Finite Group Databasebeta

← #15786056

Subgroups — #15786056

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×#11718648C211yesmaximal, characteristic
5C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
6C2×C4×#6103C211yesmaximal, characteristic
7#13113105C212yesmaximal, complemented
8#13113078C212yesmaximal
9#13113072C212yesmaximal
10#13113065C212yesmaximal, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C23×Dic26C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4×Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C2×#88151—24no—
27C2×#88151—24no—
28C2×#88151C418yescomplemented
29C13×#389—24no—
30C2×C13×#95C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38C2×#88071C2211yescharacteristic
39#11718648—24no—
40C4⋊C4×Dic13—24no—
41#11718635—24no—
42C4×#6103—24no—
43#11718590—24no—
44C24×D13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2312yes—
49C23×C4×C13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2312yes—
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—24no—
70C2×C13×C4⋊C4—22no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—42no—
75C2×C13×C4⋊C4C2×C414yes—
76C2×C13×C4⋊C4D414yes—
77C2×C13×C4⋊C4D414yes—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×C42×C13—22no—
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—22no—
97C2×C4⋊Dic13C2×C418yes—
98C2×C4⋊Dic13D414yes—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13—24no—
102C2×C4×Dic13—24no—
103C2×C4×Dic13—42no—
104C2×C4×Dic13D414yes—
105#88151—232no—
106C13×#95—24no—
107#88071—24no—
108#88071—24no—
109#88071—24no—
110#88071—22no—
111#88071—22no—
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—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13C22×C414yes—
156C22×C4×C13C22×C412yes—
157C22×C4×C13C2×D414yes—
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—21no—
171C22×Dic13—21no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—22no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—22no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—22no—
195C22×Dic13C22×C412yes—
196C22×Dic13C22×C414yes—
197C22×Dic13C2×D412yes—
198C22×Dic13C2×D414yes—
199C22×Dic13C2×D412yes—
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—48no—
217C13×C4⋊C4—44no—
218C13×C4⋊C4C22⋊C4116yescomplemented
219C42×C13—44no—
220#6103—28no—
221#6103—216no—
222#6103—28no—
223#6103—48no—
224C4⋊Dic13—216no—
225C4⋊Dic13—28no—
226C4×Dic13—28no—
227C4×Dic13—48no—
228C22×C22⋊Q8—131no—
229C2×#391—131no—
230C2×#391—131no—
231C2×#389D1311yescharacteristic, complemented
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—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—24no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
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—42no—
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×C13C2×C22⋊C418yes—
317C2×C4×C13C2×C22⋊C414yes—
318C2×C4×C13C4×D414yes—
319C2×C4×C13C4×D414yes—
320C2×C4×C13#12114yes—
321C2×C4×C13#12114yes—
322C2×C4×C13#12414yes—
323C2×C4×C13#12714yes—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—24no—
332C2×Dic13—24no—
333C2×Dic13—24no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—24no—
338C2×Dic13—22no—
339C2×Dic13—22no—
340C2×Dic13—24no—
341C2×Dic13—24no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—42no—
347C2×Dic13—41no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13—41no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—42no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358C2×Dic13C22⋊Q814yescomplemented
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⋊C4C2×D1311yescharacteristic
369C22×C4⋊C4C2×D1312yes—
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—264no—
379#391—264no—
380#389—24no—
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—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—42no—
445C4×C13—42no—
446C4×C13—82no—
447C4×C13#39018yes—
448Dic13—24no—
449Dic13—42no—
450Dic13—44no—
451Dic13—44no—
452Dic13—42no—
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—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×D1311yescharacteristic
475C23×C4C22×D1311yescharacteristic
476C23×C4C22×D1312yes—
477C23×C4C22×D1311yescharacteristic
478C22⋊Q8—2632no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—138no—
486C2×C4⋊C4—134no—
487C2×C4⋊C4—264no—
488C2×C4⋊C4—262no—
489C2×C4⋊C4—262no—
490C2×C4⋊C4—264no—
491C2×C4⋊C4C4×D1314yes—
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—262no—
499C2×C22⋊C4—262no—
500C2×C22⋊C4—264no—
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—22no—
509C2×C42—134no—
510C2×C42—262no—
511C2×C42—262no—
512C2×C42—264no—
513C2×C42—264no—
514C2×C42—522no—
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—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
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—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—132no—
587C22×C4—132no—
588C22×C4—132no—
589C22×C4—134no—
590C22×C4—132no—
591C22×C4—132no—
592C22×C4—134no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—261no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—261no—
606C22×C4—262no—
607C22×C4—261no—
608C22×C4—262no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—261no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—261no—
617C22×C4—262no—
618C22×C4—261no—
619C22×C4—262no—
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×C4C2×D5214yes—
631C22×C4C2×D5212yes—
632C22×C4D4×D1312yes—
633C22×C4D4×D1312yes—
634C22×C4#612912yes—
635C22×C4Q8×D1312yes—
636C22×C4#613112yes—
637C22×C4#613112yes—
638C22×C4C2×C22⋊D1314yes—
639C22×C4C2×C22⋊D1312yes—
640C4⋊C4—48no—
641C4⋊C4—44no—
642C4⋊C4—268no—
643C4⋊C4—2616no—
644C4⋊C4#6103116yescomplemented
645C22⋊C4—268no—
646C22⋊C4—268no—
647C22⋊C4—2616no—
648C22⋊C4—528no—
649C42—44no—
650C42—268no—
651C42—528no—
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
690C23C2×D4×D1311yescharacteristic
691C23C2×D4×D1311yescharacteristic
692C23C2×#612911yescharacteristic
693C23#8825111yescharacteristic
694C23C2×Q8×D1311yescharacteristic
695C23C2×#613111yescharacteristic
696C23C2×#613111yescharacteristic
697C23#8825411yescharacteristic
698C23#41×D1311yescharacteristic
699C23#41×D1311yescharacteristic
700C23#8825711yescharacteristic
701C23#8825711yescharacteristic
702C23C22×C22⋊D1311yescharacteristic
703Q8—5216no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
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—134no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—262no—
739C2×C4—262no—
740C2×C4—264no—
741C2×C4—264no—
742C2×C4—262no—
743C2×C4—264no—
744C2×C4—264no—
745C2×C4—262no—
746C2×C4—262no—
747C2×C4—264no—
748C2×C4—262no—
749C2×C4—264no—
750C2×C4—521no—
751C2×C4—522no—
752C2×C4—521no—
753C2×C4—521no—
754C2×C4—522no—
755C2×C4—522no—
756C2×C4—521no—
757C2×C4—522no—
758C2×C4—522no—
759C2×C4—521no—
760C2×C4—521no—
761C2×C4—522no—
762C2×C4—521no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4—521no—
766C2×C4—5216no—
767C2×C4#8814714yes—
768C2×C4#8814714yes—
769C2×C4#8814914yes—
770C2×C4#8814914yes—
771C2×C4C2×#610318yes—
772C2×C4C2×#610314yes—
773C2×C4#8819414yes—
774C2×C4#8820114yes—
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×#8814711yescharacteristic
791C22C2×#8814711yescharacteristic
792C22C2×#8814911yescharacteristic
793C22C2×#8814911yescharacteristic
794C22C4×#612911yescharacteristic
795C22#1171925111yescharacteristic
796C22#1171925911yescharacteristic
797C22#1171926011yescharacteristic
798C22C4×Q8×D1311yescharacteristic
799C22#1171927711yescharacteristic
800C22Q8×D5211yescharacteristic
801C22#1171928111yescharacteristic
802C22#1171930311yescharacteristic
803C22#1171931111yescharacteristic
804C22#1171931311yescharacteristic
805C22#1171931711yescharacteristic
806C22D13×C22⋊Q811yescharacteristic
807C22#1171933311yescharacteristic
808C22#1171933611yescharacteristic
809C22#1171933711yescharacteristic
810C22#1171939611yescharacteristic
811C22#1171939911yescharacteristic
812C22#1171939911yescharacteristic
813C22#1171940211yescharacteristic
814C22#1171943311yescharacteristic
815C22#1171943511yescharacteristic
816C22#1171943711yescharacteristic
817C22#1171943811yescharacteristic
818C22C22×#610311yescharacteristic
819C22C2×#8819411yescharacteristic
820C22#1171951111yescharacteristic
821C22C2×#8820111yescharacteristic
822C22Q8×C22⋊D1311yescharacteristic
823C22#1171952911yescharacteristic
824C22#1171953611yescharacteristic
825C4—28no—
826C4—42no—
827C4—42no—
828C4—82no—
829C4—264no—
830C4—522no—
831C4—522no—
832C4—524no—
833C4—524no—
834C4#1171864918yes—
835C2—524no—
836C2C2×#1171864911yescharacteristic
837C2#1311736611yescharacteristic
838C2#1311751611yescharacteristic
839C2#1311766111yescharacteristic
840C2Q8×#610311yescharacteristic
841C2#1311784011yescharacteristic
842C2#1311786211yescharacteristic
843C2#1311826311yescharacteristic
844C2#1311828511yescharacteristic
845C2#1311841111yescharacteristic
846C2#1311843311yescharacteristic
847C2#1311918011yescharacteristic
848C2#1311921311yescharacteristic
849C2#1311977211yescharacteristic
850C2#1311978611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#13997
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11718590C2semidirect
3. C2×#11718635C2semidirect
5. C2×C4⋊C4×Dic13C2semidirect
7. #13113105C2semidirect
10. #13113065C2semidirect
11. C2×C13×#389C2semidirect
28. C2×#88151C4semidirect
92. C2×#6103Q8semidirect
218. C13×C4⋊C4C22⋊C4semidirect
231. C2×#389D13semidirect
358. C2×Dic13C22⋊Q8semidirect
644. C4⋊C4#6103semidirect
652. C13#13997semidirect

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×#117186482
C2×C4⋊C4×Dic132
C2×C4×#61032
#131131052
#131130782
#131130722
#131130652
C2×C13×#3892
#1399713