Finite Group Databasebeta

← #15769728

Subgroups — #15769728

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#6107C211yesmaximal, characteristic
2C22×#88075C211yesmaximal, characteristic
3C22×#88050C211yesmaximal, characteristic
4C2×#11718590C211yesmaximal, characteristic
5C2×#11718121C211yesmaximal, characteristic
6C2×#11718116C211yesmaximal, characteristic
7C2×C13×#391C211yesmaximal, characteristic
8C23×Q8×C13C2211yescharacteristic
9C23×Dic26C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C42×C13C2211yescharacteristic
12C22×#6107—22no—
13C22×#6107—22no—
14C22×#6107—22no—
15C22×#6107—22no—
16C22×#6107—22no—
17C22×#6107—22no—
18C22×#6107C414yescomplemented
19C22×C4⋊Dic13C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C13×#391—22no—
23C13×#391—22no—
24C2×C13×#95—22no—
25C2×#88075—22no—
26C2×#88075—22no—
27C2×#88075—22no—
28C2×#88071—22no—
29C2×#88050—22no—
30C2×#88050—22no—
31C2×#88050—22no—
32#11718590—22no—
33#11718590—22no—
34#11718121—22no—
35#11718116—22no—
36C22×Q8×C13—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×C13C2×C412yes—
48C22×Q8×C13D412yes—
49C22×Q8×C13D412yes—
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13D412yes—
53C23×C4×C13C2311yescharacteristic
54C23×Dic13—21no—
55C23×Dic13—21no—
56C22×Dic26—21no—
57C22×Dic26—21no—
58C22×Dic26—21no—
59C22×Dic26—21no—
60C22×Dic26—21no—
61C22×Dic26—21no—
62C22×Dic26—21no—
63C22×Dic26—21no—
64C22×Dic26—21no—
65C22×Dic26—21no—
66C22×Dic26—21no—
67C22×Dic26C2×C412yes—
68C22×Dic26D412yes—
69C22×Dic26D412yes—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4D412yes—
76C2×C42×C13—21no—
77C2×C42×C13—21no—
78C2×C42×C13—21no—
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×#6107—28no—
83C2×#6107—28no—
84C2×#6107—28no—
85C2×#6107—28no—
86C2×#6107—28no—
87C2×#6107—28no—
88C2×#6107—28no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13D412yes—
95C22×#1055—21no—
96C22×#1055—21no—
97C22×#1055—21no—
98C22×#1055—21no—
99C22×#1055—21no—
100C22×#1055—21no—
101C22×#1055—21no—
102C22×#1055—21no—
103C22×#1055—21no—
104C22×#1055—21no—
105C22×#1055C2×C412yes—
106C22×#1055D412yes—
107C22×#1055D412yes—
108C22×#1055D412yes—
109C13×#95—28no—
110#88075—28no—
111#88071—28no—
112#88050—28no—
113#11024—131nomaximal, Sylow
114C24×C13C2×D411yescharacteristic
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13—22no—
122C2×Q8×C13—22no—
123C2×Q8×C13—22no—
124C2×Q8×C13—22no—
125C2×Q8×C13—22no—
126C2×Q8×C13—22no—
127C2×Q8×C13—22no—
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13—41no—
131C2×Q8×C13—41no—
132C2×Q8×C13—41no—
133C2×Q8×C13—41no—
134C2×Q8×C13—41no—
135C2×Q8×C13—41no—
136C2×Q8×C13—41no—
137C2×Q8×C13—41no—
138C2×Q8×C13—41no—
139C2×Q8×C13—41no—
140C2×Q8×C13—41no—
141C2×Q8×C13—41no—
142C2×Q8×C13C22⋊C414yes—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—41no—
154C22×C4×C13—41no—
155C22×C4×C13—41no—
156C22×C4×C13—41no—
157C22×C4×C13—41no—
158C22×C4×C13—41no—
159C22×C4×C13—42no—
160C22×C4×C13—42no—
161C22×C4×C13Q1614yescomplemented
162C22×C4×C13C22×C411yescharacteristic
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13#4111yescharacteristic
173C22×C4×C13#4111yescharacteristic
174C22×C4×C13#4111yescharacteristic
175C22×C4×C13#4111yescharacteristic
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—41no—
181C22×Dic13—41no—
182C22×Dic13—41no—
183C22×Dic13—41no—
184C22×Dic13—41no—
185C22×Dic13—41no—
186C22×Dic13—42no—
187C22×Dic13—42no—
188C2×Dic26—22no—
189C2×Dic26—22no—
190C2×Dic26—22no—
191C2×Dic26—22no—
192C2×Dic26—22no—
193C2×Dic26—22no—
194C2×Dic26—22no—
195C2×Dic26—22no—
196C2×Dic26—22no—
197C2×Dic26—22no—
198C2×Dic26—22no—
199C2×Dic26—22no—
200C2×Dic26—22no—
201C2×Dic26—22no—
202C2×Dic26—22no—
203C2×Dic26—41no—
204C2×Dic26—41no—
205C2×Dic26—41no—
206C2×Dic26—41no—
207C2×Dic26—41no—
208C2×Dic26—41no—
209C2×Dic26—41no—
210C2×Dic26—41no—
211C2×Dic26—41no—
212C2×Dic26—41no—
213C2×Dic26—41no—
214C2×Dic26—41no—
215C2×Dic26C22⋊C414yes—
216C13×C4⋊C4—22no—
217C13×C4⋊C4—22no—
218C13×C4⋊C4—41no—
219C13×C4⋊C4—41no—
220C42×C13—41no—
221C42×C13—41no—
222C42×C13—41no—
223C42×C13—41no—
224#6107—232no—
225C4⋊Dic13—22no—
226C4⋊Dic13—22no—
227C4⋊Dic13—41no—
228C4⋊Dic13—41no—
229C2×#1055—22no—
230C2×#1055—22no—
231C2×#1055—22no—
232C2×#1055—22no—
233C2×#1055—22no—
234C2×#1055—22no—
235C2×#1055—22no—
236C2×#1055—22no—
237C2×#1055—22no—
238C2×#1055—41no—
239C2×#1055—41no—
240C2×#1055—41no—
241C2×#1055—41no—
242C2×#1055C22⋊C414yes—
243C23×Q16—131no—
244C22×#103—131no—
245C22×#103—131no—
246C2×#391—131no—
247C2×#391D1311yescharacteristic
248C2×#340—131no—
249C2×#336—131no—
250C23×C13C4×D411yescharacteristic
251C23×C13#12011yescharacteristic
252C23×C13#12011yescharacteristic
253C23×C13#12111yescharacteristic
254C23×C13#12111yescharacteristic
255C23×C13#12111yescharacteristic
256C23×C13#12711yescharacteristic
257C23×C13C2×Q1612yes—
258C23×C13#13512yes—
259C23×C13#13712yes—
260C23×C13#13712yes—
261Q8×C13—24no—
262Q8×C13—24no—
263Q8×C13—42no—
264Q8×C13—42no—
265Q8×C13—42no—
266Q8×C13—42no—
267Q8×C13—42no—
268Q8×C13—42no—
269C2×C4×C13—24no—
270C2×C4×C13—24no—
271C2×C4×C13—24no—
272C2×C4×C13—24no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—42no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—44no—
285C2×C4×C13—82no—
286C2×C4×C13—81no—
287C2×C4×C13—81no—
288C2×C4×C13C2×C22⋊C411yescharacteristic
289C2×C4×C13C2×C22⋊C411yescharacteristic
290C2×C4×C13C2×C22⋊C411yescharacteristic
291C2×C4×C13C4×D411yescharacteristic
292C2×C4×C13C4×D411yescharacteristic
293C2×C4×C13C4×D411yescharacteristic
294C2×C4×C13#12011yescharacteristic
295C2×C4×C13#12011yescharacteristic
296C2×C4×C13#12011yescharacteristic
297C2×C4×C13#12011yescharacteristic
298C2×C4×C13#12011yescharacteristic
299C2×C4×C13#12011yescharacteristic
300C2×C4×C13#12111yescharacteristic
301C2×C4×C13#12111yescharacteristic
302C2×C4×C13#12111yescharacteristic
303C2×C4×C13#12111yescharacteristic
304C2×C4×C13#12111yescharacteristic
305C2×C4×C13#12111yescharacteristic
306C2×C4×C13#12111yescharacteristic
307C2×C4×C13#12111yescharacteristic
308C2×C4×C13#12111yescharacteristic
309C2×C4×C13#12311yescharacteristic
310C2×C4×C13#12311yescharacteristic
311C2×C4×C13#12311yescharacteristic
312C2×C4×C13#12311yescharacteristic
313C2×C4×C13#12411yescharacteristic
314C2×C4×C13#12411yescharacteristic
315C2×C4×C13#12711yescharacteristic
316C2×Dic13—24no—
317C2×Dic13—42no—
318C2×Dic13—42no—
319C2×Dic13—42no—
320C2×Dic13—42no—
321C2×Dic13—42no—
322C2×Dic13—42no—
323C2×Dic13—42no—
324C2×Dic13—44no—
325C2×Dic13—82no—
326C2×Dic13—81no—
327C2×Dic13—81no—
328Dic26—24no—
329Dic26—24no—
330Dic26—42no—
331Dic26—42no—
332Dic26—42no—
333Dic26—42no—
334Dic26—42no—
335Dic26—42no—
336#1055—24no—
337#1055—42no—
338C23×Q8—131no—
339C23×Q8C2×D1311yescharacteristic
340C22×Q16—134no—
341C22×Q16—262no—
342C22×Q16—262no—
343C22×Q16—262no—
344C22×Q16—262no—
345C22×Q16—262no—
346C22×Q16—262no—
347C23×C8—131no—
348C23×C8—131no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4C2×D1311yescharacteristic
351C22×C42C2×D1311yescharacteristic
352C2×#103—262no—
353C2×#103—262no—
354C2×#103—262no—
355C2×#103—262no—
356C2×#103—262no—
357C2×#103—262no—
358#391—22no—
359#391—22no—
360#391—262no—
361#391—262no—
362C2×#95—22no—
363C2×#95—262no—
364#340—262no—
365#336—262no—
366C22×C13#38611yescharacteristic
367C22×C13#38611yescharacteristic
368C22×C13#39011yescharacteristic
369C22×C13#39211yescharacteristic
370C22×C13#39211yescharacteristic
371C22×C13#39211yescharacteristic
372C22×C13#39411yescharacteristic
373C22×C13C4×Q1612yes—
374C22×C13#44112yes—
375C22×C13#45112yes—
376C22×C13#45112yes—
377C22×C13#45212yes—
378C22×C13#45212yes—
379C22×C13#46212yes—
380C22×C13#46212yes—
381C22×C13#46412yes—
382C22×C13#46412yes—
383C22×C13#46712yes—
384C22×C13#47012yes—
385C22×C13#49411yescharacteristic
386C22×C13#49511yescharacteristic
387C22×C13#49711yescharacteristic
388C22×C13#49711yescharacteristic
389C4×C13—44no—
390C4×C13—44no—
391C4×C13—82no—
392C4×C13#37911yescharacteristic
393C4×C13#38611yescharacteristic
394C4×C13#38611yescharacteristic
395C4×C13#39011yescharacteristic
396C4×C13#39211yescharacteristic
397C4×C13#39411yescharacteristic
398C4×C13#39411yescharacteristic
399C4×C13#39411yescharacteristic
400Dic13—44no—
401Dic13—82no—
402C22×Q8—21no—
403C22×Q8—21no—
404C22×Q8—21no—
405C22×Q8—21no—
406C22×Q8—21no—
407C22×Q8—21no—
408C22×Q8—21no—
409C22×Q8—21no—
410C22×Q8—21no—
411C22×Q8—21no—
412C22×Q8—21no—
413C22×Q8—132no—
414C22×Q8—132no—
415C22×Q8—132no—
416C22×Q8—261no—
417C22×Q8—261no—
418C22×Q8—261no—
419C22×Q8—261no—
420C22×Q8—261no—
421C22×Q8—261no—
422C22×Q8—261no—
423C22×Q8—261no—
424C22×Q8—261no—
425C22×Q8—261no—
426C22×Q8—261no—
427C22×Q8C4×D1312yes—
428C22×Q8D5212yes—
429C22×Q8C22⋊D1312yes—
430C23×C4—21no—
431C23×C4—21no—
432C23×C4—261no—
433C23×C4—261no—
434C23×C4C22⋊D1312yes—
435C23×C4C22×D1311yescharacteristic
436C2×Q16—268no—
437C2×Q16—268no—
438C2×Q16—268no—
439C2×Q16—268no—
440C2×Q16—268no—
441C2×Q16—268no—
442C2×Q16—268no—
443C22×C8—132no—
444C22×C8—132no—
445C22×C8—132no—
446C22×C8—132no—
447C22×C8—261no—
448C22×C8—261no—
449C22×C8—261no—
450C22×C8—261no—
451C22×C8—261no—
452C22×C8—261no—
453C22×C8—261no—
454C22×C8—261no—
455C22×C8—261no—
456C22×C8—261no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—132no—
463C2×C4⋊C4—261no—
464C2×C4⋊C4—261no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4—261no—
468C2×C4⋊C4C22⋊D1312yes—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475#103—268no—
476#103—268no—
477#95—28no—
478#95—268no—
479C2×C13#143811yescharacteristic
480C2×C13#187812yes—
481C2×C13#187812yes—
482C2×C13#196911yescharacteristic
483C2×C13#197111yescharacteristic
484C2×C13#200112yes—
485C2×C13#201511yescharacteristic
486C2×C13#201511yescharacteristic
487C2×C13#201611yescharacteristic
488C2×C13#201611yescharacteristic
489C2×C13#205612yes—
490C24C2×C22⋊D1311yescharacteristic
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—22no—
500C2×Q8—22no—
501C2×Q8—22no—
502C2×Q8—22no—
503C2×Q8—22no—
504C2×Q8—22no—
505C2×Q8—22no—
506C2×Q8—41no—
507C2×Q8—41no—
508C2×Q8—41no—
509C2×Q8—41no—
510C2×Q8—41no—
511C2×Q8—41no—
512C2×Q8—41no—
513C2×Q8—41no—
514C2×Q8—41no—
515C2×Q8—41no—
516C2×Q8—41no—
517C2×Q8—41no—
518C2×Q8—134no—
519C2×Q8—262no—
520C2×Q8—262no—
521C2×Q8—262no—
522C2×Q8—262no—
523C2×Q8—262no—
524C2×Q8—262no—
525C2×Q8—262no—
526C2×Q8—262no—
527C2×Q8—262no—
528C2×Q8—262no—
529C2×Q8—262no—
530C2×Q8—262no—
531C2×Q8—262no—
532C2×Q8—262no—
533C2×Q8—262no—
534C2×Q8—521no—
535C2×Q8—521no—
536C2×Q8—521no—
537C2×Q8—521no—
538C2×Q8—521no—
539C2×Q8—521no—
540C2×Q8—521no—
541C2×Q8—521no—
542C2×Q8—521no—
543C2×Q8—521no—
544C2×Q8—521no—
545C2×Q8—521no—
546C2×Q8#610314yes—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—521no—
570C22×C4—521no—
571C22×C4—521no—
572C22×C4—521no—
573C22×C4—521no—
574C22×C4—521no—
575C22×C4—522no—
576C22×C4—522no—
577C22×C4#610714yescomplemented
578C22×C4C2×C4×D1311yescharacteristic
579C22×C4C2×D5211yescharacteristic
580C22×C4#612711yescharacteristic
581C22×C4#612711yescharacteristic
582C22×C4D4×D1311yescharacteristic
583C22×C4D4×D1311yescharacteristic
584C22×C4D4×D1311yescharacteristic
585C22×C4D4×D1311yescharacteristic
586C22×C4D4×D1311yescharacteristic
587C22×C4D4×D1311yescharacteristic
588C22×C4#612911yescharacteristic
589C22×C4#612911yescharacteristic
590C22×C4C2×C22⋊D1311yescharacteristic
591C22×C4C2×C22⋊D1311yescharacteristic
592Q16—2632no—
593C2×C8—134no—
594C2×C8—262no—
595C2×C8—262no—
596C2×C8—262no—
597C2×C8—262no—
598C2×C8—262no—
599C2×C8—262no—
600C2×C8—262no—
601C2×C8—262no—
602C2×C8—262no—
603C2×C8—521no—
604C2×C8—521no—
605C2×C8—521no—
606C2×C8—521no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—41no—
610C4⋊C4—41no—
611C4⋊C4—262no—
612C4⋊C4—262no—
613C4⋊C4—521no—
614C4⋊C4—521no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C13#1102411yescharacteristic, complemented, Sylow
620C23C4×C22⋊D1311yescharacteristic
621C23#8818411yescharacteristic
622C23#8819111yescharacteristic
623C23#8819211yescharacteristic
624C23#8819311yescharacteristic
625C23#8819411yescharacteristic
626C23#8819612yes—
627C23C2×#610712yes—
628C23#8820412yes—
629C23#8820512yes—
630C23#8820711yescharacteristic
631Q8—24no—
632Q8—24no—
633Q8—42no—
634Q8—42no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—42no—
639Q8—264no—
640Q8—264no—
641Q8—522no—
642Q8—522no—
643Q8—522no—
644Q8—522no—
645Q8—522no—
646Q8—522no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—44no—
663C2×C4—82no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—264no—
667C2×C4—522no—
668C2×C4—522no—
669C2×C4—522no—
670C2×C4—522no—
671C2×C4—522no—
672C2×C4—522no—
673C2×C4—524no—
674C2×C4—522no—
675C2×C4—1042no—
676C2×C4—1041no—
677C2×C4—1041no—
678C2×C4C22⋊C4×D1311yescharacteristic
679C2×C4C22⋊C4×D1311yescharacteristic
680C2×C4#8813511yescharacteristic
681C2×C4#8813511yescharacteristic
682C2×C4#8813611yescharacteristic
683C2×C4#8813611yescharacteristic
684C2×C4#8813611yescharacteristic
685C2×C4#8813711yescharacteristic
686C2×C4#8813711yescharacteristic
687C2×C4#8813811yescharacteristic
688C2×C4#8813811yescharacteristic
689C2×C4#8813811yescharacteristic
690C2×C4#8813811yescharacteristic
691C2×C4#8813911yescharacteristic
692C2×C4#8813911yescharacteristic
693C2×C4#8814011yescharacteristic
694C2×C4C2×#610311yescharacteristic
695C2×C4C4×C22⋊D1311yescharacteristic
696C2×C4#8818311yescharacteristic
697C2×C4#8818411yescharacteristic
698C2×C4#8819111yescharacteristic
699C2×C4#8819111yescharacteristic
700C2×C4#8819111yescharacteristic
701C2×C4#8819211yescharacteristic
702C2×C4#8819311yescharacteristic
703C2×C4#8819311yescharacteristic
704C2×C4#8819311yescharacteristic
705C2×C4#8819411yescharacteristic
706C8—264no—
707C8—522no—
708C22#1171861711yescharacteristic
709C22#1171861811yescharacteristic
710C22#1171862111yescharacteristic
711C22#1171862211yescharacteristic
712C22#1171868912yes—
713C22C4×#610712yes—
714C22#1171869112yes—
715C22#1171869212yes—
716C22#1171870812yes—
717C22#1171871112yes—
718C22#1171871212yes—
719C22#1171871312yes—
720C22#1171871512yes—
721C22#1171872011yescharacteristic
722C22#1171872111yescharacteristic
723C22#1171874711yescharacteristic
724C22#1171875112yes—
725C22#1171875311yescharacteristic
726C22#1171887411yescharacteristic
727C22#1171888411yescharacteristic
728C22#1171888411yescharacteristic
729C22#1171888912yes—
730C22#1171890012yes—
731C4—44no—
732C4—44no—
733C4—82no—
734C4—524no—
735C4—1042no—
736C4#1171861611yescharacteristic
737C4#1171861711yescharacteristic
738C4#1171861811yescharacteristic
739C4#1171861911yescharacteristic
740C4#1171862011yescharacteristic
741C4#1171862011yescharacteristic
742C4#1171862111yescharacteristic
743C4#1171862211yescharacteristic
744C2#1311307511yescharacteristic
745C2#1311517712yes—
746C2#1311518012yes—
747C2#1311569611yescharacteristic
748C2#1311570611yescharacteristic
749C2#1311584412yes—
750C2#1311592911yescharacteristic
751C2#1311593011yescharacteristic
752C2#1311593511yescharacteristic
753C2#1311593611yescharacteristic
754C2#1311615812yes—
subgroupG/H
centerC24C2×C22⋊D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#391C2
socle, prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#391D13
hypocenterC13#11024
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
18. C22×#6107C4semidirect
161. C22×C4×C13Q16semidirect
577. C22×C4#6107semidirect
619. C13#11024semidirect

Maximal subgroups

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

subgroupindex
C23×#61072
C22×#880752
C22×#880502
C2×#117185902
C2×#117181212
C2×#117181162
C2×C13×#3912
#1102413