Finite Group Databasebeta

← #15789346

Subgroups — #15789346

Order 3328.

1926 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88126C211yesmaximal, characteristic
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718589C211yesmaximal, characteristic, complemented
4C2×#11718648C211yesmaximal, characteristic
5C2×#11718648C211yesmaximal, characteristic
6#13113100C212yesmaximal, complemented
7#13113091C212yesmaximal, complemented
8#13113082C212yesmaximal
9#13113080C212yesmaximal
10#13113065C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×#6101C2212yes—
26C22×C4×Dic13C2211yescharacteristic
27C2×#88126—24no—
28C2×#88126—24no—
29C2×#88126—24no—
30C2×C13×#95C2212yes—
31C2×C13×#95C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718648—24no—
39#11718648C418yescomplemented
40#11718646—24no—
41#11718589—24no—
42C24×D13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13C2×C414yes—
58C22×C4×D13D414yes—
59C22×C4×D13Q814yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4C2×C414yes—
66C2×C42×C13—22no—
67C2×C42×C13—22no—
68C2×C42×C13D414yes—
69C2×#6103—22no—
70C2×#6103—22no—
71C2×#6103—22no—
72C2×#6103—22no—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×#6103—24no—
76C2×#6103—42no—
77C2×#6103—42no—
78C2×#6103—42no—
79C2×#6103—42no—
80C2×#6103C2×C418yes—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—24no—
87C2×C4⋊Dic13—42no—
88C2×C4⋊Dic13—42no—
89C2×C4⋊Dic13C2×C414yes—
90C2×#6101—22no—
91C2×#6101—22no—
92C2×#6101—22no—
93C2×#6101—22no—
94C2×#6101—22no—
95C2×#6101—22no—
96C2×#6101—24no—
97C2×#6101—42no—
98C2×#6101—42no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13D414yes—
102#88126—232no—
103C13×#95—42no—
104C13×#95—42no—
105#88071—24no—
106#88071—24no—
107#88071—24no—
108#88071—42no—
109#88071—42no—
110#88071C2×C418yes—
111#14264—131nomaximal, Sylow
112C24×C13C2411yescharacteristic
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13—21no—
117C23×D13—21no—
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—21no—
122C23×D13—21no—
123C23×D13—21no—
124C23×D13—21no—
125C23×D13C22×C412yes—
126C23×D13C2×D412yes—
127C23×D13C2×Q812yes—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
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×C13C22×C414yes—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×Q812yes—
161C22×C4×C13#4112yes—
162C22×C4×C13#4112yes—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—22no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—22no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13C22×C414yes—
193C22×Dic13C22×C412yes—
194C22×Dic13C2×D412yes—
195C22×Dic13C2×D412yes—
196C22×Dic13C2×D412yes—
197C22×Dic13C2×Q812yes—
198C2×C4×D13—28no—
199C2×C4×D13—28no—
200C2×C4×D13—28no—
201C2×C4×D13—28no—
202C2×C4×D13—28no—
203C2×C4×D13—28no—
204C2×C4×D13C4⋊C4116yescomplemented
205C13×C4⋊C4—28no—
206C13×C4⋊C4—44no—
207C42×C13—28no—
208#6103—28no—
209#6103—28no—
210#6103—48no—
211#6103—48no—
212C4⋊Dic13—28no—
213C4⋊Dic13—48no—
214C4⋊Dic13—44no—
215#6101—28no—
216#6101—28no—
217#6101—48no—
218C4×Dic13—28no—
219C22×#117—131no—
220C2×#389—131no—
221C2×#389—131no—
222C2×#380—131no—
223C2×#380—131no—
224#1444—132no—
225#1442—132no—
226#1439—132no—
227#1439—132no—
228C4⋊#95—131no—
229C4⋊#95D1311yescharacteristic, complemented
230C23×C13C23×C411yescharacteristic
231C23×C13C22×D411yescharacteristic
232C23×C13C22×D411yescharacteristic
233C23×C13C22×D411yescharacteristic
234C23×C13C22×Q811yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13H(5,𝔽2)11yescharacteristic
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C13H(5,𝔽2)11yescharacteristic
241C23×C132−1+411yescharacteristic
242C23×C132−1+411yescharacteristic
243C23×C132−1+411yescharacteristic
244C23×C132−1+411yescharacteristic
245C22×D13—22no—
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—41no—
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×D13C2×C4⋊C414yes—
280C2×C4×C13—24no—
281C2×C4×C13—24no—
282C2×C4×C13—24no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—42no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13C2×C4⋊C414yes—
309C2×C4×C13C4×D414yes—
310C2×C4×C13C4×D414yes—
311C2×C4×C13#12014yes—
312C2×C4×C13C22⋊Q814yes—
313C2×C4×C13C22⋊Q814yes—
314C2×C4×C13#12314yes—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—24no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—22no—
330C2×Dic13—42no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—42no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13C2×C4⋊C414yes—
350C4×D13—232no—
351C24×C4—131no—
352C2×#117—264no—
353C2×#117—264no—
354C2×#117—264no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—131no—
357C22×C4⋊C4—131no—
358C22×C4⋊C4—131no—
359C22×C4⋊C4—132no—
360C22×C4⋊C4—132no—
361C22×C4⋊C4C2×D1311yescharacteristic
362C22×C4⋊C4C2×D1311yescharacteristic
363C22×C22⋊C4—132no—
364C22×C22⋊C4—131no—
365C22×C22⋊C4—131no—
366C22×C22⋊C4—132no—
367C22×C42—131no—
368C22×C42C2×D1311yescharacteristic
369#389—264no—
370#389—264no—
371#380—138no—
372#380—264no—
373C2×#95—132no—
374C2×#95—132no—
375C2×#95—132no—
376C2×#95—132no—
377C2×#95—132no—
378C2×#95—132no—
379C2×#95C2×D1312yes—
380C2×#95C2×D1312yes—
381C22×C13C22×C4⋊C411yescharacteristic
382C22×C13C2×C4×D411yescharacteristic
383C22×C13C2×C4×D411yescharacteristic
384C22×C13#51811yescharacteristic
385C22×C13#51911yescharacteristic
386C22×C13#52011yescharacteristic
387C22×C13#52011yescharacteristic
388C22×C13C2×#12011yescharacteristic
389C22×C13C2×C22⋊Q811yescharacteristic
390C22×C13C2×C22⋊Q811yescharacteristic
391C22×C13C2×#12311yescharacteristic
392C22×C13#53511yescharacteristic
393C22×C13#53511yescharacteristic
394C22×C13#53511yescharacteristic
395C22×C13#53611yescharacteristic
396C22×C13#53611yescharacteristic
397C22×C13#53611yescharacteristic
398C22×C13#53711yescharacteristic
399C22×C13#53711yescharacteristic
400C22×C13#53711yescharacteristic
401C22×C13#53711yescharacteristic
402C22×C13#53711yescharacteristic
403C22×C13#53711yescharacteristic
404C22×C13#54011yescharacteristic
405C22×C13#54011yescharacteristic
406C22×C13#54111yescharacteristic
407C22×C13#54111yescharacteristic
408C22×C13#54211yescharacteristic
409C22×C13#54211yescharacteristic
410C22×C13#54211yescharacteristic
411C22×C13#54211yescharacteristic
412C22×C13#54411yescharacteristic
413C22×C13#54411yescharacteristic
414C22×C13#54411yescharacteristic
415C22×C13#54411yescharacteristic
416C2×D13—24no—
417C2×D13—24no—
418C2×D13—24no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C2×D13—42no—
429C2×D13—42no—
430C2×D13—42no—
431C4×C13—44no—
432C4×C13—42no—
433C4×C13—42no—
434C4×C13—82no—
435C4×C13#38518yes—
436Dic13—24no—
437Dic13—44no—
438Dic13—42no—
439Dic13—42no—
440Dic13—82no—
441C25—131no—
442C23×C4—131no—
443C23×C4—134no—
444C23×C4—134no—
445C23×C4—134no—
446C23×C4—131no—
447C23×C4—132no—
448C23×C4—131no—
449C23×C4—132no—
450C23×C4—262no—
451C23×C4—262no—
452C23×C4—262no—
453C23×C4—262no—
454C23×C4C22×D1312yes—
455C23×C4C22×D1312yes—
456C23×C4C22×D1311yescharacteristic
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459#117—2632no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—262no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4—262no—
474C2×C4⋊C4—264no—
475C2×C4⋊C4—264no—
476C2×C4⋊C4—262no—
477C2×C4⋊C4—262no—
478C2×C4⋊C4—262no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4—522no—
481C2×C4⋊C4—522no—
482C2×C4⋊C4—522no—
483C2×C4⋊C4C4×D1314yes—
484C2×C22⋊C4—138no—
485C2×C22⋊C4—262no—
486C2×C22⋊C4—262no—
487C2×C22⋊C4—262no—
488C2×C22⋊C4—262no—
489C2×C22⋊C4—262no—
490C2×C22⋊C4—262no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4—522no—
493C2×C22⋊C4—522no—
494C2×C22⋊C4—522no—
495C2×C22⋊C4—522no—
496C2×C42—22no—
497C2×C42—22no—
498C2×C42—134no—
499C2×C42—262no—
500C2×C42—262no—
501C2×C42D5214yes—
502#95—42no—
503#95—42no—
504#95—138no—
505#95—264no—
506#95—264no—
507#95—264no—
508#95—522no—
509#95—522no—
510C2×C13C2×#38511yescharacteristic
511C2×C13#231611yescharacteristic
512C2×C13#231711yescharacteristic
513C2×C13#232311yescharacteristic
514C2×C13#232311yescharacteristic
515C2×C13#232411yescharacteristic
516C2×C13#232411yescharacteristic
517C2×C13#261511yescharacteristic
518C2×C13#261611yescharacteristic
519C2×C13#262411yescharacteristic
520C2×C13#262511yescharacteristic
521C2×C13#262811yescharacteristic
522C2×C13#262811yescharacteristic
523C2×C13#262911yescharacteristic
524C2×C13#262911yescharacteristic
525D13—44no—
526C24—132no—
527C24—132no—
528C24—132no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24—261no—
533C24—261no—
534C24—261no—
535C24—261no—
536C24—261no—
537C24—261no—
538C24—261no—
539C24—261no—
540C24—261no—
541C24C23×D1311yescharacteristic
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—1316no—
571C22×C4—134no—
572C22×C4—132no—
573C22×C4—132no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—268no—
579C22×C4—268no—
580C22×C4—268no—
581C22×C4—268no—
582C22×C4—268no—
583C22×C4—268no—
584C22×C4—262no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—262no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—262no—
592C22×C4—261no—
593C22×C4—262no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4—262no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—262no—
608C22×C4—262no—
609C22×C4C2×C4×D1314yes—
610C22×C4C2×C4×D1312yes—
611C22×C4C2×D5212yes—
612C22×C4C2×D5212yes—
613C22×C4C2×D5212yes—
614C22×C4#612712yes—
615C22×C4D4×D1312yes—
616C22×C4D4×D1312yes—
617C22×C4#612912yes—
618C22×C4Q8×D1312yes—
619C4⋊C4—28no—
620C4⋊C4—44no—
621C4⋊C4—268no—
622C4⋊C4—268no—
623C4⋊C4—268no—
624C4⋊C4—528no—
625C4⋊C4—528no—
626C4⋊C4—524no—
627C22⋊C4—268no—
628C22⋊C4—268no—
629C22⋊C4—528no—
630C22⋊C4—528no—
631C42—28no—
632C42—268no—
633C13#1426411yescharacteristic, complemented, Sylow
634C23—134no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23—262no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23—262no—
643C23—262no—
644C23—262no—
645C23—262no—
646C23—262no—
647C23—262no—
648C23—262no—
649C23—262no—
650C23—262no—
651C23—262no—
652C23—262no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23—521no—
659C23—521no—
660C23—521no—
661C23—521no—
662C23—521no—
663C23—521no—
664C23—521no—
665C23—521no—
666C23—521no—
667C23—521no—
668C23—521no—
669C23C22×C4×D1311yescharacteristic
670C23C22×D5211yescharacteristic
671C23C2×#612711yescharacteristic
672C23C2×D4×D1311yescharacteristic
673C23C2×D4×D1311yescharacteristic
674C23C2×#612911yescharacteristic
675C23#8825111yescharacteristic
676C23#8825111yescharacteristic
677C23C2×Q8×D1311yescharacteristic
678C23#8825411yescharacteristic
679C23#8825411yescharacteristic
680C23#8825611yescharacteristic
681C23#8825611yescharacteristic
682C23#8825711yescharacteristic
683C23#8825711yescharacteristic
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—134no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—2632no—
720C2×C4—264no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—264no—
724C2×C4—264no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—262no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—521no—
738C2×C4—521no—
739C2×C4—521no—
740C2×C4—521no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4—522no—
747C2×C4—522no—
748C2×C4C4×D5214yes—
749C2×C4#8813514yes—
750C2×C4#8813614yes—
751C2×C4#8813714yes—
752C2×C4C4⋊C4×D1314yes—
753C2×C4#8815014yes—
754C2×C4#8815114yes—
755C22—264no—
756C22—264no—
757C22—264no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22—522no—
765C22—522no—
766C22—522no—
767C22—522no—
768C22—522no—
769C22—522no—
770C22C2×C4×D5211yescharacteristic
771C22C2×#8813511yescharacteristic
772C22C2×#8813611yescharacteristic
773C22C2×#8813711yescharacteristic
774C22C2×C4⋊C4×D1311yescharacteristic
775C22C2×#8815011yescharacteristic
776C22C2×#8815111yescharacteristic
777C22#1171921511yescharacteristic
778C22#1171921511yescharacteristic
779C22#1171923011yescharacteristic
780C22#1171923111yescharacteristic
781C22#1171925011yescharacteristic
782C22#1171925111yescharacteristic
783C22#1171926611yescharacteristic
784C22#1171926711yescharacteristic
785C22#1171927711yescharacteristic
786C22#1171927911yescharacteristic
787C22#1171928711yescharacteristic
788C22#1171928811yescharacteristic
789C22#1171931211yescharacteristic
790C22#1171931211yescharacteristic
791C22#1171931311yescharacteristic
792C22#1171931311yescharacteristic
793C22#1171933311yescharacteristic
794C22#1171933311yescharacteristic
795C22#1171933411yescharacteristic
796C22#1171933411yescharacteristic
797C22#1171938711yescharacteristic
798C22#1171938711yescharacteristic
799C22#1171939411yescharacteristic
800C22#1171939411yescharacteristic
801C22#1171942411yescharacteristic
802C22#1171943411yescharacteristic
803C22#1171943411yescharacteristic
804C22#1171943611yescharacteristic
805C4—42no—
806C4—42no—
807C4—44no—
808C4—82no—
809C4—264no—
810C4—522no—
811C4—522no—
812C4—524no—
813C4—1042no—
814C4#1171832918yes—
815C2—524no—
816C2C2×#1171832911yescharacteristic
817C2#1311745111yescharacteristic
818C2#1311745811yescharacteristic
819C2#1311751911yescharacteristic
820C2#1311752111yescharacteristic
821C2#1311753011yescharacteristic
822C2#1311753211yescharacteristic
823C2#1312056211yescharacteristic
824C2#1312056711yescharacteristic
825C2#1312062811yescharacteristic
826C2#1312063611yescharacteristic
827C2#1312066011yescharacteristic
828C2#1312066311yescharacteristic
829C2#1312066911yescharacteristic
830C2#1312067111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#14264
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718646C2semidirect
3. C2×#11718589C2semidirect
6. #13113100C2semidirect
7. #13113091C2semidirect
10. #13113065C2semidirect
11. C13×C4⋊#95C2semidirect
39. #11718648C4semidirect
204. C2×C4×D13C4⋊C4semidirect
229. C4⋊#95D13semidirect
633. C13#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#881262
C2×#117186462
C2×#117185892
C2×#117186482
#131131002
#131130912
#131130822
#131130802
#131130652
C13×C4⋊#952
#1426413