Finite Group Databasebeta

← #15770728

Subgroups — #15770728

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×#88072C211yesmaximal, characteristic
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718143C211yesmaximal, characteristic, complemented
4C2×#11718121C211yesmaximal, characteristic, complemented
5C2×#11718142C211yesmaximal, characteristic, complemented
6#13113065C211yesmaximal, characteristic, complemented
7C22×C13×#102C211yesmaximal, characteristic
8C23×D4×C13C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C22⋊Dic13—21no—
12C22×C22⋊Dic13—21no—
13C22×C4⋊Dic13C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×C4×Dic13C2211yescharacteristic
16C23×#1055C2211yescharacteristic
17C2×C13×#102—22no—
18C2×C13×#102—22no—
19C2×C13×#102—22no—
20#11718882—22no—
21#11718882—22no—
22C2×#88072—22no—
23C2×#88072—22no—
24C2×#88072C414yescomplemented
25C2×#88071—21no—
26C2×#88071—21no—
27#11718143—22no—
28#11718142—22no—
29#11718121—22no—
30C25×C13—21no—
31C22×D4×C13—21no—
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13—21no—
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—21no—
38C22×D4×C13—21no—
39C22×D4×C13—21no—
40C22×D4×C13—21no—
41C22×D4×C13—21no—
42C22×D4×C13C2×C412yes—
43C22×D4×C13D412yes—
44C22×D4×C13D412yes—
45C23×C4×C13—21no—
46C23×C4×C13C2311yescharacteristic
47C23×Dic13—21no—
48C23×Dic13—21no—
49C23×Dic13D411yescharacteristic
50C23×Dic13D411yescharacteristic
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⋊C4D412yes—
64C2×C22⋊Dic13—24no—
65C2×C22⋊Dic13—24no—
66C2×C22⋊Dic13—42no—
67C2×C22⋊Dic13—42no—
68C2×C22⋊Dic13—42no—
69C2×C22⋊Dic13—42no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13—21no—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13C2×C412yes—
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—
95C13×#102—28no—
96#88072—28no—
97#88071—42no—
98#88071—42no—
99#11189—131nomaximal, Sylow
100C24×C13—22no—
101C24×C13—22no—
102C24×C13—22no—
103C24×C13—41no—
104C24×C13—41no—
105C24×C13—41no—
106C24×C13—41no—
107C24×C13—41no—
108C24×C13—41no—
109C24×C13—41no—
110C24×C13—41no—
111C24×C13—41no—
112C24×C13—41no—
113C24×C13—41no—
114C24×C13—41no—
115C24×C13C2×D411yescharacteristic
116C2×D4×C13—22no—
117C2×D4×C13—22no—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—22no—
128C2×D4×C13—22no—
129C2×D4×C13—22no—
130C2×D4×C13—22no—
131C2×D4×C13—41no—
132C2×D4×C13—41no—
133C2×D4×C13—41no—
134C2×D4×C13—41no—
135C2×D4×C13—41no—
136C2×D4×C13—41no—
137C2×D4×C13—41no—
138C2×D4×C13—41no—
139C2×D4×C13—41no—
140C2×D4×C13—41no—
141C2×D4×C13—41no—
142C2×D4×C13—41no—
143C2×D4×C13C22⋊C414yes—
144C22×C4×C13—22no—
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×C13C22×C411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13#4111yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C22×C4×C13#4111yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C22×C4×C13#4111yescharacteristic
162C22×C4×C13#4111yescharacteristic
163C22×C4×C13#4111yescharacteristic
164C22×C4×C13#4111yescharacteristic
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—22no—
178C22×Dic13—22no—
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×Dic13—41no—
188C22×Dic13—41no—
189C22×Dic13—41no—
190C22×Dic13—41no—
191C22×Dic13D812yes—
192C22×Dic13SD1612yes—
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—41no—
203C13×C4⋊C4—41no—
204C22⋊Dic13—48no—
205C22⋊Dic13—48no—
206C4⋊Dic13—22no—
207C4⋊Dic13—22no—
208C4⋊Dic13—22no—
209C4⋊Dic13—22no—
210C4⋊Dic13—41no—
211C4⋊Dic13—41no—
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×#102D1311yescharacteristic
227C2×#390—131no—
228C2×#340—131no—
229C2×#340—131no—
230C2×#336—131no—
231C4⋊#95—131no—
232C23×C13—24no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—42no—
236C23×C13—42no—
237C23×C13—42no—
238C23×C13—42no—
239C23×C13—42no—
240C23×C13—42no—
241C23×C13—42no—
242C23×C13—42no—
243C23×C13—42no—
244C23×C13—42no—
245C23×C13—42no—
246C23×C13—42no—
247C23×C13—42no—
248C23×C13—42no—
249C23×C13—42no—
250C23×C13—42no—
251C23×C13—81no—
252C23×C13—81no—
253C23×C13—81no—
254C23×C13—81no—
255C23×C13—81no—
256C23×C13—81no—
257C23×C13—81no—
258C23×C13—81no—
259C23×C13—81no—
260C23×C13—81no—
261C23×C13—81no—
262C23×C13—81no—
263C23×C13—81no—
264C23×C13—81no—
265C23×C13—81no—
266C23×C13—81no—
267C23×C13C4×D411yescharacteristic
268C23×C13#12011yescharacteristic
269C23×C13#12111yescharacteristic
270C23×C13#12111yescharacteristic
271C23×C13#12111yescharacteristic
272C23×C13#12311yescharacteristic
273C23×C13#12411yescharacteristic
274C23×C13C2×D811yescharacteristic
275C23×C13C2×SD1611yescharacteristic
276C23×C13#13511yescharacteristic
277C23×C13#13511yescharacteristic
278C23×C13AGL(1,ℤ/8)11yescharacteristic
279C23×C13AGL(1,ℤ/8)11yescharacteristic
280C23×C13AGL(1,ℤ/8)11yescharacteristic
281C23×C13#13711yescharacteristic
282D4×C13—24no—
283D4×C13—24no—
284D4×C13—42no—
285D4×C13—42no—
286D4×C13—42no—
287D4×C13—42no—
288D4×C13—42no—
289D4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—81no—
294C2×C4×C13—81no—
295C2×C4×C13—81no—
296C2×C4×C13—81no—
297C2×C4×C13C2×C22⋊C411yescharacteristic
298C2×C4×C13#11711yescharacteristic
299C2×C4×C13#11711yescharacteristic
300C2×C4×C13C4×D411yescharacteristic
301C2×C4×C13C4×D411yescharacteristic
302C2×C4×C13C4×D411yescharacteristic
303C2×C4×C13#12011yescharacteristic
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#12311yescharacteristic
314C2×C4×C13#12311yescharacteristic
315C2×C4×C13#12311yescharacteristic
316C2×C4×C13#12311yescharacteristic
317C2×C4×C13#12311yescharacteristic
318C2×C4×C13#12411yescharacteristic
319C2×C4×C13#12411yescharacteristic
320C2×C4×C13#12411yescharacteristic
321C2×C4×C13#12611yescharacteristic
322C2×C4×C13#12611yescharacteristic
323C2×C4×C13#12611yescharacteristic
324C2×C4×C13#12611yescharacteristic
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—22no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—81no—
346C2×Dic13—81no—
347C2×Dic13—81no—
348C2×Dic13—81no—
349C2×Dic13—81no—
350C2×Dic13—81no—
351C2×Dic13—81no—
352C2×Dic13—81no—
353C8×C13—42no—
354#1055—42no—
355C23×D4C2×D1311yescharacteristic
356C23×C8—131no—
357C23×C8C2×D1311yescharacteristic
358C22×C4⋊C4—131no—
359C22×C4⋊C4—131no—
360C22×C4⋊C4C2×D1311yescharacteristic
361C22×C22⋊C4—261no—
362C22×C22⋊C4—261no—
363C22×C42—131no—
364C2×#102—22no—
365C2×#102—22no—
366C2×#102—22no—
367C2×#102—134no—
368C2×#102—262no—
369C2×#102—262no—
370#390—262no—
371#390—262no—
372C2×#95—261no—
373C2×#95—261no—
374#340—262no—
375#340—262no—
376#336—262no—
377C22×C13—44no—
378C22×C13—44no—
379C22×C13—44no—
380C22×C13—82no—
381C22×C13—82no—
382C22×C13—82no—
383C22×C13—82no—
384C22×C13—82no—
385C22×C13—82no—
386C22×C13—82no—
387C22×C13—82no—
388C22×C13—82no—
389C22×C13—82no—
390C22×C13—82no—
391C22×C13—82no—
392C22×C13#38611yescharacteristic
393C22×C13#38811yescharacteristic
394C22×C13#38811yescharacteristic
395C22×C13#39411yescharacteristic
396C22×C13#39411yescharacteristic
397C22×C13#39411yescharacteristic
398C22×C13#39711yescharacteristic
399C22×C13C4×D811yescharacteristic
400C22×C13C4×SD1611yescharacteristic
401C22×C13#44011yescharacteristic
402C22×C13#44211yescharacteristic
403C22×C13#44711yescharacteristic
404C22×C13#44911yescharacteristic
405C22×C13#45011yescharacteristic
406C22×C13#45211yescharacteristic
407C22×C13#45911yescharacteristic
408C22×C13#45911yescharacteristic
409C22×C13#46011yescharacteristic
410C22×C13#46111yescharacteristic
411C22×C13#46311yescharacteristic
412C22×C13#46311yescharacteristic
413C22×C13#46311yescharacteristic
414C22×C13#46411yescharacteristic
415C22×C13#46511yescharacteristic
416C22×C13#46611yescharacteristic
417C22×C13#46811yescharacteristic
418C22×C13#46911yescharacteristic
419C22×C13#48011yescharacteristic
420C22×C13#48111yescharacteristic
421C22×C13#48211yescharacteristic
422C22×C13#48211yescharacteristic
423C22×C13#48611yescharacteristic
424C22×C13#48811yescharacteristic
425C22×C13#48911yescharacteristic
426C22×C13#49011yescharacteristic
427C4×C13—82no—
428C4×C13#38111yescharacteristic
429C4×C13#38611yescharacteristic
430C4×C13#38811yescharacteristic
431C4×C13#38811yescharacteristic
432C4×C13#39411yescharacteristic
433C4×C13#39711yescharacteristic
434C4×C13#39711yescharacteristic
435C4×C13#39711yescharacteristic
436Dic13—42no—
437Dic13—42no—
438Dic13—82no—
439Dic13—82no—
440C25—21no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C4×D1312yes—
453C22×D4D5212yes—
454C22×D4C22⋊D1312yes—
455C23×C4—21no—
456C23×C4—131no—
457C23×C4—131no—
458C23×C4—261no—
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×C8C22⋊D1312yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—132no—
481C2×C4⋊C4—132no—
482C2×C4⋊C4—261no—
483C2×C4⋊C4—261no—
484C2×C4⋊C4—261no—
485C2×C4⋊C4—261no—
486C2×C4⋊C4—261no—
487C2×C4⋊C4—261no—
488C2×C4⋊C4—261no—
489C2×C4⋊C4—261no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4—261no—
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—28no—
506#102—268no—
507#95—522no—
508#95—522no—
509C2×C13—84no—
510C2×C13#144011yescharacteristic
511C2×C13#187711yescharacteristic
512C2×C13#187911yescharacteristic
513C2×C13#192511yescharacteristic
514C2×C13#192611yescharacteristic
515C2×C13#193411yescharacteristic
516C2×C13#193611yescharacteristic
517C2×C13#203311yescharacteristic
518C2×C13#203411yescharacteristic
519C2×C13#204111yescharacteristic
520C2×C13#204211yescharacteristic
521C2×C13#205411yescharacteristic
522C2×C13#205511yescharacteristic
523C2×C13#207111yescharacteristic
524C2×C13#207311yescharacteristic
525C24—22no—
526C24—22no—
527C24—22no—
528C24—41no—
529C24—41no—
530C24—41no—
531C24—41no—
532C24—41no—
533C24—41no—
534C24—41no—
535C24—41no—
536C24—41no—
537C24—41no—
538C24—41no—
539C24—41no—
540C24D4×D1311yescharacteristic
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4#610314yes—
569C22×C4—22no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—41no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—132no—
577C22×C4—132no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—521no—
593C22×C4—521no—
594C22×C4—521no—
595C22×C4—521no—
596C22×C4—521no—
597C22×C4—521no—
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×C4D4×D1311yescharacteristic
609C22×C4#612911yescharacteristic
610C22×C4#612911yescharacteristic
611C22×C4#612911yescharacteristic
612C22×C4#612911yescharacteristic
613C22×C4#612911yescharacteristic
614C22×C4#612911yescharacteristic
615C22×C4C2×C22⋊D1311yescharacteristic
616C22×C4C2×C22⋊D1311yescharacteristic
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—41no—
635C4⋊C4—41no—
636C4⋊C4—262no—
637C4⋊C4—262no—
638C4⋊C4—262no—
639C4⋊C4—262no—
640C4⋊C4—521no—
641C4⋊C4—521no—
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—24no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23—81no—
675C23—81no—
676C23—81no—
677C23—81no—
678C23—81no—
679C23—81no—
680C23—81no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23—81no—
685C23—81no—
686C23#8813511yescharacteristic
687C23#8813611yescharacteristic
688C23#8813711yescharacteristic
689C23#8813911yescharacteristic
690C23D8×D1311yescharacteristic
691C23#8816511yescharacteristic
692C23#8816511yescharacteristic
693C23#8816611yescharacteristic
694C23SD16×D1311yescharacteristic
695C23#8816811yescharacteristic
696C23#8816911yescharacteristic
697C23#8817011yescharacteristic
698C23#8819211yescharacteristic
699C23#8819311yescharacteristic
700C23#8819311yescharacteristic
701D4—24no—
702D4—24no—
703D4—42no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—521no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—1041no—
737C2×C4—1041no—
738C2×C4—1041no—
739C2×C4—1041no—
740C2×C4—1041no—
741C2×C4—1041no—
742C2×C4—1041no—
743C2×C4—1041no—
744C2×C4#8813111yescharacteristic
745C2×C4#8813111yescharacteristic
746C2×C4#8813311yescharacteristic
747C2×C4#8813311yescharacteristic
748C2×C4#8813311yescharacteristic
749C2×C4#8813311yescharacteristic
750C2×C4#8813511yescharacteristic
751C2×C4#8813711yescharacteristic
752C2×C4#8813911yescharacteristic
753C2×C4#8814011yescharacteristic
754C2×C4#8814011yescharacteristic
755C2×C4#8814011yescharacteristic
756C2×C4C2×#610311yescharacteristic
757C2×C4C4×C22⋊D1311yescharacteristic
758C2×C4C4×C22⋊D1311yescharacteristic
759C2×C4#8818311yescharacteristic
760C2×C4#8818411yescharacteristic
761C2×C4#8818411yescharacteristic
762C2×C4#8818911yescharacteristic
763C2×C4#8818911yescharacteristic
764C2×C4#8818911yescharacteristic
765C2×C4#8818911yescharacteristic
766C2×C4#8819011yescharacteristic
767C2×C4#8819011yescharacteristic
768C2×C4#8819211yescharacteristic
769C2×C4#8819311yescharacteristic
770C2×C4#8819311yescharacteristic
771C2×C4#8820711yescharacteristic
772C8—42no—
773C8—522no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—82no—
789C22#1171841711yescharacteristic
790C22#1171841811yescharacteristic
791C22#1171841911yescharacteristic
792C22#1171842111yescharacteristic
793C22#1171842511yescharacteristic
794C22#1171842611yescharacteristic
795C22#1171842911yescharacteristic
796C22#1171843411yescharacteristic
797C22#1171843511yescharacteristic
798C22#1171843711yescharacteristic
799C22#1171843811yescharacteristic
800C22#1171844011yescharacteristic
801C22#1171844211yescharacteristic
802C22#1171844411yescharacteristic
803C22#1171844511yescharacteristic
804C22#1171844611yescharacteristic
805C22#1171860511yescharacteristic
806C22#1171860611yescharacteristic
807C22#1171861311yescharacteristic
808C22#1171861911yescharacteristic
809C22#1171862211yescharacteristic
810C22#1171862211yescharacteristic
811C22#1171881111yescharacteristic
812C22#1171881111yescharacteristic
813C22#1171881411yescharacteristic
814C22#1171881411yescharacteristic
815C22#1171881811yescharacteristic
816C22#1171882011yescharacteristic
817C22#1171882311yescharacteristic
818C22#1171882411yescharacteristic
819C22#1171882611yescharacteristic
820C22#1171882711yescharacteristic
821C22#1171883211yescharacteristic
822C22#1171883511yescharacteristic
823C22#1171888311yescharacteristic
824C4—82no—
825C4—522no—
826C4—522no—
827C4—1042no—
828C4—1042no—
829C4#1171860411yescharacteristic
830C4#1171860511yescharacteristic
831C4#1171860611yescharacteristic
832C4#1171861311yescharacteristic
833C4#1171861411yescharacteristic
834C4#1171861411yescharacteristic
835C4#1171887411yescharacteristic
836C4#1171888311yescharacteristic
837C2—84no—
838C2#1311308311yescharacteristic
839C2#1311516811yescharacteristic
840C2#1311518211yescharacteristic
841C2#1311545911yescharacteristic
842C2#1311546611yescharacteristic
843C2#1311551611yescharacteristic
844C2#1311553011yescharacteristic
845C2#1311601711yescharacteristic
846C2#1311602411yescharacteristic
847C2#1311606911yescharacteristic
848C2#1311607611yescharacteristic
849C2#1311614411yescharacteristic
850C2#1311614911yescharacteristic
851C2#1311624211yescharacteristic
852C2#1311625211yescharacteristic
subgroupG/H
centerC24D4×D13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC22×C13×#102C2
socleC24×C13C2×D4
prime radicalC23×D4×C13C22
cosocleC23×C4×C13C23
hypercenterC22×#102D13
hypocenterC13#11189
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
3. C2×#11718143C2semidirect
4. C2×#11718121C2semidirect
5. C2×#11718142C2semidirect
6. #13113065C2semidirect
24. C2×#88072C4semidirect
650. C13#11189semidirect

Maximal subgroups

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

subgroupindex
C22×#880722
C2×#117188822
C2×#117181432
C2×#117181212
C2×#117181422
#131130652
C22×C13×#1022
#1118913