Finite Group Databasebeta

← #15770734

Subgroups — #15770734

Order 3328.

1210 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×#88061C211yesmaximal, characteristic
2C22×#88049C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718121C211yesmaximal, characteristic, complemented
5C2×#11718142C211yesmaximal, characteristic, complemented
6#13113065C211yesmaximal, characteristic, complemented
7C2×C13×#340C211yesmaximal, characteristic, complemented
8C23×D52C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C13×C4⋊C4C2211yescharacteristic
12C22×#6103—21no—
13C22×#6103—21no—
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4×Dic13C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C2×#88071—21no—
18C2×#88071—21no—
19C2×#88061—22no—
20C2×#88061—22no—
21C2×#88061—22no—
22#11718649—22no—
23#11718649—22no—
24C2×#88049—22no—
25C2×#88049—22no—
26C2×#88049C414yescomplemented
27C13×#340—22no—
28#11718142—22no—
29#11718121—22no—
30C24×D13—21no—
31C23×C4×C13—21no—
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C23×Dic13—21no—
35C23×Dic13D411yescharacteristic
36C23×Dic13D411yescharacteristic
37C22×D52—21no—
38C22×D52—21no—
39C22×D52—21no—
40C22×D52—21no—
41C22×D52—21no—
42C22×D52—21no—
43C22×D52—21no—
44C22×D52—21no—
45C22×D52—21no—
46C22×D52—21no—
47C22×D52—21no—
48C22×D52C2×C412yes—
49C22×D52D412yes—
50C22×D52D412yes—
51C22×C8×C13—21no—
52C22×C8×C13—21no—
53C22×C8×C13—21no—
54C22×C8×C13—21no—
55C22×C8×C13—21no—
56C22×C8×C13—21no—
57C22×C8×C13D412yes—
58C2×C13×C4⋊C4—21no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4—21no—
62C2×C13×C4⋊C4—21no—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—21no—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4C2×C412yes—
69C2×C13×C4⋊C4D412yes—
70C2×#6103—24no—
71C2×#6103—24no—
72C2×#6103—42no—
73C2×#6103—42no—
74C2×#6103—42no—
75C2×#6103—42no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13D412yes—
82C2×C4×Dic13—21no—
83C2×C4×Dic13—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C22×#1055—21no—
89C22×#1055—21no—
90C22×#1055—21no—
91C22×#1055—21no—
92C22×#1055—21no—
93C22×#1055—21no—
94C22×#1055C2×C412yes—
95#88071—42no—
96#88071—42no—
97#88061—28no—
98#88049—28no—
99#11189—131nomaximal, Sylow
100C24×C13C2×D411yescharacteristic
101C23×D13—22no—
102C23×D13—22no—
103C23×D13—22no—
104C23×D13—41no—
105C23×D13—41no—
106C23×D13—41no—
107C23×D13—41no—
108C23×D13—41no—
109C23×D13—41no—
110C23×D13—41no—
111C23×D13—41no—
112C23×D13—41no—
113C23×D13—41no—
114C23×D13—41no—
115C23×D13—41no—
116C22×C4×C13—22no—
117C22×C4×C13—22no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—41no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13—41no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13#4111yescharacteristic
137C22×C4×C13#4111yescharacteristic
138C22×C4×C13#4111yescharacteristic
139C22×C4×C13#4111yescharacteristic
140C22×C4×C13#4111yescharacteristic
141C22×C4×C13#4111yescharacteristic
142C22×C4×C13#4111yescharacteristic
143C22×C4×C13#4111yescharacteristic
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—22no—
157C22×Dic13—41no—
158C22×Dic13—41no—
159C22×Dic13—41no—
160C22×Dic13—41no—
161C22×Dic13—41no—
162C22×Dic13—41no—
163C22×Dic13D812yes—
164C22×Dic13SD1612yes—
165C2×D52—22no—
166C2×D52—22no—
167C2×D52—22no—
168C2×D52—22no—
169C2×D52—22no—
170C2×D52—22no—
171C2×D52—22no—
172C2×D52—22no—
173C2×D52—22no—
174C2×D52—22no—
175C2×D52—22no—
176C2×D52—22no—
177C2×D52—22no—
178C2×D52—22no—
179C2×D52—22no—
180C2×D52—41no—
181C2×D52—41no—
182C2×D52—41no—
183C2×D52—41no—
184C2×D52—41no—
185C2×D52—41no—
186C2×D52—41no—
187C2×D52—41no—
188C2×D52—41no—
189C2×D52—41no—
190C2×D52—41no—
191C2×D52—41no—
192C2×D52C22⋊C414yes—
193C2×C8×C13—22no—
194C2×C8×C13—22no—
195C2×C8×C13—22no—
196C2×C8×C13—41no—
197C2×C8×C13—41no—
198C2×C8×C13—41no—
199C2×C8×C13—41no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—22no—
204C13×C4⋊C4—41no—
205C13×C4⋊C4—41no—
206C13×C4⋊C4—41no—
207C13×C4⋊C4—41no—
208#6103—48no—
209#6103—48no—
210C4⋊Dic13—22no—
211C4⋊Dic13—22no—
212C4⋊Dic13—41no—
213C4⋊Dic13—41no—
214C4×Dic13—41no—
215C4×Dic13—41no—
216C4×Dic13—41no—
217C4×Dic13—41no—
218C2×#1055—22no—
219C2×#1055—22no—
220C2×#1055—22no—
221C2×#1055—41no—
222C2×#1055—41no—
223C2×#1055—41no—
224C2×#1055—41no—
225C22×#102—131no—
226C22×#102—131no—
227C2×#390—131no—
228C2×#340—131no—
229C2×#340D1311yescharacteristic, complemented
230C2×#336—131no—
231C4⋊#95—131no—
232C23×C13C4×D411yescharacteristic
233C23×C13#12011yescharacteristic
234C23×C13#12111yescharacteristic
235C23×C13#12111yescharacteristic
236C23×C13#12111yescharacteristic
237C23×C13#12311yescharacteristic
238C23×C13#12411yescharacteristic
239C23×C13C2×D811yescharacteristic
240C23×C13C2×SD1611yescharacteristic
241C23×C13#13511yescharacteristic
242C23×C13#13511yescharacteristic
243C23×C13AGL(1,ℤ/8)11yescharacteristic
244C23×C13AGL(1,ℤ/8)11yescharacteristic
245C23×C13AGL(1,ℤ/8)11yescharacteristic
246C23×C13#13711yescharacteristic
247C22×D13—24no—
248C22×D13—42no—
249C22×D13—42no—
250C22×D13—42no—
251C22×D13—42no—
252C22×D13—42no—
253C22×D13—42no—
254C22×D13—42no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13—42no—
259C22×D13—42no—
260C22×D13—42no—
261C22×D13—42no—
262C22×D13—42no—
263C22×D13—42no—
264C22×D13—42no—
265C22×D13—42no—
266C22×D13—81no—
267C22×D13—81no—
268C22×D13—81no—
269C22×D13—81no—
270C22×D13—81no—
271C22×D13—81no—
272C22×D13—81no—
273C22×D13—81no—
274C22×D13—81no—
275C22×D13—81no—
276C22×D13—81no—
277C22×D13—81no—
278C22×D13—81no—
279C22×D13—81no—
280C22×D13—81no—
281C22×D13—81no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—81no—
289C2×C4×C13—81no—
290C2×C4×C13—81no—
291C2×C4×C13—81no—
292C2×C4×C13—81no—
293C2×C4×C13—81no—
294C2×C4×C13—81no—
295C2×C4×C13—81no—
296C2×C4×C13C2×C22⋊C411yescharacteristic
297C2×C4×C13#11711yescharacteristic
298C2×C4×C13#11711yescharacteristic
299C2×C4×C13C4×D411yescharacteristic
300C2×C4×C13C4×D411yescharacteristic
301C2×C4×C13C4×D411yescharacteristic
302C2×C4×C13#12011yescharacteristic
303C2×C4×C13#12111yescharacteristic
304C2×C4×C13#12111yescharacteristic
305C2×C4×C13#12111yescharacteristic
306C2×C4×C13#12111yescharacteristic
307C2×C4×C13#12111yescharacteristic
308C2×C4×C13#12311yescharacteristic
309C2×C4×C13#12311yescharacteristic
310C2×C4×C13#12311yescharacteristic
311C2×C4×C13#12311yescharacteristic
312C2×C4×C13#12311yescharacteristic
313C2×C4×C13#12311yescharacteristic
314C2×C4×C13#12311yescharacteristic
315C2×C4×C13#12311yescharacteristic
316C2×C4×C13#12311yescharacteristic
317C2×C4×C13#12411yescharacteristic
318C2×C4×C13#12411yescharacteristic
319C2×C4×C13#12411yescharacteristic
320C2×C4×C13#12611yescharacteristic
321C2×C4×C13#12611yescharacteristic
322C2×C4×C13#12611yescharacteristic
323C2×C4×C13#12611yescharacteristic
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—81no—
342C2×Dic13—81no—
343C2×Dic13—81no—
344C2×Dic13—81no—
345D52—24no—
346D52—24no—
347D52—42no—
348D52—42no—
349D52—42no—
350D52—42no—
351D52—42no—
352D52—42no—
353C8×C13—42no—
354#1055—42no—
355C23×D4—131no—
356C23×C8—131no—
357C23×C8C2×D1311yescharacteristic
358C22×C4⋊C4—131no—
359C22×C4⋊C4C2×D1311yescharacteristic
360C22×C4⋊C4C2×D1311yescharacteristic
361C22×C22⋊C4—261no—
362C22×C22⋊C4—261no—
363C22×C42—131no—
364C2×#102—134no—
365C2×#102—262no—
366C2×#102—262no—
367C2×#102—262no—
368C2×#102—262no—
369C2×#102—262no—
370#390—262no—
371#390—262no—
372C2×#95—261no—
373C2×#95—261no—
374#340—22no—
375#340—262no—
376#336—262no—
377C22×C13#38611yescharacteristic
378C22×C13#38811yescharacteristic
379C22×C13#38811yescharacteristic
380C22×C13#39411yescharacteristic
381C22×C13#39411yescharacteristic
382C22×C13#39411yescharacteristic
383C22×C13#39711yescharacteristic
384C22×C13C4×D811yescharacteristic
385C22×C13C4×SD1611yescharacteristic
386C22×C13#44011yescharacteristic
387C22×C13#44211yescharacteristic
388C22×C13#44711yescharacteristic
389C22×C13#44911yescharacteristic
390C22×C13#45011yescharacteristic
391C22×C13#45211yescharacteristic
392C22×C13#45911yescharacteristic
393C22×C13#45911yescharacteristic
394C22×C13#46011yescharacteristic
395C22×C13#46111yescharacteristic
396C22×C13#46311yescharacteristic
397C22×C13#46311yescharacteristic
398C22×C13#46311yescharacteristic
399C22×C13#46411yescharacteristic
400C22×C13#46511yescharacteristic
401C22×C13#46611yescharacteristic
402C22×C13#46811yescharacteristic
403C22×C13#46911yescharacteristic
404C22×C13#48011yescharacteristic
405C22×C13#48111yescharacteristic
406C22×C13#48211yescharacteristic
407C22×C13#48211yescharacteristic
408C22×C13#48611yescharacteristic
409C22×C13#48811yescharacteristic
410C22×C13#48911yescharacteristic
411C22×C13#49011yescharacteristic
412C2×D13—44no—
413C2×D13—44no—
414C2×D13—44no—
415C2×D13—82no—
416C2×D13—82no—
417C2×D13—82no—
418C2×D13—82no—
419C2×D13—82no—
420C2×D13—82no—
421C2×D13—82no—
422C2×D13—82no—
423C2×D13—82no—
424C2×D13—82no—
425C2×D13—82no—
426C2×D13—82no—
427C4×C13—82no—
428C4×C13—82no—
429C4×C13#38111yescharacteristic
430C4×C13#38611yescharacteristic
431C4×C13#38811yescharacteristic
432C4×C13#38811yescharacteristic
433C4×C13#39411yescharacteristic
434C4×C13#39711yescharacteristic
435C4×C13#39711yescharacteristic
436C4×C13#39711yescharacteristic
437Dic13—42no—
438Dic13—42no—
439Dic13—82no—
440C25—261no—
441C22×D4—132no—
442C22×D4—132no—
443C22×D4—132no—
444C22×D4—261no—
445C22×D4—261no—
446C22×D4—261no—
447C22×D4—261no—
448C22×D4—261no—
449C22×D4—261no—
450C22×D4—261no—
451C22×D4—261no—
452C22×D4—261no—
453C22×D4—261no—
454C22×D4—261no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—131no—
458C23×C4—131no—
459C23×C4—261no—
460C23×C4C22×D1311yescharacteristic
461C22×C8—21no—
462C22×C8—21no—
463C22×C8—21no—
464C22×C8—21no—
465C22×C8—21no—
466C22×C8—21no—
467C22×C8—132no—
468C22×C8—261no—
469C22×C8—261no—
470C22×C8—261no—
471C22×C8—261no—
472C22×C8—261no—
473C22×C8—261no—
474C22×C8D5212yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—132no—
486C2×C4⋊C4—261no—
487C2×C4⋊C4—261no—
488C2×C4⋊C4—261no—
489C2×C4⋊C4—261no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4C4×D1312yes—
492C2×C4⋊C4C22⋊D1312yes—
493C2×C22⋊C4—264no—
494C2×C22⋊C4—264no—
495C2×C22⋊C4—522no—
496C2×C22⋊C4—522no—
497C2×C22⋊C4—522no—
498C2×C22⋊C4—522no—
499C2×C42—261no—
500C2×C42—261no—
501C2×C42—261no—
502C2×C42—261no—
503C2×C42—261no—
504C2×C42—261no—
505#102—268no—
506#102—268no—
507#95—522no—
508#95—522no—
509C2×C13#144011yescharacteristic
510C2×C13#187711yescharacteristic
511C2×C13#187911yescharacteristic
512C2×C13#192511yescharacteristic
513C2×C13#192611yescharacteristic
514C2×C13#193411yescharacteristic
515C2×C13#193611yescharacteristic
516C2×C13#203311yescharacteristic
517C2×C13#203411yescharacteristic
518C2×C13#204111yescharacteristic
519C2×C13#204211yescharacteristic
520C2×C13#205411yescharacteristic
521C2×C13#205511yescharacteristic
522C2×C13#207111yescharacteristic
523C2×C13#207311yescharacteristic
524D13—84no—
525C24—262no—
526C24—262no—
527C24—262no—
528C24—521no—
529C24—521no—
530C24—521no—
531C24—521no—
532C24—521no—
533C24—521no—
534C24—521no—
535C24—521no—
536C24—521no—
537C24—521no—
538C24—521no—
539C24—521no—
540C24D4×D1311yescharacteristic
541C2×D4—134no—
542C2×D4—262no—
543C2×D4—262no—
544C2×D4—262no—
545C2×D4—262no—
546C2×D4—262no—
547C2×D4—262no—
548C2×D4—262no—
549C2×D4—262no—
550C2×D4—262no—
551C2×D4—262no—
552C2×D4—262no—
553C2×D4—262no—
554C2×D4—262no—
555C2×D4—262no—
556C2×D4—262no—
557C2×D4—521no—
558C2×D4—521no—
559C2×D4—521no—
560C2×D4—521no—
561C2×D4—521no—
562C2×D4—521no—
563C2×D4—521no—
564C2×D4—521no—
565C2×D4—521no—
566C2×D4—521no—
567C2×D4—521no—
568C2×D4—521no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4—132no—
584C22×C4—132no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—521no—
599C22×C4—521no—
600C22×C4—521no—
601C22×C4—521no—
602C22×C4—521no—
603C22×C4—521no—
604C22×C4C2×C4×D1311yescharacteristic
605C22×C4C2×D5211yescharacteristic
606C22×C4#612711yescharacteristic
607C22×C4#612711yescharacteristic
608C22×C4#612711yescharacteristic
609C22×C4#612711yescharacteristic
610C22×C4D4×D1311yescharacteristic
611C22×C4D4×D1311yescharacteristic
612C22×C4D4×D1311yescharacteristic
613C22×C4#612911yescharacteristic
614C22×C4#612911yescharacteristic
615C22×C4#613111yescharacteristic
616C22×C4#613111yescharacteristic
617C22×C4C2×C22⋊D1311yescharacteristic
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—22no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—41no—
624C2×C8—41no—
625C2×C8—262no—
626C2×C8—262no—
627C2×C8—262no—
628C2×C8—521no—
629C2×C8—521no—
630C2×C8—521no—
631C2×C8—521no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—41no—
639C4⋊C4—41no—
640C4⋊C4—262no—
641C4⋊C4—262no—
642C4⋊C4—521no—
643C4⋊C4—521no—
644C22⋊C4—528no—
645C22⋊C4—528no—
646C42—521no—
647C42—521no—
648C42—521no—
649C42—521no—
650C13#1118911yescharacteristic, complemented, Sylow
651C23—264no—
652C23—522no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23—522no—
657C23—522no—
658C23—522no—
659C23—522no—
660C23—522no—
661C23—522no—
662C23—522no—
663C23—522no—
664C23—522no—
665C23—522no—
666C23—522no—
667C23—522no—
668C23—522no—
669C23—522no—
670C23—1041no—
671C23—1041no—
672C23—1041no—
673C23—1041no—
674C23—1041no—
675C23—1041no—
676C23—1041no—
677C23—1041no—
678C23—1041no—
679C23—1041no—
680C23—1041no—
681C23—1041no—
682C23—1041no—
683C23—1041no—
684C23—1041no—
685C23—1041no—
686C23#8813511yescharacteristic
687C23#8813811yescharacteristic
688C23#8813811yescharacteristic
689C23#8813911yescharacteristic
690C23#8814811yescharacteristic
691C23#8814911yescharacteristic
692C23D8×D1311yescharacteristic
693C23#8816511yescharacteristic
694C23SD16×D1311yescharacteristic
695C23#8816811yescharacteristic
696C23#8816811yescharacteristic
697C23#8817011yescharacteristic
698C23#8817211yescharacteristic
699C23#8817311yescharacteristic
700C23#8819111yescharacteristic
701D4—264no—
702D4—264no—
703D4—522no—
704D4—522no—
705D4—522no—
706D4—522no—
707D4—522no—
708D4—522no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—521no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—1041no—
741C2×C4—1041no—
742C2×C4—1041no—
743C2×C4—1041no—
744C2×C4#8812611yescharacteristic
745C2×C4C4×D5211yescharacteristic
746C2×C4#8812911yescharacteristic
747C2×C4#8813011yescharacteristic
748C2×C4C22⋊C4×D1311yescharacteristic
749C2×C4#8813611yescharacteristic
750C2×C4#8813711yescharacteristic
751C2×C4#8813711yescharacteristic
752C2×C4#8813711yescharacteristic
753C2×C4#8813811yescharacteristic
754C2×C4#8813911yescharacteristic
755C2×C4#8814011yescharacteristic
756C2×C4#8814611yescharacteristic
757C2×C4#8814711yescharacteristic
758C2×C4#8814811yescharacteristic
759C2×C4#8814811yescharacteristic
760C2×C4#8814811yescharacteristic
761C2×C4#8814811yescharacteristic
762C2×C4#8814911yescharacteristic
763C2×C4#8815211yescharacteristic
764C2×C4#8815211yescharacteristic
765C2×C4#8815211yescharacteristic
766C2×C4C4×C22⋊D1311yescharacteristic
767C2×C4#8818311yescharacteristic
768C2×C4#8818411yescharacteristic
769C2×C4#8819211yescharacteristic
770C2×C4#8819311yescharacteristic
771C2×C4#8820111yescharacteristic
772C8—42no—
773C8—522no—
774C22—524no—
775C22—524no—
776C22—524no—
777C22—1042no—
778C22—1042no—
779C22—1042no—
780C22—1042no—
781C22—1042no—
782C22—1042no—
783C22—1042no—
784C22—1042no—
785C22—1042no—
786C22—1042no—
787C22—1042no—
788C22—1042no—
789C22#1171833011yescharacteristic
790C22#1171833111yescharacteristic
791C22#1171833311yescharacteristic
792C22#1171833611yescharacteristic
793C22#1171841711yescharacteristic
794C22#1171842111yescharacteristic
795C22#1171842311yescharacteristic
796C22#1171842511yescharacteristic
797C22#1171844611yescharacteristic
798C22#1171844711yescharacteristic
799C22#1171844711yescharacteristic
800C22#1171844811yescharacteristic
801C22#1171844911yescharacteristic
802C22#1171845611yescharacteristic
803C22#1171845911yescharacteristic
804C22#1171846111yescharacteristic
805C22#1171847811yescharacteristic
806C22#1171847911yescharacteristic
807C22#1171848011yescharacteristic
808C22#1171848011yescharacteristic
809C22#1171852411yescharacteristic
810C22#1171852511yescharacteristic
811C22#1171852611yescharacteristic
812C22#1171852711yescharacteristic
813C22#1171854311yescharacteristic
814C22#1171854411yescharacteristic
815C22#1171854611yescharacteristic
816C22#1171854711yescharacteristic
817C22#1171861711yescharacteristic
818C22#1171862011yescharacteristic
819C22#1171865211yescharacteristic
820C22#1171881711yescharacteristic
821C22#1171883011yescharacteristic
822C22#1171883311yescharacteristic
823C22#1171884811yescharacteristic
824C4—82no—
825C4—82no—
826C4—522no—
827C4—522no—
828C4—1042no—
829C4#1171832511yescharacteristic
830C4#1171832611yescharacteristic
831C4#1171833511yescharacteristic
832C4#1171833611yescharacteristic
833C4#1171860111yescharacteristic
834C4#1171862211yescharacteristic
835C4#1171865111yescharacteristic
836C4#1171865411yescharacteristic
837C2—1044no—
838C2#1311308411yescharacteristic
839C2#1311516711yescharacteristic
840C2#1311518111yescharacteristic
841C2#1311545411yescharacteristic
842C2#1311546111yescharacteristic
843C2#1311552011yescharacteristic
844C2#1311553411yescharacteristic
845C2#1311602011yescharacteristic
846C2#1311602711yescharacteristic
847C2#1311606811yescharacteristic
848C2#1311607311yescharacteristic
849C2#1311614811yescharacteristic
850C2#1311615511yescharacteristic
851C2#1311624311yescharacteristic
852C2#1311625311yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#340C2
socleC24×C13C2×D4
prime radicalC23×D52C22
cosocleC23×C4×C13C23
hypercenterC2×#340D13
hypocenterC13#11189
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
4. C2×#11718121C2semidirect
5. C2×#11718142C2semidirect
6. #13113065C2semidirect
7. C2×C13×#340C2semidirect
26. C2×#88049C4semidirect
229. C2×#340D13semidirect
650. C13#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#880612
C22×#880492
C2×#117186492
C2×#117181212
C2×#117181422
#131130652
C2×C13×#3402
#1118913