Finite Group Databasebeta

← #15785169

Subgroups — #15785169

Order 3328.

2366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718648C211yesmaximal, characteristic
4C2×#11718648C212yesmaximal
5C2×C4×#6103C211yesmaximal, characteristic
6#13113090C212yesmaximal, complemented
7#13113086C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113057C212yesmaximal
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×C4×D13C2212yes—
13C23×C4×D13C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2212yes—
16C22×C13×C4⋊C4C2211yescharacteristic
17C22×C42×C13C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C2×C4⋊C4×D13—24no—
27C2×C4⋊C4×D13—24no—
28C2×C4⋊C4×D13C418yescomplemented
29C13×#389—24no—
30C2×C13×#95C2212yes—
31C2×#88071C2211yescharacteristic
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39#11718648—24no—
40#11718648—28no—
41#11718646—24no—
42C4×#6103—24no—
43C24×D13C2311yescharacteristic
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2312yes—
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2312yes—
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—24no—
59C22×C4×D13—24no—
60C22×C4×D13—24no—
61C22×C4×D13—24no—
62C22×C4×D13—42no—
63C22×C4×D13—42no—
64C22×C4×D13C2×C418yes—
65C22×C4×D13C2×C414yes—
66C22×C4×D13D414yes—
67C22×C4×D13Q814yes—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—22no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—42no—
74C2×C13×C4⋊C4C2×C414yes—
75C2×C13×C4⋊C4D414yes—
76C2×C13×C4⋊C4D414yes—
77C2×C42×C13—22no—
78C2×C42×C13—22no—
79C2×C42×C13—22no—
80C2×#6103—22no—
81C2×#6103—22no—
82C2×#6103—22no—
83C2×#6103—22no—
84C2×#6103—24no—
85C2×#6103—24no—
86C2×#6103—24no—
87C2×#6103D414yes—
88C2×#6103Q814yes—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—24no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13—22no—
95C2×C4⋊Dic13—24no—
96C2×C4⋊Dic13—42no—
97C2×C4⋊Dic13C2×C414yes—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101C2×C418yes—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C4⋊C4×D13—232no—
105C13×#95—24no—
106#88071—24no—
107#88071—24no—
108#88071—22no—
109#88071—22no—
110#88071—24no—
111#88071—24no—
112#88071—42no—
113#88071—42no—
114#13907—131nomaximal, Sylow
115C24×C13C2411yescharacteristic
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×D13C22×C412yes—
125C23×D13C2×D412yes—
126C23×D13C2×D412yes—
127C23×D13C2×Q812yes—
128C23×D13C2×Q812yes—
129C23×D13#4112yes—
130C23×D13#4112yes—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
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×C13—22no—
154C22×C4×C13C22×C414yes—
155C22×C4×C13C22×C412yes—
156C22×C4×C13C2×D414yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2×D414yes—
161C22×C4×C13C2×D412yes—
162C22×C4×C13C2×Q812yes—
163C22×C4×C13C2×Q812yes—
164C22×C4×C13#4112yes—
165C22×C4×C13#4112yes—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—22no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—21no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13C22×C414yes—
196C22×Dic13C22×C412yes—
197C22×Dic13C2×D412yes—
198C22×Dic13C2×D412yes—
199C22×Dic13C2×Q812yes—
200C22×Dic13C2×Q812yes—
201C2×C4×D13—28no—
202C2×C4×D13—28no—
203C2×C4×D13—28no—
204C2×C4×D13—28no—
205C2×C4×D13—28no—
206C2×C4×D13—28no—
207C2×C4×D13—216no—
208C2×C4×D13—216no—
209C2×C4×D13—48no—
210C2×C4×D13—48no—
211C2×C4×D13—48no—
212C2×C4×D13—48no—
213C2×C4×D13—48no—
214C2×C4×D13C4⋊C4116yescomplemented
215C13×C4⋊C4—48no—
216C13×C4⋊C4—44no—
217C13×C4⋊C4C22⋊C4116yescomplemented
218C42×C13—44no—
219#6103—28no—
220#6103—28no—
221#6103—48no—
222C4⋊Dic13—28no—
223C4⋊Dic13—48no—
224C4⋊Dic13—44no—
225#6101—216no—
226C4×Dic13—44no—
227C23×C4⋊C4—131no—
228C2×#389—131no—
229C2×#389D1311yescharacteristic, complemented
230C2×#380—132no—
231C2×#380—131no—
232C2×C4×C22⋊C4—131no—
233#1441—132no—
234#1441—132no—
235C4⋊#95—131no—
236C4⋊#95—131no—
237C22⋊#95—132no—
238C23×C13C23×C411yescharacteristic
239C23×C13C22×D411yescharacteristic
240C23×C13C22×D411yescharacteristic
241C23×C13C22×D411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C13C22×Q811yescharacteristic
244C23×C13C22×Q811yescharacteristic
245C23×C13C2×#4111yescharacteristic
246C23×C13C2×#4111yescharacteristic
247C23×C13C2×#4111yescharacteristic
248C23×C13C2×#4111yescharacteristic
249C23×C13H(5,𝔽2)11yescharacteristic
250C23×C13H(5,𝔽2)11yescharacteristic
251C23×C132−1+411yescharacteristic
252C23×C132−1+411yescharacteristic
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—22no—
265C22×D13—22no—
266C22×D13—22no—
267C22×D13—22no—
268C22×D13—22no—
269C22×D13—22no—
270C22×D13—22no—
271C22×D13—22no—
272C22×D13—22no—
273C22×D13—22no—
274C22×D13—22no—
275C22×D13—22no—
276C22×D13—22no—
277C22×D13—22no—
278C22×D13—22no—
279C22×D13—22no—
280C22×D13—22no—
281C22×D13C2×C4⋊C414yes—
282C22×D13C4×D414yes—
283C22×D13C4×Q814yes—
284C22×D13#12114yes—
285C22×D13C22⋊Q814yes—
286C22×D13#12514yes—
287C22×D13C4⋊Q814yes—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—24no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—42no—
309C2×C4×C13—42no—
310C2×C4×C13—42no—
311C2×C4×C13—42no—
312C2×C4×C13—42no—
313C2×C4×C13—42no—
314C2×C4×C13—42no—
315C2×C4×C13C2×C22⋊C418yes—
316C2×C4×C13C2×C22⋊C414yes—
317C2×C4×C13C2×C4⋊C414yes—
318C2×C4×C13#11714yes—
319C2×C4×C13#12114yes—
320C2×C4×C13#12114yes—
321C2×C4×C13C22⋊Q814yes—
322C2×C4×C13C22⋊Q814yes—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—24no—
330C2×Dic13—24no—
331C2×Dic13—24no—
332C2×Dic13—22no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—22no—
337C2×Dic13—22no—
338C2×Dic13—41no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—41no—
350C2×Dic13—42no—
351C2×Dic13—42no—
352C2×Dic13—42no—
353C2×Dic13—42no—
354C2×Dic13—42no—
355C2×Dic13—42no—
356C2×Dic13—42no—
357C2×Dic13C2×C4⋊C414yes—
358C4×D13—232no—
359C4×D13—432no—
360C24×C4—131no—
361C24×C4—132no—
362C22×C4⋊C4—132no—
363C22×C4⋊C4—131no—
364C22×C4⋊C4—138no—
365C22×C4⋊C4—131no—
366C22×C4⋊C4—132no—
367C22×C4⋊C4—264no—
368C22×C4⋊C4—264no—
369C22×C4⋊C4C2×D1311yescharacteristic
370C22×C4⋊C4C2×D1312yes—
371C22×C4⋊C4C2×D1311yescharacteristic
372C22×C22⋊C4—131no—
373C22×C22⋊C4—131no—
374C22×C22⋊C4—132no—
375C22×C42—131no—
376C22×C42C2×D1311yescharacteristic
377#389—24no—
378#389—264no—
379#380—268no—
380#380—264no—
381C4×C22⋊C4—264no—
382C2×#95—132no—
383C2×#95—132no—
384C2×#95—132no—
385C2×#95—131no—
386C2×#95—131no—
387C2×#95—132no—
388C2×#95—132no—
389C2×#95—132no—
390C2×#95C2×D1312yes—
391C22×C13C22×C22⋊C411yescharacteristic
392C22×C13C22×C4⋊C411yescharacteristic
393C22×C13C2×#11711yescharacteristic
394C22×C13C2×C4×D411yescharacteristic
395C22×C13C2×C4×Q811yescharacteristic
396C22×C13#51811yescharacteristic
397C22×C13#51911yescharacteristic
398C22×C13C2×#12111yescharacteristic
399C22×C13C2×#12111yescharacteristic
400C22×C13C2×#12111yescharacteristic
401C22×C13C2×C22⋊Q811yescharacteristic
402C22×C13C2×C22⋊Q811yescharacteristic
403C22×C13C2×C22⋊Q811yescharacteristic
404C22×C13C2×#12511yescharacteristic
405C22×C13C2×C4⋊Q811yescharacteristic
406C22×C13#53711yescharacteristic
407C22×C13#53711yescharacteristic
408C22×C13#54411yescharacteristic
409C22×C13#54411yescharacteristic
410C22×C13D4211yescharacteristic
411C22×C13D4211yescharacteristic
412C22×C13#54611yescharacteristic
413C22×C13#54611yescharacteristic
414C22×C13#54711yescharacteristic
415C22×C13#54711yescharacteristic
416C22×C13#54811yescharacteristic
417C22×C13#54811yescharacteristic
418C22×C13D4×Q811yescharacteristic
419C22×C13D4×Q811yescharacteristic
420C22×C13#55211yescharacteristic
421C22×C13#55211yescharacteristic
422C22×C13#55311yescharacteristic
423C22×C13#55311yescharacteristic
424C22×C13#55411yescharacteristic
425C22×C13#55411yescharacteristic
426C2×D13—24no—
427C2×D13—24no—
428C2×D13—24no—
429C2×D13—24no—
430C2×D13—24no—
431C2×D13—24no—
432C2×D13—24no—
433C2×D13—24no—
434C2×D13—24no—
435C2×D13—24no—
436C2×D13—24no—
437C2×D13—24no—
438C2×D13—24no—
439C2×D13—24no—
440C2×D13#38918yescomplemented
441C4×C13—28no—
442C4×C13—42no—
443C4×C13—42no—
444C4×C13—82no—
445C4×C13#38018yescomplemented
446Dic13—24no—
447Dic13—44no—
448Dic13—42no—
449Dic13—42no—
450Dic13—82no—
451C25—131no—
452C23×C4—131no—
453C23×C4—134no—
454C23×C4—134no—
455C23×C4—134no—
456C23×C4—131no—
457C23×C4—131no—
458C23×C4—132no—
459C23×C4—138no—
460C23×C4—132no—
461C23×C4—264no—
462C23×C4—264no—
463C23×C4—262no—
464C23×C4—262no—
465C23×C4—262no—
466C23×C4—262no—
467C23×C4—264no—
468C23×C4—264no—
469C23×C4—522no—
470C23×C4—522no—
471C23×C4C22×D1312yes—
472C23×C4C22×D1311yescharacteristic
473C23×C4C22×D1311yescharacteristic
474C23×C4C22×D1312yes—
475C23×C4C22×D1311yescharacteristic
476C2×C4⋊C4—24no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—138no—
483C2×C4⋊C4—134no—
484C2×C4⋊C4—264no—
485C2×C4⋊C4—262no—
486C2×C4⋊C4—264no—
487C2×C4⋊C4—262no—
488C2×C4⋊C4—2632no—
489C2×C4⋊C4—264no—
490C2×C4⋊C4—264no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—262no—
494C2×C4⋊C4—522no—
495C2×C4⋊C4C4×D1314yes—
496C2×C4⋊C4D5214yes—
497C2×C4⋊C4C22⋊D1314yes—
498C2×C22⋊C4—134no—
499C2×C22⋊C4—134no—
500C2×C22⋊C4—262no—
501C2×C22⋊C4—262no—
502C2×C22⋊C4—262no—
503C2×C22⋊C4—262no—
504C2×C22⋊C4—264no—
505C2×C22⋊C4—264no—
506C2×C22⋊C4—264no—
507C2×C42—22no—
508C2×C42—22no—
509C2×C42—22no—
510C2×C42—262no—
511C2×C42—262no—
512C2×C42—262no—
513#95—24no—
514#95—262no—
515#95—262no—
516#95—264no—
517#95—264no—
518#95—264no—
519#95—264no—
520#95—522no—
521#95—522no—
522C2×C13C2×#38011yescharacteristic
523C2×C13C2×#38911yescharacteristic
524C2×C13#231611yescharacteristic
525C2×C13D4×C22⋊C411yescharacteristic
526C2×C13Q8×C22⋊C411yescharacteristic
527C2×C13#234411yescharacteristic
528C2×C13#234511yescharacteristic
529C2×C13#241611yescharacteristic
530C2×C13#241611yescharacteristic
531C2×C13#241711yescharacteristic
532C2×C13#241711yescharacteristic
533C2×C13#244011yescharacteristic
534C2×C13#244011yescharacteristic
535C2×C13#244211yescharacteristic
536C2×C13#244211yescharacteristic
537D13—28no—
538C24—132no—
539C24—132no—
540C24—132no—
541C24—132no—
542C24—132no—
543C24—132no—
544C24—132no—
545C24—261no—
546C24—261no—
547C24—261no—
548C24—261no—
549C24—261no—
550C24—261no—
551C24—261no—
552C24—261no—
553C24C23×D1311yescharacteristic
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—132no—
578C22×C4—132no—
579C22×C4—132no—
580C22×C4—1316no—
581C22×C4—134no—
582C22×C4—132no—
583C22×C4—132no—
584C22×C4—2616no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—268no—
590C22×C4—268no—
591C22×C4—268no—
592C22×C4—268no—
593C22×C4—268no—
594C22×C4—268no—
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—261no—
604C22×C4—261no—
605C22×C4—261no—
606C22×C4—261no—
607C22×C4—261no—
608C22×C4—262no—
609C22×C4—262no—
610C22×C4—261no—
611C22×C4—261no—
612C22×C4—262no—
613C22×C4—2616no—
614C22×C4—262no—
615C22×C4—262no—
616C22×C4—262no—
617C22×C4—262no—
618C22×C4—262no—
619C22×C4—262no—
620C22×C4—262no—
621C22×C4—528no—
622C22×C4—528no—
623C22×C4—528no—
624C22×C4—528no—
625C22×C4—528no—
626C22×C4C2×C4×D1314yes—
627C22×C4C2×C4×D1312yes—
628C22×C4C2×D5214yes—
629C22×C4C2×D5212yes—
630C22×C4D4×D1312yes—
631C22×C4D4×D1312yes—
632C22×C4#612912yes—
633C22×C4Q8×D1312yes—
634C22×C4Q8×D1312yes—
635C22×C4#613112yes—
636C22×C4C2×C22⋊D1314yes—
637C22×C4C2×C22⋊D1312yes—
638C4⋊C4—48no—
639C4⋊C4—44no—
640C4⋊C4—2616no—
641C4⋊C4—268no—
642C4⋊C4—528no—
643C4⋊C4—524no—
644C4⋊C4#6103116yescomplemented
645C22⋊C4—268no—
646C22⋊C4—268no—
647C22⋊C4—528no—
648C42—44no—
649C42—524no—
650C13#1390711yescharacteristic, complemented, Sylow
651C23—134no—
652C23—134no—
653C23—134no—
654C23—134no—
655C23—134no—
656C23—134no—
657C23—134no—
658C23—262no—
659C23—262no—
660C23—262no—
661C23—262no—
662C23—262no—
663C23—262no—
664C23—262no—
665C23—262no—
666C23—262no—
667C23—262no—
668C23—262no—
669C23—262no—
670C23—262no—
671C23—262no—
672C23—262no—
673C23—262no—
674C23—262no—
675C23—262no—
676C23—262no—
677C23—262no—
678C23—262no—
679C23—262no—
680C23—262no—
681C23—262no—
682C23—262no—
683C23—262no—
684C23—262no—
685C23—262no—
686C23C22×C4×D1311yescharacteristic
687C23C22×D5211yescharacteristic
688C23C2×D4×D1311yescharacteristic
689C23C2×D4×D1311yescharacteristic
690C23C2×#612911yescharacteristic
691C23#8825111yescharacteristic
692C23C2×Q8×D1311yescharacteristic
693C23C2×Q8×D1311yescharacteristic
694C23C2×#613111yescharacteristic
695C23#8825411yescharacteristic
696C23#41×D1311yescharacteristic
697C23#41×D1311yescharacteristic
698C23#8825611yescharacteristic
699C23#8825711yescharacteristic
700C23C22×C22⋊D1311yescharacteristic
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—134no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—2632no—
736C2×C4—262no—
737C2×C4—262no—
738C2×C4—264no—
739C2×C4—264no—
740C2×C4—264no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—5232no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—522no—
749C2×C4—522no—
750C2×C4—521no—
751C2×C4—522no—
752C2×C4—522no—
753C2×C4—521no—
754C2×C4—521no—
755C2×C4—521no—
756C2×C4—521no—
757C2×C4—521no—
758C2×C4—522no—
759C2×C4—522no—
760C2×C4—522no—
761C2×C4—522no—
762C2×C4—522no—
763C2×C4—522no—
764C2×C4—522no—
765C2×C4C4⋊C4×D1314yes—
766C2×C4#8814614yes—
767C2×C4#8814914yes—
768C2×C4#8815114yes—
769C2×C4C2×#610318yes—
770C2×C4C2×#610314yes—
771C2×C4#8819214yes—
772C2×C4#8820014yes—
773C22—138no—
774C22—264no—
775C22—264no—
776C22—264no—
777C22—264no—
778C22—264no—
779C22—264no—
780C22—264no—
781C22—264no—
782C22—264no—
783C22—264no—
784C22—264no—
785C22—264no—
786C22—264no—
787C22—264no—
788C22C2×C4⋊C4×D1311yescharacteristic
789C22C2×#8814611yescharacteristic
790C22C2×#8814911yescharacteristic
791C22C2×#8815111yescharacteristic
792C22C4×D4×D1311yescharacteristic
793C22#1171925011yescharacteristic
794C22D4×D5211yescharacteristic
795C22#1171925911yescharacteristic
796C22C4×Q8×D1311yescharacteristic
797C22#1171927711yescharacteristic
798C22Q8×D5211yescharacteristic
799C22#1171928111yescharacteristic
800C22D13×#12111yescharacteristic
801C22#1171931311yescharacteristic
802C22#1171931611yescharacteristic
803C22#1171931911yescharacteristic
804C22D13×C22⋊Q811yescharacteristic
805C22#1171933411yescharacteristic
806C22#1171934011yescharacteristic
807C22#1171934411yescharacteristic
808C22D13×#12511yescharacteristic
809C22#1171939411yescharacteristic
810C22#1171939911yescharacteristic
811C22#1171940011yescharacteristic
812C22D13×C4⋊Q811yescharacteristic
813C22#1171943111yescharacteristic
814C22#1171943411yescharacteristic
815C22#1171943511yescharacteristic
816C22C22×#610311yescharacteristic
817C22C2×#8819211yescharacteristic
818C22D4×C22⋊D1311yescharacteristic
819C22C2×#8820011yescharacteristic
820C22Q8×C22⋊D1311yescharacteristic
821C22#1171953411yescharacteristic
822C22#1171953611yescharacteristic
823C4—28no—
824C4—42no—
825C4—42no—
826C4—82no—
827C4—264no—
828C4—522no—
829C4—522no—
830C4—524no—
831C4—1042no—
832C4#1171864818yescomplemented
833C2—268no—
834C2C2×#1171864811yescharacteristic
835C2D13×#38911yescharacteristic
836C2#1311745111yescharacteristic
837C2D4×#610311yescharacteristic
838C2Q8×#610311yescharacteristic
839C2#1311770411yescharacteristic
840C2#1311771211yescharacteristic
841C2#1311827211yescharacteristic
842C2#1311827411yescharacteristic
843C2#1311828311yescharacteristic
844C2#1311828511yescharacteristic
845C2#1311853411yescharacteristic
846C2#1311853611yescharacteristic
847C2#1311855611yescharacteristic
848C2#1311855811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#13907
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11718646C2semidirect
6. #13113090C2semidirect
7. #13113086C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
11. C2×C13×#389C2semidirect
28. C2×C4⋊C4×D13C4semidirect
214. C2×C4×D13C4⋊C4semidirect
217. C13×C4⋊C4C22⋊C4semidirect
229. C2×#389D13semidirect
440. C2×D13#389semidirect
445. C4×C13#380semidirect
644. C4⋊C4#6103semidirect
650. C13#13907semidirect
832. C4#11718648semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C2×#117186462
C2×#117186482
C2×C4×#61032
#131130902
#131130862
#131130662
#131130652
#131130572
C2×C13×#3892
#1390713