Finite Group Databasebeta

← #15786014

Subgroups — #15786014

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718634C211yesmaximal, characteristic, complemented
2C2×#11718601C212yesmaximal
3C2×#11718648C211yesmaximal, characteristic
4C2×#11718648C211yesmaximal, characteristic
5C2×C4×#6103C211yesmaximal, characteristic
6#13113091C212yesmaximal, complemented
7#13113084C212yesmaximal
8#13113066C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113063C212yesmaximal, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C4×C13×C4⋊C4—24no—
26C2×C13×#95C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718648—24no—
37#11718648C418yescomplemented
38#11718634—24no—
39#11718601—28no—
40C4×#6103—24no—
41C24×D13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13C2×C414yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4C2×C414yes—
64C2×C13×C4⋊C4D414yes—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—24no—
68C2×C42×C13—24no—
69C2×C42×C13—24no—
70C2×C42×C13D414yes—
71C2×#6103—24no—
72C2×#6103—22no—
73C2×#6103—24no—
74C2×#6103—22no—
75C2×#6103—22no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—42no—
81C2×#6103C2×C418yes—
82C2×#6103D414yes—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13C2×C414yes—
89C2×#6101—24no—
90C2×#6101—24no—
91C2×#6101—42no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13—22no—
95C13×#95—24no—
96#88071—22no—
97#88071—22no—
98#88071—24no—
99#88071—24no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—42no—
104#88071C2×C418yes—
105#13994—131nomaximal, Sylow
106C24×C13C2411yescharacteristic
107C23×D13—21no—
108C23×D13—21no—
109C23×D13—21no—
110C23×D13—21no—
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×D13C22×C412yes—
120C23×D13C2×D412yes—
121C23×D13#4112yes—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13C22×C414yes—
145C22×C4×C13C22×C412yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—22no—
163C22×Dic13—22no—
164C22×Dic13—21no—
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—22no—
176C22×Dic13—21no—
177C22×Dic13—22no—
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×C412yes—
189C22×Dic13C22×C414yes—
190C22×Dic13C2×D412yes—
191C22×Dic13#4112yes—
192C2×C4×D13—28no—
193C2×C4×D13—28no—
194C2×C4×D13—28no—
195C2×C4×D13—44no—
196C2×C4×D13—44no—
197C2×C4×D13—44no—
198C2×C4×D13—44no—
199C13×C4⋊C4—28no—
200C13×C4⋊C4—28no—
201C42×C13—28no—
202C42×C13—48no—
203#6103—28no—
204#6103—216no—
205#6103—28no—
206#6103—48no—
207C4⋊Dic13—28no—
208C4⋊Dic13—44no—
209#6101—48no—
210C4×Dic13—44no—
211C2×#389—131no—
212C2×#388—132no—
213C2×#380—131no—
214C2×#380—131no—
215C2×C4×C4⋊C4D1311yescharacteristic, complemented
216C2×C4×C22⋊C4—131no—
217#1442—132no—
218#1440—132no—
219C4⋊#95—131no—
220C4⋊#95—131no—
221#1434—132no—
222C23×C13C23×C411yescharacteristic
223C23×C13C22×D411yescharacteristic
224C23×C13C22×D411yescharacteristic
225C23×C13C22×D411yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13C2×#4111yescharacteristic
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4111yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13H(5,𝔽2)11yescharacteristic
234C23×C132−1+411yescharacteristic
235C23×C132−1+411yescharacteristic
236C23×C132−1+411yescharacteristic
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—22no—
240C22×D13—22no—
241C22×D13—22no—
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—41no—
256C22×D13—41no—
257C22×D13—41no—
258C22×D13—41no—
259C22×D13—41no—
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×D13C4×D414yes—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—24no—
281C2×C4×C13—24no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—42no—
298C2×C4×C13—41no—
299C2×C4×C13#11714yes—
300C2×C4×C13C4×D414yes—
301C2×C4×C13C4×D414yes—
302C2×C4×C13#12114yes—
303C2×C4×C13#12114yes—
304C2×C4×C13#12314yes—
305C2×C4×C13#12414yes—
306C2×C4×C13#12614yes—
307C2×Dic13—22no—
308C2×Dic13—24no—
309C2×Dic13—24no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—24no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—41no—
330C2×Dic13—42no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—42no—
334C2×Dic13—41no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C4×D13—416no—
343C24×C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4—131no—
346C22×C4⋊C4—132no—
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C4⋊C4C2×D1311yescharacteristic
349C22×C22⋊C4—132no—
350C22×C22⋊C4—131no—
351C22×C22⋊C4—131no—
352C22×C22⋊C4—132no—
353C22×C42—131no—
354C22×C42C2×D1312yes—
355C22×C42C2×D1311yescharacteristic
356#389—264no—
357#388—268no—
358#380—138no—
359#380—264no—
360C4×C4⋊C4—24no—
361C4×C22⋊C4—264no—
362C2×#95—132no—
363C2×#95—131no—
364C2×#95—132no—
365C2×#95—132no—
366C2×#95—132no—
367C2×#95—132no—
368C2×#95—132no—
369C2×#95—131no—
370C2×#95—132no—
371C2×#95C2×D1312yes—
372C22×C13C2×#11711yescharacteristic
373C22×C13C2×C4×D411yescharacteristic
374C22×C13C2×C4×D411yescharacteristic
375C22×C13C2×C4×D411yescharacteristic
376C22×C13C4×#4111yescharacteristic
377C22×C13#51911yescharacteristic
378C22×C13#52011yescharacteristic
379C22×C13C2×#12111yescharacteristic
380C22×C13C2×#12111yescharacteristic
381C22×C13C2×#12311yescharacteristic
382C22×C13#52511yescharacteristic
383C22×C13C2×#12411yescharacteristic
384C22×C13C2×#12611yescharacteristic
385C22×C13#52911yescharacteristic
386C22×C13#53211yescharacteristic
387C22×C13#53611yescharacteristic
388C22×C13#53711yescharacteristic
389C22×C13#54111yescharacteristic
390C22×C13#54211yescharacteristic
391C22×C13D4211yescharacteristic
392C22×C13#54711yescharacteristic
393C22×C13#54711yescharacteristic
394C22×C13#54711yescharacteristic
395C22×C13#54711yescharacteristic
396C22×C13#54811yescharacteristic
397C22×C13#54811yescharacteristic
398C22×C13#55211yescharacteristic
399C22×C13#55211yescharacteristic
400C22×C13#55211yescharacteristic
401C22×C13#55211yescharacteristic
402C22×C13#55211yescharacteristic
403C22×C13#55311yescharacteristic
404C22×C13#55511yescharacteristic
405C22×C13#55511yescharacteristic
406C22×C13#55611yescharacteristic
407C2×D13—24no—
408C2×D13—24no—
409C2×D13—24no—
410C2×D13—42no—
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C4×C13—24no—
423C4×C13—42no—
424C4×C13—44no—
425C4×C13—44no—
426C4×C13#38818yescomplemented
427Dic13—44no—
428Dic13—42no—
429Dic13—42no—
430Dic13—42no—
431Dic13—82no—
432C25—131no—
433C23×C4—132no—
434C23×C4—131no—
435C23×C4—131no—
436C23×C4—131no—
437C23×C4—134no—
438C23×C4—132no—
439C23×C4—262no—
440C23×C4—262no—
441C23×C4—262no—
442C23×C4—262no—
443C23×C4—262no—
444C23×C4—262no—
445C23×C4C22×D1312yes—
446C23×C4C22×D1312yes—
447C23×C4C22×D1311yescharacteristic
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4—264no—
459C2×C4⋊C4—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—522no—
463C2×C4⋊C4C4×D1314yes—
464C2×C4⋊C4D5214yes—
465C2×C22⋊C4—138no—
466C2×C22⋊C4—134no—
467C2×C22⋊C4—262no—
468C2×C22⋊C4—264no—
469C2×C22⋊C4—262no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—262no—
472C2×C22⋊C4—262no—
473C2×C22⋊C4—262no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—264no—
476C2×C22⋊C4—522no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—24no—
480C2×C42—24no—
481C2×C42—24no—
482C2×C42—262no—
483C2×C42—262no—
484C2×C42—262no—
485C2×C42C22⋊D1314yes—
486#95—24no—
487#95—138no—
488#95—264no—
489#95—264no—
490#95—264no—
491#95—264no—
492#95—264no—
493#95—262no—
494#95—262no—
495#95—522no—
496C2×C13C2×#38811yescharacteristic
497C2×C13C4×#12111yescharacteristic
498C2×C13#232311yescharacteristic
499C2×C13#234411yescharacteristic
500C2×C13#234611yescharacteristic
501C2×C13#236111yescharacteristic
502C2×C13#236211yescharacteristic
503C2×C13#248511yescharacteristic
504C2×C13#248611yescharacteristic
505C2×C13#248911yescharacteristic
506C2×C13#249111yescharacteristic
507C2×C13#249511yescharacteristic
508C2×C13#249611yescharacteristic
509C2×C13#253611yescharacteristic
510C2×C13#253711yescharacteristic
511D13—44no—
512C24—132no—
513C24—132no—
514C24—132no—
515C24—261no—
516C24—261no—
517C24—261no—
518C24—261no—
519C24—261no—
520C24—261no—
521C24—261no—
522C24—261no—
523C24—261no—
524C24—261no—
525C24—261no—
526C24—261no—
527C24C23×D1311yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—132no—
551C22×C4—134no—
552C22×C4—132no—
553C22×C4—132no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—262no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—262no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—262no—
566C22×C4—261no—
567C22×C4—262no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—262no—
571C22×C4—261no—
572C22×C4—262no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—268no—
579C22×C4—268no—
580C22×C4—268no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—524no—
589C22×C4—524no—
590C22×C4—524no—
591C22×C4—524no—
592C22×C4C2×C4×D1314yes—
593C22×C4C2×C4×D1312yes—
594C22×C4C2×D5214yes—
595C22×C4C2×D5212yes—
596C22×C4#612712yes—
597C22×C4#612712yes—
598C22×C4#612712yes—
599C22×C4#612712yes—
600C22×C4D4×D1312yes—
601C22×C4#612912yes—
602C22×C4C2×C22⋊D1312yes—
603C22×C4C2×C22⋊D1312yes—
604C22×C4C2×C22⋊D1312yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—268no—
608C4⋊C4—528no—
609C4⋊C4—524no—
610C22⋊C4—2616no—
611C22⋊C4—268no—
612C22⋊C4—268no—
613C22⋊C4—528no—
614C42—28no—
615C42—48no—
616C42—524no—
617C13#1399411yescharacteristic, complemented, Sylow
618C23—134no—
619C23—262no—
620C23—262no—
621C23—262no—
622C23—262no—
623C23—262no—
624C23—262no—
625C23—262no—
626C23—262no—
627C23—262no—
628C23—262no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—521no—
638C23—521no—
639C23—521no—
640C23—521no—
641C23—521no—
642C23—521no—
643C23—521no—
644C23—521no—
645C23—521no—
646C23—521no—
647C23—521no—
648C23—521no—
649C23—521no—
650C23—521no—
651C23—521no—
652C23—521no—
653C23C22×C4×D1311yescharacteristic
654C23C22×D5211yescharacteristic
655C23C2×#612711yescharacteristic
656C23C2×#612711yescharacteristic
657C23C2×#612711yescharacteristic
658C23C2×#612711yescharacteristic
659C23C2×D4×D1311yescharacteristic
660C23C2×#612911yescharacteristic
661C23#8825411yescharacteristic
662C23#8825411yescharacteristic
663C23#41×D1311yescharacteristic
664C23#41×D1311yescharacteristic
665C23#8825611yescharacteristic
666C23#8825711yescharacteristic
667C23C22×C22⋊D1311yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—262no—
696C2×C4—264no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—264no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—264no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—522no—
710C2×C4—522no—
711C2×C4—521no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—522no—
716C2×C4—521no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—522no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—5216no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4#8812614yes—
732C2×C4C4×D5214yes—
733C2×C4#8812914yes—
734C2×C4#8813014yes—
735C2×C4C4×C22⋊D1314yes—
736C2×C4#8818314yes—
737C2×C4#8818414yes—
738C2×C4#8819214yes—
739C22—264no—
740C22—264no—
741C22—264no—
742C22—522no—
743C22—522no—
744C22—522no—
745C22—522no—
746C22—522no—
747C22—522no—
748C22—522no—
749C22—522no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—522no—
754C22C2×#8812611yescharacteristic
755C22C2×C4×D5211yescharacteristic
756C22C2×#8812911yescharacteristic
757C22C2×#8813011yescharacteristic
758C22#1171921211yescharacteristic
759C22#1171921211yescharacteristic
760C22#1171921811yescharacteristic
761C22#1171921811yescharacteristic
762C22#1171923411yescharacteristic
763C22#1171923511yescharacteristic
764C22#1171923711yescharacteristic
765C22#1171923811yescharacteristic
766C22C4×#612911yescharacteristic
767C22C4×D4×D1311yescharacteristic
768C22#1171925311yescharacteristic
769C22D4×D5211yescharacteristic
770C22#1171925611yescharacteristic
771C22#1171926011yescharacteristic
772C22#1171926211yescharacteristic
773C22#1171926811yescharacteristic
774C22#1171927711yescharacteristic
775C22#1171927911yescharacteristic
776C22#1171928111yescharacteristic
777C22#1171928111yescharacteristic
778C22#1171928611yescharacteristic
779C22#1171928611yescharacteristic
780C22#1171928711yescharacteristic
781C22#1171928811yescharacteristic
782C22C2×C4×C22⋊D1311yescharacteristic
783C22C2×#8818311yescharacteristic
784C22C2×#8818411yescharacteristic
785C22C2×#8819211yescharacteristic
786C22#1171952111yescharacteristic
787C22#1171953311yescharacteristic
788C22#1171953811yescharacteristic
789C4—24no—
790C4—44no—
791C4—42no—
792C4—44no—
793C4—522no—
794C4—522no—
795C4—524no—
796C4—522no—
797C4—1042no—
798C4#1171860118yescomplemented
799C2—524no—
800C2C2×#1171860111yescharacteristic
801C2C4×#8819211yescharacteristic
802C2#1311751211yescharacteristic
803C2#1311770111yescharacteristic
804C2#1311771711yescharacteristic
805C2#1311785411yescharacteristic
806C2#1311786511yescharacteristic
807C2#1311912711yescharacteristic
808C2#1311913811yescharacteristic
809C2#1311917111yescharacteristic
810C2#1311919311yescharacteristic
811C2#1311924111yescharacteristic
812C2#1311925211yescharacteristic
813C2#1311974111yescharacteristic
814C2#1311974911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#13994
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718634C2semidirect
6. #13113091C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
10. #13113063C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
37. #11718648C4semidirect
215. C2×C4×C4⋊C4D13semidirect
426. C4×C13#388semidirect
617. C13#13994semidirect
798. C4#11718601semidirect

Maximal subgroups

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

subgroupindex
C2×#117186342
C2×#117186012
C2×#117186482
C2×C4×#61032
#131130912
#131130842
#131130662
#131130652
#131130632
C2×C4×C13×C4⋊C42
#1399413