Finite Group Databasebeta

← #15785716

Subgroups — #15785716

Order 3328.

2266 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88200C211yesmaximal, characteristic
2C22×Q8×Dic13C211yesmaximal, characteristic, complemented
3C2×#11718648C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5#13113090C212yesmaximal, complemented
6#13113082C212yesmaximal
7#13113072C212yesmaximal
8#13113071C212yesmaximal, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, 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
19C2×Q8×Dic13—24no—
20C2×Q8×Dic13—24no—
21C2×Q8×Dic13—24no—
22C22×#6103C2211yescharacteristic
23C22×#6103C2212yes—
24C22×#6103C2212yes—
25C22×#6103C2211yescharacteristic
26C22×C4⋊Dic13C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×#6101C2212yes—
30C22×C4×Dic13C2212yes—
31C22×C4×Dic13C2211yescharacteristic
32C13×#391—24no—
33C2×C13×#95C2212yes—
34C2×C13×#95C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2211yescharacteristic
40C2×#88071C2212yes—
41C2×#88071C2212yes—
42#11718648—24no—
43C4×#6103—24no—
44C24×D13C2311yescharacteristic
45C22×Q8×C13—22no—
46C22×Q8×C13—22no—
47C22×Q8×C13—22no—
48C22×Q8×C13—22no—
49C22×Q8×C13C2×C414yes—
50C22×Q8×C13D414yes—
51C22×Q8×C13D414yes—
52C23×C4×C13C2312yes—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2312yes—
56C23×C4×C13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2312yes—
59C23×Dic13C2312yes—
60C23×Dic13C2311yescharacteristic
61C23×Dic13C2311yescharacteristic
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×C13—22no—
75#88200—232no—
76Q8×Dic13—232no—
77C2×#6103—22no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×#6103—24no—
85C2×#6103—24no—
86C2×#6103—42no—
87C2×#6103C2×C418yes—
88C2×#6103Q814yescomplemented
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—24no—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13C2×C414yes—
97C2×C4⋊Dic13D414yes—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101C2×C418yes—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—24no—
105C2×C4×Dic13—24no—
106C2×C4×Dic13D414yes—
107C13×#95—24no—
108C13×#95—24no—
109#88071—24no—
110#88071—22no—
111#88071—22no—
112#88071—24no—
113#88071—24no—
114#88071—42no—
115#88071—42no—
116#13969—131nomaximal, Sylow
117C24×C13C2411yescharacteristic
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×D13—21no—
130C23×D13C22×C412yes—
131C23×D13C2×Q812yes—
132C23×D13#4112yes—
133C2×Q8×C13—28no—
134C2×Q8×C13—28no—
135C2×Q8×C13—28no—
136C2×Q8×C13—28no—
137C2×Q8×C13—28no—
138C2×Q8×C13—28no—
139C2×Q8×C13C22⋊C4116yescomplemented
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
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×C13—22no—
163C22×C4×C13C22×C414yes—
164C22×C4×C13C22×C412yes—
165C22×C4×C13C2×D414yes—
166C22×C4×C13C2×D412yes—
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2×D412yes—
169C22×C4×C13C2×D414yes—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×Q812yes—
172C22×C4×C13#4112yes—
173C22×C4×C13#4112yes—
174C22×C4×C13#4112yes—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—21no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—22no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—22no—
198C22×Dic13—21no—
199C22×Dic13—22no—
200C22×Dic13—22no—
201C22×Dic13—21no—
202C22×Dic13—22no—
203C22×Dic13C22×C412yes—
204C22×Dic13C22×C414yes—
205C22×Dic13C2×D414yes—
206C22×Dic13C2×D412yes—
207C22×Dic13C2×D412yes—
208C22×Dic13C2×Q812yes—
209C22×Dic13#4112yes—
210C2×C4×D13—28no—
211C2×C4×D13—28no—
212C2×C4×D13—28no—
213C2×C4×D13—44no—
214C2×C4×D13—44no—
215C2×C4×D13—44no—
216C2×C4×D13—44no—
217C13×C4⋊C4—44no—
218C42×C13—44no—
219#6103—28no—
220#6103—216no—
221#6103—28no—
222#6103—48no—
223C4⋊Dic13—216no—
224C4⋊Dic13—28no—
225C4⋊Dic13—28no—
226#6101—216no—
227C4×Dic13—216no—
228C4×Dic13—28no—
229C22×C22⋊Q8—131no—
230C22×C4×Q8—131no—
231C2×#391D1311yescharacteristic, complemented
232C2×#380—131no—
233C2×C4×C22⋊C4—131no—
234#1441—132no—
235#1439—132no—
236#1437—132no—
237#1436—132no—
238C4⋊#95—131no—
239C4⋊#95—131no—
240C23×C13C23×C411yescharacteristic
241C23×C13C22×D411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C13C22×D411yescharacteristic
244C23×C13C22×D411yescharacteristic
245C23×C13C22×Q811yescharacteristic
246C23×C13C2×#4111yescharacteristic
247C23×C13C2×#4111yescharacteristic
248C23×C13C2×#4111yescharacteristic
249C23×C13C2×#4111yescharacteristic
250C23×C13C2×#4111yescharacteristic
251C23×C13H(5,𝔽2)11yescharacteristic
252C23×C132−1+411yescharacteristic
253C23×C132−1+411yescharacteristic
254C23×C132−1+411yescharacteristic
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—22no—
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×D13—41no—
289C22×D13C4×Q814yescomplemented
290Q8×C13—232no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—24no—
296C2×C4×C13—24no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
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×C13—42no—
318C2×C4×C13C2×C22⋊C418yes—
319C2×C4×C13C2×C22⋊C414yes—
320C2×C4×C13C4×D414yes—
321C2×C4×C13C4×D414yes—
322C2×C4×C13#12014yes—
323C2×C4×C13#12114yes—
324C2×C4×C13#12114yes—
325C2×C4×C13#12314yes—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—24no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—24no—
337C2×Dic13—24no—
338C2×Dic13—24no—
339C2×Dic13—22no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—24no—
343C2×Dic13—24no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—41no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13—42no—
358C2×Dic13—42no—
359C2×Dic13—41no—
360C2×Dic13C22⋊Q814yescomplemented
361C4×D13—416no—
362C23×Q8C2×D1311yescharacteristic
363C24×C4—131no—
364C2×C22⋊Q8—138no—
365C2×C22⋊Q8—264no—
366C2×C22⋊Q8—264no—
367C2×C4×Q8—264no—
368C2×C4×Q8—264no—
369C2×C4×Q8—264no—
370C22×C4⋊C4—132no—
371C22×C4⋊C4—131no—
372C22×C4⋊C4—131no—
373C22×C4⋊C4—132no—
374C22×C4⋊C4C2×D1311yescharacteristic
375C22×C22⋊C4—132no—
376C22×C22⋊C4—131no—
377C22×C22⋊C4—131no—
378C22×C22⋊C4—132no—
379C22×C42—131no—
380C22×C42—132no—
381C22×C42C2×D1311yescharacteristic
382#391—24no—
383#380—264no—
384C4×C22⋊C4—264no—
385C2×#95—132no—
386C2×#95—132no—
387C2×#95—131no—
388C2×#95—132no—
389C2×#95—131no—
390C2×#95—132no—
391C2×#95—132no—
392C2×#95C2×D1312yes—
393C2×#95C2×D1312yes—
394C22×C13C22×C22⋊C411yescharacteristic
395C22×C13C2×C4×D411yescharacteristic
396C22×C13C2×C4×D411yescharacteristic
397C22×C13C2×C4×Q811yescharacteristic
398C22×C13C4×#4111yescharacteristic
399C22×C13#51911yescharacteristic
400C22×C13#52011yescharacteristic
401C22×C13C2×#12011yescharacteristic
402C22×C13C2×#12111yescharacteristic
403C22×C13C2×#12111yescharacteristic
404C22×C13C2×C22⋊Q811yescharacteristic
405C22×C13C2×#12311yescharacteristic
406C22×C13#52511yescharacteristic
407C22×C13#52911yescharacteristic
408C22×C13#53311yescharacteristic
409C22×C13#53611yescharacteristic
410C22×C13#53711yescharacteristic
411C22×C13#54111yescharacteristic
412C22×C13#54211yescharacteristic
413C22×C13#54611yescharacteristic
414C22×C13#54711yescharacteristic
415C22×C13#54811yescharacteristic
416C22×C13#54811yescharacteristic
417C22×C13#54811yescharacteristic
418C22×C13#54811yescharacteristic
419C22×C13#54811yescharacteristic
420C22×C13D4×Q811yescharacteristic
421C22×C13D4×Q811yescharacteristic
422C22×C13D4×Q811yescharacteristic
423C22×C13#55011yescharacteristic
424C22×C13#55011yescharacteristic
425C22×C13#55211yescharacteristic
426C22×C13#55211yescharacteristic
427C22×C13#55411yescharacteristic
428C22×C13#55611yescharacteristic
429C2×D13—24no—
430C2×D13—24no—
431C2×D13—24no—
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—
443C2×D13—42no—
444C4×C13—28no—
445C4×C13—42no—
446C4×C13—42no—
447C4×C13—82no—
448C4×C13#38618yes—
449Dic13—24no—
450Dic13—44no—
451Dic13—42no—
452Dic13—44no—
453Dic13—42no—
454C25—131no—
455C22×Q8—22no—
456C22×Q8—22no—
457C22×Q8—22no—
458C22×Q8—22no—
459C22×Q8C4×D1314yes—
460C22×Q8D5214yes—
461C22×Q8C22⋊D1314yes—
462C23×C4—131no—
463C23×C4—132no—
464C23×C4—131no—
465C23×C4—132no—
466C23×C4—131no—
467C23×C4—134no—
468C23×C4—262no—
469C23×C4—262no—
470C23×C4—262no—
471C23×C4—262no—
472C23×C4—262no—
473C23×C4—262no—
474C23×C4C22×D1312yes—
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1311yescharacteristic
477C23×C4C22×D1312yes—
478C23×C4C22×D1311yescharacteristic
479C22⋊Q8—2632no—
480C4×Q8—2632no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—138no—
485C2×C4⋊C4—134no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—264no—
489C2×C4⋊C4—264no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—264no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—264no—
495C2×C4⋊C4—262no—
496C2×C22⋊C4—138no—
497C2×C22⋊C4—134no—
498C2×C22⋊C4—262no—
499C2×C22⋊C4—262no—
500C2×C22⋊C4—262no—
501C2×C22⋊C4—262no—
502C2×C22⋊C4—264no—
503C2×C22⋊C4—262no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C22⋊C4—522no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—22no—
511C2×C42—134no—
512C2×C42—264no—
513C2×C42—264no—
514C2×C42—264no—
515C2×C42—262no—
516C2×C42—262no—
517#95—24no—
518#95—24no—
519#95—264no—
520#95—262no—
521#95—262no—
522#95—264no—
523#95—264no—
524#95—522no—
525#95—522no—
526C2×C13C2×#38611yescharacteristic
527C2×C13C4×C22⋊Q811yescharacteristic
528C2×C13#232311yescharacteristic
529C2×C13Q8×C22⋊C411yescharacteristic
530C2×C13#234111yescharacteristic
531C2×C13#236011yescharacteristic
532C2×C13#236211yescharacteristic
533C2×C13#240711yescharacteristic
534C2×C13#240911yescharacteristic
535C2×C13#242111yescharacteristic
536C2×C13#242311yescharacteristic
537C2×C13#242611yescharacteristic
538C2×C13#242911yescharacteristic
539C2×C13#253611yescharacteristic
540C2×C13#253811yescharacteristic
541D13—44no—
542C24—132no—
543C24—132no—
544C24—132no—
545C24—261no—
546C24—261no—
547C24—261no—
548C24—261no—
549C24—261no—
550C24—261no—
551C24—261no—
552C24—261no—
553C24—261no—
554C24—261no—
555C24—261no—
556C24—261no—
557C24C23×D1311yescharacteristic
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—28no—
561C2×Q8—28no—
562C2×Q8—28no—
563C2×Q8—28no—
564C2×Q8#6103116yescomplemented
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—132no—
589C22×C4—132no—
590C22×C4—132no—
591C22×C4—134no—
592C22×C4—132no—
593C22×C4—132no—
594C22×C4—134no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—262no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—262no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—261no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—261no—
615C22×C4—262no—
616C22×C4—261no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—261no—
620C22×C4—262no—
621C22×C4—262no—
622C22×C4—261no—
623C22×C4—268no—
624C22×C4—268no—
625C22×C4—268no—
626C22×C4—524no—
627C22×C4—524no—
628C22×C4—524no—
629C22×C4—524no—
630C22×C4C2×C4×D1314yes—
631C22×C4C2×C4×D1312yes—
632C22×C4C2×D5214yes—
633C22×C4C2×D5212yes—
634C22×C4D4×D1312yes—
635C22×C4D4×D1312yes—
636C22×C4#612912yes—
637C22×C4#612912yes—
638C22×C4Q8×D1312yes—
639C22×C4#613112yes—
640C22×C4C2×C22⋊D1314yes—
641C22×C4C2×C22⋊D1312yes—
642C4⋊C4—44no—
643C4⋊C4—2616no—
644C4⋊C4—268no—
645C4⋊C4—2616no—
646C4⋊C4—268no—
647C22⋊C4—268no—
648C22⋊C4—268no—
649C22⋊C4—2616no—
650C22⋊C4—528no—
651C42—44no—
652C42—2616no—
653C42—268no—
654C13#1396911yescharacteristic, complemented, Sylow
655C23—134no—
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—262no—
673C23—262no—
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—
688C23—521no—
689C23—521no—
690C23C22×C4×D1311yescharacteristic
691C23C22×D5211yescharacteristic
692C23C2×D4×D1311yescharacteristic
693C23C2×D4×D1311yescharacteristic
694C23C2×#612911yescharacteristic
695C23C2×#612911yescharacteristic
696C23C2×Q8×D1311yescharacteristic
697C23C2×#613111yescharacteristic
698C23#8825411yescharacteristic
699C23#8825411yescharacteristic
700C23#41×D1311yescharacteristic
701C23#41×D1311yescharacteristic
702C23#8825611yescharacteristic
703C23#8825711yescharacteristic
704C23C22×C22⋊D1311yescharacteristic
705Q8—232no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—134no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—264no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—264no—
744C2×C4—262no—
745C2×C4—264no—
746C2×C4—262no—
747C2×C4—264no—
748C2×C4—264no—
749C2×C4—262no—
750C2×C4—262no—
751C2×C4—264no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4—521no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—521no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—522no—
766C2×C4—522no—
767C2×C4—521no—
768C2×C4—5216no—
769C2×C4#8813514yes—
770C2×C4#8813514yes—
771C2×C4#8813614yes—
772C2×C4#8814014yes—
773C2×C4C2×#610318yes—
774C2×C4C2×#610314yes—
775C2×C4#8819314yes—
776C2×C4#8819314yes—
777C22—264no—
778C22—264no—
779C22—264no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—522no—
784C22—522no—
785C22—522no—
786C22—522no—
787C22—522no—
788C22—522no—
789C22—522no—
790C22—522no—
791C22—522no—
792C22C2×#8813511yescharacteristic
793C22C2×#8813511yescharacteristic
794C22C2×#8813611yescharacteristic
795C22C2×#8814011yescharacteristic
796C22C4×Q8×D1311yescharacteristic
797C22#1171927711yescharacteristic
798C22C4×#613111yescharacteristic
799C22#1171927911yescharacteristic
800C22Q8×D5211yescharacteristic
801C22#1171928111yescharacteristic
802C22#1171928111yescharacteristic
803C22#1171928211yescharacteristic
804C22D13×C22⋊Q811yescharacteristic
805C22#1171933211yescharacteristic
806C22#1171933311yescharacteristic
807C22#1171933411yescharacteristic
808C22#1171934011yescharacteristic
809C22#1171934411yescharacteristic
810C22#1171934611yescharacteristic
811C22#1171934711yescharacteristic
812C22#1171938111yescharacteristic
813C22#1171938211yescharacteristic
814C22#1171938511yescharacteristic
815C22#1171938711yescharacteristic
816C22#1171943111yescharacteristic
817C22#1171943211yescharacteristic
818C22#1171943311yescharacteristic
819C22#1171943611yescharacteristic
820C22C22×#610311yescharacteristic
821C22C2×#8819311yescharacteristic
822C22C2×#8819311yescharacteristic
823C22Q8×C22⋊D1311yescharacteristic
824C22#1171952211yescharacteristic
825C22#1171953611yescharacteristic
826C22#1171953911yescharacteristic
827C4—28no—
828C4—42no—
829C4—42no—
830C4—82no—
831C4—264no—
832C4—522no—
833C4—524no—
834C4—522no—
835C4—524no—
836C4#1171861918yes—
837C2—524no—
838C2C2×#1171861911yescharacteristic
839C2#1311737411yescharacteristic
840C2#1311752111yescharacteristic
841C2Q8×#610311yescharacteristic
842C2#1311767411yescharacteristic
843C2#1311784611yescharacteristic
844C2#1311786811yescharacteristic
845C2#1311818411yescharacteristic
846C2#1311819911yescharacteristic
847C2#1311833711yescharacteristic
848C2#1311835911yescharacteristic
849C2#1311840511yescharacteristic
850C2#1311843811yescharacteristic
851C2#1311974311yescharacteristic
852C2#1311975511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#391C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#391D13
hypocenterC13#13969
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic13C2semidirect
5. #13113090C2semidirect
8. #13113071C2semidirect
9. #13113066C2semidirect
10. #13113065C2semidirect
11. C2×C13×#391C2semidirect
18. C2×#88200C4semidirect
88. C2×#6103Q8semidirect
139. C2×Q8×C13C22⋊C4semidirect
231. C2×#391D13semidirect
289. C22×D13C4×Q8semidirect
360. C2×Dic13C22⋊Q8semidirect
564. C2×Q8#6103semidirect
654. C13#13969semidirect

Maximal subgroups

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

subgroupindex
C22×#882002
C22×Q8×Dic132
C2×#117186482
C2×C4×#61032
#131130902
#131130822
#131130722
#131130712
#131130662
#131130652
C2×C13×#3912
#1396913