Finite Group Databasebeta

← #15769431

Subgroups — #15769431

Order 3328.

1578 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88151C211yesmaximal, characteristic
2C22×#88056C211yesmaximal, characteristic, complemented
3C22×#88050C211yesmaximal, characteristic, complemented
4C22×#88060C211yesmaximal, characteristic
5C2×#11718648C211yesmaximal, characteristic
6C2×#11718121C211yesmaximal, characteristic, complemented
7C2×C13×#340C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
9C23×Dic26C2211yescharacteristic
10C23×C8×C13C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×C13×C4⋊C4C2211yescharacteristic
13C22×#6103—21no—
14C22×#6103—21no—
15C22×C4⋊Dic13—21no—
16C22×C4⋊Dic13C2211yescharacteristic
17C23×#1055C2211yescharacteristic
18C2×#88151—22no—
19C2×#88151—22no—
20C2×#88151—22no—
21C2×#88151—22no—
22C2×#88151—22no—
23C2×#88151C414yescomplemented
24C2×#88071—21no—
25C2×#88060—22no—
26C2×#88060—22no—
27C2×#88060—22no—
28C2×#88056—22no—
29C2×#88056—22no—
30C2×#88056—22no—
31#11718648—22no—
32#11718648—22no—
33C2×#88050—22no—
34C2×#88050—22no—
35C2×#88050—22no—
36C13×#340—22no—
37#11718121—22no—
38C24×D13D411yescharacteristic
39C23×C4×C13—21no—
40C23×C4×C13—21no—
41C23×C4×C13C2311yescharacteristic
42C23×Dic13—21no—
43C23×Dic13—21no—
44C23×Dic13D411yescharacteristic
45C22×C4×D13—21no—
46C22×C4×D13—21no—
47C22×C4×D13—21no—
48C22×C4×D13—21no—
49C22×C4×D13—21no—
50C22×C4×D13—21no—
51C22×C4×D13—21no—
52C22×C4×D13—21no—
53C22×C4×D13—21no—
54C22×C4×D13—21no—
55C22×C4×D13—21no—
56C22×C4×D13—21no—
57C22×C4×D13C2×C412yes—
58C22×C4×D13D412yes—
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×Dic26—21no—
68C22×Dic26—21no—
69C22×Dic26—21no—
70C22×Dic26C2×C412yes—
71C22×Dic26D412yes—
72C22×Dic26D412yes—
73C22×C8×C13—21no—
74C22×C8×C13—21no—
75C22×C8×C13—21no—
76C22×C8×C13—21no—
77C22×C8×C13—21no—
78C22×C8×C13—21no—
79C22×C8×C13D412yes—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—21no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—21no—
88C2×C13×C4⋊C4C2×C412yes—
89C2×C13×C4⋊C4D412yes—
90C2×C13×C4⋊C4D412yes—
91C2×C13×C4⋊C4D412yes—
92C2×#6103—24no—
93C2×#6103—24no—
94C2×#6103—24no—
95C2×#6103—24no—
96C2×#6103—42no—
97C2×#6103—42no—
98C2×C4⋊Dic13—24no—
99C2×C4⋊Dic13—24no—
100C2×C4⋊Dic13—24no—
101C2×C4⋊Dic13—21no—
102C2×C4⋊Dic13—21no—
103C2×C4⋊Dic13—21no—
104C2×C4⋊Dic13—21no—
105C2×C4⋊Dic13—21no—
106C2×C4⋊Dic13D412yes—
107C22×#1055—21no—
108C22×#1055—21no—
109C22×#1055—21no—
110C22×#1055—21no—
111C22×#1055—21no—
112C22×#1055—21no—
113C22×#1055D412yes—
114#88151—28no—
115#88151—28no—
116#88151—28no—
117#88151—28no—
118#88071—24no—
119#88060—28no—
120#88056—28no—
121#88050—28no—
122#10970—131nomaximal, Sylow
123C24×C13C2×D411yescharacteristic
124C23×D13—21no—
125C23×D13—21no—
126C23×D13—21no—
127C23×D13—21no—
128C23×D13—21no—
129C23×D13—21no—
130C23×D13—21no—
131C23×D13—21no—
132C23×D13—21no—
133C23×D13—21no—
134C23×D13—21no—
135C23×D13—21no—
136C23×D13C22⋊C412yes—
137C23×D13SD1612yes—
138C23×D13Q1612yes—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—41no—
144C22×C4×C13—41no—
145C22×C4×C13—41no—
146C22×C4×C13—41no—
147C22×C4×C13—41no—
148C22×C4×C13—41no—
149C22×C4×C13—41no—
150C22×C4×C13—41no—
151C22×C4×C13—41no—
152C22×C4×C13—41no—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D411yescharacteristic
163C22×C4×C13#4111yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C22×C4×C13#4111yescharacteristic
166C22×C4×C13#4111yescharacteristic
167C22×Dic13—22no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—22no—
177C22×Dic13—41no—
178C22×Dic13—41no—
179C22×Dic13—41no—
180C22×Dic13—41no—
181C22×Dic13—41no—
182C22×Dic13—41no—
183C22×Dic13—41no—
184C22×Dic13—41no—
185C22×Dic13—41no—
186C22×Dic13—41no—
187C22×Dic13C22⋊C412yes—
188C2×C4×D13—22no—
189C2×C4×D13—22no—
190C2×C4×D13—22no—
191C2×C4×D13—22no—
192C2×C4×D13—22no—
193C2×C4×D13—22no—
194C2×C4×D13—22no—
195C2×C4×D13—22no—
196C2×C4×D13—22no—
197C2×C4×D13—22no—
198C2×C4×D13—22no—
199C2×C4×D13—22no—
200C2×C4×D13—41no—
201C2×C4×D13—41no—
202C2×C4×D13—41no—
203C2×C4×D13—41no—
204C2×C4×D13—41no—
205C2×C4×D13—41no—
206C2×C4×D13—41no—
207C2×C4×D13—41no—
208C2×C4×D13—41no—
209C2×C4×D13—41no—
210C2×C4×D13—41no—
211C2×C4×D13—41no—
212C2×C4×D13—41no—
213C2×C4×D13—41no—
214C2×C4×D13—41no—
215C2×C4×D13—41no—
216C2×Dic26—22no—
217C2×Dic26—22no—
218C2×Dic26—22no—
219C2×Dic26—22no—
220C2×Dic26—22no—
221C2×Dic26—22no—
222C2×Dic26—22no—
223C2×Dic26—22no—
224C2×Dic26—22no—
225C2×Dic26—22no—
226C2×Dic26—22no—
227C2×Dic26—22no—
228C2×Dic26—22no—
229C2×Dic26—22no—
230C2×Dic26—22no—
231C2×Dic26—41no—
232C2×Dic26—41no—
233C2×Dic26—41no—
234C2×Dic26—41no—
235C2×Dic26—41no—
236C2×Dic26—41no—
237C2×Dic26—41no—
238C2×Dic26—41no—
239C2×Dic26—41no—
240C2×Dic26—41no—
241C2×Dic26—41no—
242C2×Dic26—41no—
243C2×Dic26C22⋊C414yescomplemented
244C2×C8×C13—22no—
245C2×C8×C13—22no—
246C2×C8×C13—22no—
247C2×C8×C13—41no—
248C2×C8×C13—41no—
249C2×C8×C13—41no—
250C2×C8×C13—41no—
251C13×C4⋊C4—22no—
252C13×C4⋊C4—22no—
253C13×C4⋊C4—22no—
254C13×C4⋊C4—22no—
255C13×C4⋊C4—22no—
256C13×C4⋊C4—41no—
257C13×C4⋊C4—41no—
258C13×C4⋊C4C22⋊C414yescomplemented
259#6103—216no—
260#6103—48no—
261C4⋊Dic13—216no—
262C4⋊Dic13—22no—
263C4⋊Dic13—22no—
264C4⋊Dic13—41no—
265C4⋊Dic13—41no—
266C2×#1055—22no—
267C2×#1055—22no—
268C2×#1055—22no—
269C2×#1055—41no—
270C2×#1055—41no—
271C2×#1055—41no—
272C2×#1055—41no—
273C22×C22⋊Q8—131no—
274C22×#103—131no—
275C22×#103—131no—
276C22×C22⋊C8—131no—
277C2×#380—131no—
278C2×#340—131no—
279C2×#340D1311yescharacteristic, complemented
280C23×C13C2×C22⋊C411yescharacteristic
281C23×C13#12011yescharacteristic
282C23×C13#12011yescharacteristic
283C23×C13#12011yescharacteristic
284C23×C13#12111yescharacteristic
285C23×C13#12111yescharacteristic
286C23×C13#12311yescharacteristic
287C23×C13C2×SD1611yescharacteristic
288C23×C13C2×Q1611yescharacteristic
289C23×C13#13511yescharacteristic
290C23×C13#13511yescharacteristic
291C23×C13AGL(1,ℤ/8)11yescharacteristic
292C23×C13#13711yescharacteristic
293C23×C13#13711yescharacteristic
294C23×C13#13711yescharacteristic
295C22×D13—22no—
296C22×D13—22no—
297C22×D13—22no—
298C22×D13—22no—
299C22×D13—22no—
300C22×D13—22no—
301C22×D13—22no—
302C22×D13—22no—
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—22no—
306C22×D13—22no—
307C22×D13—22no—
308C22×D13—22no—
309C22×D13—22no—
310C22×D13—22no—
311C22×D13—22no—
312C22×D13—22no—
313C22×D13—41no—
314C22×D13—41no—
315C22×D13—41no—
316C22×D13—41no—
317C22×D13—41no—
318C22×D13—41no—
319C22×D13—41no—
320C22×D13—41no—
321C22×D13—41no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13#10314yescomplemented
330C2×C4×C13—24no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—42no—
337C2×C4×C13—42no—
338C2×C4×C13—42no—
339C2×C4×C13—42no—
340C2×C4×C13—81no—
341C2×C4×C13—81no—
342C2×C4×C13—81no—
343C2×C4×C13—81no—
344C2×C4×C13C2×C22⋊C411yescharacteristic
345C2×C4×C13C2×C22⋊C411yescharacteristic
346C2×C4×C13C4×D411yescharacteristic
347C2×C4×C13C4×D411yescharacteristic
348C2×C4×C13C4×D411yescharacteristic
349C2×C4×C13C4×D411yescharacteristic
350C2×C4×C13#12011yescharacteristic
351C2×C4×C13#12011yescharacteristic
352C2×C4×C13#12011yescharacteristic
353C2×C4×C13#12011yescharacteristic
354C2×C4×C13#12011yescharacteristic
355C2×C4×C13#12111yescharacteristic
356C2×C4×C13#12111yescharacteristic
357C2×C4×C13#12111yescharacteristic
358C2×C4×C13#12111yescharacteristic
359C2×C4×C13#12111yescharacteristic
360C2×C4×C13#12111yescharacteristic
361C2×C4×C13#12111yescharacteristic
362C2×C4×C13#12111yescharacteristic
363C2×C4×C13#12111yescharacteristic
364C2×C4×C13#12111yescharacteristic
365C2×C4×C13#12311yescharacteristic
366C2×C4×C13#12311yescharacteristic
367C2×C4×C13#12311yescharacteristic
368C2×C4×C13#12411yescharacteristic
369C2×C4×C13#12411yescharacteristic
370C2×C4×C13#12711yescharacteristic
371C2×C4×C13#12711yescharacteristic
372C2×Dic13—22no—
373C2×Dic13—24no—
374C2×Dic13—22no—
375C2×Dic13—22no—
376C2×Dic13—42no—
377C2×Dic13—42no—
378C2×Dic13—42no—
379C2×Dic13—42no—
380C2×Dic13—41no—
381C2×Dic13—41no—
382C2×Dic13—42no—
383C2×Dic13—42no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—42no—
387C2×Dic13—42no—
388C2×Dic13—42no—
389C2×Dic13—81no—
390C2×Dic13—81no—
391C2×Dic13—81no—
392C2×Dic13—81no—
393C4×D13—42no—
394C4×D13—42no—
395C4×D13—42no—
396C4×D13—42no—
397C4×D13—42no—
398C4×D13—42no—
399C4×D13—42no—
400C4×D13—42no—
401Dic26—24no—
402Dic26—24no—
403Dic26—42no—
404Dic26—42no—
405Dic26—42no—
406Dic26—42no—
407Dic26—42no—
408Dic26—42no—
409C8×C13—42no—
410#1055—42no—
411C23×Q8—131no—
412C24×C4—131no—
413C23×C8—131no—
414C23×C8C2×D1311yescharacteristic
415C2×C22⋊Q8—134no—
416C2×C22⋊Q8—262no—
417C2×C22⋊Q8—262no—
418C2×C22⋊Q8—262no—
419C2×C22⋊Q8—262no—
420C2×C22⋊Q8—262no—
421C22×C4⋊C4—131no—
422C22×C4⋊C4—261no—
423C22×C4⋊C4C2×D1311yescharacteristic
424C22×C4⋊C4C2×D1311yescharacteristic
425C22×C22⋊C4—261no—
426C22×C22⋊C4—261no—
427C2×#103—262no—
428C2×#103—262no—
429C2×#103—262no—
430C2×#103—262no—
431C2×#103—262no—
432C2×#103—262no—
433C2×C22⋊C8—262no—
434C2×C22⋊C8—262no—
435C2×C22⋊C8—262no—
436#380—262no—
437#380—262no—
438C2×#95—261no—
439#340—22no—
440#340—262no—
441C22×C13#37911yescharacteristic
442C22×C13#38611yescharacteristic
443C22×C13#38611yescharacteristic
444C22×C13#39211yescharacteristic
445C22×C13#39211yescharacteristic
446C22×C13#39411yescharacteristic
447C22×C13#39411yescharacteristic
448C22×C13C2×#10311yescharacteristic
449C22×C13#41611yescharacteristic
450C22×C13#41711yescharacteristic
451C22×C13#41911yescharacteristic
452C22×C13#44811yescharacteristic
453C22×C13#44811yescharacteristic
454C22×C13#44911yescharacteristic
455C22×C13#44911yescharacteristic
456C22×C13#45011yescharacteristic
457C22×C13#45111yescharacteristic
458C22×C13#45111yescharacteristic
459C22×C13#45111yescharacteristic
460C22×C13#45211yescharacteristic
461C22×C13#45211yescharacteristic
462C22×C13#45211yescharacteristic
463C22×C13#45211yescharacteristic
464C22×C13#46511yescharacteristic
465C22×C13#46511yescharacteristic
466C22×C13#46711yescharacteristic
467C22×C13#46711yescharacteristic
468C22×C13#46811yescharacteristic
469C22×C13#46811yescharacteristic
470C22×C13#47011yescharacteristic
471C22×C13#47011yescharacteristic
472C22×C13#48311yescharacteristic
473C22×C13#48411yescharacteristic
474C22×C13#48511yescharacteristic
475C22×C13#48511yescharacteristic
476C2×D13—24no—
477C2×D13—24no—
478C2×D13—24no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—42no—
483C2×D13—42no—
484C2×D13—42no—
485C2×D13—42no—
486C2×D13—42no—
487C2×D13—42no—
488C2×D13—42no—
489C2×D13—42no—
490C2×D13—42no—
491C4×C13—44no—
492C4×C13—82no—
493C4×C13#38611yescharacteristic
494C4×C13#38611yescharacteristic
495C4×C13#39011yescharacteristic
496C4×C13#39011yescharacteristic
497C4×C13#39211yescharacteristic
498C4×C13#39211yescharacteristic
499C4×C13#39411yescharacteristic
500C4×C13#39411yescharacteristic
501Dic13—44no—
502Dic13—42no—
503Dic13—82no—
504C25—131no—
505C22×Q8—132no—
506C22×Q8—132no—
507C22×Q8—132no—
508C22×Q8—261no—
509C22×Q8—261no—
510C22×Q8—261no—
511C22×Q8—261no—
512C22×Q8—261no—
513C22×Q8—261no—
514C22×Q8—261no—
515C22×Q8—261no—
516C22×Q8—261no—
517C22×Q8—261no—
518C22×Q8—261no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—131no—
522C23×C4—132no—
523C23×C4—132no—
524C23×C4—261no—
525C23×C4—261no—
526C23×C4—261no—
527C23×C4—261no—
528C23×C4—261no—
529C23×C4—261no—
530C23×C4—261no—
531C23×C4—261no—
532C23×C4—261no—
533C23×C4—261no—
534C23×C4—261no—
535C23×C4—261no—
536C23×C4—261no—
537C23×C4—261no—
538C23×C4C22×D1311yescharacteristic
539C22×C8—21no—
540C22×C8—21no—
541C22×C8—21no—
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8—132no—
546C22×C8—261no—
547C22×C8—261no—
548C22×C8—261no—
549C22×C8—261no—
550C22×C8—261no—
551C22×C8—261no—
552C22×C8D5212yes—
553C22⋊Q8—268no—
554C22⋊Q8—268no—
555C22⋊Q8—268no—
556C22⋊Q8—268no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—132no—
566C2×C4⋊C4—264no—
567C2×C4⋊C4—264no—
568C2×C4⋊C4—264no—
569C2×C4⋊C4—261no—
570C2×C4⋊C4—261no—
571C2×C4⋊C4—261no—
572C2×C4⋊C4—261no—
573C2×C4⋊C4—261no—
574C2×C4⋊C4C4×D1312yes—
575C2×C4⋊C4D5212yes—
576C2×C4⋊C4D5212yes—
577C2×C4⋊C4C22⋊D1312yes—
578C2×C22⋊C4—264no—
579C2×C22⋊C4—264no—
580C2×C22⋊C4—264no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—522no—
583C2×C22⋊C4—522no—
584#103—268no—
585#103—268no—
586C22⋊C8—268no—
587#95—264no—
588C2×C13#143811yescharacteristic
589C2×C13#178711yescharacteristic
590C2×C13#178811yescharacteristic
591C2×C13#187211yescharacteristic
592C2×C13#187311yescharacteristic
593C2×C13#189211yescharacteristic
594C2×C13#189411yescharacteristic
595C2×C13#200011yescharacteristic
596C2×C13#200011yescharacteristic
597C2×C13#200111yescharacteristic
598C2×C13#200111yescharacteristic
599C2×C13#203511yescharacteristic
600C2×C13#203511yescharacteristic
601C2×C13#203611yescharacteristic
602C2×C13#203611yescharacteristic
603D13—44no—
604C24—132no—
605C24—132no—
606C24—132no—
607C24—261no—
608C24—261no—
609C24—261no—
610C24—261no—
611C24—261no—
612C24—261no—
613C24—261no—
614C24—261no—
615C24—261no—
616C24—261no—
617C24—261no—
618C24—261no—
619C24D4×D1311yescharacteristic
620C2×Q8—134no—
621C2×Q8—262no—
622C2×Q8—262no—
623C2×Q8—262no—
624C2×Q8—262no—
625C2×Q8—262no—
626C2×Q8—262no—
627C2×Q8—262no—
628C2×Q8—262no—
629C2×Q8—262no—
630C2×Q8—262no—
631C2×Q8—262no—
632C2×Q8—262no—
633C2×Q8—262no—
634C2×Q8—262no—
635C2×Q8—262no—
636C2×Q8—521no—
637C2×Q8—521no—
638C2×Q8—521no—
639C2×Q8—521no—
640C2×Q8—521no—
641C2×Q8—521no—
642C2×Q8—521no—
643C2×Q8—521no—
644C2×Q8—521no—
645C2×Q8—521no—
646C2×Q8—521no—
647C2×Q8—521no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—132no—
663C22×C4—262no—
664C22×C4—261no—
665C22×C4—262no—
666C22×C4—261no—
667C22×C4—261no—
668C22×C4—261no—
669C22×C4—261no—
670C22×C4—262no—
671C22×C4—261no—
672C22×C4—262no—
673C22×C4—262no—
674C22×C4—262no—
675C22×C4—262no—
676C22×C4—262no—
677C22×C4—262no—
678C22×C4—262no—
679C22×C4—262no—
680C22×C4—262no—
681C22×C4—262no—
682C22×C4—262no—
683C22×C4—262no—
684C22×C4—262no—
685C22×C4—521no—
686C22×C4—521no—
687C22×C4—521no—
688C22×C4—521no—
689C22×C4—521no—
690C22×C4—521no—
691C22×C4—521no—
692C22×C4—521no—
693C22×C4—521no—
694C22×C4—521no—
695C22×C4—521no—
696C22×C4—521no—
697C22×C4—521no—
698C22×C4—521no—
699C22×C4—521no—
700C22×C4—521no—
701C22×C4—521no—
702C22×C4—521no—
703C22×C4—521no—
704C22×C4—521no—
705C22×C4—521no—
706C22×C4—521no—
707C22×C4—521no—
708C22×C4—521no—
709C22×C4—521no—
710C22×C4—521no—
711C22×C4C2×C4×D1311yescharacteristic
712C22×C4C2×D5211yescharacteristic
713C22×C4C2×D5211yescharacteristic
714C22×C4C2×D5211yescharacteristic
715C22×C4#612711yescharacteristic
716C22×C4#612711yescharacteristic
717C22×C4D4×D1311yescharacteristic
718C22×C4D4×D1311yescharacteristic
719C22×C4D4×D1311yescharacteristic
720C22×C4D4×D1311yescharacteristic
721C22×C4D4×D1311yescharacteristic
722C22×C4#613111yescharacteristic
723C22×C4#613111yescharacteristic
724C22×C4C2×C22⋊D1311yescharacteristic
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—41no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—262no—
733C2×C8—262no—
734C2×C8—262no—
735C2×C8—521no—
736C2×C8—521no—
737C2×C8—521no—
738C2×C8—521no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—41no—
745C4⋊C4—41no—
746C4⋊C4—2616no—
747C4⋊C4—262no—
748C4⋊C4—262no—
749C4⋊C4—521no—
750C4⋊C4—521no—
751C4⋊C4#610314yescomplemented
752C22⋊C4—2616no—
753C22⋊C4—528no—
754C13#1097011yescharacteristic, complemented, Sylow
755C23—134no—
756C23—262no—
757C23—262no—
758C23—262no—
759C23—262no—
760C23—262no—
761C23—262no—
762C23—262no—
763C23—262no—
764C23—262no—
765C23—262no—
766C23—262no—
767C23—262no—
768C23—262no—
769C23—262no—
770C23—262no—
771C23—262no—
772C23—262no—
773C23—262no—
774C23—521no—
775C23—521no—
776C23—521no—
777C23—521no—
778C23—521no—
779C23—521no—
780C23—521no—
781C23—521no—
782C23—521no—
783C23—521no—
784C23—521no—
785C23—521no—
786C23—521no—
787C23—521no—
788C23—521no—
789C23—521no—
790C23C22⋊C4×D1311yescharacteristic
791C23#8813611yescharacteristic
792C23#8813611yescharacteristic
793C23#8813811yescharacteristic
794C23#8814811yescharacteristic
795C23#8814911yescharacteristic
796C23#8816511yescharacteristic
797C23#8816611yescharacteristic
798C23SD16×D1311yescharacteristic
799C23#8816911yescharacteristic
800C23#8816911yescharacteristic
801C23#8817011yescharacteristic
802C23Q16×D1311yescharacteristic
803C23#8817211yescharacteristic
804C23#8819111yescharacteristic
805Q8—264no—
806Q8—264no—
807Q8—522no—
808Q8—522no—
809Q8—522no—
810Q8—522no—
811Q8—522no—
812Q8—522no—
813C2×C4—24no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—262no—
828C2×C4—262no—
829C2×C4—264no—
830C2×C4—262no—
831C2×C4—522no—
832C2×C4—522no—
833C2×C4—521no—
834C2×C4—522no—
835C2×C4—521no—
836C2×C4—522no—
837C2×C4—521no—
838C2×C4—522no—
839C2×C4—521no—
840C2×C4—522no—
841C2×C4—522no—
842C2×C4—522no—
843C2×C4—522no—
844C2×C4—522no—
845C2×C4—522no—
846C2×C4—522no—
847C2×C4—522no—
848C2×C4—522no—
849C2×C4—522no—
850C2×C4—522no—
851C2×C4—522no—
852C2×C4—1041no—
853C2×C4—1041no—
854C2×C4—1041no—
855C2×C4—1041no—
856C2×C4C4×D5211yescharacteristic
857C2×C4C4×D5211yescharacteristic
858C2×C4#8812811yescharacteristic
859C2×C4#8812911yescharacteristic
860C2×C4C22⋊C4×D1311yescharacteristic
861C2×C4#8813611yescharacteristic
862C2×C4#8813611yescharacteristic
863C2×C4#8813611yescharacteristic
864C2×C4#8813611yescharacteristic
865C2×C4#8813811yescharacteristic
866C2×C4#8813811yescharacteristic
867C2×C4#8813811yescharacteristic
868C2×C4#8814711yescharacteristic
869C2×C4#8814711yescharacteristic
870C2×C4#8814811yescharacteristic
871C2×C4#8814811yescharacteristic
872C2×C4#8814811yescharacteristic
873C2×C4#8814911yescharacteristic
874C2×C4#8814911yescharacteristic
875C2×C4#8814911yescharacteristic
876C2×C4#8814911yescharacteristic
877C2×C4#8814911yescharacteristic
878C2×C4C2×#610311yescharacteristic
879C2×C4#8818411yescharacteristic
880C2×C4#8818411yescharacteristic
881C2×C4#8819111yescharacteristic
882C2×C4#8819411yescharacteristic
883C2×C4#8820111yescharacteristic
884C8—42no—
885C8—522no—
886C22—264no—
887C22—264no—
888C22—264no—
889C22—522no—
890C22—522no—
891C22—522no—
892C22—522no—
893C22—522no—
894C22—522no—
895C22—522no—
896C22—522no—
897C22—522no—
898C22—522no—
899C22—522no—
900C22—522no—
901C22#1171832611yescharacteristic
902C22#1171832611yescharacteristic
903C22#1171833211yescharacteristic
904C22#1171833311yescharacteristic
905C22#1171843211yescharacteristic
906C22#1171843311yescharacteristic
907C22#1171843711yescharacteristic
908C22#1171843911yescharacteristic
909C22#1171844111yescharacteristic
910C22#1171844211yescharacteristic
911C22#1171844411yescharacteristic
912C22#1171844411yescharacteristic
913C22D13×#10311yescharacteristic
914C22#1171846311yescharacteristic
915C22#1171846711yescharacteristic
916C22#1171846911yescharacteristic
917C22#1171846911yescharacteristic
918C22#1171847111yescharacteristic
919C22#1171847411yescharacteristic
920C22#1171847711yescharacteristic
921C22#1171852311yescharacteristic
922C22#1171852511yescharacteristic
923C22#1171852811yescharacteristic
924C22#1171852911yescharacteristic
925C22#1171854511yescharacteristic
926C22#1171854711yescharacteristic
927C22#1171854811yescharacteristic
928C22#1171854911yescharacteristic
929C22#1171861611yescharacteristic
930C22#1171862111yescharacteristic
931C22#1171865211yescharacteristic
932C22#1171881911yescharacteristic
933C22#1171883111yescharacteristic
934C22#1171883411yescharacteristic
935C22#1171884711yescharacteristic
936C4—44no—
937C4—82no—
938C4—522no—
939C4—524no—
940C4—1042no—
941C4#1171832611yescharacteristic
942C4#1171832611yescharacteristic
943C4#1171833211yescharacteristic
944C4#1171833311yescharacteristic
945C4#1171860011yescharacteristic
946C4#1171862111yescharacteristic
947C4#1171864911yescharacteristic
948C4#1171865211yescharacteristic
949C2—524no—
950C2#1311307611yescharacteristic
951C2#1311476911yescharacteristic
952C2#1311477311yescharacteristic
953C2#1311514211yescharacteristic
954C2#1311514711yescharacteristic
955C2#1311525811yescharacteristic
956C2#1311526811yescharacteristic
957C2#1311584011yescharacteristic
958C2#1311584211yescharacteristic
959C2#1311584511yescharacteristic
960C2#1311584711yescharacteristic
961C2#1311603411yescharacteristic
962C2#1311603511yescharacteristic
963C2#1311604111yescharacteristic
964C2#1311604211yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC24×D13D4
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#10970
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#88056C2semidirect
3. C22×#88050C2semidirect
6. C2×#11718121C2semidirect
7. C2×C13×#340C2semidirect
23. C2×#88151C4semidirect
243. C2×Dic26C22⋊C4semidirect
258. C13×C4⋊C4C22⋊C4semidirect
279. C2×#340D13semidirect
329. C22×D13#103semidirect
751. C4⋊C4#6103semidirect
754. C13#10970semidirect

Maximal subgroups

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

subgroupindex
C22×#881512
C22×#880562
C22×#880502
C22×#880602
C2×#117186482
C2×#117181212
C2×C13×#3402
#1097013