Finite Group Databasebeta

← #15793010

Subgroups — #15793010

Order 3328.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718608C211yesmaximal, characteristic
2C2×#11718635C211yesmaximal, characteristic, complemented
3C2×#11718307C211yesmaximal, characteristic, complemented
4C2×#11718871C211yesmaximal, characteristic
5#13113099C211yesmaximal, characteristic, complemented
6#13113099C211yesmaximal, characteristic, complemented
7#13113095C211yesmaximal, characteristic, complemented
8#13113091C211yesmaximal, characteristic, complemented
9#13113079C211yesmaximal, characteristic
10#13113073C211yesmaximal, characteristic
11#13113073C211yesmaximal, characteristic
12#13113061C211yesmaximal, characteristic, complemented
13#13113060C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic
15C2×C13×#385C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29C22×C4×Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C13×#385—24no—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34#11718871—24no—
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53#11718635—24no—
54#11718608C418yescomplemented
55#11718307—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
78C22×Dic26—22no—
79C22×Dic26—22no—
80C22×Dic26—22no—
81C22×Dic26—22no—
82C22×Dic26—41no—
83C22×Dic26—41no—
84C22×Dic26C2×C414yescomplemented
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—41no—
89C2×C13×C4⋊C4—41no—
90C2×C13×C4⋊C4—41no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—41no—
96C2×C13×C22⋊C4C2×C414yes—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—41no—
102C2×C22⋊Dic13—41no—
103C2×C22⋊Dic13—41no—
104C2×C22⋊Dic13—41no—
105C2×C22⋊Dic13—41no—
106C2×C22⋊Dic13C2×C414yes—
107C2×C22⋊Dic13C2×C414yes—
108C2×C22⋊Dic13Q814yescomplemented
109C2×#6101—22no—
110C2×#6101—22no—
111C2×#6101—22no—
112C2×#6101—41no—
113C2×#6101—41no—
114C2×#6101—41no—
115C2×#6101—41no—
116C2×#6101—41no—
117C2×#6101—41no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—41no—
123C2×C4×Dic13—41no—
124C13×#95—22no—
125C13×#95D414yes—
126#88071—22no—
127#88071—22no—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071—22no—
132#88071—22no—
133#88071—41no—
134#88071—41no—
135#88071—41no—
136#88071—41no—
137#88071—41no—
138#88071—41no—
139#88071—41no—
140#88071C2×C414yescomplemented
141#88071C2×C414yescomplemented
142#88071C2×C414yescomplemented
143#88071D414yes—
144#14575—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×Q812yes—
159C24×C13#4112yes—
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×C13C2×D412yes—
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—
266C2×Dic26—28no—
267C2×Dic26—28no—
268C2×Dic26—44no—
269C2×Dic26—44no—
270C2×Dic26—44no—
271C2×Dic26—44no—
272C2×Dic26—44no—
273C13×C4⋊C4—44no—
274C13×C4⋊C4—44no—
275C13×C22⋊C4—28no—
276C13×C22⋊C4—44no—
277C22⋊Dic13—28no—
278C22⋊Dic13—44no—
279C22⋊Dic13—44no—
280C22⋊Dic13—44no—
281#6101—44no—
282#6101—44no—
283#6101—44no—
284C4×Dic13—44no—
285C4×Dic13—44no—
286C2×#393—131no—
287C2×#391—131no—
288C2×#391—131no—
289C2×#385—131no—
290C2×#385D1311yescharacteristic
291#1444—131no—
292#1444—131no—
293#1442—131no—
294#1442—131no—
295#1439—131no—
296#1437—131no—
297#1437—131no—
298#1434—131no—
299#1434—131no—
300C22⋊#95—131no—
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—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
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×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13C4×Q814yes—
336C23×C13C23×C411yescharacteristic
337C23×C13C22×D411yescharacteristic
338C23×C13C22×D411yescharacteristic
339C23×C13C22×Q811yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C13H(5,𝔽2)11yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C13H(5,𝔽2)11yescharacteristic
348C23×C132−1+411yescharacteristic
349C23×C132−1+411yescharacteristic
350C23×C132−1+411yescharacteristic
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—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—416no—
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×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13C4×D414yes—
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—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
414C2×Dic13—22no—
415C2×Dic13—22no—
416C2×Dic13—22no—
417C2×Dic13—22no—
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×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13C4×D414yes—
450Dic26—416no—
451C23×Q8—131no—
452C24×C4C2×D1311yescharacteristic
453C22×C4⋊C4—131no—
454C22×C4⋊C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4C2×D1311yescharacteristic
457C22×C4⋊C4C2×D1311yescharacteristic
458C22×C22⋊C4—131no—
459C22×C22⋊C4—131no—
460C22×C22⋊C4—131no—
461C22×C22⋊C4—131no—
462C22×C22⋊C4C2×D1311yescharacteristic
463C22×C22⋊C4C2×D1311yescharacteristic
464C22×C42—131no—
465C22×C42—131no—
466#393—138no—
467#391—264no—
468#391—264no—
469#385—24no—
470#385—264no—
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×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95C2×D1311yescharacteristic
490C2×#95C2×D1311yescharacteristic
491C22×C13—24no—
492C22×C13—24no—
493C22×C13—24no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13C2×C4×D411yescharacteristic
507C22×C13C2×C4×D411yescharacteristic
508C22×C13C2×C4×Q811yescharacteristic
509C22×C13#51811yescharacteristic
510C22×C13#52011yescharacteristic
511C22×C13#52011yescharacteristic
512C22×C13#52011yescharacteristic
513C22×C13#53511yescharacteristic
514C22×C13#53511yescharacteristic
515C22×C13#53611yescharacteristic
516C22×C13#53611yescharacteristic
517C22×C13#53811yescharacteristic
518C22×C13#53911yescharacteristic
519C22×C13#54211yescharacteristic
520C22×C13#54211yescharacteristic
521C22×C13#54211yescharacteristic
522C22×C13#54211yescharacteristic
523C22×C13#54311yescharacteristic
524C22×C13#54411yescharacteristic
525C22×C13D4211yescharacteristic
526C22×C13#54611yescharacteristic
527C22×C13#54611yescharacteristic
528C22×C13#54611yescharacteristic
529C22×C13#54611yescharacteristic
530C22×C13D4×Q811yescharacteristic
531C22×C13D4×Q811yescharacteristic
532C22×C13#55111yescharacteristic
533C22×C13#55211yescharacteristic
534C22×C13#55211yescharacteristic
535C22×C13#55411yescharacteristic
536C22×C13#55411yescharacteristic
537C22×C13H(3,𝔽4)11yescharacteristic
538C22×C13#56211yescharacteristic
539C22×C13#56211yescharacteristic
540C22×C13#56311yescharacteristic
541C4×C13—24no—
542C4×C13—42no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—81no—
547Dic13—24no—
548Dic13—42no—
549Dic13—42no—
550Dic13—42no—
551Dic13—42no—
552Dic13—42no—
553Dic13—42no—
554Dic13—81no—
555C25C22×D1311yescharacteristic
556C22×Q8—134no—
557C22×Q8—262no—
558C22×Q8—262no—
559C22×Q8—262no—
560C22×Q8—262no—
561C22×Q8—521no—
562C22×Q8—521no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—41no—
567C23×C4—41no—
568C23×C4—41no—
569C23×C4—41no—
570C23×C4—131no—
571C23×C4—131no—
572C23×C4—131no—
573C23×C4—131no—
574C23×C4—131no—
575C23×C4—131no—
576C23×C4—131no—
577C23×C4—131no—
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C23×C4C22×D1311yescharacteristic
583C23×C4C22×D1311yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4—41no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—521no—
594C2×C4⋊C4—521no—
595C2×C4⋊C4—521no—
596C2×C4⋊C4—521no—
597C2×C4⋊C4—521no—
598C2×C4⋊C4—521no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—134no—
605C2×C22⋊C4—134no—
606C2×C22⋊C4—134no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—262no—
609C2×C22⋊C4—262no—
610C2×C22⋊C4—262no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4—521no—
613C2×C22⋊C4—521no—
614C2×C22⋊C4—521no—
615C2×C22⋊C4—521no—
616C2×C22⋊C4C4×D1314yes—
617C2×C42—262no—
618C2×C42—262no—
619C2×C42—262no—
620C2×C42—262no—
621C2×C42—521no—
622C2×C42—521no—
623#95—22no—
624#95—134no—
625#95—134no—
626#95—134no—
627#95—134no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—521no—
636#95—521no—
637#95—521no—
638#95—521no—
639#95—521no—
640#95—521no—
641#95—521no—
642#95C22⋊D1314yes—
643C2×C13—44no—
644C2×C13#232611yescharacteristic
645C2×C13#232611yescharacteristic
646C2×C13#232911yescharacteristic
647C2×C13#235811yescharacteristic
648C2×C13#236011yescharacteristic
649C2×C13#236011yescharacteristic
650C2×C13#237911yescharacteristic
651C2×C13#267011yescharacteristic
652C2×C13#267711yescharacteristic
653C2×C13#268711yescharacteristic
654C2×C13#268711yescharacteristic
655C2×C13#269211yescharacteristic
656C2×C13#269211yescharacteristic
657C2×C13#276311yescharacteristic
658C2×C13#276411yescharacteristic
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24C2×C4×D1312yes—
672C24#612912yes—
673C24Q8×D1312yes—
674C24C23×D1311yescharacteristic
675C2×Q8—268no—
676C2×Q8—268no—
677C2×Q8—524no—
678C2×Q8—524no—
679C2×Q8—524no—
680C2×Q8—524no—
681C2×Q8—524no—
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—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—44no—
718C22×C4—44no—
719C22×C4—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—132no—
725C22×C4—132no—
726C22×C4—132no—
727C22×C4—132no—
728C22×C4—132no—
729C22×C4—132no—
730C22×C4—132no—
731C22×C4—132no—
732C22×C4—132no—
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×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×C4C2×C4×D1312yes—
781C22×C4C2×C4×D1312yes—
782C22×C4#612712yes—
783C22×C4D4×D1312yes—
784C22×C4C2×C22⋊D1312yes—
785C22×C4C2×C22⋊D1312yes—
786C22×C4C2×C22⋊D1312yes—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—524no—
790C4⋊C4—524no—
791C4⋊C4—524no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—268no—
795C22⋊C4—524no—
796C22⋊C4—524no—
797C22⋊C4—524no—
798C42—524no—
799C42—524no—
800C13#1457511yescharacteristic, complemented, Sylow
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23#8814114yes—
836C23C22×C4×D1311yescharacteristic
837C23C2×#612711yescharacteristic
838C23C2×D4×D1311yescharacteristic
839C23C2×#612911yescharacteristic
840C23#8825111yescharacteristic
841C23#8825111yescharacteristic
842C23#8825111yescharacteristic
843C23#8825111yescharacteristic
844C23C2×Q8×D1311yescharacteristic
845C23#8825411yescharacteristic
846C23#41×D1311yescharacteristic
847C23#8825611yescharacteristic
848C23#8825711yescharacteristic
849C23#8825711yescharacteristic
850C23C22×C22⋊D1311yescharacteristic
851Q8—5216no—
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—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—416no—
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—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—134no—
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—262no—
908C2×C4—262no—
909C2×C4—262no—
910C2×C4—262no—
911C2×C4—262no—
912C2×C4—262no—
913C2×C4—262no—
914C2×C4—262no—
915C2×C4—262no—
916C2×C4—262no—
917C2×C4—262no—
918C2×C4—262no—
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×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4C4×C22⋊D1314yes—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22C2×#8814111yescharacteristic
967C22#1171920911yescharacteristic
968C22#1171921611yescharacteristic
969C22#1171921811yescharacteristic
970C22C4×D4×D1311yescharacteristic
971C22#1171925011yescharacteristic
972C22#1171925111yescharacteristic
973C22#1171925111yescharacteristic
974C22#1171925511yescharacteristic
975C22#1171926111yescharacteristic
976C22#1171926611yescharacteristic
977C22#1171926611yescharacteristic
978C22#1171929611yescharacteristic
979C22#1171929711yescharacteristic
980C22#1171929811yescharacteristic
981C22#1171929911yescharacteristic
982C22#1171932811yescharacteristic
983C22#1171933311yescharacteristic
984C22#1171933711yescharacteristic
985C22#1171933911yescharacteristic
986C22#1171934111yescharacteristic
987C22#1171934511yescharacteristic
988C22#1171935111yescharacteristic
989C22#1171935211yescharacteristic
990C22#1171935511yescharacteristic
991C22#1171936711yescharacteristic
992C22#1171937011yescharacteristic
993C22#1171937211yescharacteristic
994C22C2×C4×C22⋊D1311yescharacteristic
995C22D4×C22⋊D1311yescharacteristic
996C22#1171951011yescharacteristic
997C22#1171951111yescharacteristic
998C22Q8×C22⋊D1311yescharacteristic
999C22#1171953011yescharacteristic
1000C22#1171953411yescharacteristic
1001C4—24no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—81no—
1007C4—264no—
1008C4—522no—
1009C4—522no—
1010C4—522no—
1011C4—522no—
1012C4—522no—
1013C4—522no—
1014C4—1041no—
1015C2—44no—
1016C2#1311754211yescharacteristic
1017C2#1311754811yescharacteristic
1018C2#1311756711yescharacteristic
1019C2#1311781311yescharacteristic
1020C2#1311783611yescharacteristic
1021C2#1311784111yescharacteristic
1022C2#1311800911yescharacteristic
1023C2#1312105811yescharacteristic
1024C2#1312114711yescharacteristic
1025C2#1312125111yescharacteristic
1026C2#1312126011yescharacteristic
1027C2#1312132611yescharacteristic
1028C2#1312133511yescharacteristic
1029C2#1312224811yescharacteristic
1030C2#1312225711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14575
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#11718635C2semidirect
3. C2×#11718307C2semidirect
5. #13113099C2semidirect
6. #13113099C2semidirect
7. #13113095C2semidirect
8. #13113091C2semidirect
12. #13113061C2semidirect
13. #13113060C2semidirect
54. #11718608C4semidirect
84. C22×Dic26C2×C4semidirect
108. C2×C22⋊Dic13Q8semidirect
140. #88071C2×C4semidirect
141. #88071C2×C4semidirect
142. #88071C2×C4semidirect
800. C13#14575semidirect

Maximal subgroups

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

subgroupindex
C2×#117186082
C2×#117186352
C2×#117183072
C2×#117188712
#131130992
#131130952
#131130912
#131130792
#131130732
#131130612
#131130602
#131130592
C2×C13×#3852
#1457513