Finite Group Databasebeta

← #15787014

Subgroups — #15787014

Order 3328.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88180C211yesmaximal, characteristic
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718612C211yesmaximal, characteristic
4C2×#11718642C211yesmaximal, characteristic, complemented
5#13113093C211yesmaximal, characteristic, complemented
6#13113089C211yesmaximal, characteristic, complemented
7#13113085C211yesmaximal, characteristic
8#13113081C211yesmaximal, characteristic
9#13113073C211yesmaximal, characteristic
10#13113070C211yesmaximal, characteristic, complemented
11#13113070C211yesmaximal, characteristic, complemented
12#13113068C211yesmaximal, characteristic, complemented
13#13113059C211yesmaximal, characteristic
14#95×Dic13C211yesmaximal, characteristic, complemented
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
25C2×#88180—24no—
26C2×#88180—24no—
27C2×#88180—24no—
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C13×#385C418yescomplemented
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55#11718646—24no—
56#11718642—24no—
57#11718612—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13C2×C414yes—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4C2×C414yes—
85C2×C13×C4⋊C4C2×C414yes—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4C2×C414yes—
91C2×C13×C22⋊C4C2×C414yes—
92C2×C22⋊Dic13—22no—
93C2×C22⋊Dic13—22no—
94C2×C22⋊Dic13—22no—
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—22no—
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⋊Dic13D414yes—
104#88180—232no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13—22no—
115C2×C4⋊Dic13—41no—
116C2×C4⋊Dic13D414yes—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—22no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—22no—
121C2×C4×Dic13—22no—
122C2×C4×Dic13—22no—
123C2×C4×Dic13—22no—
124C2×C4×Dic13—22no—
125C2×C4×Dic13—22no—
126C2×C4×Dic13—41no—
127C2×C4×Dic13—41no—
128C2×C4×Dic13D414yes—
129C13×#95C2×C414yes—
130C13×#95C2×C414yes—
131#88071—22no—
132#88071—22no—
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—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—41no—
147#14072—131nomaximal, Sylow
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×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13C22×C412yes—
161C24×C13C2×D412yes—
162C24×C13#4112yes—
163C24×C13C2411yescharacteristic
164C22×C4×C13—28no—
165C22×C4×C13—28no—
166C22×C4×C13—28no—
167C22×C4×C13—28no—
168C22×C4×C13—28no—
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—28no—
182C22×C4×C13—28no—
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×C13C22×C412yes—
202C22×C4×C13C22×C412yes—
203C22×C4×C13C22×C412yes—
204C22×C4×C13C22×C412yes—
205C22×C4×C13C22×C412yes—
206C22×C4×C13C22×C412yes—
207C22×C4×C13C2×D412yes—
208C22×C4×C13C2×D412yes—
209C22×C4×C13#4112yes—
210C22×C4×C13#4112yes—
211C22×C4×C13#4112yes—
212C22×C4×C13#4112yes—
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×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13C2×D412yes—
262C22×Dic13C2×D412yes—
263C22×Dic13C2×D412yes—
264C22×Dic13C2×D412yes—
265C22×Dic13C2×D412yes—
266C22×Dic13C2×D412yes—
267C22×Dic13#4112yes—
268C22×Dic13#4112yes—
269C13×C4⋊C4—28no—
270C13×C4⋊C4—28no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4—28no—
273C22⋊Dic13—28no—
274C22⋊Dic13—28no—
275C22⋊Dic13—44no—
276C22⋊Dic13—44no—
277C4⋊Dic13—28no—
278C4⋊Dic13—28no—
279C4⋊Dic13—44no—
280C4⋊Dic13—44no—
281C4×Dic13—28no—
282C4×Dic13—28no—
283C4×Dic13—44no—
284C4×Dic13—44no—
285C22×#117—131no—
286C2×#389—131no—
287C2×#388—131no—
288C2×#387—131no—
289C2×#385D1311yescharacteristic
290#1442—131no—
291#1441—131no—
292#1440—131no—
293#1439—131no—
294#1437—131no—
295#1436—131no—
296#1436—131no—
297#1436—131no—
298C22⋊#95—131no—
299C4×#95—131no—
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—22no—
316C23×C13—22no—
317C23×C13—22no—
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×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13C4×D414yes—
335C23×C13C23×C411yescharacteristic
336C23×C13C22×D411yescharacteristic
337C23×C13C22×D411yescharacteristic
338C23×C13C22×D411yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13C2×#4111yescharacteristic
344C23×C13C2×#4111yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C132−1+411yescharacteristic
348C23×C132−1+411yescharacteristic
349C23×C132−1+411yescharacteristic
350C2×C4×C13—232no—
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—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—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#11714yescomplemented
391C2×C4×C13C4×D414yes—
392C2×C4×C13C4×D414yes—
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—22no—
412C2×Dic13—22no—
413C2×Dic13—22no—
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×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13#12014yes—
449C24×C4C2×D1311yescharacteristic
450C2×#117—264no—
451C2×#117—264no—
452C2×#117—264no—
453C22×C4⋊C4—131no—
454C22×C4⋊C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4C2×D1311yescharacteristic
458C22×C4⋊C4C2×D1311yescharacteristic
459C22×C22⋊C4—131no—
460C22×C22⋊C4—131no—
461C22×C22⋊C4—131no—
462C22×C22⋊C4—131no—
463C22×C22⋊C4C2×D1311yescharacteristic
464C22×C22⋊C4C2×D1311yescharacteristic
465C22×C42—131no—
466C22×C42—131no—
467C22×C42—131no—
468C22×C42—131no—
469#389—264no—
470#388—264no—
471#387—264no—
472#385Dic1318yescomplemented
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×#11711yescharacteristic
507C22×C13C2×C4×D411yescharacteristic
508C22×C13C2×C4×D411yescharacteristic
509C22×C13C2×C4×D411yescharacteristic
510C22×C13C4×#4111yescharacteristic
511C22×C13#51911yescharacteristic
512C22×C13#52011yescharacteristic
513C22×C13C2×#12011yescharacteristic
514C22×C13#52511yescharacteristic
515C22×C13#52511yescharacteristic
516C22×C13#52511yescharacteristic
517C22×C13#52911yescharacteristic
518C22×C13#52911yescharacteristic
519C22×C13#53211yescharacteristic
520C22×C13#53211yescharacteristic
521C22×C13#53611yescharacteristic
522C22×C13#53711yescharacteristic
523C22×C13#54111yescharacteristic
524C22×C13#54211yescharacteristic
525C22×C13#54611yescharacteristic
526C22×C13#54611yescharacteristic
527C22×C13#54711yescharacteristic
528C22×C13#54711yescharacteristic
529C22×C13#54711yescharacteristic
530C22×C13#54711yescharacteristic
531C22×C13#54811yescharacteristic
532C22×C13#54811yescharacteristic
533C22×C13#55111yescharacteristic
534C22×C13#55211yescharacteristic
535C22×C13#55211yescharacteristic
536C22×C13#55211yescharacteristic
537C22×C13#55211yescharacteristic
538C22×C13#55211yescharacteristic
539C22×C13#55311yescharacteristic
540C22×C13#55611yescharacteristic
541C4×C13—24no—
542C4×C13—24no—
543C4×C13—24no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—42no—
547Dic13—24no—
548Dic13—42no—
549Dic13—42no—
550Dic13—42no—
551Dic13—42no—
552Dic13—42no—
553Dic13—81no—
554Dic13—81no—
555C25C22×D1311yescharacteristic
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—131no—
570C23×C4C2×Dic1314yes—
571C23×C4C22×D1311yescharacteristic
572C23×C4C22×D1311yescharacteristic
573C23×C4C22×D1311yescharacteristic
574C23×C4C22×D1311yescharacteristic
575C23×C4C22×D1311yescharacteristic
576C23×C4C22×D1311yescharacteristic
577#117—2632no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—134no—
583C2×C4⋊C4—262no—
584C2×C4⋊C4—262no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—262no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—521no—
594C2×C4⋊C4C2×Dic1314yes—
595C2×C4⋊C4C2×Dic1314yes—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—134no—
601C2×C22⋊C4—262no—
602C2×C22⋊C4—262no—
603C2×C22⋊C4—262no—
604C2×C22⋊C4—262no—
605C2×C22⋊C4—262no—
606C2×C22⋊C4—262no—
607C2×C22⋊C4—262no—
608C2×C22⋊C4—262no—
609C2×C22⋊C4—262no—
610C2×C22⋊C4—521no—
611C2×C22⋊C4—521no—
612C2×C22⋊C4C2×Dic1314yes—
613C2×C22⋊C4C2×Dic1314yes—
614C2×C42—134no—
615C2×C42—262no—
616C2×C42—262no—
617C2×C42—262no—
618C2×C42—262no—
619C2×C42—262no—
620C2×C42—262no—
621C2×C42—262no—
622C2×C42—262no—
623C2×C42—262no—
624C2×C42—521no—
625C2×C42—521no—
626#95—262no—
627#95—262no—
628#95—262no—
629#95—262no—
630#95—262no—
631#95—262no—
632#95—262no—
633#95—262no—
634#95—262no—
635#95—262no—
636#95—262no—
637#95—262no—
638#95—262no—
639#95—262no—
640#95—262no—
641#95—521no—
642#95C2×Dic1314yes—
643#95C2×Dic1314yes—
644C2×C13—44no—
645C2×C13#229311yescharacteristic
646C2×C13C4×#12011yescharacteristic
647C2×C13#232311yescharacteristic
648C2×C13#234411yescharacteristic
649C2×C13#235211yescharacteristic
650C2×C13#235911yescharacteristic
651C2×C13#236211yescharacteristic
652C2×C13#243011yescharacteristic
653C2×C13#243211yescharacteristic
654C2×C13#247011yescharacteristic
655C2×C13#247511yescharacteristic
656C2×C13#247711yescharacteristic
657C2×C13#247811yescharacteristic
658C2×C13#260111yescharacteristic
659C2×C13#261111yescharacteristic
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24D4×D1312yes—
673C24#612912yes—
674C24C22×Dic1312yes—
675C24C23×D1311yescharacteristic
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
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—28no—
694C22×C4—28no—
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—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×C4—261no—
769C22×C4#612712yes—
770C22×C4#612712yes—
771C22×C4D4×D1312yes—
772C22×C4D4×D1312yes—
773C22×C4#612912yes—
774C22×C4#612912yes—
775C22×C4C22×Dic1312yes—
776C22×C4C22×Dic1312yes—
777C22×C4C22×Dic1312yes—
778C22×C4C22×Dic1312yes—
779C22×C4C22×Dic1312yes—
780C22×C4C22×Dic1312yes—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—268no—
784C4⋊C4—268no—
785C4⋊C4—524no—
786C4⋊C4—524no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—268no—
790C22⋊C4—268no—
791C22⋊C4—524no—
792C22⋊C4—524no—
793C42—268no—
794C42—268no—
795C42—524no—
796C42—524no—
797C13#1407211yescharacteristic, complemented, Sylow
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—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
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—
832C23D4×Dic1314yes—
833C23C2×#612711yescharacteristic
834C23C2×#612711yescharacteristic
835C23C2×D4×D1311yescharacteristic
836C23C2×D4×D1311yescharacteristic
837C23C2×D4×D1311yescharacteristic
838C23C2×#612911yescharacteristic
839C23C2×#612911yescharacteristic
840C23C2×#612911yescharacteristic
841C23#8825411yescharacteristic
842C23#8825411yescharacteristic
843C23#41×D1311yescharacteristic
844C23#41×D1311yescharacteristic
845C23#8825611yescharacteristic
846C23#8825711yescharacteristic
847C23C23×Dic1311yescharacteristic
848C2×C4—232no—
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—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—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
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—134no—
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—262no—
908C2×C4—262no—
909C2×C4—262no—
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×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4#8818014yescomplemented
945C2×C4D4×Dic1314yes—
946C2×C4D4×Dic1314yes—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22#1171921211yescharacteristic
963C22#1171921211yescharacteristic
964C22#1171921811yescharacteristic
965C22#1171921811yescharacteristic
966C22#1171924611yescharacteristic
967C22#1171925311yescharacteristic
968C22#1171925311yescharacteristic
969C22#1171925511yescharacteristic
970C22#1171925711yescharacteristic
971C22#1171926211yescharacteristic
972C22#1171926211yescharacteristic
973C22#1171927011yescharacteristic
974C22#1171929111yescharacteristic
975C22#1171929111yescharacteristic
976C22#1171929111yescharacteristic
977C22D13×#12011yescharacteristic
978C22#1171933011yescharacteristic
979C22#1171933311yescharacteristic
980C22#1171933411yescharacteristic
981C22#1171933611yescharacteristic
982C22#1171933811yescharacteristic
983C22#1171934411yescharacteristic
984C22#1171934611yescharacteristic
985C22#1171934811yescharacteristic
986C22#1171935511yescharacteristic
987C22#1171935911yescharacteristic
988C22#1171936011yescharacteristic
989C22#1171936311yescharacteristic
990C22C2×#8818011yescharacteristic
991C22C2×D4×Dic1311yescharacteristic
992C22C2×D4×Dic1311yescharacteristic
993C22C2×D4×Dic1311yescharacteristic
994C22#1171951711yescharacteristic
995C22#41×Dic1311yescharacteristic
996C22#1171953211yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—264no—
1004C4—522no—
1005C4—522no—
1006C4—522no—
1007C4—522no—
1008C4—522no—
1009C4—1041no—
1010C4—1041no—
1011C2—44no—
1012C2#1311730111yescharacteristic
1013C2#120×Dic1311yescharacteristic
1014C2#1311752011yescharacteristic
1015C2#1311770511yescharacteristic
1016C2#1311776511yescharacteristic
1017C2#1311783211yescharacteristic
1018C2#1311786711yescharacteristic
1019C2#1311844511yescharacteristic
1020C2#1311846211yescharacteristic
1021C2#1311893111yescharacteristic
1022C2#1311900611yescharacteristic
1023C2#1311903611yescharacteristic
1024C2#1311905111yescharacteristic
1025C2#1312043711yescharacteristic
1026C2#1312053011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#385C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#385D13
hypocenterC13#14072
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C2×#11718646C2semidirect
4. C2×#11718642C2semidirect
5. #13113093C2semidirect
6. #13113089C2semidirect
10. #13113070C2semidirect
11. #13113070C2semidirect
12. #13113068C2semidirect
14. #95×Dic13C2semidirect
36. C13×#385C4semidirect
390. C2×C4×C13#117semidirect
472. #385Dic13semidirect
797. C13#14072semidirect
944. C2×C4#88180semidirect

Maximal subgroups

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

subgroupindex
C22×#881802
C2×#117186462
C2×#117186122
C2×#117186422
#131130932
#131130892
#131130852
#131130812
#131130732
#131130702
#131130682
#131130592
#95×Dic132
C2×C13×#3852
#1407213