Finite Group Databasebeta

← #15785572

Subgroups — #15785572

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88146C211yesmaximal, characteristic
2C2×#11718589C211yesmaximal, characteristic, complemented
3C2×#11718634C211yesmaximal, characteristic, complemented
4C2×#11718648C211yesmaximal, characteristic
5C2×C4×#6103C211yesmaximal, characteristic
6#13113080C212yesmaximal
7#13113080C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113064C212yesmaximal, complemented
10#13113061C212yesmaximal, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101C2212yes—
23C22×#6101C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2212yes—
26C2×#88146—24no—
27C2×#88146—24no—
28C2×#88146C418yescomplemented
29C2×C13×#95C2212yes—
30C2×C13×#95C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38#11718648—24no—
39#11718634—24no—
40C4×#6103—24no—
41#11718589—24no—
42C24×D13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13C2×C414yes—
58C22×C4×D13D414yes—
59C22×C4×D13Q814yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4C2×C414yes—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×#6103—22no—
70C2×#6103—22no—
71C2×#6103—22no—
72C2×#6103—22no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—22no—
76C2×#6103—22no—
77C2×#6103—24no—
78C2×#6103—42no—
79C2×#6103—42no—
80C2×#6103C2×C418yes—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13C2×C414yes—
85C2×C4⋊Dic13D414yes—
86C2×C4⋊Dic13D414yes—
87C2×#6101—24no—
88C2×#6101—24no—
89C2×#6101—24no—
90C2×#6101—24no—
91C2×#6101—42no—
92C2×#6101—42no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13C2×C418yes—
99#88146—232no—
100C13×#95—24no—
101C13×#95—42no—
102#88071—24no—
103#88071—22no—
104#88071—22no—
105#88071—24no—
106#88071—24no—
107#88071—24no—
108#88071—42no—
109#13951—131nomaximal, Sylow
110C24×C13C2411yescharacteristic
111C23×D13—21no—
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13—21no—
117C23×D13—21no—
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—21no—
122C23×D13—21no—
123C23×D13C22×C412yes—
124C23×D13C2×D412yes—
125C23×D13C2×Q812yes—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13C22×C414yes—
152C22×C4×C13C22×C412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×Q812yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—22no—
164C22×Dic13—22no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13C22×C414yes—
189C22×Dic13C22×C412yes—
190C22×Dic13C2×D414yes—
191C22×Dic13C2×D414yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×Q812yes—
194C22×Dic13#4112yes—
195C22×Dic13#4112yes—
196C2×C4×D13—28no—
197C2×C4×D13—28no—
198C2×C4×D13—28no—
199C2×C4×D13—28no—
200C2×C4×D13—28no—
201C2×C4×D13—28no—
202C2×C4×D13C4⋊C4116yescomplemented
203C13×C4⋊C4—28no—
204C13×C4⋊C4—44no—
205C42×C13—44no—
206#6103—28no—
207#6103—28no—
208#6103—216no—
209#6103—48no—
210C4⋊Dic13—44no—
211C4⋊Dic13C22⋊C4116yescomplemented
212#6101—48no—
213#6101—48no—
214C4×Dic13—216no—
215C4×Dic13—44no—
216C22×#117—131no—
217C2×#389—131no—
218C2×#389—131no—
219C2×#380—131no—
220C2×C4×C22⋊C4—131no—
221#1439—132no—
222#1439—132no—
223C4⋊#95—132no—
224C4⋊#95—131no—
225C4⋊#95D1311yescharacteristic, complemented
226#1434—132no—
227C23×C13C23×C411yescharacteristic
228C23×C13C22×D411yescharacteristic
229C23×C13C22×D411yescharacteristic
230C23×C13C22×D411yescharacteristic
231C23×C13C22×Q811yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13C2×#4111yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C132−1+411yescharacteristic
241C23×C132−1+411yescharacteristic
242C22×D13—22no—
243C22×D13—22no—
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—22no—
253C22×D13—22no—
254C22×D13—22no—
255C22×D13—22no—
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—41no—
261C22×D13—41no—
262C22×D13—41no—
263C22×D13—41no—
264C22×D13—41no—
265C22×D13—41no—
266C22×D13—41no—
267C22×D13—41no—
268C22×D13—41no—
269C22×D13—41no—
270C22×D13—41no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13C2×C4⋊C414yes—
277C2×C4×C13—24no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13C2×C22⋊C414yes—
306C2×C4×C13C2×C4⋊C414yes—
307C2×C4×C13#11714yes—
308C2×C4×C13#12114yes—
309C2×C4×C13#12114yes—
310C2×C4×C13C22⋊Q814yes—
311C2×C4×C13C22⋊Q814yes—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—24no—
315C2×Dic13—24no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—24no—
321C2×Dic13—24no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13C2×C22⋊C418yes—
346C2×Dic13C2×C4⋊C414yes—
347C4×D13—232no—
348C24×C4—131no—
349C2×#117—138no—
350C2×#117—264no—
351C2×#117—264no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—132no—
355C22×C4⋊C4—132no—
356C22×C4⋊C4C2×D1311yescharacteristic
357C22×C4⋊C4C2×D1311yescharacteristic
358C22×C22⋊C4—132no—
359C22×C22⋊C4—131no—
360C22×C22⋊C4—131no—
361C22×C22⋊C4—132no—
362C22×C42—132no—
363C22×C42—131no—
364C22×C42C2×D1311yescharacteristic
365#389—264no—
366#389—264no—
367#380—264no—
368C4×C22⋊C4—264no—
369C2×#95—131no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95—131no—
375C2×#95—132no—
376C2×#95C2×D1312yes—
377C2×#95C2×D1312yes—
378C22×C13C22×C22⋊C411yescharacteristic
379C22×C13C22×C4⋊C411yescharacteristic
380C22×C13C2×#11711yescharacteristic
381C22×C13C4×#4111yescharacteristic
382C22×C13C4×#4111yescharacteristic
383C22×C13#52011yescharacteristic
384C22×C13#52011yescharacteristic
385C22×C13C2×#12111yescharacteristic
386C22×C13C2×#12111yescharacteristic
387C22×C13C2×C22⋊Q811yescharacteristic
388C22×C13C2×C22⋊Q811yescharacteristic
389C22×C13#52511yescharacteristic
390C22×C13#52511yescharacteristic
391C22×C13#53311yescharacteristic
392C22×C13#53311yescharacteristic
393C22×C13#53511yescharacteristic
394C22×C13#53611yescharacteristic
395C22×C13#54411yescharacteristic
396C22×C13#54411yescharacteristic
397C22×C13#54611yescharacteristic
398C22×C13#54611yescharacteristic
399C22×C13#54711yescharacteristic
400C22×C13#54711yescharacteristic
401C22×C13#54811yescharacteristic
402C22×C13#54811yescharacteristic
403C22×C13#55011yescharacteristic
404C22×C13#55011yescharacteristic
405C22×C13#55211yescharacteristic
406C22×C13#55211yescharacteristic
407C22×C13#55311yescharacteristic
408C22×C13#55311yescharacteristic
409C22×C13#55511yescharacteristic
410C22×C13#55511yescharacteristic
411C22×C13#55611yescharacteristic
412C22×C13#55611yescharacteristic
413C2×D13—24no—
414C2×D13—24no—
415C2×D13—24no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C4×C13—44no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13—82no—
432C4×C13#38018yes—
433Dic13—28no—
434Dic13—24no—
435Dic13—42no—
436Dic13—42no—
437Dic13—82no—
438C25—131no—
439C23×C4—132no—
440C23×C4—131no—
441C23×C4—134no—
442C23×C4—134no—
443C23×C4—134no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—132no—
447C23×C4—262no—
448C23×C4—262no—
449C23×C4—262no—
450C23×C4—262no—
451C23×C4C22×D1312yes—
452C23×C4C22×D1312yes—
453C23×C4C22×D1311yescharacteristic
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1311yescharacteristic
456#117—2632no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—134no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—264no—
466C2×C4⋊C4—264no—
467C2×C4⋊C4—264no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—264no—
472C2×C4⋊C4—522no—
473C2×C4⋊C4—522no—
474C2×C4⋊C4C4×D1314yes—
475C2×C22⋊C4—138no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—262no—
479C2×C22⋊C4—262no—
480C2×C22⋊C4—262no—
481C2×C22⋊C4—262no—
482C2×C22⋊C4—262no—
483C2×C22⋊C4—262no—
484C2×C22⋊C4—264no—
485C2×C22⋊C4—522no—
486C2×C22⋊C4—522no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—138no—
491C2×C42—264no—
492C2×C42—264no—
493C2×C42—262no—
494C2×C42—262no—
495C2×C42—262no—
496#95—24no—
497#95—42no—
498#95—264no—
499#95—262no—
500#95—262no—
501#95—264no—
502#95—264no—
503#95—264no—
504#95—522no—
505C2×C13C2×#38011yescharacteristic
506C2×C13#229611yescharacteristic
507C2×C13#231711yescharacteristic
508C2×C13#233911yescharacteristic
509C2×C13#234111yescharacteristic
510C2×C13#234611yescharacteristic
511C2×C13#234711yescharacteristic
512C2×C13#241411yescharacteristic
513C2×C13#241411yescharacteristic
514C2×C13#241511yescharacteristic
515C2×C13#241511yescharacteristic
516C2×C13#243911yescharacteristic
517C2×C13#243911yescharacteristic
518C2×C13#244111yescharacteristic
519C2×C13#244111yescharacteristic
520D13—44no—
521C24—132no—
522C24—132no—
523C24—132no—
524C24—261no—
525C24—261no—
526C24—261no—
527C24—261no—
528C24—261no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24—261no—
533C24—261no—
534C24—261no—
535C24—261no—
536C24C23×D1311yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—132no—
563C22×C4—134no—
564C22×C4—132no—
565C22×C4—134no—
566C22×C4—134no—
567C22×C4—132no—
568C22×C4—1316no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—268no—
580C22×C4—268no—
581C22×C4—268no—
582C22×C4—268no—
583C22×C4—268no—
584C22×C4—268no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4C2×C4×D1314yes—
605C22×C4C2×C4×D1312yes—
606C22×C4#612712yes—
607C22×C4#612712yes—
608C22×C4D4×D1312yes—
609C22×C4D4×D1312yes—
610C22×C4D4×D1312yes—
611C22×C4#612912yes—
612C22×C4Q8×D1312yes—
613C22×C4#613112yes—
614C4⋊C4—28no—
615C4⋊C4—44no—
616C4⋊C4—1316no—
617C4⋊C4—528no—
618C4⋊C4—528no—
619C4⋊C4—524no—
620C22⋊C4—2616no—
621C22⋊C4—268no—
622C22⋊C4—268no—
623C22⋊C4—528no—
624C42—44no—
625C42—2616no—
626C42—524no—
627C13#1395111yescharacteristic, complemented, Sylow
628C23—134no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23—262no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23—262no—
643C23—262no—
644C23—262no—
645C23—262no—
646C23—262no—
647C23—521no—
648C23—521no—
649C23—521no—
650C23—521no—
651C23—521no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23—521no—
659C23—521no—
660C23—521no—
661C23—521no—
662C23—521no—
663C23C22×C4×D1311yescharacteristic
664C23C2×#612711yescharacteristic
665C23C2×#612711yescharacteristic
666C23C2×D4×D1311yescharacteristic
667C23C2×D4×D1311yescharacteristic
668C23C2×D4×D1311yescharacteristic
669C23C2×#612911yescharacteristic
670C23#8825111yescharacteristic
671C23C2×Q8×D1311yescharacteristic
672C23C2×#613111yescharacteristic
673C23#8825411yescharacteristic
674C23#41×D1311yescharacteristic
675C23#41×D1311yescharacteristic
676C23#8825611yescharacteristic
677C23#8825711yescharacteristic
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—138no—
707C2×C4—134no—
708C2×C4—264no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—264no—
716C2×C4—264no—
717C2×C4—264no—
718C2×C4—264no—
719C2×C4—264no—
720C2×C4—2632no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—521no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4#8812614yes—
743C2×C4C22⋊C4×D1314yes—
744C2×C4#8813814yes—
745C2×C4#8813814yes—
746C2×C4C4⋊C4×D1314yes—
747C2×C4#8815014yes—
748C2×C4#8815014yes—
749C22—264no—
750C22—264no—
751C22—264no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22C2×#8812611yescharacteristic
765C22C2×C22⋊C4×D1311yescharacteristic
766C22C2×#8813811yescharacteristic
767C22C2×#8813811yescharacteristic
768C22C2×C4⋊C4×D1311yescharacteristic
769C22C2×#8815011yescharacteristic
770C22C2×#8815011yescharacteristic
771C22#1171921811yescharacteristic
772C22#1171921911yescharacteristic
773C22#1171923711yescharacteristic
774C22#1171923811yescharacteristic
775C22C4×#612911yescharacteristic
776C22#1171925111yescharacteristic
777C22#1171926311yescharacteristic
778C22#1171926811yescharacteristic
779C22C4×#613111yescharacteristic
780C22#1171927911yescharacteristic
781C22#1171928611yescharacteristic
782C22#1171928911yescharacteristic
783C22#1171930311yescharacteristic
784C22#1171930411yescharacteristic
785C22#1171931111yescharacteristic
786C22#1171931211yescharacteristic
787C22#1171933211yescharacteristic
788C22#1171933311yescharacteristic
789C22#1171933511yescharacteristic
790C22#1171933611yescharacteristic
791C22#1171938111yescharacteristic
792C22#1171938211yescharacteristic
793C22#1171939311yescharacteristic
794C22#1171939411yescharacteristic
795C22#1171942311yescharacteristic
796C22#1171943111yescharacteristic
797C22#1171943311yescharacteristic
798C22#1171943411yescharacteristic
799C4—42no—
800C4—42no—
801C4—44no—
802C4—82no—
803C4—264no—
804C4—268no—
805C4—522no—
806C4—522no—
807C4—1042no—
808C4#1171832818yes—
809C2—524no—
810C2C2×#1171832811yescharacteristic
811C2#1311731711yescharacteristic
812C2#1311745811yescharacteristic
813C2#1311766511yescharacteristic
814C2#1311767511yescharacteristic
815C2#1311771711yescharacteristic
816C2#1311772511yescharacteristic
817C2#1311825611yescharacteristic
818C2#1311825711yescharacteristic
819C2#1311826711yescharacteristic
820C2#1311826811yescharacteristic
821C2#1311852911yescharacteristic
822C2#1311853011yescharacteristic
823C2#1311855111yescharacteristic
824C2#1311855211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#13951
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718589C2semidirect
3. C2×#11718634C2semidirect
8. #13113065C2semidirect
9. #13113064C2semidirect
10. #13113061C2semidirect
11. C13×C4⋊#95C2semidirect
28. C2×#88146C4semidirect
202. C2×C4×D13C4⋊C4semidirect
211. C4⋊Dic13C22⋊C4semidirect
225. C4⋊#95D13semidirect
627. C13#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#881462
C2×#117185892
C2×#117186342
C2×#117186482
C2×C4×#61032
#131130802
#131130652
#131130642
#131130612
C13×C4⋊#952
#1395113