Finite Group Databasebeta

← #15786054

Subgroups — #15786054

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×#88200C211yesmaximal, characteristic
2C2×#11718891C211yesmaximal, characteristic, complemented
3C2×#11718634C211yesmaximal, characteristic, complemented
4C2×#11718648C211yesmaximal, characteristic
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
6C2×C4×#6103C211yesmaximal, characteristic
7#13113102C212yesmaximal, complemented
8#13113080C212yesmaximal
9#13113072C212yesmaximal
10#13113064C212yesmaximal, complemented
11C2×C13×#391C211yesmaximal, characteristic, complemented
12C23×Q8×C13C2211yescharacteristic
13C23×C4×D13C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C2×#88200—24no—
17C2×#88200—24no—
18C2×#88200C418yescomplemented
19C22×#6103C2211yescharacteristic
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2212yes—
26C22×#6101C2212yes—
27C22×C4×Dic13C2211yescharacteristic
28C22×C4×Dic13C2212yes—
29C13×#391—24no—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32#11718891—24no—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2211yescharacteristic
40#11718648—24no—
41#11718634—24no—
42C4×#6103—24no—
43C4×C4⋊Dic13—24no—
44C24×D13C2311yescharacteristic
45C22×Q8×C13—22no—
46C22×Q8×C13—22no—
47C22×Q8×C13—22no—
48C22×Q8×C13—22no—
49C22×Q8×C13—22no—
50C22×Q8×C13—22no—
51C22×Q8×C13C2×C414yes—
52C23×C4×C13C2312yes—
53C23×C4×C13C2312yes—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2312yes—
59C23×Dic13C2311yescharacteristic
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2312yes—
62C22×C4×D13—22no—
63C22×C4×D13—22no—
64C22×C4×D13—22no—
65C22×C4×D13—22no—
66C22×C4×D13—22no—
67C22×C4×D13—22no—
68C22×C4×D13C2×C414yes—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C42×C13—22no—
73C2×C42×C13—22no—
74C2×C42×C13D414yes—
75#88200—232no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—22no—
83C2×#6103—24no—
84C2×#6103—24no—
85C2×#6103—42no—
86C2×#6103C2×C418yes—
87C2×#6103Q814yescomplemented
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13C2×C414yes—
91C2×C4⋊Dic13D414yes—
92C2×C4⋊Dic13D414yes—
93C2×C4⋊Dic13D414yes—
94C2×#6101—24no—
95C2×#6101—24no—
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—42no—
99C2×#6101C2×C418yes—
100C2×C4×Dic13—22no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—24no—
104C2×C4×Dic13—24no—
105C2×C4×Dic13—42no—
106C13×#95—24no—
107C13×#95—24no—
108#88071—22no—
109#88071—22no—
110#88071—24no—
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—
132C2×Q8×C13—28no—
133C2×Q8×C13—28no—
134C2×Q8×C13—28no—
135C2×Q8×C13—44no—
136C2×Q8×C13—44no—
137C2×Q8×C13—44no—
138C2×Q8×C13—44no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13C22×C414yes—
163C22×C4×C13C22×C412yes—
164C22×C4×C13C2×D412yes—
165C22×C4×C13C2×D412yes—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D412yes—
170C22×C4×C13C2×Q812yes—
171C22×C4×C13#4112yes—
172C22×C4×C13#4112yes—
173C22×C4×C13#4112yes—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—22no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—22no—
197C22×Dic13—21no—
198C22×Dic13—22no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13C22×C412yes—
203C22×Dic13C22×C414yes—
204C22×Dic13C2×D414yes—
205C22×Dic13C2×D414yes—
206C22×Dic13C2×D414yes—
207C22×Dic13C2×Q812yes—
208C22×Dic13#4112yes—
209C2×C4×D13—28no—
210C2×C4×D13—28no—
211C2×C4×D13—28no—
212C2×C4×D13—44no—
213C2×C4×D13—44no—
214C2×C4×D13—44no—
215C2×C4×D13—44no—
216C13×C4⋊C4—44no—
217C42×C13—28no—
218#6103—28no—
219#6103—28no—
220#6103—216no—
221#6103—48no—
222C4⋊Dic13—28no—
223C4⋊Dic13C22⋊C4116yescomplemented
224#6101—216no—
225#6101—48no—
226C4×Dic13—48no—
227C4×Dic13—44no—
228C22×C22⋊Q8—131no—
229C2×#391—131no—
230C2×#391D1311yescharacteristic, complemented
231C2×#389—131no—
232C2×#380—131no—
233C2×C4×C4⋊C4—131no—
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—
289Q8×C13—416no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—24no—
297C2×C4×C13—24no—
298C2×C4×C13—24no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13—42no—
316C2×C4×C13—42no—
317C2×C4×C13C2×C22⋊C414yes—
318C2×C4×C13C4×D414yes—
319C2×C4×C13C4×D414yes—
320C2×C4×C13#12114yes—
321C2×C4×C13#12114yes—
322C2×C4×C13C22⋊Q814yescomplemented
323C2×C4×C13#12414yes—
324C2×C4×C13#12714yes—
325C2×Dic13—24no—
326C2×Dic13—24no—
327C2×Dic13—24no—
328C2×Dic13—24no—
329C2×Dic13—24no—
330C2×Dic13—24no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—24no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—24no—
339C2×Dic13—24no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—42no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—42no—
358C2×Dic13—41no—
359C2×Dic13C2×C22⋊C418yes—
360C4×D13—416no—
361C23×Q8C2×D1311yescharacteristic
362C24×C4—131no—
363C2×C22⋊Q8—138no—
364C2×C22⋊Q8—264no—
365C2×C22⋊Q8—264no—
366C22×C4⋊C4—131no—
367C22×C4⋊C4—132no—
368C22×C4⋊C4—131no—
369C22×C4⋊C4—132no—
370C22×C4⋊C4C2×D1311yescharacteristic
371C22×C22⋊C4—132no—
372C22×C22⋊C4—131no—
373C22×C22⋊C4—131no—
374C22×C22⋊C4—132no—
375C22×C42—131no—
376C22×C42—132no—
377C22×C42C2×D1311yescharacteristic
378#391—24no—
379#391—264no—
380#389—264no—
381#380—264no—
382C4×C4⋊C4—264no—
383C4×C22⋊C4—264no—
384C2×#95—131no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95—131no—
391C2×#95C2×D1312yes—
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—24no—
444C4×C13—42no—
445C4×C13—44no—
446C4×C13—82no—
447C4×C13#39018yes—
448Dic13—28no—
449Dic13—44no—
450Dic13—42no—
451Dic13—42no—
452Dic13—42no—
453C25—131no—
454C22×Q8—22no—
455C22×Q8—22no—
456C22×Q8—22no—
457C22×Q8—22no—
458C22×Q8—22no—
459C22×Q8—22no—
460C22×Q8C4×D1314yes—
461C23×C4—132no—
462C23×C4—131no—
463C23×C4—132no—
464C23×C4—131no—
465C23×C4—131no—
466C23×C4—134no—
467C23×C4—262no—
468C23×C4—262no—
469C23×C4—262no—
470C23×C4—262no—
471C23×C4—262no—
472C23×C4—262no—
473C23×C4C22×D1312yes—
474C23×C4C22×D1312yes—
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1311yescharacteristic
478C22⋊Q8—2632no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—134no—
483C2×C4⋊C4—134no—
484C2×C4⋊C4—134no—
485C2×C4⋊C4—138no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—262no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—264no—
492C2×C4⋊C4—264no—
493C2×C4⋊C4—522no—
494C2×C22⋊C4—138no—
495C2×C22⋊C4—134no—
496C2×C22⋊C4—264no—
497C2×C22⋊C4—264no—
498C2×C22⋊C4—262no—
499C2×C22⋊C4—262no—
500C2×C22⋊C4—262no—
501C2×C22⋊C4—262no—
502C2×C22⋊C4—262no—
503C2×C22⋊C4—264no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—522no—
506C2×C42—22no—
507C2×C42—22no—
508C2×C42—264no—
509C2×C42—262no—
510C2×C42—262no—
511C2×C42—264no—
512C2×C42—262no—
513C2×C42—522no—
514C2×C42C22⋊D1314yes—
515#95—24no—
516#95—24no—
517#95—264no—
518#95—264no—
519#95—264no—
520#95—264no—
521#95—264no—
522#95—262no—
523#95—262no—
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—28no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—44no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—134no—
587C22×C4—134no—
588C22×C4—134no—
589C22×C4—132no—
590C22×C4—134no—
591C22×C4—132no—
592C22×C4—132no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—262no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—262no—
609C22×C4—261no—
610C22×C4—262no—
611C22×C4—261no—
612C22×C4—261no—
613C22×C4—261no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—261no—
617C22×C4—261no—
618C22×C4—261no—
619C22×C4—261no—
620C22×C4—261no—
621C22×C4—268no—
622C22×C4—268no—
623C22×C4—268no—
624C22×C4—524no—
625C22×C4—524no—
626C22×C4—524no—
627C22×C4—524no—
628C22×C4C2×C4×D1314yes—
629C22×C4C2×C4×D1312yes—
630C22×C4#612712yes—
631C22×C4D4×D1312yes—
632C22×C4D4×D1312yes—
633C22×C4D4×D1312yes—
634C22×C4#612912yes—
635C22×C4Q8×D1312yes—
636C22×C4#613112yes—
637C22×C4C2×C22⋊D1312yes—
638C22×C4C2×C22⋊D1312yes—
639C22×C4C2×C22⋊D1312yes—
640C4⋊C4—44no—
641C4⋊C4—1316no—
642C4⋊C4—2616no—
643C4⋊C4—268no—
644C4⋊C4—528no—
645C22⋊C4—2616no—
646C22⋊C4—268no—
647C22⋊C4—268no—
648C22⋊C4—528no—
649C42—28no—
650C42—528no—
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
689C23C2×#612711yescharacteristic
690C23C2×D4×D1311yescharacteristic
691C23C2×D4×D1311yescharacteristic
692C23C2×D4×D1311yescharacteristic
693C23C2×#612911yescharacteristic
694C23C2×Q8×D1311yescharacteristic
695C23C2×#613111yescharacteristic
696C23#8825411yescharacteristic
697C23#8825411yescharacteristic
698C23#41×D1311yescharacteristic
699C23#41×D1311yescharacteristic
700C23#8825611yescharacteristic
701C23#8825711yescharacteristic
702C23C22×C22⋊D1311yescharacteristic
703Q8—416no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—138no—
732C2×C4—264no—
733C2×C4—264no—
734C2×C4—264no—
735C2×C4—264no—
736C2×C4—264no—
737C2×C4—264no—
738C2×C4—264no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—264no—
744C2×C4—262no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—264no—
748C2×C4—262no—
749C2×C4—262no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—521no—
759C2×C4—521no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—521no—
765C2×C4—521no—
766C2×C4—5216no—
767C2×C4C22⋊C4×D1314yes—
768C2×C4#8813514yes—
769C2×C4#8813814yes—
770C2×C4#8813914yes—
771C2×C4C4×C22⋊D1314yes—
772C2×C4#8819314yes—
773C2×C4#8819414yes—
774C2×C4#8820014yescomplemented
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×C22⋊C4×D1311yescharacteristic
791C22C2×#8813511yescharacteristic
792C22C2×#8813811yescharacteristic
793C22C2×#8813911yescharacteristic
794C22C4×Q8×D1311yescharacteristic
795C22#1171927711yescharacteristic
796C22C4×#613111yescharacteristic
797C22#1171927911yescharacteristic
798C22#1171928311yescharacteristic
799C22#1171928511yescharacteristic
800C22#1171928711yescharacteristic
801C22#1171928811yescharacteristic
802C22#1171933511yescharacteristic
803C22#1171933611yescharacteristic
804C22#1171933711yescharacteristic
805C22#1171933811yescharacteristic
806C22#1171934011yescharacteristic
807C22#1171934411yescharacteristic
808C22#1171934611yescharacteristic
809C22#1171934711yescharacteristic
810C22#1171938111yescharacteristic
811C22#1171938111yescharacteristic
812C22#1171938211yescharacteristic
813C22#1171938211yescharacteristic
814C22#1171943111yescharacteristic
815C22#1171943111yescharacteristic
816C22#1171943211yescharacteristic
817C22#1171943211yescharacteristic
818C22C2×C4×C22⋊D1311yescharacteristic
819C22C2×#8819311yescharacteristic
820C22C2×#8819411yescharacteristic
821C22C2×#8820011yescharacteristic
822C22#1171952111yescharacteristic
823C22#1171953311yescharacteristic
824C22#1171953811yescharacteristic
825C4—24no—
826C4—42no—
827C4—44no—
828C4—82no—
829C4—268no—
830C4—522no—
831C4—522no—
832C4—522no—
833C4—524no—
834C4#1171861818yes—
835C2—524no—
836C2C2×#1171861811yescharacteristic
837C2C4×#8820011yescharacteristic
838C2#1311751211yescharacteristic
839C2#1311766511yescharacteristic
840C2#1311767011yescharacteristic
841C2#1311784611yescharacteristic
842C2#1311786811yescharacteristic
843C2#1311826611yescharacteristic
844C2#1311828811yescharacteristic
845C2#1311841411yescharacteristic
846C2#1311843611yescharacteristic
847C2#1311917811yescharacteristic
848C2#1311921111yescharacteristic
849C2#1311977611yescharacteristic
850C2#1311979011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#391C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#391D13
hypocenterC13#13997
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#11718891C2semidirect
3. C2×#11718634C2semidirect
5. C2×C4×C4⋊Dic13C2semidirect
7. #13113102C2semidirect
10. #13113064C2semidirect
11. C2×C13×#391C2semidirect
18. C2×#88200C4semidirect
87. C2×#6103Q8semidirect
223. C4⋊Dic13C22⋊C4semidirect
230. C2×#391D13semidirect
322. C2×C4×C13C22⋊Q8semidirect
652. C13#13997semidirect
774. C2×C4#88200semidirect

Maximal subgroups

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

subgroupindex
C22×#882002
C2×#117188912
C2×#117186342
C2×#117186482
C2×C4×C4⋊Dic132
C2×C4×#61032
#131131022
#131130802
#131130722
#131130642
C2×C13×#3912
#1399713