Finite Group Databasebeta

← #15790855

Subgroups — #15790855

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718606C211yesmaximal, characteristic
2C2×#11718605C211yesmaximal, characteristic
3C2×#11718871C211yesmaximal, characteristic
4C2×#11718311C211yesmaximal, characteristic, complemented
5#13113099C211yesmaximal, characteristic, complemented
6#13113099C211yesmaximal, characteristic, complemented
7#13113094C211yesmaximal, characteristic, complemented
8#13113086C211yesmaximal, characteristic, complemented
9#13113081C211yesmaximal, characteristic
10#13113079C211yesmaximal, characteristic
11#13113070C211yesmaximal, characteristic, complemented
12#13113065C211yesmaximal, characteristic, complemented
13#13113064C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C2×C13×#385C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×#6101C2211yescharacteristic
30C22×#6101C2211yescharacteristic
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C13×#385—24no—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36#11718871—24no—
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
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718606—24no—
54#11718605C418yescomplemented
55#11718311—24no—
56C25×C13C2311yescharacteristic
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—41no—
61C23×C4×C13—41no—
62C23×C4×C13—41no—
63C23×C4×C13—41no—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×Dic13C2311yescharacteristic
71C23×Dic13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C22⋊Dic13—22no—
91C2×C22⋊Dic13—22no—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—41no—
94C2×C22⋊Dic13—41no—
95C2×C22⋊Dic13—41no—
96C2×C22⋊Dic13—41no—
97C2×C22⋊Dic13—41no—
98C2×C22⋊Dic13C2×C414yes—
99C2×C22⋊Dic13C2×C414yes—
100C2×C22⋊Dic13D414yes—
101C2×C22⋊Dic13Q814yes—
102C2×C4⋊Dic13—22no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—41no—
105C2×#6101—22no—
106C2×#6101—22no—
107C2×#6101—22no—
108C2×#6101—22no—
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—41no—
112C2×#6101—41no—
113C2×#6101—41no—
114C2×#6101—41no—
115C2×#6101—41no—
116C2×#6101—41no—
117C2×#6101—41no—
118C2×#6101—41no—
119C2×#6101C2×C414yescomplemented
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—41no—
125C2×C4×Dic13C2×C414yescomplemented
126C13×#95—22no—
127C13×#95D414yes—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—22no—
134#88071—22no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071—41no—
141#88071—41no—
142#88071C2×C414yescomplemented
143#88071C2×C414yescomplemented
144#14403—131nomaximal, Sylow
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13C22×C412yes—
158C24×C13C2×D412yes—
159C24×C13C2×Q812yes—
160C24×C13C2411yescharacteristic
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×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—44no—
197C22×C4×C13—44no—
198C22×C4×C13—44no—
199C22×C4×C13—44no—
200C22×C4×C13—44no—
201C22×C4×C13—44no—
202C22×C4×C13—44no—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C2×D412yes—
206C22×C4×C13C2×D412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13#4112yes—
209C22×C4×C13#4112yes—
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×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×Dic13C22×C412yes—
258C22×Dic13C22×C412yes—
259C22×Dic13C22×C412yes—
260C22×Dic13C22×C412yes—
261C22×Dic13C2×D412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×Q812yes—
264C22×Dic13C2×Q812yes—
265C22×Dic13#4112yes—
266C13×C4⋊C4—44no—
267C13×C4⋊C4—44no—
268C13×C22⋊C4—28no—
269C13×C22⋊C4—44no—
270C22⋊Dic13—44no—
271C22⋊Dic13—44no—
272C22⋊Dic13—44no—
273C22⋊Dic13C4⋊C4116yescomplemented
274C4⋊Dic13—44no—
275#6101—44no—
276#6101—44no—
277#6101—44no—
278#6101—44no—
279#6101—44no—
280C4×Dic13—28no—
281C4×Dic13—44no—
282C2×#388—131no—
283C2×#388—131no—
284C2×#385—131no—
285C2×#385D1311yescharacteristic
286C2×#382—131no—
287#1444—131no—
288#1444—131no—
289#1442—131no—
290#1441—131no—
291#1439—131no—
292#1439—131no—
293#1436—131no—
294C4⋊#95—131no—
295C4⋊#95—131no—
296C22⋊#95—131no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13C2×C4⋊C414yes—
332C23×C13C23×C411yescharacteristic
333C23×C13C22×D411yescharacteristic
334C23×C13C22×D411yescharacteristic
335C23×C13C22×Q811yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13H(5,𝔽2)11yescharacteristic
340C23×C13H(5,𝔽2)11yescharacteristic
341C23×C13H(5,𝔽2)11yescharacteristic
342C23×C13H(5,𝔽2)11yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C132−1+411yescharacteristic
345C23×C132−1+411yescharacteristic
346C23×C132−1+411yescharacteristic
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—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—416no—
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—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
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×C13C4×D414yes—
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—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—22no—
410C2×Dic13—22no—
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×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
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×Dic13C2×C4⋊C414yes—
445C2×Dic13C2×C4⋊C414yes—
446C24×C4C2×D1311yescharacteristic
447C22×C4⋊C4—131no—
448C22×C4⋊C4—131no—
449C22×C4⋊C4—131no—
450C22×C4⋊C4—131no—
451C22×C4⋊C4—131no—
452C22×C4⋊C4—131no—
453C22×C4⋊C4C2×D1311yescharacteristic
454C22×C4⋊C4C2×D1311yescharacteristic
455C22×C22⋊C4—131no—
456C22×C22⋊C4—131no—
457C22×C22⋊C4—131no—
458C22×C22⋊C4—131no—
459C22×C22⋊C4C2×D1311yescharacteristic
460C22×C22⋊C4C2×D1311yescharacteristic
461C22×C42—131no—
462C22×C42—131no—
463#388—138no—
464#388—264no—
465#385—24no—
466#385—264no—
467#382—264no—
468C2×#95—131no—
469C2×#95—131no—
470C2×#95—131no—
471C2×#95—131no—
472C2×#95—131no—
473C2×#95—131no—
474C2×#95—131no—
475C2×#95—131no—
476C2×#95—131no—
477C2×#95—131no—
478C2×#95—131no—
479C2×#95—131no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95C2×D1311yescharacteristic
485C2×#95C2×D1311yescharacteristic
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13C22×C4⋊C411yescharacteristic
502C22×C13C2×C4×D411yescharacteristic
503C22×C13C4×#4111yescharacteristic
504C22×C13#51811yescharacteristic
505C22×C13#52011yescharacteristic
506C22×C13#52011yescharacteristic
507C22×C13#52011yescharacteristic
508C22×C13#53511yescharacteristic
509C22×C13#53511yescharacteristic
510C22×C13#53611yescharacteristic
511C22×C13#53711yescharacteristic
512C22×C13#53811yescharacteristic
513C22×C13#53911yescharacteristic
514C22×C13#54011yescharacteristic
515C22×C13#54111yescharacteristic
516C22×C13#54211yescharacteristic
517C22×C13#54211yescharacteristic
518C22×C13#54411yescharacteristic
519C22×C13#54411yescharacteristic
520C22×C13D4211yescharacteristic
521C22×C13#54611yescharacteristic
522C22×C13#54611yescharacteristic
523C22×C13#54611yescharacteristic
524C22×C13#54711yescharacteristic
525C22×C13#54711yescharacteristic
526C22×C13D4×Q811yescharacteristic
527C22×C13#55111yescharacteristic
528C22×C13#55211yescharacteristic
529C22×C13#55411yescharacteristic
530C22×C13#55411yescharacteristic
531C22×C13#55411yescharacteristic
532C22×C13H(3,𝔽4)11yescharacteristic
533C22×C13#56211yescharacteristic
534C22×C13#56211yescharacteristic
535C22×C13#56311yescharacteristic
536C4×C13—24no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—81no—
542Dic13—24no—
543Dic13—24no—
544Dic13—42no—
545Dic13—42no—
546Dic13—42no—
547Dic13—81no—
548Dic13—81no—
549Dic13—81no—
550C25C22×D1311yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—41no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4—41no—
558C23×C4—131no—
559C23×C4—131no—
560C23×C4—131no—
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4C22×D1311yescharacteristic
567C23×C4C22×D1311yescharacteristic
568C23×C4C22×D1311yescharacteristic
569C23×C4C22×D1311yescharacteristic
570C23×C4C22×D1311yescharacteristic
571C23×C4C22×D1311yescharacteristic
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—134no—
579C2×C4⋊C4—262no—
580C2×C4⋊C4—262no—
581C2×C4⋊C4—262no—
582C2×C4⋊C4—262no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—521no—
588C2×C4⋊C4—521no—
589C2×C4⋊C4—521no—
590C2×C4⋊C4—521no—
591C2×C4⋊C4—521no—
592C2×C4⋊C4—521no—
593C2×C4⋊C4—521no—
594C2×C4⋊C4—521no—
595C2×C4⋊C4—521no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—134no—
602C2×C22⋊C4—134no—
603C2×C22⋊C4—134no—
604C2×C22⋊C4—134no—
605C2×C22⋊C4—262no—
606C2×C22⋊C4—262no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—521no—
609C2×C22⋊C4—521no—
610C2×C22⋊C4—521no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4—521no—
613C2×C22⋊C4C4×D1314yes—
614C2×C42—134no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—262no—
618C2×C42—262no—
619C2×C42—521no—
620#95—22no—
621#95—134no—
622#95—134no—
623#95—262no—
624#95—262no—
625#95—262no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—521no—
631#95—521no—
632#95—521no—
633#95—521no—
634#95—521no—
635#95—521no—
636#95—521no—
637#95C22⋊D1314yes—
638C2×C13—44no—
639C2×C13#231711yescharacteristic
640C2×C13#232411yescharacteristic
641C2×C13#233411yescharacteristic
642C2×C13D4×C4⋊C411yescharacteristic
643C2×C13#234911yescharacteristic
644C2×C13#235911yescharacteristic
645C2×C13#237911yescharacteristic
646C2×C13#267011yescharacteristic
647C2×C13#267211yescharacteristic
648C2×C13#269811yescharacteristic
649C2×C13#270411yescharacteristic
650C2×C13#270611yescharacteristic
651C2×C13#272011yescharacteristic
652C2×C13#276311yescharacteristic
653C2×C13#276811yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C2×C4×D1312yes—
667C24D4×D1312yes—
668C24Q8×D1312yes—
669C24C23×D1311yescharacteristic
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—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
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—44no—
706C22×C4—44no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—44no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—132no—
717C22×C4—132no—
718C22×C4—132no—
719C22×C4—132no—
720C22×C4—132no—
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×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
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×C4C2×C4×D1312yes—
769C22×C4C2×C4×D1312yes—
770C22×C4#612712yes—
771C22×C4#612912yes—
772C22×C4C2×C22⋊D1312yes—
773C22×C4C2×C22⋊D1312yes—
774C22×C4C2×C22⋊D1312yes—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—524no—
778C4⋊C4—524no—
779C4⋊C4—524no—
780C4⋊C4—524no—
781C4⋊C4—524no—
782C4⋊C4—524no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—1316no—
786C22⋊C4—524no—
787C22⋊C4—524no—
788C22⋊C4—524no—
789C42—268no—
790C42—524no—
791C13#1440311yescharacteristic, complemented, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4⋊C4×D1314yes—
827C23C22×C4×D1311yescharacteristic
828C23C2×#612711yescharacteristic
829C23C2×D4×D1311yescharacteristic
830C23C2×#612911yescharacteristic
831C23#8825111yescharacteristic
832C23#8825111yescharacteristic
833C23#8825111yescharacteristic
834C23#8825111yescharacteristic
835C23C2×Q8×D1311yescharacteristic
836C23#8825411yescharacteristic
837C23#41×D1311yescharacteristic
838C23#8825611yescharacteristic
839C23#8825711yescharacteristic
840C23#8825711yescharacteristic
841C23C22×C22⋊D1311yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—416no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—134no—
885C2×C4—134no—
886C2×C4—262no—
887C2×C4—262no—
888C2×C4—262no—
889C2×C4—262no—
890C2×C4—262no—
891C2×C4—262no—
892C2×C4—262no—
893C2×C4—262no—
894C2×C4—262no—
895C2×C4—262no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—521no—
908C2×C4—521no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4C4×C22⋊D1314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C4⋊C4×D1311yescharacteristic
957C22#1171920911yescharacteristic
958C22#1171921211yescharacteristic
959C22#1171921611yescharacteristic
960C22C4×#612911yescharacteristic
961C22#1171924611yescharacteristic
962C22#1171925011yescharacteristic
963C22#1171925111yescharacteristic
964C22#1171925111yescharacteristic
965C22#1171926111yescharacteristic
966C22#1171926611yescharacteristic
967C22#1171926711yescharacteristic
968C22#1171929611yescharacteristic
969C22#1171929711yescharacteristic
970C22#1171929811yescharacteristic
971C22#1171929911yescharacteristic
972C22#1171932811yescharacteristic
973C22#1171932811yescharacteristic
974C22#1171933011yescharacteristic
975C22#1171934011yescharacteristic
976C22#1171934111yescharacteristic
977C22#1171934311yescharacteristic
978C22#1171935111yescharacteristic
979C22#1171935211yescharacteristic
980C22#1171935311yescharacteristic
981C22#1171935911yescharacteristic
982C22#1171936711yescharacteristic
983C22#1171937211yescharacteristic
984C22C2×C4×C22⋊D1311yescharacteristic
985C22D4×C22⋊D1311yescharacteristic
986C22#1171951011yescharacteristic
987C22#1171951111yescharacteristic
988C22Q8×C22⋊D1311yescharacteristic
989C22#1171952911yescharacteristic
990C22#1171953811yescharacteristic
991C4—24no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—81no—
997C4—264no—
998C4—264no—
999C4—522no—
1000C4—522no—
1001C4—522no—
1002C4—1041no—
1003C4—1041no—
1004C4—1041no—
1005C2—44no—
1006C2#1311745511yescharacteristic
1007C2#1311752311yescharacteristic
1008C2#1311761211yescharacteristic
1009C2C4⋊C4×C22⋊D1311yescharacteristic
1010C2#1311774211yescharacteristic
1011C2#1311782211yescharacteristic
1012C2#1311800911yescharacteristic
1013C2#1312105811yescharacteristic
1014C2#1312108711yescharacteristic
1015C2#1312141411yescharacteristic
1016C2#1312149011yescharacteristic
1017C2#1312152511yescharacteristic
1018C2#1312171011yescharacteristic
1019C2#1312224811yescharacteristic
1020C2#1312231411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14403
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#11718311C2semidirect
5. #13113099C2semidirect
6. #13113099C2semidirect
7. #13113094C2semidirect
8. #13113086C2semidirect
11. #13113070C2semidirect
12. #13113065C2semidirect
13. #13113064C2semidirect
54. #11718605C4semidirect
119. C2×#6101C2×C4semidirect
125. C2×C4×Dic13C2×C4semidirect
142. #88071C2×C4semidirect
143. #88071C2×C4semidirect
273. C22⋊Dic13C4⋊C4semidirect
791. C13#14403semidirect

Maximal subgroups

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

subgroupindex
C2×#117186062
C2×#117186052
C2×#117188712
C2×#117183112
#131130992
#131130942
#131130862
#131130812
#131130792
#131130702
#131130652
#131130642
#131130592
C2×C13×#3852
#1440313