Finite Group Databasebeta

← #15786066

Subgroups — #15786066

Order 3328.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718882C211yesmaximal, characteristic, complemented
2C2×#11718882C212yesmaximal, complemented
3C2×#11718882C211yesmaximal, characteristic, complemented
4C2×#11718646C211yesmaximal, characteristic, complemented
5C2×#11718873C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
8#13113081C212yesmaximal, complemented
9#13113077C212yesmaximal, complemented
10#13113073C212yesmaximal, complemented
11C22×C13×#121C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C23×D4×C13C2212yes—
14C24×C4×C13C2211yescharacteristic
15C2×C13×#121—24no—
16C2×C13×#121—24no—
17C2×C13×#121C418yescomplemented
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×C22⋊Dic13C2211yescharacteristic
22C22×C22⋊Dic13C2212yes—
23C22×C22⋊Dic13C2212yes—
24C22×C22⋊Dic13C2212yes—
25C22×C22⋊Dic13C2211yescharacteristic
26C22×C22⋊Dic13C2212yes—
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2212yes—
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4×Dic13C2211yescharacteristic
31C22×C4×Dic13C2212yes—
32C22×C4×Dic13C2211yescharacteristic
33#11718882—28no—
34#11718882—24no—
35#11718882—24no—
36#11718873—24no—
37C4×C22⋊Dic13—24no—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2212yes—
43#11718646—24no—
44C4⋊C4×Dic13—24no—
45C25×C13C2312yes—
46C25×C13C2311yescharacteristic
47C22×D4×C13—24no—
48C22×D4×C13—24no—
49C22×D4×C13—24no—
50C22×D4×C13—24no—
51C22×D4×C13—22no—
52C22×D4×C13—22no—
53C22×D4×C13—22no—
54C22×D4×C13—22no—
55C22×D4×C13—22no—
56C22×D4×C13—22no—
57C22×D4×C13—42no—
58C22×D4×C13—42no—
59C22×D4×C13C2×C414yes—
60C22×D4×C13C2×C418yes—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13C2×C414yes—
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2312yes—
70C23×C4×C13C2311yescharacteristic
71C23×Dic13C2312yes—
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2312yes—
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C13×#121—232no—
78C2×C13×C4⋊C4C2×C414yes—
79C2×C13×C4⋊C4D414yes—
80C2×C13×C4⋊C4D414yes—
81C2×C13×C22⋊C4—24no—
82C2×C13×C22⋊C4—24no—
83C2×C13×C22⋊C4C2×C418yes—
84C2×C22⋊Dic13—22no—
85C2×C22⋊Dic13—22no—
86C2×C22⋊Dic13—22no—
87C2×C22⋊Dic13—22no—
88C2×C22⋊Dic13—22no—
89C2×C22⋊Dic13—24no—
90C2×C22⋊Dic13—24no—
91C2×C22⋊Dic13—24no—
92C2×C22⋊Dic13—24no—
93C2×C22⋊Dic13—24no—
94C2×C22⋊Dic13—24no—
95C2×C22⋊Dic13—24no—
96C2×C22⋊Dic13—24no—
97C2×C22⋊Dic13—24no—
98C2×C22⋊Dic13—24no—
99C2×C22⋊Dic13—42no—
100C2×C22⋊Dic13—42no—
101C2×C22⋊Dic13—42no—
102C2×C22⋊Dic13—42no—
103C2×C22⋊Dic13—42no—
104C2×C22⋊Dic13D414yescomplemented
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—24no—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—24no—
112C2×C4⋊Dic13—42no—
113C2×C4⋊Dic13D414yescomplemented
114C2×C4×Dic13—22no—
115C2×C4×Dic13—22no—
116C2×C4×Dic13—22no—
117C2×C4×Dic13—22no—
118C2×C4×Dic13—24no—
119C2×C4×Dic13—22no—
120C2×C4×Dic13—24no—
121C2×C4×Dic13—42no—
122C2×C4×Dic13D414yescomplemented
123#88071—24no—
124#88071—24no—
125#88071—22no—
126#88071—22no—
127#88071—24no—
128#13998—131nomaximal, Sylow
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—22no—
142C24×C13—22no—
143C24×C13—22no—
144C24×C13—22no—
145C24×C13—22no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
150C24×C13—22no—
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13C22×C414yes—
156C24×C13C22×C412yes—
157C24×C13C2×D412yes—
158C24×C13#4112yes—
159C24×C13C2411yescharacteristic
160C2×D4×C13—216no—
161C2×D4×C13—216no—
162C2×D4×C13—28no—
163C2×D4×C13—28no—
164C2×D4×C13—28no—
165C2×D4×C13—48no—
166C2×D4×C13—48no—
167C2×D4×C13—48no—
168C2×D4×C13—48no—
169C2×D4×C13—48no—
170C2×D4×C13—44no—
171C2×D4×C13—44no—
172C2×D4×C13—44no—
173C2×D4×C13—44no—
174C22×C4×C13—22no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—28no—
185C22×C4×C13—28no—
186C22×C4×C13—28no—
187C22×C4×C13—44no—
188C22×C4×C13—44no—
189C22×C4×C13—44no—
190C22×C4×C13—44no—
191C22×C4×C13C22×C412yes—
192C22×C4×C13C22×C414yes—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C2×D412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D414yes—
197C22×C4×C13C2×D414yes—
198C22×C4×C13C2×D412yes—
199C22×C4×C13C2×D412yes—
200C22×C4×C13#4112yes—
201C22×C4×C13#4112yes—
202C22×Dic13—21no—
203C22×Dic13—21no—
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—21no—
207C22×Dic13—21no—
208C22×Dic13—22no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—22no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—22no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—22no—
222C22×Dic13—22no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—22no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—22no—
231C22×Dic13—22no—
232C22×Dic13—22no—
233C22×Dic13—22no—
234C22×Dic13—22no—
235C22×Dic13—22no—
236C22×Dic13—22no—
237C22×Dic13C2×D412yes—
238C22×Dic13C2×D414yes—
239C22×Dic13C2×D412yes—
240C22×Dic13C2×D412yes—
241C22×Dic13C2×D412yes—
242C22×Dic13#4112yes—
243C22×Dic13#4112yes—
244C13×C4⋊C4C22⋊C4116yescomplemented
245C13×C22⋊C4—216no—
246C22⋊Dic13—28no—
247C22⋊Dic13—28no—
248C22⋊Dic13—48no—
249C22⋊Dic13—48no—
250C22⋊Dic13—48no—
251C22⋊Dic13—48no—
252C22⋊Dic13—48no—
253C4⋊Dic13—28no—
254C4⋊Dic13—48no—
255C4⋊Dic13—44no—
256C4×Dic13—28no—
257C4×Dic13—48no—
258C4×Dic13—44no—
259C22×#121D1311yescharacteristic
260C2×#390—132no—
261C2×#390—131no—
262C2×#390—131no—
263C2×#389—131no—
264C2×#380—131no—
265C2×C4×C4⋊C4—131no—
266C2×C4×C22⋊C4—131no—
267#1439—132no—
268#1438—132no—
269#1437—132no—
270C23×C13—22no—
271C23×C13—22no—
272C23×C13—22no—
273C23×C13—22no—
274C23×C13—22no—
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—24no—
289C23×C13—24no—
290C23×C13—24no—
291C23×C13—24no—
292C23×C13—24no—
293C23×C13—24no—
294C23×C13—24no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—42no—
312C23×C13—42no—
313C23×C13—42no—
314C23×C13—42no—
315C23×C13—42no—
316C23×C13—42no—
317C23×C13—42no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13—42no—
321C23×C13—42no—
322C23×C13—42no—
323C23×C13—42no—
324C23×C13—42no—
325C23×C13—42no—
326C23×C13—42no—
327C23×C13—42no—
328C23×C13—42no—
329C23×C13—42no—
330C23×C13—42no—
331C23×C13—42no—
332C23×C13—42no—
333C23×C13—42no—
334C23×C13—42no—
335C23×C13—42no—
336C23×C13—42no—
337C23×C13—42no—
338C23×C13—42no—
339C23×C13C4×D414yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×D411yescharacteristic
345C23×C13C22×D411yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13C2×#4111yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13H(5,𝔽2)11yescharacteristic
352C23×C13H(5,𝔽2)11yescharacteristic
353C23×C13H(5,𝔽2)11yescharacteristic
354C23×C132−1+411yescharacteristic
355D4×C13—432no—
356D4×C13—416no—
357C2×C4×C13—24no—
358C2×C4×C13—24no—
359C2×C4×C13—24no—
360C2×C4×C13—24no—
361C2×C4×C13—24no—
362C2×C4×C13—24no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—416no—
371C2×C4×C13C2×C22⋊C418yes—
372C2×C4×C13C2×C22⋊C414yes—
373C2×C4×C13C4×D414yes—
374C2×C4×C13C4×D414yes—
375C2×C4×C13#12114yes—
376C2×C4×C13#12114yes—
377C2×C4×C13#12414yes—
378C2×C4×C13#12714yes—
379C2×Dic13—22no—
380C2×Dic13—22no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—22no—
384C2×Dic13—22no—
385C2×Dic13—22no—
386C2×Dic13—24no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389C2×Dic13—22no—
390C2×Dic13—22no—
391C2×Dic13—22no—
392C2×Dic13—24no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—24no—
396C2×Dic13—22no—
397C2×Dic13—41no—
398C2×Dic13—41no—
399C2×Dic13—42no—
400C2×Dic13—41no—
401C2×Dic13—41no—
402C2×Dic13—42no—
403C2×Dic13—42no—
404C2×Dic13—41no—
405C2×Dic13—41no—
406C2×Dic13—41no—
407C2×Dic13—41no—
408C2×Dic13—42no—
409C2×Dic13—41no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—42no—
414C2×Dic13—42no—
415C2×Dic13—42no—
416C2×Dic13—42no—
417C2×Dic13—42no—
418C2×Dic13—42no—
419C2×Dic13—42no—
420C2×Dic13#12114yescomplemented
421C23×D4C2×D1311yescharacteristic
422C23×D4C2×D1312yes—
423C24×C4C2×D1311yescharacteristic
424C2×#121—24no—
425C2×#121—24no—
426C2×#121Dic1318yescomplemented
427C22×C4⋊C4—131no—
428C22×C4⋊C4—131no—
429C22×C4⋊C4—132no—
430C22×C4⋊C4C2×D1311yescharacteristic
431C22×C22⋊C4—131no—
432C22×C22⋊C4—132no—
433C22×C22⋊C4—131no—
434C22×C22⋊C4—132no—
435C22×C22⋊C4—132no—
436C22×C22⋊C4—132no—
437C22×C22⋊C4—132no—
438C22×C22⋊C4C2×D1312yes—
439C22×C42—131no—
440C22×C42—131no—
441C22×C42—132no—
442#390—264no—
443#390—268no—
444#390—264no—
445#389—264no—
446#380—264no—
447C4×C4⋊C4—264no—
448C4×C22⋊C4—264no—
449C2×#95—131no—
450C2×#95—132no—
451C2×#95—132no—
452C2×#95—132no—
453C2×#95—131no—
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—42no—
458C22×C13—42no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—44no—
470C22×C13—44no—
471C22×C13—44no—
472C22×C13—44no—
473C22×C13—44no—
474C22×C13—44no—
475C22×C13—44no—
476C22×C13—82no—
477C22×C13—82no—
478C22×C13—82no—
479C22×C13—82no—
480C22×C13—82no—
481C22×C13—82no—
482C22×C13—82no—
483C22×C13—82no—
484C22×C13C22×C22⋊C411yescharacteristic
485C22×C13C2×C4×D411yescharacteristic
486C22×C13C2×C4×D411yescharacteristic
487C22×C13C2×C4×D411yescharacteristic
488C22×C13C4×#4111yescharacteristic
489C22×C13#51811yescharacteristic
490C22×C13#52011yescharacteristic
491C22×C13C2×#12111yescharacteristic
492C22×C13C2×#12111yescharacteristic
493C22×C13C2×#12111yescharacteristic
494C22×C13#52511yescharacteristic
495C22×C13C2×#12411yescharacteristic
496C22×C13#52911yescharacteristic
497C22×C13C2×#12711yescharacteristic
498C22×C13#53211yescharacteristic
499C22×C13#53511yescharacteristic
500C22×C13#53711yescharacteristic
501C22×C13#54011yescharacteristic
502C22×C13#54211yescharacteristic
503C22×C13D4211yescharacteristic
504C22×C13D4211yescharacteristic
505C22×C13D4211yescharacteristic
506C22×C13#54611yescharacteristic
507C22×C13#54611yescharacteristic
508C22×C13#54611yescharacteristic
509C22×C13#54711yescharacteristic
510C22×C13#54811yescharacteristic
511C22×C13#54811yescharacteristic
512C22×C13#54811yescharacteristic
513C22×C13#55011yescharacteristic
514C22×C13#55011yescharacteristic
515C22×C13#55011yescharacteristic
516C22×C13#55311yescharacteristic
517C22×C13#55311yescharacteristic
518C22×C13#55511yescharacteristic
519C4×C13—28no—
520C4×C13—42no—
521C4×C13#39018yescomplemented
522Dic13—24no—
523Dic13—42no—
524Dic13—44no—
525Dic13—42no—
526Dic13—42no—
527Dic13—82no—
528C25C22×D1312yes—
529C25C22×D1311yescharacteristic
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4C2×Dic1314yes—
543C22×D4C2×Dic1318yes—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—131no—
551C23×C4—131no—
552C23×C4—132no—
553C23×C4—131no—
554C23×C4—131no—
555C23×C4—132no—
556C23×C4C2×Dic1314yes—
557C23×C4C22×D1311yescharacteristic
558C23×C4C22×D1312yes—
559C23×C4C22×D1311yescharacteristic
560#121—232no—
561C2×C4⋊C4—134no—
562C2×C4⋊C4—262no—
563C2×C4⋊C4—262no—
564C2×C4⋊C4—264no—
565C2×C4⋊C4—262no—
566C2×C4⋊C4—262no—
567C2×C4⋊C4—264no—
568C2×C4⋊C4—262no—
569C2×C4⋊C4—522no—
570C2×C4⋊C4C2×Dic1314yes—
571C2×C4⋊C4C22⋊D1314yes—
572C2×C4⋊C4C22⋊D1314yes—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—134no—
576C2×C22⋊C4—262no—
577C2×C22⋊C4—262no—
578C2×C22⋊C4—262no—
579C2×C22⋊C4—262no—
580C2×C22⋊C4—262no—
581C2×C22⋊C4—264no—
582C2×C22⋊C4—264no—
583C2×C22⋊C4—264no—
584C2×C22⋊C4—264no—
585C2×C22⋊C4—264no—
586C2×C22⋊C4—264no—
587C2×C22⋊C4—264no—
588C2×C22⋊C4—264no—
589C2×C22⋊C4—264no—
590C2×C22⋊C4—264no—
591C2×C22⋊C4—522no—
592C2×C22⋊C4—522no—
593C2×C22⋊C4—522no—
594C2×C22⋊C4—522no—
595C2×C22⋊C4—522no—
596C2×C22⋊C4C2×Dic1318yes—
597C2×C42—134no—
598C2×C42—262no—
599C2×C42—262no—
600C2×C42—264no—
601C2×C42—262no—
602C2×C42—262no—
603C2×C42—264no—
604C2×C42—262no—
605C2×C42—522no—
606#95—262no—
607#95—262no—
608#95—264no—
609#95—264no—
610#95—264no—
611C2×C13—44no—
612C2×C13—84no—
613C2×C13C2×#39011yescharacteristic
614C2×C13C4×#12111yescharacteristic
615C2×C13#232411yescharacteristic
616C2×C13D4×C22⋊C411yescharacteristic
617C2×C13#234111yescharacteristic
618C2×C13#236111yescharacteristic
619C2×C13#236311yescharacteristic
620C2×C13#241411yescharacteristic
621C2×C13#241611yescharacteristic
622C2×C13#242611yescharacteristic
623C2×C13#242811yescharacteristic
624C2×C13#249011yescharacteristic
625C2×C13#249111yescharacteristic
626C2×C13#254011yescharacteristic
627C2×C13#254111yescharacteristic
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24D4×D1312yes—
655C24#612912yes—
656C24C22×Dic1314yes—
657C24C22×Dic1312yes—
658C24C23×D1311yescharacteristic
659C2×D4—216no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—216no—
663C2×D4—28no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—132no—
691C22×C4—132no—
692C22×C4—132no—
693C22×C4—132no—
694C22×C4—134no—
695C22×C4—132no—
696C22×C4—132no—
697C22×C4—261no—
698C22×C4—261no—
699C22×C4—261no—
700C22×C4—261no—
701C22×C4—261no—
702C22×C4—261no—
703C22×C4—262no—
704C22×C4—261no—
705C22×C4—261no—
706C22×C4—261no—
707C22×C4—261no—
708C22×C4—261no—
709C22×C4—262no—
710C22×C4—262no—
711C22×C4—261no—
712C22×C4—261no—
713C22×C4—261no—
714C22×C4—261no—
715C22×C4—261no—
716C22×C4—262no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—262no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—262no—
724C22×C4—261no—
725C22×C4—262no—
726C22×C4—262no—
727C22×C4—262no—
728C22×C4—262no—
729C22×C4—262no—
730C22×C4—262no—
731C22×C4—262no—
732C22×C4D4×D1312yes—
733C22×C4D4×D1312yes—
734C22×C4#612912yes—
735C22×C4#612912yes—
736C22×C4C22×Dic1312yes—
737C22×C4C22×Dic1314yes—
738C22×C4C22×Dic1312yes—
739C22×C4C2×C22⋊D1314yes—
740C22×C4C2×C22⋊D1314yes—
741C22×C4C2×C22⋊D1312yes—
742C22×C4C2×C22⋊D1312yes—
743C4⋊C4—268no—
744C4⋊C4—528no—
745C4⋊C4—524no—
746C4⋊C4C22⋊Dic13116yescomplemented
747C22⋊C4—216no—
748C22⋊C4—268no—
749C22⋊C4—268no—
750C22⋊C4—528no—
751C22⋊C4—528no—
752C22⋊C4—528no—
753C22⋊C4—528no—
754C22⋊C4—528no—
755C42—268no—
756C42—528no—
757C42—524no—
758C13#1399811yescharacteristic, complemented, Sylow
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23D4×Dic1314yes—
829C23C2×D4×D1311yescharacteristic
830C23C2×D4×D1311yescharacteristic
831C23C2×D4×D1311yescharacteristic
832C23C2×#612911yescharacteristic
833C23C2×#612911yescharacteristic
834C23C2×#612911yescharacteristic
835C23#8825111yescharacteristic
836C23#8825111yescharacteristic
837C23#41×D1311yescharacteristic
838C23#41×D1311yescharacteristic
839C23#8825611yescharacteristic
840C23#8825711yescharacteristic
841C23C23×Dic1311yescharacteristic
842C23C22×C22⋊D1311yescharacteristic
843C23C22×C22⋊D1311yescharacteristic
844D4—432no—
845D4—416no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—416no—
860C2×C4—134no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—262no—
867C2×C4—262no—
868C2×C4—264no—
869C2×C4—262no—
870C2×C4—262no—
871C2×C4—262no—
872C2×C4—262no—
873C2×C4—262no—
874C2×C4—262no—
875C2×C4—262no—
876C2×C4—264no—
877C2×C4—262no—
878C2×C4—264no—
879C2×C4—522no—
880C2×C4—521no—
881C2×C4—521no—
882C2×C4—521no—
883C2×C4—521no—
884C2×C4—521no—
885C2×C4—521no—
886C2×C4—522no—
887C2×C4—522no—
888C2×C4—521no—
889C2×C4—521no—
890C2×C4—521no—
891C2×C4—521no—
892C2×C4—521no—
893C2×C4—521no—
894C2×C4—522no—
895C2×C4—522no—
896C2×C4—522no—
897C2×C4—522no—
898C2×C4—522no—
899C2×C4—522no—
900C2×C4—522no—
901C2×C4—522no—
902C2×C4D4×Dic1314yes—
903C2×C4D4×Dic1314yes—
904C2×C4#8819014yes—
905C2×C4#8819214yes—
906C2×C4#8819214yes—
907C2×C4#8819414yes—
908C2×C4C2×C22⋊Dic1318yes—
909C2×C4C2×C22⋊Dic1314yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22#1171930111yescharacteristic
941C22#1171930311yescharacteristic
942C22#1171930411yescharacteristic
943C22#1171930511yescharacteristic
944C22#1171930811yescharacteristic
945C22D13×#12111yescharacteristic
946C22#1171931111yescharacteristic
947C22#1171931211yescharacteristic
948C22#1171931311yescharacteristic
949C22#1171931411yescharacteristic
950C22#1171931611yescharacteristic
951C22#1171931711yescharacteristic
952C22#1171931911yescharacteristic
953C22#1171932111yescharacteristic
954C22#1171932311yescharacteristic
955C22#1171932411yescharacteristic
956C22C2×D4×Dic1311yescharacteristic
957C22C2×D4×Dic1311yescharacteristic
958C22C2×D4×Dic1311yescharacteristic
959C22C2×#8819011yescharacteristic
960C22#1171950311yescharacteristic
961C22C2×#8819211yescharacteristic
962C22C2×#8819211yescharacteristic
963C22D4×C22⋊D1311yescharacteristic
964C22D4×C22⋊D1311yescharacteristic
965C22C2×#8819411yescharacteristic
966C22#1171951111yescharacteristic
967C22#1171951111yescharacteristic
968C22#41×Dic1311yescharacteristic
969C22#1171953211yescharacteristic
970C22#1171953611yescharacteristic
971C22#1171953611yescharacteristic
972C22#1171953911yescharacteristic
973C22#1171953911yescharacteristic
974C22C22×C22⋊Dic1311yescharacteristic
975C4—28no—
976C4—42no—
977C4—264no—
978C4—522no—
979C4—522no—
980C4—522no—
981C4—524no—
982C4—1042no—
983C4#1171888218yescomplemented
984C2—44no—
985C2—84no—
986C2C2×#1171888211yescharacteristic
987C2#121×Dic1311yescharacteristic
988C2#1311753111yescharacteristic
989C2D4×C22⋊Dic1311yescharacteristic
990C2#1311767711yescharacteristic
991C2#1311785611yescharacteristic
992C2#1311787811yescharacteristic
993C2#1311825011yescharacteristic
994C2#1311827211yescharacteristic
995C2#1311839811yescharacteristic
996C2#1311842011yescharacteristic
997C2#1311919011yescharacteristic
998C2#1311920111yescharacteristic
999C2#1311977211yescharacteristic
1000C2#1311977911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
Fitting, prime radicalC22×C13×#121C2
socle, cosocleC24×C13C24
hypercenterC22×#121D13
hypocenterC13#13998
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11718882C2semidirect
2. C2×#11718882C2semidirect
3. C2×#11718882C2semidirect
4. C2×#11718646C2semidirect
5. C2×#11718873C2semidirect
6. C2×C4⋊C4×Dic13C2semidirect
7. C2×C4×C22⋊Dic13C2semidirect
8. #13113081C2semidirect
9. #13113077C2semidirect
10. #13113073C2semidirect
17. C2×C13×#121C4semidirect
104. C2×C22⋊Dic13D4semidirect
113. C2×C4⋊Dic13D4semidirect
122. C2×C4×Dic13D4semidirect
244. C13×C4⋊C4C22⋊C4semidirect
420. C2×Dic13#121semidirect
426. C2×#121Dic13semidirect
521. C4×C13#390semidirect
746. C4⋊C4C22⋊Dic13semidirect
758. C13#13998semidirect
983. C4#11718882semidirect

Maximal subgroups

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

subgroupindex
C2×#117188822
C2×#117186462
C2×#117188732
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
#131130812
#131130772
#131130732
C22×C13×#1212
#1399813