Finite Group Databasebeta

← #15786047

Subgroups — #15786047

Order 3328.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C2×#11718590C211yesmaximal, characteristic, complemented
3C2×#11718635C211yesmaximal, characteristic, complemented
4C2×#11718646C211yesmaximal, characteristic, complemented
5C2×#11718648C211yesmaximal, characteristic
6C2×C4×#6103C211yesmaximal, characteristic
7#13113103C212yesmaximal, complemented
8#13113082C212yesmaximal
9#13113074C212yesmaximal
10#13113066C212yesmaximal, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C23×Dic26C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2212yes—
17C22×C42×C13C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2212yes—
24C22×C4⋊Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C2×#88151—24no—
27C2×#88151—24no—
28C2×#88151C418yescomplemented
29C4×C13×C4⋊C4—24no—
30C2×C13×#95C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2211yescharacteristic
39#11718648—24no—
40#11718646—24no—
41#11718635—24no—
42C4×#6103—24no—
43#11718590—24no—
44C24×D13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C23×C4×C13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2312yes—
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2311yescharacteristic
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—22no—
60C22×C4×D13—22no—
61C22×C4×D13C2×C414yes—
62C22×Dic26—22no—
63C22×Dic26—22no—
64C22×Dic26—22no—
65C22×Dic26—22no—
66C22×Dic26—22no—
67C22×Dic26—22no—
68C22×Dic26C2×C414yes—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4C2×C414yes—
72C2×C13×C4⋊C4D414yes—
73C2×C13×C4⋊C4D414yes—
74C2×C13×C4⋊C4D414yes—
75C2×C42×C13—22no—
76C2×C42×C13—22no—
77C2×C42×C13—24no—
78C2×C42×C13—24no—
79C2×C42×C13—42no—
80C2×C42×C13D414yes—
81C2×#6103—22no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×#6103—22no—
85C2×#6103—22no—
86C2×#6103—22no—
87C2×#6103—22no—
88C2×#6103—24no—
89C2×#6103—24no—
90C2×#6103—42no—
91C2×#6103C2×C418yes—
92C2×#6103Q814yescomplemented
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13—24no—
95C2×C4⋊Dic13—22no—
96C2×C4⋊Dic13—24no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—22no—
99C2×C4⋊Dic13—24no—
100C2×C4⋊Dic13—42no—
101C2×C4⋊Dic13C2×C418yes—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105#88151—232no—
106C13×#95—24no—
107#88071—24no—
108#88071—24no—
109#88071—22no—
110#88071—22no—
111#88071—24no—
112#88071—24no—
113#88071—24no—
114#88071—24no—
115#13997—131nomaximal, Sylow
116C24×C13C2411yescharacteristic
117C23×D13—21no—
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—21no—
122C23×D13—21no—
123C23×D13—21no—
124C23×D13—21no—
125C23×D13—21no—
126C23×D13—21no—
127C23×D13—21no—
128C23×D13—21no—
129C23×D13C22×C412yes—
130C23×D13C2×Q812yes—
131C23×D13#4112yes—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13C22×C414yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D414yes—
156C22×C4×C13C2×D414yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D412yes—
161C22×C4×C13C2×D414yes—
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2×Q812yes—
164C22×C4×C13#4112yes—
165C22×C4×C13#4112yes—
166C22×C4×C13#4112yes—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13—22no—
197C22×Dic13—22no—
198C22×Dic13C22×C412yes—
199C22×Dic13C22×C414yes—
200C22×Dic13C2×Q812yes—
201C22×Dic13#4112yes—
202C2×C4×D13—28no—
203C2×C4×D13—28no—
204C2×C4×D13—28no—
205C2×C4×D13—44no—
206C2×C4×D13—44no—
207C2×C4×D13—44no—
208C2×C4×D13—44no—
209C2×Dic26—28no—
210C2×Dic26—28no—
211C2×Dic26—28no—
212C2×Dic26—44no—
213C2×Dic26—44no—
214C2×Dic26—44no—
215C2×Dic26—44no—
216C13×C4⋊C4—28no—
217C13×C4⋊C4C22⋊C4116yescomplemented
218C42×C13—28no—
219C42×C13—48no—
220#6103—28no—
221#6103—216no—
222#6103—28no—
223#6103—48no—
224C4⋊Dic13—216no—
225C4⋊Dic13—48no—
226C4⋊Dic13—44no—
227C4×Dic13—44no—
228C22×C22⋊Q8—131no—
229C2×#391—131no—
230C2×#391—131no—
231C2×#389—131no—
232C2×#380—131no—
233C2×C4×C4⋊C4D1311yescharacteristic, complemented
234C2×C4×C22⋊C4—131no—
235#1445—132no—
236#1439—132no—
237#1437—132no—
238C4⋊#95—132no—
239C23×C13C23×C411yescharacteristic
240C23×C13C22×D411yescharacteristic
241C23×C13C22×D411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C13C22×D411yescharacteristic
244C23×C13C22×Q811yescharacteristic
245C23×C13C2×#4111yescharacteristic
246C23×C13C2×#4111yescharacteristic
247C23×C13C2×#4111yescharacteristic
248C23×C13C2×#4111yescharacteristic
249C23×C13C2×#4111yescharacteristic
250C23×C13H(5,𝔽2)11yescharacteristic
251C23×C132−1+411yescharacteristic
252C23×C132−1+411yescharacteristic
253C23×C132−1+411yescharacteristic
254C22×D13—22no—
255C22×D13—22no—
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—22no—
261C22×D13—22no—
262C22×D13—22no—
263C22×D13—22no—
264C22×D13—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—22no—
271C22×D13—22no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13—41no—
281C22×D13—41no—
282C22×D13—41no—
283C22×D13—41no—
284C22×D13—41no—
285C22×D13—41no—
286C22×D13—41no—
287C22×D13—41no—
288C22×D13C4×Q814yes—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—24no—
294C2×C4×C13—22no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—24no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—24no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—24no—
306C2×C4×C13—24no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—42no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13C2×C22⋊C418yes—
316C2×C4×C13C2×C22⋊C414yes—
317C2×C4×C13C4×D414yes—
318C2×C4×C13C4×D414yes—
319C2×C4×C13#12114yes—
320C2×C4×C13#12114yes—
321C2×C4×C13C22⋊Q814yescomplemented
322C2×C4×C13#12414yes—
323C2×C4×C13#12714yes—
324C2×Dic13—22no—
325C2×Dic13—24no—
326C2×Dic13—24no—
327C2×Dic13—24no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—42no—
341C2×Dic13—41no—
342C2×Dic13—41no—
343C2×Dic13—41no—
344C2×Dic13—42no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C4×D13—416no—
360Dic26—416no—
361C23×Q8—131no—
362C24×C4—131no—
363C2×C22⋊Q8—138no—
364C2×C22⋊Q8—264no—
365C2×C22⋊Q8—264no—
366C22×C4⋊C4—132no—
367C22×C4⋊C4—131no—
368C22×C4⋊C4—132no—
369C22×C4⋊C4C2×D1311yescharacteristic
370C22×C4⋊C4C2×D1311yescharacteristic
371C22×C22⋊C4—132no—
372C22×C22⋊C4—131no—
373C22×C22⋊C4—131no—
374C22×C22⋊C4—132no—
375C22×C42—131no—
376C22×C42C2×D1312yes—
377C22×C42C2×D1311yescharacteristic
378#391—264no—
379#391—264no—
380#389—264no—
381#380—264no—
382C4×C4⋊C4—24no—
383C4×C22⋊C4—264no—
384C2×#95—131no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—132no—
391C2×#95—131no—
392C2×#95C2×D1312yes—
393C22×C13C22×C22⋊C411yescharacteristic
394C22×C13C2×C4×D411yescharacteristic
395C22×C13C2×C4×D411yescharacteristic
396C22×C13C2×C4×Q811yescharacteristic
397C22×C13C4×#4111yescharacteristic
398C22×C13#51911yescharacteristic
399C22×C13#52011yescharacteristic
400C22×C13C2×#12111yescharacteristic
401C22×C13C2×#12111yescharacteristic
402C22×C13C2×C22⋊Q811yescharacteristic
403C22×C13#52511yescharacteristic
404C22×C13C2×#12411yescharacteristic
405C22×C13#52911yescharacteristic
406C22×C13C2×#12711yescharacteristic
407C22×C13#53311yescharacteristic
408C22×C13#53611yescharacteristic
409C22×C13#53711yescharacteristic
410C22×C13#54111yescharacteristic
411C22×C13#54211yescharacteristic
412C22×C13#54611yescharacteristic
413C22×C13#54611yescharacteristic
414C22×C13#54611yescharacteristic
415C22×C13#54711yescharacteristic
416C22×C13#54711yescharacteristic
417C22×C13#54711yescharacteristic
418C22×C13#54811yescharacteristic
419C22×C13#54811yescharacteristic
420C22×C13#54811yescharacteristic
421C22×C13D4×Q811yescharacteristic
422C22×C13D4×Q811yescharacteristic
423C22×C13D4×Q811yescharacteristic
424C22×C13#55211yescharacteristic
425C22×C13#55211yescharacteristic
426C22×C13#55411yescharacteristic
427C22×C13#55611yescharacteristic
428C2×D13—24no—
429C2×D13—24no—
430C2×D13—24no—
431C2×D13—42no—
432C2×D13—42no—
433C2×D13—42no—
434C2×D13—42no—
435C2×D13—42no—
436C2×D13—42no—
437C2×D13—42no—
438C2×D13—42no—
439C2×D13—42no—
440C2×D13—42no—
441C2×D13—42no—
442C2×D13—42no—
443C4×C13—28no—
444C4×C13—24no—
445C4×C13—42no—
446C4×C13—44no—
447C4×C13#39018yes—
448Dic13—42no—
449Dic13—42no—
450Dic13—44no—
451Dic13—42no—
452Dic13—82no—
453C25—131no—
454C22×Q8—134no—
455C22×Q8—262no—
456C22×Q8—262no—
457C22×Q8—262no—
458C22×Q8—262no—
459C22×Q8—262no—
460C22×Q8—262no—
461C23×C4—131no—
462C23×C4—132no—
463C23×C4—131no—
464C23×C4—131no—
465C23×C4—134no—
466C23×C4—132no—
467C23×C4—262no—
468C23×C4—262no—
469C23×C4—262no—
470C23×C4—262no—
471C23×C4—262no—
472C23×C4—262no—
473C23×C4C22×D1312yes—
474C23×C4C22×D1311yescharacteristic
475C23×C4C22×D1312yes—
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C22⋊Q8—2632no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—138no—
482C2×C4⋊C4—264no—
483C2×C4⋊C4—264no—
484C2×C4⋊C4—264no—
485C2×C4⋊C4—262no—
486C2×C4⋊C4—264no—
487C2×C4⋊C4—262no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—522no—
490C2×C4⋊C4C4×D1314yes—
491C2×C4⋊C4D5214yes—
492C2×C4⋊C4D5214yes—
493C2×C4⋊C4C22⋊D1314yes—
494C2×C22⋊C4—138no—
495C2×C22⋊C4—134no—
496C2×C22⋊C4—262no—
497C2×C22⋊C4—262no—
498C2×C22⋊C4—264no—
499C2×C22⋊C4—262no—
500C2×C22⋊C4—262no—
501C2×C22⋊C4—262no—
502C2×C22⋊C4—264no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—522no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—24no—
509C2×C42—24no—
510C2×C42—42no—
511C2×C42—262no—
512C2×C42—262no—
513C2×C42—262no—
514C2×C42D5214yes—
515#95—24no—
516#95—262no—
517#95—262no—
518#95—264no—
519#95—264no—
520#95—264no—
521#95—264no—
522#95—264no—
523#95—264no—
524C2×C13C2×#39011yescharacteristic
525C2×C13C4×C22⋊Q811yescharacteristic
526C2×C13#232311yescharacteristic
527C2×C13#233911yescharacteristic
528C2×C13Q8×C22⋊C411yescharacteristic
529C2×C13#236011yescharacteristic
530C2×C13#236211yescharacteristic
531C2×C13#241511yescharacteristic
532C2×C13#241711yescharacteristic
533C2×C13#242711yescharacteristic
534C2×C13#242911yescharacteristic
535C2×C13#248911yescharacteristic
536C2×C13#249211yescharacteristic
537C2×C13#254011yescharacteristic
538C2×C13#254211yescharacteristic
539D13—44no—
540C24—132no—
541C24—132no—
542C24—132no—
543C24—261no—
544C24—261no—
545C24—261no—
546C24—261no—
547C24—261no—
548C24—261no—
549C24—261no—
550C24—261no—
551C24—261no—
552C24—261no—
553C24—261no—
554C24—261no—
555C24C23×D1311yescharacteristic
556C2×Q8—268no—
557C2×Q8—268no—
558C2×Q8—268no—
559C2×Q8—524no—
560C2×Q8—524no—
561C2×Q8—524no—
562C2×Q8—524no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—134no—
584C22×C4—132no—
585C22×C4—132no—
586C22×C4—132no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—262no—
610C22×C4—261no—
611C22×C4—268no—
612C22×C4—268no—
613C22×C4—268no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—524no—
622C22×C4—524no—
623C22×C4—524no—
624C22×C4—524no—
625C22×C4C2×C4×D1314yes—
626C22×C4C2×C4×D1312yes—
627C22×C4C2×D5212yes—
628C22×C4C2×D5214yes—
629C22×C4C2×D5212yes—
630C22×C4C2×D5214yes—
631C22×C4C2×D5212yes—
632C22×C4C2×D5212yes—
633C22×C4C2×D5212yes—
634C22×C4#612712yes—
635C22×C4#612712yes—
636C22×C4#612912yes—
637C22×C4Q8×D1312yes—
638C22×C4C2×C22⋊D1314yes—
639C22×C4C2×C22⋊D1312yes—
640C4⋊C4—28no—
641C4⋊C4—2616no—
642C4⋊C4—528no—
643C4⋊C4—524no—
644C4⋊C4#6103116yescomplemented
645C22⋊C4—268no—
646C22⋊C4—268no—
647C22⋊C4—2616no—
648C22⋊C4—528no—
649C42—28no—
650C42—48no—
651C42—524no—
652C13#1399711yescharacteristic, complemented, Sylow
653C23—134no—
654C23—262no—
655C23—262no—
656C23—262no—
657C23—262no—
658C23—262no—
659C23—262no—
660C23—262no—
661C23—262no—
662C23—262no—
663C23—262no—
664C23—262no—
665C23—262no—
666C23—262no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—521no—
673C23—521no—
674C23—521no—
675C23—521no—
676C23—521no—
677C23—521no—
678C23—521no—
679C23—521no—
680C23—521no—
681C23—521no—
682C23—521no—
683C23—521no—
684C23—521no—
685C23—521no—
686C23—521no—
687C23—521no—
688C23C22×C4×D1311yescharacteristic
689C23C22×D5211yescharacteristic
690C23C22×D5211yescharacteristic
691C23C22×D5211yescharacteristic
692C23C2×#612711yescharacteristic
693C23C2×#612711yescharacteristic
694C23C2×#612911yescharacteristic
695C23#8825111yescharacteristic
696C23C2×Q8×D1311yescharacteristic
697C23#8825411yescharacteristic
698C23#41×D1311yescharacteristic
699C23#41×D1311yescharacteristic
700C23#8825711yescharacteristic
701C23#8825711yescharacteristic
702C23C22×C22⋊D1311yescharacteristic
703Q8—5216no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—264no—
733C2×C4—264no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—264no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—521no—
743C2×C4—521no—
744C2×C4—521no—
745C2×C4—522no—
746C2×C4—521no—
747C2×C4—522no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—522no—
753C2×C4—522no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—5216no—
759C2×C4—522no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4C4×D5214yes—
767C2×C4C4×D5214yes—
768C2×C4#8812814yes—
769C2×C4#8812914yes—
770C2×C4#8815114yescomplemented
771C2×C4C2×#610318yes—
772C2×C4C2×#610314yes—
773C2×C4#8818414yes—
774C2×C4#8818414yes—
775C22—264no—
776C22—264no—
777C22—264no—
778C22—522no—
779C22—522no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—522no—
784C22—522no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—522no—
789C22—522no—
790C22C2×C4×D5211yescharacteristic
791C22C2×C4×D5211yescharacteristic
792C22C2×#8812811yescharacteristic
793C22C2×#8812911yescharacteristic
794C22C2×#8815111yescharacteristic
795C22#1171921511yescharacteristic
796C22#1171921611yescharacteristic
797C22#1171921811yescharacteristic
798C22#1171922911yescharacteristic
799C22#1171923111yescharacteristic
800C22#1171923411yescharacteristic
801C22#1171923811yescharacteristic
802C22C4×#612911yescharacteristic
803C22#1171925111yescharacteristic
804C22#1171925911yescharacteristic
805C22#1171925911yescharacteristic
806C22#1171926011yescharacteristic
807C22#1171926011yescharacteristic
808C22#1171926211yescharacteristic
809C22#1171926611yescharacteristic
810C22C4×Q8×D1311yescharacteristic
811C22#1171927711yescharacteristic
812C22Q8×D5211yescharacteristic
813C22Q8×D5211yescharacteristic
814C22#1171928111yescharacteristic
815C22#1171928111yescharacteristic
816C22#1171928311yescharacteristic
817C22#1171928811yescharacteristic
818C22C22×#610311yescharacteristic
819C22C2×#8818411yescharacteristic
820C22C2×#8818411yescharacteristic
821C22#1171951111yescharacteristic
822C22Q8×C22⋊D1311yescharacteristic
823C22#1171952911yescharacteristic
824C22#1171953611yescharacteristic
825C4—24no—
826C4—28no—
827C4—42no—
828C4—44no—
829C4—522no—
830C4—522no—
831C4—522no—
832C4—524no—
833C4—1042no—
834C4#1171860018yes—
835C2—524no—
836C2C2×#1171860011yescharacteristic
837C2C4×#8815111yescharacteristic
838C2#1311751911yescharacteristic
839C2#1311766111yescharacteristic
840C2Q8×#610311yescharacteristic
841C2#1311784311yescharacteristic
842C2#1311786511yescharacteristic
843C2#1311825911yescharacteristic
844C2#1311828111yescharacteristic
845C2#1311840711yescharacteristic
846C2#1311842911yescharacteristic
847C2#1311917111yescharacteristic
848C2#1311920411yescharacteristic
849C2#1311977011yescharacteristic
850C2#1311978511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#13997
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718590C2semidirect
3. C2×#11718635C2semidirect
4. C2×#11718646C2semidirect
7. #13113103C2semidirect
10. #13113066C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
28. C2×#88151C4semidirect
92. C2×#6103Q8semidirect
217. C13×C4⋊C4C22⋊C4semidirect
233. C2×C4×C4⋊C4D13semidirect
321. C2×C4×C13C22⋊Q8semidirect
644. C4⋊C4#6103semidirect
652. C13#13997semidirect
770. C2×C4#88151semidirect

Maximal subgroups

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

subgroupindex
C22×#881512
C2×#117185902
C2×#117186352
C2×#117186462
C2×#117186482
C2×C4×#61032
#131131032
#131130822
#131130742
#131130662
C2×C4×C13×C4⋊C42
#1399713