Finite Group Databasebeta

← #15790240

Subgroups — #15790240

Order 3328.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718882C211yesmaximal, characteristic
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718642C211yesmaximal, characteristic, complemented
4C2×#11718873C211yesmaximal, characteristic, complemented
5#13113089C211yesmaximal, characteristic, complemented
6#13113081C211yesmaximal, characteristic, complemented
7#13113081C211yesmaximal, characteristic, complemented
8#13113081C211yesmaximal, characteristic, complemented
9#13113081C211yesmaximal, characteristic, complemented
10#13113077C211yesmaximal, characteristic
11#13113073C211yesmaximal, characteristic, complemented
12#13113073C211yesmaximal, characteristic, complemented
13#13113068C211yesmaximal, characteristic, complemented
14#13113059C211yesmaximal, characteristic, complemented
15C22×C13×#123C211yesmaximal, characteristic
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×#123—24no—
19C2×C13×#123—24no—
20C2×C13×#123C418yescomplemented
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic13C2211yescharacteristic
27C22×C22⋊Dic13C2211yescharacteristic
28C22×C22⋊Dic13C2211yescharacteristic
29C22×C22⋊Dic13C2211yescharacteristic
30C22×C22⋊Dic13C2211yescharacteristic
31C22×C22⋊Dic13C2211yescharacteristic
32C22×C22⋊Dic13C2211yescharacteristic
33C22×C22⋊Dic13C2211yescharacteristic
34C22×C4⋊Dic13C2211yescharacteristic
35C22×C4⋊Dic13C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37C22×C4⋊Dic13C2211yescharacteristic
38C22×C4×Dic13C2211yescharacteristic
39C22×C4×Dic13C2211yescharacteristic
40#11718882—24no—
41#11718873—24no—
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52C2×#88071C2211yescharacteristic
53C2×#88071C2211yescharacteristic
54C2×#88071C2211yescharacteristic
55C2×#88071C2211yescharacteristic
56#11718646—24no—
57#11718642—24no—
58C25×C13C2311yescharacteristic
59C25×C13C2311yescharacteristic
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—41no—
65C22×D4×C13—41no—
66C22×D4×C13C2×C414yes—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—41no—
72C23×C4×C13—41no—
73C23×C4×C13C2×C414yes—
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C13×#123—232no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4C2×C414yes—
91C2×C13×C4⋊C4C2×C414yes—
92C2×C13×C4⋊C4D414yes—
93C2×C13×C4⋊C4D414yes—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4C2×C414yes—
101C2×C13×C22⋊C4C2×C414yes—
102C2×C13×C22⋊C4C2×C414yes—
103C2×C22⋊Dic13—22no—
104C2×C22⋊Dic13—22no—
105C2×C22⋊Dic13—22no—
106C2×C22⋊Dic13—22no—
107C2×C22⋊Dic13—22no—
108C2×C22⋊Dic13—22no—
109C2×C22⋊Dic13—22no—
110C2×C22⋊Dic13—22no—
111C2×C22⋊Dic13—22no—
112C2×C22⋊Dic13—41no—
113C2×C22⋊Dic13—41no—
114C2×C22⋊Dic13—41no—
115C2×C22⋊Dic13—41no—
116C2×C22⋊Dic13—41no—
117C2×C22⋊Dic13—41no—
118C2×C22⋊Dic13—41no—
119C2×C22⋊Dic13—41no—
120C2×C22⋊Dic13—41no—
121C2×C22⋊Dic13—41no—
122C2×C22⋊Dic13—41no—
123C2×C22⋊Dic13—41no—
124C2×C22⋊Dic13—41no—
125C2×C22⋊Dic13—41no—
126C2×C22⋊Dic13D414yes—
127C2×C4⋊Dic13—22no—
128C2×C4⋊Dic13—22no—
129C2×C4⋊Dic13—22no—
130C2×C4⋊Dic13—22no—
131C2×C4⋊Dic13—22no—
132C2×C4⋊Dic13—22no—
133C2×C4⋊Dic13—22no—
134C2×C4⋊Dic13—41no—
135C2×C4⋊Dic13—41no—
136C2×C4⋊Dic13—41no—
137C2×C4⋊Dic13—41no—
138C2×C4⋊Dic13—41no—
139C2×C4×Dic13—22no—
140C2×C4×Dic13—22no—
141C2×C4×Dic13—22no—
142C2×C4×Dic13—41no—
143C2×C4×Dic13—41no—
144C2×C4×Dic13—41no—
145#88071—22no—
146#88071—22no—
147#88071—22no—
148#88071—22no—
149#88071—22no—
150#88071—22no—
151#88071—22no—
152#88071—22no—
153#88071—22no—
154#88071—22no—
155#88071—41no—
156#88071—41no—
157#88071—41no—
158#88071—41no—
159#14360—131nomaximal, Sylow
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13C22×C412yes—
187C24×C13C22×C412yes—
188C24×C13C2×D412yes—
189C24×C13#4112yes—
190C24×C13C2411yescharacteristic
191C2×D4×C13—28no—
192C2×D4×C13—28no—
193C2×D4×C13—44no—
194C2×D4×C13—44no—
195C2×D4×C13—44no—
196C2×D4×C13—44no—
197C2×D4×C13—44no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—28no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—28no—
224C22×C4×C13—44no—
225C22×C4×C13—44no—
226C22×C4×C13—44no—
227C22×C4×C13—44no—
228C22×C4×C13—44no—
229C22×C4×C13C22×C412yes—
230C22×C4×C13C22×C412yes—
231C22×C4×C13C22×C412yes—
232C22×C4×C13C22×C412yes—
233C22×C4×C13C22×C412yes—
234C22×C4×C13C2×D412yes—
235C22×C4×C13C2×D412yes—
236C22×C4×C13C2×D412yes—
237C22×C4×C13C2×D412yes—
238C22×C4×C13C2×D412yes—
239C22×C4×C13C2×D412yes—
240C22×Dic13—21no—
241C22×Dic13—21no—
242C22×Dic13—21no—
243C22×Dic13—21no—
244C22×Dic13—21no—
245C22×Dic13—21no—
246C22×Dic13—21no—
247C22×Dic13—21no—
248C22×Dic13—21no—
249C22×Dic13—21no—
250C22×Dic13—21no—
251C22×Dic13—21no—
252C22×Dic13—21no—
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—21no—
257C22×Dic13—21no—
258C22×Dic13—21no—
259C22×Dic13—21no—
260C22×Dic13—21no—
261C22×Dic13—21no—
262C22×Dic13—21no—
263C22×Dic13—21no—
264C22×Dic13—21no—
265C22×Dic13—21no—
266C22×Dic13—21no—
267C22×Dic13—21no—
268C22×Dic13—21no—
269C22×Dic13—21no—
270C22×Dic13—21no—
271C22×Dic13—21no—
272C22×Dic13—21no—
273C22×Dic13—21no—
274C22×Dic13—21no—
275C22×Dic13—21no—
276C22×Dic13—21no—
277C22×Dic13—21no—
278C22×Dic13—21no—
279C22×Dic13—21no—
280C22×Dic13—21no—
281C22×Dic13—21no—
282C22×Dic13—21no—
283C22×Dic13—21no—
284C22×Dic13—21no—
285C22×Dic13—21no—
286C22×Dic13—21no—
287C22×Dic13—21no—
288C22×Dic13—21no—
289C22×Dic13—21no—
290C22×Dic13—21no—
291C22×Dic13—21no—
292C22×Dic13C2×D412yes—
293C22×Dic13C2×D412yes—
294C22×Dic13#4112yes—
295C22×Dic13#4112yes—
296C13×C4⋊C4—28no—
297C13×C4⋊C4C22⋊C4116yescomplemented
298C13×C22⋊C4—28no—
299C13×C22⋊C4—28no—
300C13×C22⋊C4—28no—
301C22⋊Dic13—44no—
302C22⋊Dic13—44no—
303C22⋊Dic13—44no—
304C22⋊Dic13—44no—
305C22⋊Dic13—44no—
306C22⋊Dic13—44no—
307C22⋊Dic13—44no—
308C22⋊Dic13—44no—
309C4⋊Dic13—44no—
310C4⋊Dic13—44no—
311C4⋊Dic13—44no—
312C4⋊Dic13—44no—
313C4×Dic13—44no—
314C4×Dic13—44no—
315C22×#123D1311yescharacteristic
316C2×#390—131no—
317C2×#389—131no—
318C2×#387—131no—
319C2×#380—131no—
320#1441—131no—
321#1439—131no—
322#1439—131no—
323#1439—131no—
324#1439—131no—
325#1438—131no—
326#1437—131no—
327#1437—131no—
328#1436—131no—
329C22⋊#95—131no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13—22no—
354C23×C13—22no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—41no—
395C23×C13—41no—
396C23×C13—41no—
397C23×C13—41no—
398C23×C13—41no—
399C23×C13C4×D414yes—
400C23×C13C23×C411yescharacteristic
401C23×C13C22×D411yescharacteristic
402C23×C13C22×D411yescharacteristic
403C23×C13C22×D411yescharacteristic
404C23×C13C2×#4111yescharacteristic
405C23×C13C2×#4111yescharacteristic
406C23×C13C2×#4111yescharacteristic
407C23×C13H(5,𝔽2)11yescharacteristic
408C23×C13H(5,𝔽2)11yescharacteristic
409C23×C13H(5,𝔽2)11yescharacteristic
410C23×C13H(5,𝔽2)11yescharacteristic
411C23×C13H(5,𝔽2)11yescharacteristic
412C23×C132−1+411yescharacteristic
413C23×C132−1+411yescharacteristic
414C23×C132−1+411yescharacteristic
415D4×C13—416no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—22no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—416no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13C2×C22⋊C414yes—
450C2×C4×C13C2×C22⋊C414yes—
451C2×C4×C13C2×C22⋊C414yes—
452C2×Dic13—22no—
453C2×Dic13—22no—
454C2×Dic13—22no—
455C2×Dic13—22no—
456C2×Dic13—22no—
457C2×Dic13—22no—
458C2×Dic13—22no—
459C2×Dic13—22no—
460C2×Dic13—22no—
461C2×Dic13—22no—
462C2×Dic13—22no—
463C2×Dic13—22no—
464C2×Dic13—41no—
465C2×Dic13—41no—
466C2×Dic13—41no—
467C2×Dic13—41no—
468C2×Dic13—41no—
469C2×Dic13—41no—
470C2×Dic13—41no—
471C2×Dic13—41no—
472C2×Dic13—41no—
473C2×Dic13—41no—
474C2×Dic13—41no—
475C2×Dic13—41no—
476C2×Dic13—41no—
477C2×Dic13—41no—
478C2×Dic13—41no—
479C2×Dic13—41no—
480C2×Dic13—41no—
481C2×Dic13—41no—
482C2×Dic13—41no—
483C2×Dic13—41no—
484C2×Dic13—41no—
485C2×Dic13—41no—
486C2×Dic13—41no—
487C2×Dic13—41no—
488C2×Dic13—41no—
489C2×Dic13—41no—
490C2×Dic13—41no—
491C2×Dic13—41no—
492C2×Dic13—41no—
493C2×Dic13—41no—
494C2×Dic13—41no—
495C2×Dic13—41no—
496C2×Dic13—41no—
497C2×Dic13—41no—
498C2×Dic13—41no—
499C2×Dic13—41no—
500C2×Dic13—41no—
501C2×Dic13—41no—
502C2×Dic13—41no—
503C2×Dic13—41no—
504C2×Dic13—41no—
505C2×Dic13—41no—
506C2×Dic13—41no—
507C2×Dic13—41no—
508C23×D4C2×D1311yescharacteristic
509C24×C4C2×D1311yescharacteristic
510C2×#123—24no—
511C2×#123—24no—
512C2×#123Dic1318yescomplemented
513C22×C4⋊C4—131no—
514C22×C4⋊C4—131no—
515C22×C4⋊C4—131no—
516C22×C4⋊C4—131no—
517C22×C4⋊C4C2×D1311yescharacteristic
518C22×C4⋊C4C2×D1311yescharacteristic
519C22×C22⋊C4—131no—
520C22×C22⋊C4—131no—
521C22×C22⋊C4—131no—
522C22×C22⋊C4—131no—
523C22×C22⋊C4—131no—
524C22×C22⋊C4—131no—
525C22×C22⋊C4—131no—
526C22×C22⋊C4—131no—
527C22×C22⋊C4C2×D1311yescharacteristic
528C22×C22⋊C4C2×D1311yescharacteristic
529C22×C22⋊C4C2×D1311yescharacteristic
530C22×C42—131no—
531C22×C42—131no—
532#390—264no—
533#389—264no—
534#387—264no—
535#380—264no—
536C2×#95—131no—
537C2×#95—131no—
538C2×#95—131no—
539C2×#95—131no—
540C2×#95—131no—
541C2×#95—131no—
542C2×#95—131no—
543C2×#95—131no—
544C2×#95—131no—
545C2×#95—131no—
546C2×#95—131no—
547C2×#95—131no—
548C2×#95—131no—
549C2×#95—131no—
550C22×C13—24no—
551C22×C13—24no—
552C22×C13—24no—
553C22×C13—42no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—42no—
557C22×C13—42no—
558C22×C13—42no—
559C22×C13—42no—
560C22×C13—42no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—42no—
564C22×C13—42no—
565C22×C13—42no—
566C22×C13—42no—
567C22×C13—42no—
568C22×C13—42no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—42no—
572C22×C13—81no—
573C22×C13—81no—
574C22×C13—81no—
575C22×C13—81no—
576C22×C13—81no—
577C22×C13—81no—
578C22×C13—81no—
579C22×C13—81no—
580C22×C13C22×C22⋊C411yescharacteristic
581C22×C13C2×C4×D411yescharacteristic
582C22×C13C4×#4111yescharacteristic
583C22×C13#51811yescharacteristic
584C22×C13#52011yescharacteristic
585C22×C13#52011yescharacteristic
586C22×C13#52011yescharacteristic
587C22×C13#53411yescharacteristic
588C22×C13#53511yescharacteristic
589C22×C13#53611yescharacteristic
590C22×C13#53611yescharacteristic
591C22×C13#53711yescharacteristic
592C22×C13#53711yescharacteristic
593C22×C13#53811yescharacteristic
594C22×C13#53911yescharacteristic
595C22×C13#53911yescharacteristic
596C22×C13#53911yescharacteristic
597C22×C13#54011yescharacteristic
598C22×C13#54211yescharacteristic
599C22×C13D4211yescharacteristic
600C22×C13D4211yescharacteristic
601C22×C13#54611yescharacteristic
602C22×C13#54611yescharacteristic
603C22×C13#54611yescharacteristic
604C22×C13#54711yescharacteristic
605C22×C13#54811yescharacteristic
606C22×C13#54811yescharacteristic
607C22×C13#55011yescharacteristic
608C22×C13#55011yescharacteristic
609C22×C13#55111yescharacteristic
610C22×C13#55211yescharacteristic
611C22×C13#56011yescharacteristic
612C22×C13#56211yescharacteristic
613C22×C13#56211yescharacteristic
614C22×C13#56311yescharacteristic
615C4×C13—24no—
616C4×C13—24no—
617C4×C13—24no—
618C4×C13—42no—
619C4×C13—42no—
620Dic13—42no—
621Dic13—42no—
622Dic13—42no—
623Dic13—42no—
624Dic13—81no—
625Dic13—81no—
626Dic13—81no—
627Dic13—81no—
628C25C22×D1311yescharacteristic
629C25C22×D1311yescharacteristic
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—22no—
633C22×D4—22no—
634C22×D4—41no—
635C22×D4—41no—
636C22×D4C2×Dic1314yes—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—22no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4—131no—
644C23×C4—131no—
645C23×C4—131no—
646C23×C4—131no—
647C23×C4—131no—
648C23×C4—131no—
649C23×C4—131no—
650C23×C4—131no—
651C23×C4C2×Dic1314yes—
652C23×C4C22×D1311yescharacteristic
653C23×C4C22×D1311yescharacteristic
654C23×C4C22×D1311yescharacteristic
655C23×C4C22×D1311yescharacteristic
656C23×C4C22×D1311yescharacteristic
657#123—232no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—262no—
661C2×C4⋊C4—262no—
662C2×C4⋊C4—262no—
663C2×C4⋊C4—262no—
664C2×C4⋊C4—262no—
665C2×C4⋊C4—262no—
666C2×C4⋊C4—262no—
667C2×C4⋊C4—521no—
668C2×C4⋊C4—521no—
669C2×C4⋊C4—521no—
670C2×C4⋊C4—521no—
671C2×C4⋊C4—521no—
672C2×C4⋊C4C2×Dic1314yes—
673C2×C4⋊C4C2×Dic1314yes—
674C2×C4⋊C4C22⋊D1314yes—
675C2×C4⋊C4C22⋊D1314yes—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—134no—
683C2×C22⋊C4—262no—
684C2×C22⋊C4—262no—
685C2×C22⋊C4—262no—
686C2×C22⋊C4—262no—
687C2×C22⋊C4—262no—
688C2×C22⋊C4—262no—
689C2×C22⋊C4—262no—
690C2×C22⋊C4—262no—
691C2×C22⋊C4—262no—
692C2×C22⋊C4—521no—
693C2×C22⋊C4—521no—
694C2×C22⋊C4—521no—
695C2×C22⋊C4—521no—
696C2×C22⋊C4—521no—
697C2×C22⋊C4—521no—
698C2×C22⋊C4—521no—
699C2×C22⋊C4—521no—
700C2×C22⋊C4—521no—
701C2×C22⋊C4—521no—
702C2×C22⋊C4—521no—
703C2×C22⋊C4—521no—
704C2×C22⋊C4—521no—
705C2×C22⋊C4—521no—
706C2×C22⋊C4C2×Dic1314yes—
707C2×C22⋊C4C2×Dic1314yes—
708C2×C22⋊C4C2×Dic1314yes—
709C2×C42—262no—
710C2×C42—262no—
711C2×C42—262no—
712C2×C42—521no—
713C2×C42—521no—
714C2×C42—521no—
715#95—262no—
716#95—262no—
717#95—262no—
718#95—262no—
719#95—262no—
720#95—262no—
721#95—262no—
722#95—262no—
723#95—262no—
724#95—262no—
725#95—521no—
726#95—521no—
727#95—521no—
728#95—521no—
729C2×C13—44no—
730C2×C13—82no—
731C2×C13#231111yescharacteristic
732C2×C13#232211yescharacteristic
733C2×C13#233511yescharacteristic
734C2×C13D4×C22⋊C411yescharacteristic
735C2×C13#234111yescharacteristic
736C2×C13#235911yescharacteristic
737C2×C13#237611yescharacteristic
738C2×C13#267311yescharacteristic
739C2×C13#267411yescharacteristic
740C2×C13#268111yescharacteristic
741C2×C13#268211yescharacteristic
742C2×C13#269411yescharacteristic
743C2×C13#269611yescharacteristic
744C2×C13#270511yescharacteristic
745C2×C13#270711yescharacteristic
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24D4×D1312yes—
773C24#612912yes—
774C24C22×Dic1312yes—
775C24C22×Dic1312yes—
776C24C23×D1311yescharacteristic
777C2×D4—28no—
778C2×D4—28no—
779C2×D4—44no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—28no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—28no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4—44no—
815C22×C4—132no—
816C22×C4—132no—
817C22×C4—132no—
818C22×C4—132no—
819C22×C4—261no—
820C22×C4—261no—
821C22×C4—261no—
822C22×C4—261no—
823C22×C4—261no—
824C22×C4—261no—
825C22×C4—261no—
826C22×C4—261no—
827C22×C4—261no—
828C22×C4—261no—
829C22×C4—261no—
830C22×C4—261no—
831C22×C4—261no—
832C22×C4—261no—
833C22×C4—261no—
834C22×C4—261no—
835C22×C4—261no—
836C22×C4—261no—
837C22×C4—261no—
838C22×C4—261no—
839C22×C4—261no—
840C22×C4—261no—
841C22×C4—261no—
842C22×C4—261no—
843C22×C4—261no—
844C22×C4—261no—
845C22×C4—261no—
846C22×C4—261no—
847C22×C4—261no—
848C22×C4—261no—
849C22×C4—261no—
850C22×C4—261no—
851C22×C4—261no—
852C22×C4—261no—
853C22×C4—261no—
854C22×C4—261no—
855C22×C4—261no—
856C22×C4—261no—
857C22×C4—261no—
858C22×C4—261no—
859C22×C4—261no—
860C22×C4—261no—
861C22×C4—261no—
862C22×C4—261no—
863C22×C4—261no—
864C22×C4—261no—
865C22×C4—261no—
866C22×C4—261no—
867C22×C4—261no—
868C22×C4—261no—
869C22×C4—261no—
870C22×C4—261no—
871C22×C4C22×Dic1312yes—
872C22×C4C22×Dic1312yes—
873C22×C4C22×Dic1312yes—
874C22×C4C22×Dic1312yes—
875C22×C4C22×Dic1312yes—
876C22×C4C2×C22⋊D1312yes—
877C22×C4C2×C22⋊D1312yes—
878C22×C4C2×C22⋊D1312yes—
879C22×C4C2×C22⋊D1312yes—
880C22×C4C2×C22⋊D1312yes—
881C22×C4C2×C22⋊D1312yes—
882C4⋊C4—28no—
883C4⋊C4—524no—
884C4⋊C4—524no—
885C4⋊C4—524no—
886C4⋊C4—524no—
887C4⋊C4C22⋊Dic13116yescomplemented
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—524no—
892C22⋊C4—524no—
893C22⋊C4—524no—
894C22⋊C4—524no—
895C22⋊C4—524no—
896C22⋊C4—524no—
897C22⋊C4—524no—
898C22⋊C4—524no—
899C42—524no—
900C42—524no—
901C13#1436011yescharacteristic, complemented, Sylow
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23D4×Dic1314yes—
972C23C2×D4×D1311yescharacteristic
973C23C2×#612911yescharacteristic
974C23#8825111yescharacteristic
975C23#8825111yescharacteristic
976C23#41×D1311yescharacteristic
977C23#41×D1311yescharacteristic
978C23#8825611yescharacteristic
979C23#8825611yescharacteristic
980C23#8825611yescharacteristic
981C23#8825711yescharacteristic
982C23#8825711yescharacteristic
983C23#8825711yescharacteristic
984C23C23×Dic1311yescharacteristic
985C23C22×C22⋊D1311yescharacteristic
986C23C22×C22⋊D1311yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—416no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—262no—
1022C2×C4—262no—
1023C2×C4—262no—
1024C2×C4—262no—
1025C2×C4—262no—
1026C2×C4—262no—
1027C2×C4—262no—
1028C2×C4—262no—
1029C2×C4—262no—
1030C2×C4—262no—
1031C2×C4—262no—
1032C2×C4—262no—
1033C2×C4—521no—
1034C2×C4—521no—
1035C2×C4—521no—
1036C2×C4—521no—
1037C2×C4—521no—
1038C2×C4—521no—
1039C2×C4—521no—
1040C2×C4—521no—
1041C2×C4—521no—
1042C2×C4—521no—
1043C2×C4—521no—
1044C2×C4—521no—
1045C2×C4—521no—
1046C2×C4—521no—
1047C2×C4—521no—
1048C2×C4—521no—
1049C2×C4—521no—
1050C2×C4—521no—
1051C2×C4—521no—
1052C2×C4—521no—
1053C2×C4—521no—
1054C2×C4—521no—
1055C2×C4—521no—
1056C2×C4—521no—
1057C2×C4—521no—
1058C2×C4—521no—
1059C2×C4—521no—
1060C2×C4—521no—
1061C2×C4—521no—
1062C2×C4—521no—
1063C2×C4—521no—
1064C2×C4—521no—
1065C2×C4—521no—
1066C2×C4—521no—
1067C2×C4—521no—
1068C2×C4—521no—
1069C2×C4—521no—
1070C2×C4—521no—
1071C2×C4—521no—
1072C2×C4—521no—
1073C2×C4—521no—
1074C2×C4—521no—
1075C2×C4—521no—
1076C2×C4—521no—
1077C2×C4C2×C22⋊Dic1314yes—
1078C2×C4C2×C22⋊Dic1314yes—
1079C2×C4C2×C22⋊Dic1314yes—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22#1171935311yescharacteristic
1111C22#1171935511yescharacteristic
1112C22#1171935611yescharacteristic
1113C22#1171935811yescharacteristic
1114C22#1171935911yescharacteristic
1115C22#1171936011yescharacteristic
1116C22#1171936211yescharacteristic
1117C22#1171936311yescharacteristic
1118C22#1171936511yescharacteristic
1119C22#1171936711yescharacteristic
1120C22#1171936811yescharacteristic
1121C22#1171937011yescharacteristic
1122C22#1171937011yescharacteristic
1123C22#1171937111yescharacteristic
1124C22#1171937211yescharacteristic
1125C22#1171937211yescharacteristic
1126C22C2×D4×Dic1311yescharacteristic
1127C22#1171950311yescharacteristic
1128C22D4×C22⋊D1311yescharacteristic
1129C22D4×C22⋊D1311yescharacteristic
1130C22#1171951111yescharacteristic
1131C22#1171951111yescharacteristic
1132C22#1171953011yescharacteristic
1133C22#41×Dic1311yescharacteristic
1134C22#1171953211yescharacteristic
1135C22#1171953211yescharacteristic
1136C22#1171953211yescharacteristic
1137C22#1171953511yescharacteristic
1138C22#1171953611yescharacteristic
1139C22#1171953611yescharacteristic
1140C22#1171953811yescharacteristic
1141C22#1171953811yescharacteristic
1142C22#1171953911yescharacteristic
1143C22#1171953911yescharacteristic
1144C22C22×C22⋊Dic1311yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—42no—
1149C4—42no—
1150C4—522no—
1151C4—522no—
1152C4—522no—
1153C4—522no—
1154C4—1041no—
1155C4—1041no—
1156C4—1041no—
1157C4—1041no—
1158C2—44no—
1159C2—82no—
1160C2#1311742811yescharacteristic
1161C2#1311750811yescharacteristic
1162C2#1311763011yescharacteristic
1163C2D4×C22⋊Dic1311yescharacteristic
1164C2#1311767711yescharacteristic
1165C2#1311783211yescharacteristic
1166C2#1311798411yescharacteristic
1167C2#1312110211yescharacteristic
1168C2#1312111711yescharacteristic
1169C2#1312118811yescharacteristic
1170C2#1312120111yescharacteristic
1171C2#1312135211yescharacteristic
1172C2#1312138211yescharacteristic
1173C2#1312150511yescharacteristic
1174C2#1312153511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC22×C13×#123C2
socle, cosocleC24×C13C24
prime radicalC23×D4×C13C22
hypercenterC22×#123D13
hypocenterC13#14360
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C2×#11718646C2semidirect
3. C2×#11718642C2semidirect
4. C2×#11718873C2semidirect
5. #13113089C2semidirect
6. #13113081C2semidirect
7. #13113081C2semidirect
8. #13113081C2semidirect
9. #13113081C2semidirect
11. #13113073C2semidirect
12. #13113073C2semidirect
13. #13113068C2semidirect
14. #13113059C2semidirect
20. C2×C13×#123C4semidirect
297. C13×C4⋊C4C22⋊C4semidirect
512. C2×#123Dic13semidirect
887. C4⋊C4C22⋊Dic13semidirect
901. C13#14360semidirect

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×#117186422
C2×#117188732
#131130892
#131130812
#131130772
#131130732
#131130682
#131130592
C22×C13×#1232
#1436013