Finite Group Databasebeta

← #15769720

Subgroups — #15769720

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6106C211yesmaximal, characteristic
2C22×#88061C211yesmaximal, characteristic
3C2×#11718891C211yesmaximal, characteristic, complemented
4C2×#11718649C211yesmaximal, characteristic
5C2×#11718121C211yesmaximal, characteristic, complemented
6C2×#11718142C211yesmaximal, characteristic, complemented
7C22×C13×#103C211yesmaximal, characteristic, complemented
8C23×Q8×C13C2211yescharacteristic
9C23×D52C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×#6106—22no—
13C22×#6106—22no—
14C22×#6106—22no—
15C22×#6106—22no—
16C22×#6106—22no—
17C22×#6106—22no—
18C22×#6106C414yescomplemented
19C22×#6103—22no—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4×Dic13C2211yescharacteristic
22C23×#1055C2211yescharacteristic
23C2×C13×#103—22no—
24C2×C13×#103—22no—
25C2×C13×#103—22no—
26#11718891—22no—
27#11718891—22no—
28C2×#88071—22no—
29C2×#88061—22no—
30C2×#88061—22no—
31C2×#88061—22no—
32#11718649—22no—
33#11718649—22no—
34#11718142—22no—
35#11718121—22no—
36C24×D13—21no—
37C22×Q8×C13—21no—
38C22×Q8×C13—21no—
39C22×Q8×C13—21no—
40C22×Q8×C13—21no—
41C22×Q8×C13—21no—
42C22×Q8×C13—21no—
43C22×Q8×C13—21no—
44C22×Q8×C13—21no—
45C22×Q8×C13—21no—
46C22×Q8×C13—21no—
47C22×Q8×C13—21no—
48C22×Q8×C13C2×C412yes—
49C22×Q8×C13D412yes—
50C22×Q8×C13D412yes—
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C23×C4×C13C2311yescharacteristic
54C23×Dic13—21no—
55C23×Dic13D412yes—
56C22×D52—21no—
57C22×D52—21no—
58C22×D52—21no—
59C22×D52—21no—
60C22×D52—21no—
61C22×D52—21no—
62C22×D52—21no—
63C22×D52—21no—
64C22×D52—21no—
65C22×D52—21no—
66C22×D52—21no—
67C22×D52C2×C412yes—
68C22×D52D412yes—
69C22×D52D412yes—
70C22×C8×C13—21no—
71C22×C8×C13—21no—
72C22×C8×C13—21no—
73C22×C8×C13—21no—
74C22×C8×C13—21no—
75C22×C8×C13—21no—
76C22×C8×C13D412yes—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4D412yes—
83C2×#6106—28no—
84C2×#6106—28no—
85C2×#6106—28no—
86C2×#6106—28no—
87C2×#6106—28no—
88C2×#6106—28no—
89C2×#6106—28no—
90C2×#6103—28no—
91C2×#6103—44no—
92C2×#6103—44no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—21no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13—21no—
97C2×C4⋊Dic13—21no—
98C2×C4⋊Dic13D412yes—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13—21no—
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C22×#1055—21no—
106C22×#1055—21no—
107C22×#1055—21no—
108C22×#1055—21no—
109C22×#1055C2×C412yes—
110C22×#1055D412yes—
111C22×#1055D412yes—
112C13×#103—28no—
113#88071—28no—
114#88061—28no—
115#11023—131nomaximal, Sylow
116C24×C13C2×D411yescharacteristic
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—41no—
121C23×D13—41no—
122C23×D13—41no—
123C23×D13—41no—
124C23×D13—42no—
125C23×D13—42no—
126C23×D13—42no—
127C23×D13—42no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13—22no—
131C2×Q8×C13—22no—
132C2×Q8×C13—22no—
133C2×Q8×C13—22no—
134C2×Q8×C13—22no—
135C2×Q8×C13—22no—
136C2×Q8×C13—22no—
137C2×Q8×C13—22no—
138C2×Q8×C13—22no—
139C2×Q8×C13—22no—
140C2×Q8×C13—22no—
141C2×Q8×C13—22no—
142C2×Q8×C13—22no—
143C2×Q8×C13—41no—
144C2×Q8×C13—41no—
145C2×Q8×C13—41no—
146C2×Q8×C13—41no—
147C2×Q8×C13—41no—
148C2×Q8×C13—41no—
149C2×Q8×C13—41no—
150C2×Q8×C13—41no—
151C2×Q8×C13—41no—
152C2×Q8×C13—41no—
153C2×Q8×C13—41no—
154C2×Q8×C13—41no—
155C2×Q8×C13C22⋊C414yescomplemented
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—41no—
161C22×C4×C13—41no—
162C22×C4×C13—41no—
163C22×C4×C13—41no—
164C22×C4×C13—41no—
165C22×C4×C13—41no—
166C22×C4×C13—42no—
167C22×C4×C13—42no—
168C22×C4×C13C22×C411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13#4111yescharacteristic
179C22×C4×C13#4111yescharacteristic
180C22×C4×C13#4111yescharacteristic
181C22×C4×C13#4111yescharacteristic
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—41no—
190C22×Dic13—41no—
191C22×Dic13—42no—
192C22×Dic13—42no—
193C22×Dic13SD1614yescomplemented
194C2×D52—22no—
195C2×D52—22no—
196C2×D52—22no—
197C2×D52—22no—
198C2×D52—22no—
199C2×D52—22no—
200C2×D52—22no—
201C2×D52—22no—
202C2×D52—22no—
203C2×D52—22no—
204C2×D52—22no—
205C2×D52—22no—
206C2×D52—22no—
207C2×D52—22no—
208C2×D52—22no—
209C2×D52—41no—
210C2×D52—41no—
211C2×D52—41no—
212C2×D52—41no—
213C2×D52—41no—
214C2×D52—41no—
215C2×D52—41no—
216C2×D52—41no—
217C2×D52—41no—
218C2×D52—41no—
219C2×D52—41no—
220C2×D52—41no—
221C2×D52C22⋊C414yes—
222C2×C8×C13—22no—
223C2×C8×C13—22no—
224C2×C8×C13—22no—
225C2×C8×C13—41no—
226C2×C8×C13—41no—
227C2×C8×C13—41no—
228C2×C8×C13—41no—
229C13×C4⋊C4—22no—
230C13×C4⋊C4—22no—
231C13×C4⋊C4—41no—
232C13×C4⋊C4—41no—
233#6106—232no—
234#6103—416no—
235C4⋊Dic13—22no—
236C4⋊Dic13—22no—
237C4⋊Dic13—41no—
238C4⋊Dic13—41no—
239C4×Dic13—41no—
240C4×Dic13—41no—
241C4×Dic13—41no—
242C4×Dic13—41no—
243C2×#1055—22no—
244C2×#1055—22no—
245C2×#1055—22no—
246C2×#1055—22no—
247C2×#1055—22no—
248C2×#1055—22no—
249C2×#1055C22⋊C414yescomplemented
250C23×SD16—131no—
251C22×#103D1311yescharacteristic, complemented
252C22×#102—131no—
253C2×#391—131no—
254C2×#390—131no—
255C2×#340—131no—
256C2×#336—131no—
257C23×C13C4×D411yescharacteristic
258C23×C13#12011yescharacteristic
259C23×C13#12011yescharacteristic
260C23×C13#12111yescharacteristic
261C23×C13#12111yescharacteristic
262C23×C13#12111yescharacteristic
263C23×C13#12711yescharacteristic
264C23×C13C2×SD1612yes—
265C23×C13#13512yes—
266C23×C13AGL(1,ℤ/8)12yes—
267C23×C13#13712yes—
268C22×D13—24no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13—42no—
272C22×D13—42no—
273C22×D13—42no—
274C22×D13—42no—
275C22×D13—44no—
276C22×D13—44no—
277C22×D13—44no—
278C22×D13—44no—
279C22×D13—44no—
280C22×D13—44no—
281C22×D13—82no—
282C22×D13—82no—
283C22×D13—82no—
284C22×D13—82no—
285C22×D13—82no—
286C22×D13—82no—
287C22×D13—81no—
288C22×D13—81no—
289C22×D13—81no—
290C22×D13—81no—
291Q8×C13—24no—
292Q8×C13—24no—
293Q8×C13—42no—
294Q8×C13—42no—
295Q8×C13—42no—
296Q8×C13—42no—
297Q8×C13—42no—
298Q8×C13—42no—
299C2×C4×C13—24no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—44no—
308C2×C4×C13—82no—
309C2×C4×C13—81no—
310C2×C4×C13—81no—
311C2×C4×C13C2×C22⋊C411yescharacteristic
312C2×C4×C13C2×C22⋊C411yescharacteristic
313C2×C4×C13C2×C22⋊C411yescharacteristic
314C2×C4×C13C4×D411yescharacteristic
315C2×C4×C13C4×D411yescharacteristic
316C2×C4×C13C4×D411yescharacteristic
317C2×C4×C13#12011yescharacteristic
318C2×C4×C13#12011yescharacteristic
319C2×C4×C13#12011yescharacteristic
320C2×C4×C13#12011yescharacteristic
321C2×C4×C13#12011yescharacteristic
322C2×C4×C13#12011yescharacteristic
323C2×C4×C13#12111yescharacteristic
324C2×C4×C13#12111yescharacteristic
325C2×C4×C13#12111yescharacteristic
326C2×C4×C13#12111yescharacteristic
327C2×C4×C13#12111yescharacteristic
328C2×C4×C13#12111yescharacteristic
329C2×C4×C13#12111yescharacteristic
330C2×C4×C13#12111yescharacteristic
331C2×C4×C13#12111yescharacteristic
332C2×C4×C13#12311yescharacteristic
333C2×C4×C13#12311yescharacteristic
334C2×C4×C13#12311yescharacteristic
335C2×C4×C13#12311yescharacteristic
336C2×C4×C13#12411yescharacteristic
337C2×C4×C13#12411yescharacteristic
338C2×C4×C13#12711yescharacteristic
339C2×Dic13—24no—
340C2×Dic13—24no—
341C2×Dic13—24no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—44no—
348C2×Dic13—82no—
349C2×Dic13—81no—
350C2×Dic13—81no—
351D52—24no—
352D52—24no—
353D52—42no—
354D52—42no—
355D52—42no—
356D52—42no—
357D52—42no—
358D52—42no—
359C8×C13—42no—
360#1055—24no—
361C23×Q8C2×D1311yescharacteristic
362C23×D4—131no—
363C22×SD16—134no—
364C22×SD16—262no—
365C22×SD16—262no—
366C22×SD16—262no—
367C22×SD16—262no—
368C22×SD16—262no—
369C22×SD16—262no—
370C23×C8—131no—
371C23×C8C2×D1311yescharacteristic
372C22×C4⋊C4—131no—
373C22×C4⋊C4C2×D1311yescharacteristic
374C22×C22⋊C4—262no—
375C22×C42—131no—
376C2×#103—22no—
377C2×#103—22no—
378C2×#103—22no—
379C2×#102—262no—
380C2×#102—262no—
381C2×#102—262no—
382#391—262no—
383#391—262no—
384#390—262no—
385#390—262no—
386C2×#95—262no—
387#340—262no—
388#336—262no—
389C22×C13#38611yescharacteristic
390C22×C13#38611yescharacteristic
391C22×C13#39011yescharacteristic
392C22×C13#39211yescharacteristic
393C22×C13#39211yescharacteristic
394C22×C13#39211yescharacteristic
395C22×C13#39411yescharacteristic
396C22×C13C4×SD1612yes—
397C22×C13#44012yes—
398C22×C13#44812yes—
399C22×C13#44912yes—
400C22×C13#45012yes—
401C22×C13#45212yes—
402C22×C13#46012yes—
403C22×C13#46112yes—
404C22×C13#46312yes—
405C22×C13#46412yes—
406C22×C13#46512yes—
407C22×C13#46812yes—
408C22×C13#49211yescharacteristic
409C22×C13#49511yescharacteristic
410C22×C13#49611yescharacteristic
411C22×C13#49711yescharacteristic
412C2×D13—48no—
413C2×D13—44no—
414C2×D13—84no—
415C2×D13—84no—
416C2×D13—82no—
417C2×D13—82no—
418C2×D13—84no—
419C2×D13—82no—
420C2×D13—82no—
421C2×D13—82no—
422C2×D13—82no—
423C4×C13—44no—
424C4×C13—82no—
425C4×C13#37911yescharacteristic
426C4×C13#38611yescharacteristic
427C4×C13#38611yescharacteristic
428C4×C13#39011yescharacteristic
429C4×C13#39211yescharacteristic
430C4×C13#39411yescharacteristic
431C4×C13#39411yescharacteristic
432C4×C13#39411yescharacteristic
433Dic13—44no—
434Dic13—82no—
435C25—261no—
436C22×Q8—21no—
437C22×Q8—21no—
438C22×Q8—21no—
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—21no—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—21no—
445C22×Q8—21no—
446C22×Q8—21no—
447C22×Q8C4×D1312yes—
448C22×Q8D5212yes—
449C22×Q8C22⋊D1312yes—
450C22×D4—132no—
451C22×D4—132no—
452C22×D4—132no—
453C22×D4—261no—
454C22×D4—261no—
455C22×D4—261no—
456C22×D4—261no—
457C22×D4—261no—
458C22×D4—261no—
459C22×D4—261no—
460C22×D4—261no—
461C22×D4—261no—
462C22×D4—261no—
463C22×D4—261no—
464C23×C4—21no—
465C23×C4—21no—
466C23×C4—132no—
467C23×C4—261no—
468C23×C4C22×D1311yescharacteristic
469C2×SD16—268no—
470C2×SD16—268no—
471C2×SD16—268no—
472C2×SD16—268no—
473C2×SD16—268no—
474C2×SD16—268no—
475C2×SD16—268no—
476C22×C8—21no—
477C22×C8—21no—
478C22×C8—21no—
479C22×C8—21no—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—132no—
483C22×C8—132no—
484C22×C8—132no—
485C22×C8—261no—
486C22×C8—261no—
487C22×C8—261no—
488C22×C8—261no—
489C22×C8C22⋊D1312yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—132no—
496C2×C4⋊C4—261no—
497C2×C4⋊C4—261no—
498C2×C4⋊C4—261no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4C22⋊D1312yes—
502C2×C22⋊C4—268no—
503C2×C22⋊C4—524no—
504C2×C22⋊C4—524no—
505C2×C42—261no—
506C2×C42—261no—
507C2×C42—261no—
508C2×C42—261no—
509C2×C42—261no—
510C2×C42—261no—
511#103—28no—
512#102—268no—
513#95—268no—
514C2×C13#143811yescharacteristic
515C2×C13#187712yes—
516C2×C13#188012yes—
517C2×C13#196811yescharacteristic
518C2×C13#197311yescharacteristic
519C2×C13#200012yes—
520C2×C13#201211yescharacteristic
521C2×C13#201311yescharacteristic
522C2×C13#201411yescharacteristic
523C2×C13#201511yescharacteristic
524C2×C13#205512yes—
525D13—84no—
526C24—262no—
527C24—262no—
528C24—262no—
529C24—521no—
530C24—521no—
531C24—522no—
532C24—522no—
533C24—522no—
534C24—522no—
535C24—521no—
536C24—521no—
537C24D4×D1311yescharacteristic
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—41no—
563C2×Q8—41no—
564C2×Q8—41no—
565C2×Q8#610314yescomplemented
566C2×D4—134no—
567C2×D4—262no—
568C2×D4—262no—
569C2×D4—262no—
570C2×D4—262no—
571C2×D4—262no—
572C2×D4—262no—
573C2×D4—262no—
574C2×D4—262no—
575C2×D4—262no—
576C2×D4—262no—
577C2×D4—262no—
578C2×D4—262no—
579C2×D4—262no—
580C2×D4—262no—
581C2×D4—262no—
582C2×D4—521no—
583C2×D4—521no—
584C2×D4—521no—
585C2×D4—521no—
586C2×D4—521no—
587C2×D4—521no—
588C2×D4—521no—
589C2×D4—521no—
590C2×D4—521no—
591C2×D4—521no—
592C2×D4—521no—
593C2×D4—521no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—134no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—262no—
611C22×C4—262no—
612C22×C4—262no—
613C22×C4—262no—
614C22×C4—521no—
615C22×C4—522no—
616C22×C4—522no—
617C22×C4—521no—
618C22×C4C2×C4×D1311yescharacteristic
619C22×C4C2×D5211yescharacteristic
620C22×C4#612711yescharacteristic
621C22×C4#612711yescharacteristic
622C22×C4D4×D1311yescharacteristic
623C22×C4D4×D1311yescharacteristic
624C22×C4D4×D1311yescharacteristic
625C22×C4D4×D1311yescharacteristic
626C22×C4D4×D1311yescharacteristic
627C22×C4#612911yescharacteristic
628C22×C4#612911yescharacteristic
629C22×C4C2×C22⋊D1311yescharacteristic
630C22×C4C2×C22⋊D1311yescharacteristic
631C22×C4C2×C22⋊D1311yescharacteristic
632SD16—2632no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—41no—
637C2×C8—41no—
638C2×C8—41no—
639C2×C8—41no—
640C2×C8—134no—
641C2×C8—262no—
642C2×C8—262no—
643C2×C8—262no—
644C2×C8—262no—
645C2×C8—262no—
646C2×C8—262no—
647C4⋊C4—22no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C4⋊C4—262no—
652C4⋊C4—262no—
653C4⋊C4—521no—
654C4⋊C4—521no—
655C22⋊C4—5216no—
656C42—521no—
657C42—521no—
658C42—521no—
659C42—521no—
660C13#1102311yescharacteristic, complemented, Sylow
661C23—264no—
662C23—524no—
663C23—524no—
664C23—524no—
665C23—524no—
666C23—524no—
667C23—524no—
668C23—522no—
669C23—522no—
670C23—522no—
671C23—522no—
672C23—522no—
673C23—522no—
674C23—1042no—
675C23—1042no—
676C23—1042no—
677C23—1042no—
678C23—1042no—
679C23—1041no—
680C23—1041no—
681C23—1042no—
682C23—1041no—
683C23—1041no—
684C23#8813511yescharacteristic
685C23#8813611yescharacteristic
686C23#8813811yescharacteristic
687C23#8813811yescharacteristic
688C23SD16×D1312yes—
689C23#8816812yes—
690C23#8817212yes—
691C23#8817312yes—
692C23#8819111yescharacteristic
693C23#8819311yescharacteristic
694C23#8819411yescharacteristic
695Q8—24no—
696Q8—24no—
697Q8—42no—
698Q8—42no—
699Q8—42no—
700Q8—42no—
701Q8—42no—
702Q8—42no—
703D4—264no—
704D4—264no—
705D4—522no—
706D4—522no—
707D4—522no—
708D4—522no—
709D4—522no—
710D4—522no—
711C2×C4—24no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—82no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—264no—
724C2×C4—264no—
725C2×C4—264no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—524no—
731C2×C4—522no—
732C2×C4—1042no—
733C2×C4—1041no—
734C2×C4—1041no—
735C2×C4C22⋊C4×D1311yescharacteristic
736C2×C4C22⋊C4×D1311yescharacteristic
737C2×C4#8813511yescharacteristic
738C2×C4#8813611yescharacteristic
739C2×C4#8813611yescharacteristic
740C2×C4#8813711yescharacteristic
741C2×C4#8813711yescharacteristic
742C2×C4#8813811yescharacteristic
743C2×C4#8813811yescharacteristic
744C2×C4#8813911yescharacteristic
745C2×C4#8813911yescharacteristic
746C2×C4#8814011yescharacteristic
747C2×C4C2×#610311yescharacteristic
748C2×C4C4×C22⋊D1311yescharacteristic
749C2×C4C4×C22⋊D1311yescharacteristic
750C2×C4#8818311yescharacteristic
751C2×C4#8818411yescharacteristic
752C2×C4#8818411yescharacteristic
753C2×C4#8819111yescharacteristic
754C2×C4#8819111yescharacteristic
755C2×C4#8819111yescharacteristic
756C2×C4#8819211yescharacteristic
757C2×C4#8819211yescharacteristic
758C2×C4#8819311yescharacteristic
759C2×C4#8819311yescharacteristic
760C2×C4#8819311yescharacteristic
761C2×C4#8819411yescharacteristic
762C2×C4#8820711yescharacteristic
763C8—42no—
764C8—264no—
765C22—528no—
766C22—524no—
767C22—1042no—
768C22—1042no—
769C22—1042no—
770C22—1042no—
771C22—1042no—
772C22—1044no—
773C22—1042no—
774C22—1044no—
775C22—1044no—
776C22#1171844912yes—
777C22#1171846712yes—
778C22#1171846812yes—
779C22#1171847212yes—
780C22#1171847312yes—
781C22#1171847812yes—
782C22#1171847912yes—
783C22#1171848012yes—
784C22#1171861711yescharacteristic
785C22#1171861811yescharacteristic
786C22#1171861911yescharacteristic
787C22#1171862011yescharacteristic
788C22#1171862111yescharacteristic
789C22#1171862111yescharacteristic
790C22#1171882412yes—
791C22#1171883012yes—
792C22#1171883611yescharacteristic
793C22#1171883711yescharacteristic
794C22#1171884612yes—
795C22#1171884812yes—
796C22#1171885111yescharacteristic
797C22#1171885211yescharacteristic
798C22#1171888411yescharacteristic
799C4—44no—
800C4—82no—
801C4—524no—
802C4—1042no—
803C4#1171861611yescharacteristic
804C4#1171861711yescharacteristic
805C4#1171861811yescharacteristic
806C4#1171862011yescharacteristic
807C4#1171862211yescharacteristic
808C4#1171862211yescharacteristic
809C4#1171887411yescharacteristic
810C4#1171888411yescharacteristic
811C2—1044no—
812C2#1311307511yescharacteristic
813C2#1311516712yes—
814C2#1311518912yes—
815C2#1311568711yescharacteristic
816C2#1311571411yescharacteristic
817C2#1311583812yes—
818C2#1311591411yescharacteristic
819C2#1311592011yescharacteristic
820C2#1311592211yescharacteristic
821C2#1311592711yescharacteristic
822C2#1311615012yes—
subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC22×C13×#103C2
socleC24×C13C2×D4
prime radicalC23×D52C22
cosocleC23×C4×C13C23
hypercenterC22×#103D13
hypocenterC13#11023
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. C2×#11718891C2semidirect
5. C2×#11718121C2semidirect
6. C2×#11718142C2semidirect
7. C22×C13×#103C2semidirect
18. C22×#6106C4semidirect
155. C2×Q8×C13C22⋊C4semidirect
193. C22×Dic13SD16semidirect
249. C2×#1055C22⋊C4semidirect
251. C22×#103D13semidirect
565. C2×Q8#6103semidirect
660. C13#11023semidirect

Maximal subgroups

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

subgroupindex
C23×#61062
C22×#880612
C2×#117188912
C2×#117186492
C2×#117181212
C2×#117181422
C22×C13×#1032
#1102313