#1436—131no—
308#1436D1311yescharacteristic, complemented
309C22⋊#95—131no—
310C22⋊#95—131no—
311C23×C13C23×C411yescharacteristic
312C23×C13C22×D411yescharacteristic
313C23×C13C22×D411yescharacteristic
314C23×C13C22×Q811yescharacteristic
315C23×C13C22×Q811yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C13H(5,𝔽2)11yescharacteristic
325C23×C13H(5,𝔽2)11yescharacteristic
326C22×D13—22no—
327C22×D13—22no—
328C22×D13—22no—
329C22×D13—22no—
330C22×D13—22no—
331C22×D13—22no—
332C22×D13—22no—
333C22×D13—22no—
334C22×D13—22no—
335C22×D13—22no—
336C22×D13—22no—
337C22×D13—22no—
338C22×D13—22no—
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×D13C2×C4⋊C414yes—
355C22×D13C4×D414yes—
356C22×D13C4×Q814yes—
357C22×D13#12114yes—
358C22×D13C22⋊Q814yes—
359C22×D13#12514yes—
360C22×D13C4⋊Q814yes—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
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—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
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×C13C2×C4⋊C414yes—
409C2×C4×C13#11714yes—
410C2×Dic13—22no—
411C2×Dic13—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
418C2×Dic13—22no—
419C2×Dic13—22no—
420C2×Dic13—22no—
421C2×Dic13—22no—
422C2×Dic13—22no—
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—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
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×Dic13C2×C4⋊C414yes—
458C2×Dic13#11714yes—
459C4×D13—416no—
460C4×D13—416no—
461C4×D13—416no—
462C24×C4—131no—
463C24×C4—131no—
464C24×C4—131no—
465C22×C4⋊C4—131no—
466C22×C4⋊C4—131no—
467C22×C4⋊C4—131no—
468C22×C4⋊C4—131no—
469C22×C4⋊C4—131no—
470C22×C4⋊C4C2×D1311yescharacteristic
471C22×C22⋊C4—131no—
472C22×C22⋊C4—131no—
473C22×C22⋊C4—131no—
474C22×C22⋊C4—131no—
475C22×C42—131no—
476C22×C42C2×D1311yescharacteristic
477#380—264no—
478#380—264no—
479#380—264no—
480C4×C22⋊C4—264no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—138no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95—131no—
495C2×#95—131no—
496C2×#95—131no—
497C2×#95C2×D1311yescharacteristic
498C2×#95C2×D1311yescharacteristic
499C2×#95C2×D1311yescharacteristic
500C2×#95C2×D1311yescharacteristic
501C2×#95C2×D1311yescharacteristic
502C22×C13C22×C4⋊C411yescharacteristic
503C22×C13C2×#11711yescharacteristic
504C22×C13C2×#11711yescharacteristic
505C22×C13C2×C4×D411yescharacteristic
506C22×C13C2×C4×Q811yescharacteristic
507C22×C13#51811yescharacteristic
508C22×C13#51811yescharacteristic
509C22×C13C2×#12111yescharacteristic
510C22×C13C2×C22⋊Q811yescharacteristic
511C22×C13C2×#12511yescharacteristic
512C22×C13C2×C4⋊Q811yescharacteristic
513C22×C13#53211yescharacteristic
514C22×C13#53211yescharacteristic
515C22×C13#53311yescharacteristic
516C22×C13#53311yescharacteristic
517C22×C13#53411yescharacteristic
518C22×C13#53411yescharacteristic
519C22×C13#54311yescharacteristic
520C22×C13#54311yescharacteristic
521C22×C13#54611yescharacteristic
522C22×C13#54611yescharacteristic
523C22×C13#54611yescharacteristic
524C22×C13#54611yescharacteristic
525C22×C13#55111yescharacteristic
526C22×C13#55111yescharacteristic
527C22×C13#55111yescharacteristic
528C22×C13#55111yescharacteristic
529C22×C13#55311yescharacteristic
530C22×C13#55311yescharacteristic
531C22×C13#55311yescharacteristic
532C22×C13#55311yescharacteristic
533C22×C13#55411yescharacteristic
534C22×C13#55411yescharacteristic
535C22×C13#55411yescharacteristic
536C22×C13#55411yescharacteristic
537C2×D13—24no—
538C2×D13—24no—
539C2×D13—24no—
540C2×D13—24no—
541C2×D13—24no—
542C2×D13—24no—
543C2×D13—24no—
544C2×D13—24no—
545C2×D13—24no—
546C2×D13—24no—
547C2×D13—24no—
548C2×D13—24no—
549C2×D13—24no—
550C2×D13—24no—
551C2×D13#38918yes—
552C4×C13—24no—
553C4×C13—24no—
554C4×C13—42no—
555C4×C13—42no—
556C4×C13—42no—
557C4×C13—81no—
558C4×C13—81no—
559Dic13—24no—
560Dic13—24no—
561Dic13—42no—
562Dic13—42no—
563Dic13—42no—
564Dic13—81no—
565Dic13—81no—
566C25—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—134no—
570C23×C4—134no—
571C23×C4—134no—
572C23×C4—131no—
573C23×C4—131no—
574C23×C4—131no—
575C23×C4—134no—
576C23×C4—134no—
577C23×C4—131no—
578C23×C4—131no—
579C23×C4—262no—
580C23×C4—262no—
581C23×C4—262no—
582C23×C4—262no—
583C23×C4—262no—
584C23×C4—262no—
585C23×C4—262no—
586C23×C4—262no—
587C23×C4—521no—
588C23×C4—521no—
589C23×C4—521no—
590C23×C4—521no—
591C23×C4—521no—
592C23×C4—521no—
593C23×C4—521no—
594C23×C4—521no—
595C23×C4C22×D1311yescharacteristic
596C23×C4C22×D1311yescharacteristic
597C23×C4C22×D1311yescharacteristic
598C23×C4C22×D1311yescharacteristic
599C23×C4C22×D1311yescharacteristic
600C23×C4C22×D1311yescharacteristic
601C23×C4C22×D1311yescharacteristic
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—262no—
608C2×C4⋊C4—262no—
609C2×C4⋊C4—262no—
610C2×C4⋊C4—262no—
611C2×C4⋊C4—262no—
612C2×C4⋊C4—262no—
613C2×C4⋊C4—521no—
614C2×C4⋊C4—521no—
615C2×C4⋊C4—521no—
616C2×C4⋊C4—521no—
617C2×C4⋊C4—521no—
618C2×C4⋊C4—521no—
619C2×C4⋊C4—521no—
620C2×C22⋊C4—134no—
621C2×C22⋊C4—134no—
622C2×C22⋊C4—262no—
623C2×C22⋊C4—262no—
624C2×C22⋊C4—262no—
625C2×C22⋊C4—262no—
626C2×C22⋊C4—262no—
627C2×C22⋊C4—262no—
628C2×C22⋊C4—262no—
629C2×C22⋊C4—262no—
630C2×C22⋊C4—262no—
631C2×C22⋊C4—262no—
632C2×C42—22no—
633C2×C42—41no—
634C2×C42—41no—
635C2×C42—262no—
636C2×C42—521no—
637C2×C42—521no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—41no—
642#95—134no—
643#95—134no—
644#95—134no—
645#95—262no—
646#95—262no—
647#95—262no—
648#95—262no—
649#95—262no—
650#95—262no—
651#95—262no—
652#95—262no—
653#95—262no—
654#95—521no—
655#95—521no—
656#95—521no—
657#95C4×D1314yes—
658C2×C13#228511yescharacteristic
659C2×C13C2×#38911yescharacteristic
660C2×C13#231511yescharacteristic
661C2×C13#234211yescharacteristic
662C2×C13#234211yescharacteristic
663C2×C13#234511yescharacteristic
664C2×C13#234511yescharacteristic
665C2×C13#254311yescharacteristic
666C2×C13#254311yescharacteristic
667C2×C13#254911yescharacteristic
668C2×C13#254911yescharacteristic
669C2×C13#256411yescharacteristic
670C2×C13#256411yescharacteristic
671C2×C13#256911yescharacteristic
672C2×C13#256911yescharacteristic
673D13—28no—
674C24—132no—
675C24—132no—
676C24—132no—
677C24—132no—
678C24—132no—
679C24—132no—
680C24—132no—
681C24—261no—
682C24—261no—
683C24—261no—
684C24—261no—
685C24—261no—
686C24—261no—
687C24—261no—
688C24—261no—
689C24C23×D1311yescharacteristic
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
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—132no—
731C22×C4—132no—
732C22×C4—132no—
733C22×C4—132no—
734C22×C4—132no—
735C22×C4—132no—
736C22×C4—1316no—
737C22×C4—132no—
738C22×C4—132no—
739C22×C4—132no—
740C22×C4—268no—
741C22×C4—268no—
742C22×C4—268no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—261no—
769C22×C4—268no—
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—524no—
785C22×C4—524no—
786C22×C4—524no—
787C22×C4—524no—
788C22×C4—524no—
789C22×C4—524no—
790C22×C4—524no—
791C22×C4—524no—
792C22×C4—524no—
793C22×C4—524no—
794C22×C4—524no—
795C22×C4—524no—
796C22×C4—524no—
797C22×C4—524no—
798C22×C4—524no—
799C22×C4—524no—
800C22×C4C2×C4×D1312yes—
801C22×C4C2×C4×D1312yes—
802C22×C4C2×C4×D1312yes—
803C22×C4#612712yes—
804C22×C4#612712yes—
805C22×C4D4×D1312yes—
806C22×C4D4×D1312yes—
807C22×C4Q8×D1312yes—
808C22×C4Q8×D1312yes—
809C4⋊C4—44no—
810C4⋊C4—524no—
811C4⋊C4—524no—
812C4⋊C4—524no—
813C4⋊C4—524no—
814C4⋊C4—524no—
815C22⋊C4—268no—
816C22⋊C4—268no—
817C22⋊C4—524no—
818C22⋊C4—524no—
819C42—44no—
820C42—524no—
821C13#1390811yescharacteristic, complemented, Sylow
822C23—134no—
823C23—134no—
824C23—134no—
825C23—134no—
826C23—134no—
827C23—134no—
828C23—134no—
829C23—262no—
830C23—262no—
831C23—262no—
832C23—262no—
833C23—262no—
834C23—262no—
835C23—262no—
836C23—262no—
837C23—262no—
838C23—262no—
839C23—262no—
840C23—262no—
841C23—262no—
842C23—262no—
843C23—262no—
844C23—262no—
845C23—262no—
846C23—262no—
847C23—262no—
848C23—262no—
849C23—262no—
850C23—262no—
851C23—262no—
852C23—262no—
853C23—262no—
854C23—262no—
855C23—262no—
856C23—262no—
857C23C22×C4×D1311yescharacteristic
858C23C2×#612711yescharacteristic
859C23C2×#612711yescharacteristic
860C23C2×D4×D1311yescharacteristic
861C23C2×D4×D1311yescharacteristic
862C23#8825111yescharacteristic
863C23#8825111yescharacteristic
864C23C2×Q8×D1311yescharacteristic
865C23C2×Q8×D1311yescharacteristic
866C23#41×D1311yescharacteristic
867C23#41×D1311yescharacteristic
868C23#41×D1311yescharacteristic
869C23#41×D1311yescharacteristic
870C23#8825611yescharacteristic
871C23#8825611yescharacteristic
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—134no—
920C2×C4—134no—
921C2×C4—262no—
922C2×C4—262no—
923C2×C4—262no—
924C2×C4—262no—
925C2×C4—262no—
926C2×C4—262no—
927C2×C4—262no—
928C2×C4—262no—
929C2×C4—262no—
930C2×C4—262no—
931C2×C4—262no—
932C2×C4—262no—
933C2×C4—262no—
934C2×C4—262no—
935C2×C4—262no—
936C2×C4—262no—
937C2×C4—262no—
938C2×C4—262no—
939C2×C4—262no—
940C2×C4—262no—
941C2×C4—262no—
942C2×C4—5216no—
943C2×C4—5216no—
944C2×C4—5216no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4—521no—
954C2×C4—521no—
955C2×C4—521no—
956C2×C4—521no—
957C2×C4—521no—
958C2×C4—521no—
959C2×C4—521no—
960C2×C4—521no—
961C2×C4—521no—
962C2×C4—521no—
963C2×C4—521no—
964C2×C4—521no—
965C2×C4—521no—
966C2×C4—521no—
967C2×C4—521no—
968C2×C4—521no—
969C2×C4—521no—
970C2×C4—521no—
971C2×C4#8812614yes—
972C2×C4C4⋊C4×D1314yes—
973C22—138no—
974C22—264no—
975C22—264no—
976C22—264no—
977C22—264no—
978C22—264no—
979C22—264no—
980C22—264no—
981C22—264no—
982C22—264no—
983C22—264no—
984C22—264no—
985C22—264no—
986C22—264no—
987C22—264no—
988C22C2×#8812611yescharacteristic
989C22#1171919511yescharacteristic
990C22C2×C4⋊C4×D1311yescharacteristic
991C22#1171921611yescharacteristic
992C22D13×#11711yescharacteristic
993C22#1171923211yescharacteristic
994C22#1171923511yescharacteristic
995C22C4×D4×D1311yescharacteristic
996C22#1171925011yescharacteristic
997C22#1171925011yescharacteristic
998C22#1171925311yescharacteristic
999C22#1171925311yescharacteristic
1000C22#1171925511yescharacteristic
1001C22#1171926111yescharacteristic
1002C22#1171926311yescharacteristic
1003C22C4×Q8×D1311yescharacteristic
1004C22#1171928311yescharacteristic
1005C22#1171928311yescharacteristic
1006C22#1171928411yescharacteristic
1007C22#1171929411yescharacteristic
1008C22D13×#12111yescharacteristic
1009C22#1171931511yescharacteristic
1010C22D13×C22⋊Q811yescharacteristic
1011C22#1171933911yescharacteristic
1012C22#1171933911yescharacteristic
1013C22#1171934111yescharacteristic
1014C22#1171935811yescharacteristic
1015C22#1171936411yescharacteristic
1016C22#1171936611yescharacteristic
1017C22#1171938111yescharacteristic
1018C22D13×#12511yescharacteristic
1019C22#1171939511yescharacteristic
1020C22#1171941011yescharacteristic
1021C22#1171941411yescharacteristic
1022C22D13×C4⋊Q811yescharacteristic
1023C4—24no—
1024C4—24no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—81no—
1029C4—81no—
1030C4—264no—
1031C4—264no—
1032C4—522no—
1033C4—522no—
1034C4—522no—
1035C4—1041no—
1036C4—1041no—
1037C2—268no—
1038C2#1311724011yescharacteristic
1039C2D13×#38911yescharacteristic
1040C2#1311744711yescharacteristic
1041C2#1311767911yescharacteristic
1042C2#1311768411yescharacteristic
1043C2#1311770911yescharacteristic
1044C2#1311771011yescharacteristic
1045C2#1311979511yescharacteristic
1046C2#1311980111yescharacteristic
1047C2#1311984511yescharacteristic
1048C2#1311984611yescharacteristic
1049C2#1312001511yescharacteristic
1050C2#1312002111yescharacteristic
1051C2#1312005811yescharacteristic
1052C2#1312005911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1436C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1436D13
hypocenterC13#13908
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #13113100C2semidirect
7. #13113099C2semidirect
8. #13113094C2semidirect
9. #13113091C2semidirect
10. #13113070C2semidirect
11. #13113069C2semidirect
12. #13113067C2semidirect
15. C13×#1436C2semidirect
55. D13×#95C4semidirect
283. C2×C4×D13C4⋊C4semidirect
308. #1436D13semidirect
821. C13#13908semidirect

Maximal subgroups

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

subgroupindex
C2×#117183282
C2×#117186482
C2×C4×#61032
C2×D13×#952
#131131002
#131130992
#131130942
#131130912
#131130702
#131130692
#131130672
#131130572
C13×#14362
#1390813