Finite Group Databasebeta

← #15770793

Subgroups — #15770793

Order 3328.

1186 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88060C211yesmaximal, characteristic
2C2×#11718648C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4C2×#11718143C211yesmaximal, characteristic, complemented
5C2×#11718121C211yesmaximal, characteristic, complemented
6C2×#11718121C211yesmaximal, characteristic, complemented
7C2×C13×#340C211yesmaximal, characteristic, complemented
8C23×C4×D13C2211yescharacteristic
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×#88060—22no—
20C2×#88060—22no—
21C2×#88060—22no—
22#11718648—22no—
23#11718648—22no—
24#11718648—22no—
25#11718648C414yescomplemented
26C13×#340—22no—
27#11718143—22no—
28#11718121—22no—
29#11718121—22no—
30C24×D13D411yescharacteristic
31C23×C4×C13—21no—
32C23×C4×C13—21no—
33C23×C4×C13C2311yescharacteristic
34C23×Dic13—21no—
35C23×Dic13—21no—
36C23×Dic13D411yescharacteristic
37C22×C4×D13—21no—
38C22×C4×D13—21no—
39C22×C4×D13—21no—
40C22×C4×D13—21no—
41C22×C4×D13—21no—
42C22×C4×D13—21no—
43C22×C4×D13—21no—
44C22×C4×D13—21no—
45C22×C4×D13—21no—
46C22×C4×D13—21no—
47C22×C4×D13—21no—
48C22×C4×D13—21no—
49C22×C4×D13C2×C412yes—
50C22×C4×D13D412yes—
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⋊Dic13—21no—
82C2×C4⋊Dic13—21no—
83C2×C4⋊Dic13—21no—
84C2×C4⋊Dic13—21no—
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13C2×C412yes—
87C2×C4⋊Dic13D412yes—
88C22×#1055—21no—
89C22×#1055—21no—
90C22×#1055—21no—
91C22×#1055—21no—
92C22×#1055—21no—
93C22×#1055—21no—
94C22×#1055D412yes—
95#88071—24no—
96#88071—24no—
97#88060—28no—
98#11200—131nomaximal, Sylow
99C24×C13C2×D411yescharacteristic
100C23×D13—21no—
101C23×D13—21no—
102C23×D13—21no—
103C23×D13—21no—
104C23×D13—21no—
105C23×D13—21no—
106C23×D13—21no—
107C23×D13—21no—
108C23×D13—21no—
109C23×D13—21no—
110C23×D13—21no—
111C23×D13—21no—
112C23×D13C22⋊C412yes—
113C23×D13SD1612yes—
114C23×D13Q1612yes—
115C22×C4×C13—22no—
116C22×C4×C13—22no—
117C22×C4×C13—41no—
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×C13C22×C411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13#4111yescharacteristic
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×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—22no—
150C22×Dic13—22no—
151C22×Dic13—41no—
152C22×Dic13—41no—
153C22×Dic13—41no—
154C22×Dic13—41no—
155C22×Dic13—41no—
156C22×Dic13—41no—
157C22×Dic13—41no—
158C22×Dic13—41no—
159C22×Dic13—41no—
160C22×Dic13—41no—
161C22×Dic13—41no—
162C22×Dic13—41no—
163C22×Dic13C22⋊C412yes—
164C2×C4×D13—22no—
165C2×C4×D13—22no—
166C2×C4×D13—22no—
167C2×C4×D13—22no—
168C2×C4×D13—22no—
169C2×C4×D13—22no—
170C2×C4×D13—22no—
171C2×C4×D13—22no—
172C2×C4×D13—22no—
173C2×C4×D13—22no—
174C2×C4×D13—22no—
175C2×C4×D13—22no—
176C2×C4×D13—41no—
177C2×C4×D13—41no—
178C2×C4×D13—41no—
179C2×C4×D13—41no—
180C2×C4×D13—41no—
181C2×C4×D13—41no—
182C2×C4×D13—41no—
183C2×C4×D13—41no—
184C2×C4×D13—41no—
185C2×C4×D13—41no—
186C2×C4×D13—41no—
187C2×C4×D13—41no—
188C2×C4×D13—41no—
189C2×C4×D13—41no—
190C2×C4×D13—41no—
191C2×C4×D13—41no—
192C2×C8×C13—22no—
193C2×C8×C13—22no—
194C2×C8×C13—22no—
195C2×C8×C13—41no—
196C2×C8×C13—41no—
197C2×C8×C13—41no—
198C2×C8×C13—41no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—22no—
203C13×C4⋊C4—41no—
204C13×C4⋊C4—41no—
205C13×C4⋊C4—41no—
206C13×C4⋊C4—41no—
207#6103—48no—
208#6103—48no—
209C4⋊Dic13—22no—
210C4⋊Dic13—22no—
211C4⋊Dic13—22no—
212C4⋊Dic13—22no—
213C4⋊Dic13—41no—
214C4⋊Dic13—41no—
215C4⋊Dic13—41no—
216C4⋊Dic13—41no—
217C2×#1055—22no—
218C2×#1055—22no—
219C2×#1055—22no—
220C2×#1055—41no—
221C2×#1055—41no—
222C2×#1055—41no—
223C2×#1055—41no—
224C22×C22⋊C8—131no—
225C2×#380—131no—
226C2×#380—131no—
227C2×#340—131no—
228C2×#340—131no—
229C2×#340—131no—
230C2×#340D1311yescharacteristic, complemented
231C23×C13C2×C22⋊C411yescharacteristic
232C23×C13#12011yescharacteristic
233C23×C13#12111yescharacteristic
234C23×C13#12111yescharacteristic
235C23×C13#12311yescharacteristic
236C23×C13#12311yescharacteristic
237C23×C13#12311yescharacteristic
238C23×C13C2×SD1611yescharacteristic
239C23×C13C2×Q1611yescharacteristic
240C23×C13#13511yescharacteristic
241C23×C13#13511yescharacteristic
242C23×C13AGL(1,ℤ/8)11yescharacteristic
243C23×C13AGL(1,ℤ/8)11yescharacteristic
244C23×C13AGL(1,ℤ/8)11yescharacteristic
245C23×C13#13711yescharacteristic
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—22no—
253C22×D13—22no—
254C22×D13—22no—
255C22×D13—22no—
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—22no—
261C22×D13—22no—
262C22×D13—22no—
263C22×D13—22no—
264C22×D13—41no—
265C22×D13—41no—
266C22×D13—41no—
267C22×D13—41no—
268C22×D13—41no—
269C22×D13—41no—
270C22×D13—41no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13—41no—
279C22×D13—41no—
280C22×D13#10314yes—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—81no—
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#11711yescharacteristic
296C2×C4×C13#11711yescharacteristic
297C2×C4×C13C4×D411yescharacteristic
298C2×C4×C13C4×D411yescharacteristic
299C2×C4×C13C4×D411yescharacteristic
300C2×C4×C13C4×D411yescharacteristic
301C2×C4×C13#12011yescharacteristic
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#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#12411yescharacteristic
316C2×C4×C13#12411yescharacteristic
317C2×C4×C13#12411yescharacteristic
318C2×C4×C13#12411yescharacteristic
319C2×C4×C13#12611yescharacteristic
320C2×C4×C13#12611yescharacteristic
321C2×C4×C13#12611yescharacteristic
322C2×C4×C13#12611yescharacteristic
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—81no—
337C2×Dic13—81no—
338C2×Dic13—81no—
339C2×Dic13—81no—
340C2×Dic13—81no—
341C2×Dic13—81no—
342C2×Dic13—81no—
343C2×Dic13—81no—
344C4×D13—42no—
345C4×D13—42no—
346C4×D13—42no—
347C4×D13—42no—
348C4×D13—42no—
349C4×D13—42no—
350C4×D13—42no—
351C4×D13—42no—
352C8×C13—42no—
353#1055—42no—
354C24×C4—131no—
355C23×C8—131no—
356C23×C8C2×D1311yescharacteristic
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4C2×D1311yescharacteristic
360C22×C4⋊C4C2×D1311yescharacteristic
361C22×C22⋊C4—261no—
362C22×C22⋊C4—261no—
363C2×C22⋊C8—262no—
364C2×C22⋊C8—262no—
365C2×C22⋊C8—262no—
366#380—134no—
367#380—262no—
368#380—262no—
369#380—262no—
370C2×#95—261no—
371C2×#95—261no—
372#340—22no—
373#340—262no—
374#340—262no—
375#340—262no—
376C22×C13#38111yescharacteristic
377C22×C13#38611yescharacteristic
378C22×C13#38611yescharacteristic
379C22×C13#39411yescharacteristic
380C22×C13#39411yescharacteristic
381C22×C13#39711yescharacteristic
382C22×C13#39711yescharacteristic
383C22×C13C2×#10311yescharacteristic
384C22×C13#41611yescharacteristic
385C22×C13#41711yescharacteristic
386C22×C13#41811yescharacteristic
387C22×C13#44911yescharacteristic
388C22×C13#44911yescharacteristic
389C22×C13#45011yescharacteristic
390C22×C13#45111yescharacteristic
391C22×C13#46511yescharacteristic
392C22×C13#46511yescharacteristic
393C22×C13#46711yescharacteristic
394C22×C13#46711yescharacteristic
395C22×C13#46811yescharacteristic
396C22×C13#46811yescharacteristic
397C22×C13#46911yescharacteristic
398C22×C13#46911yescharacteristic
399C22×C13#48111yescharacteristic
400C22×C13#48111yescharacteristic
401C22×C13#48211yescharacteristic
402C22×C13#48211yescharacteristic
403C22×C13#48211yescharacteristic
404C22×C13#48211yescharacteristic
405C22×C13#48311yescharacteristic
406C22×C13#48411yescharacteristic
407C22×C13#48411yescharacteristic
408C22×C13#48411yescharacteristic
409C22×C13#48511yescharacteristic
410C22×C13#48511yescharacteristic
411C2×D13—24no—
412C2×D13—24no—
413C2×D13—24no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C4×C13—82no—
427C4×C13—82no—
428C4×C13#38811yescharacteristic
429C4×C13#38811yescharacteristic
430C4×C13#38811yescharacteristic
431C4×C13#38811yescharacteristic
432C4×C13#39411yescharacteristic
433C4×C13#39411yescharacteristic
434C4×C13#39711yescharacteristic
435C4×C13#39711yescharacteristic
436Dic13—42no—
437Dic13—82no—
438Dic13—82no—
439C25—131no—
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—131no—
443C23×C4—132no—
444C23×C4—132no—
445C23×C4—261no—
446C23×C4—261no—
447C23×C4—261no—
448C23×C4—261no—
449C23×C4—261no—
450C23×C4—261no—
451C23×C4—261no—
452C23×C4—261no—
453C23×C4—261no—
454C23×C4—261no—
455C23×C4—261no—
456C23×C4—261no—
457C23×C4—261no—
458C23×C4—261no—
459C23×C4C22×D1311yescharacteristic
460C22×C8—21no—
461C22×C8—21no—
462C22×C8—21no—
463C22×C8—21no—
464C22×C8—21no—
465C22×C8—21no—
466C22×C8—132no—
467C22×C8—261no—
468C22×C8—261no—
469C22×C8—261no—
470C22×C8—261no—
471C22×C8—261no—
472C22×C8—261no—
473C22×C8C22⋊D1312yes—
474C2×C4⋊C4—21no—
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—132no—
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⋊C4—261no—
492C2×C4⋊C4—261no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4—261no—
496C2×C4⋊C4C4×D1312yes—
497C2×C4⋊C4D5212yes—
498C2×C22⋊C4—264no—
499C2×C22⋊C4—264no—
500C2×C22⋊C4—522no—
501C2×C22⋊C4—522no—
502C2×C22⋊C4—522no—
503C2×C22⋊C4—522no—
504C22⋊C8—268no—
505#95—264no—
506#95—264no—
507C2×C13#144011yescharacteristic
508C2×C13#182411yescharacteristic
509C2×C13#182511yescharacteristic
510C2×C13#187211yescharacteristic
511C2×C13#187511yescharacteristic
512C2×C13#189211yescharacteristic
513C2×C13#189511yescharacteristic
514C2×C13#203411yescharacteristic
515C2×C13#203411yescharacteristic
516C2×C13#203611yescharacteristic
517C2×C13#203611yescharacteristic
518C2×C13#207611yescharacteristic
519C2×C13#207611yescharacteristic
520C2×C13#207711yescharacteristic
521C2×C13#207711yescharacteristic
522D13—44no—
523C24—132no—
524C24—132no—
525C24—132no—
526C24—261no—
527C24—261no—
528C24—261no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24—261no—
533C24—261no—
534C24—261no—
535C24—261no—
536C24—261no—
537C24—261no—
538C24D4×D1311yescharacteristic
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—41no—
552C22×C4—41no—
553C22×C4—132no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—262no—
561C22×C4—262no—
562C22×C4—262no—
563C22×C4—262no—
564C22×C4—262no—
565C22×C4—262no—
566C22×C4—262no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—521no—
575C22×C4—521no—
576C22×C4—521no—
577C22×C4—521no—
578C22×C4—521no—
579C22×C4—521no—
580C22×C4—521no—
581C22×C4—521no—
582C22×C4—521no—
583C22×C4—521no—
584C22×C4—521no—
585C22×C4—521no—
586C22×C4—521no—
587C22×C4—521no—
588C22×C4—521no—
589C22×C4—521no—
590C22×C4—521no—
591C22×C4—521no—
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×C4C2×C4×D1311yescharacteristic
603C22×C4C2×D5211yescharacteristic
604C22×C4#612711yescharacteristic
605C22×C4#612711yescharacteristic
606C22×C4#612711yescharacteristic
607C22×C4#612711yescharacteristic
608C22×C4D4×D1311yescharacteristic
609C22×C4D4×D1311yescharacteristic
610C22×C4D4×D1311yescharacteristic
611C22×C4#612911yescharacteristic
612C22×C4#612911yescharacteristic
613C22×C4#613111yescharacteristic
614C22×C4#613111yescharacteristic
615C22×C4C2×C22⋊D1311yescharacteristic
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—41no—
620C2×C8—41no—
621C2×C8—41no—
622C2×C8—41no—
623C2×C8—262no—
624C2×C8—262no—
625C2×C8—262no—
626C2×C8—521no—
627C2×C8—521no—
628C2×C8—521no—
629C2×C8—521no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4—262no—
639C4⋊C4—262no—
640C4⋊C4—262no—
641C4⋊C4—262no—
642C4⋊C4—521no—
643C4⋊C4—521no—
644C4⋊C4—521no—
645C4⋊C4—521no—
646C22⋊C4—528no—
647C22⋊C4—528no—
648C13#1120011yescharacteristic, complemented, Sylow
649C23—134no—
650C23—262no—
651C23—262no—
652C23—262no—
653C23—262no—
654C23—262no—
655C23—262no—
656C23—262no—
657C23—262no—
658C23—262no—
659C23—262no—
660C23—262no—
661C23—262no—
662C23—262no—
663C23—262no—
664C23—262no—
665C23—262no—
666C23—262no—
667C23—262no—
668C23—521no—
669C23—521no—
670C23—521no—
671C23—521no—
672C23—521no—
673C23—521no—
674C23—521no—
675C23—521no—
676C23—521no—
677C23—521no—
678C23—521no—
679C23—521no—
680C23—521no—
681C23—521no—
682C23—521no—
683C23—521no—
684C23C22⋊C4×D1311yescharacteristic
685C23#8813611yescharacteristic
686C23#8813711yescharacteristic
687C23#8813811yescharacteristic
688C23#8814811yescharacteristic
689C23#8814811yescharacteristic
690C23#8816511yescharacteristic
691C23#8816511yescharacteristic
692C23SD16×D1311yescharacteristic
693C23#8816811yescharacteristic
694C23#8816911yescharacteristic
695C23#8817011yescharacteristic
696C23Q16×D1311yescharacteristic
697C23#8817311yescharacteristic
698C23#8819211yescharacteristic
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—521no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—1041no—
735C2×C4—1041no—
736C2×C4—1041no—
737C2×C4—1041no—
738C2×C4—1041no—
739C2×C4—1041no—
740C2×C4—1041no—
741C2×C4—1041no—
742C2×C4#8812611yescharacteristic
743C2×C4C4×D5211yescharacteristic
744C2×C4#8812911yescharacteristic
745C2×C4#8813011yescharacteristic
746C2×C4#8813511yescharacteristic
747C2×C4#8813711yescharacteristic
748C2×C4#8813711yescharacteristic
749C2×C4#8813811yescharacteristic
750C2×C4#8813811yescharacteristic
751C2×C4#8813911yescharacteristic
752C2×C4#8813911yescharacteristic
753C2×C4#8814011yescharacteristic
754C2×C4#8814611yescharacteristic
755C2×C4#8814711yescharacteristic
756C2×C4#8814811yescharacteristic
757C2×C4#8814811yescharacteristic
758C2×C4#8814811yescharacteristic
759C2×C4#8814911yescharacteristic
760C2×C4#8814911yescharacteristic
761C2×C4#8815211yescharacteristic
762C2×C4#8815211yescharacteristic
763C2×C4#8815211yescharacteristic
764C2×C4C4×C22⋊D1311yescharacteristic
765C2×C4#8818311yescharacteristic
766C2×C4#8818411yescharacteristic
767C2×C4#8819111yescharacteristic
768C2×C4#8819311yescharacteristic
769C2×C4#8820111yescharacteristic
770C8—42no—
771C8—522no—
772C22—264no—
773C22—264no—
774C22—264no—
775C22—522no—
776C22—522no—
777C22—522no—
778C22—522no—
779C22—522no—
780C22—522no—
781C22—522no—
782C22—522no—
783C22—522no—
784C22—522no—
785C22—522no—
786C22—522no—
787C22#1171832511yescharacteristic
788C22#1171832611yescharacteristic
789C22#1171833311yescharacteristic
790C22#1171833611yescharacteristic
791C22#1171843111yescharacteristic
792C22#1171843211yescharacteristic
793C22#1171843711yescharacteristic
794C22#1171843811yescharacteristic
795C22#1171844011yescharacteristic
796C22#1171844111yescharacteristic
797C22#1171844211yescharacteristic
798C22#1171844311yescharacteristic
799C22D13×#10311yescharacteristic
800C22#1171846511yescharacteristic
801C22#1171846811yescharacteristic
802C22#1171846911yescharacteristic
803C22#1171847011yescharacteristic
804C22#1171847211yescharacteristic
805C22#1171847411yescharacteristic
806C22#1171847511yescharacteristic
807C22#1171852311yescharacteristic
808C22#1171852411yescharacteristic
809C22#1171852711yescharacteristic
810C22#1171852811yescharacteristic
811C22#1171854511yescharacteristic
812C22#1171854511yescharacteristic
813C22#1171854611yescharacteristic
814C22#1171854611yescharacteristic
815C22#1171861711yescharacteristic
816C22#1171862211yescharacteristic
817C22#1171865411yescharacteristic
818C22#1171882011yescharacteristic
819C22#1171883211yescharacteristic
820C22#1171883511yescharacteristic
821C22#1171884911yescharacteristic
822C4—82no—
823C4—82no—
824C4—522no—
825C4—1042no—
826C4—1042no—
827C4#1171833011yescharacteristic
828C4#1171833111yescharacteristic
829C4#1171833511yescharacteristic
830C4#1171833611yescharacteristic
831C4#1171860111yescharacteristic
832C4#1171862011yescharacteristic
833C4#1171865111yescharacteristic
834C4#1171865211yescharacteristic
835C2—524no—
836C2#1311308411yescharacteristic
837C2#1311492511yescharacteristic
838C2#1311493011yescharacteristic
839C2#1311514211yescharacteristic
840C2#1311515711yescharacteristic
841C2#1311525611yescharacteristic
842C2#1311527111yescharacteristic
843C2#1311602411yescharacteristic
844C2#1311602811yescharacteristic
845C2#1311603811yescharacteristic
846C2#1311604211yescharacteristic
847C2#1311626511yescharacteristic
848C2#1311626811yescharacteristic
849C2#1311627011yescharacteristic
850C2#1311627511yescharacteristic
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#11200
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×#11718143C2semidirect
5. C2×#11718121C2semidirect
6. C2×#11718121C2semidirect
7. C2×C13×#340C2semidirect
25. #11718648C4semidirect
230. C2×#340D13semidirect
648. C13#11200semidirect

Maximal subgroups

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

subgroupindex
C22×#880602
C2×#117186482
C2×#117181432
C2×#117181212
C2×C13×#3402
#1120013