Finite Group Databasebeta

← #15790891

Subgroups — #15790891

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic, complemented
2C2×#11718612C211yesmaximal, characteristic
3C2×#11718611C211yesmaximal, characteristic
4C2×#11718611C211yesmaximal, characteristic
5C2×#11718611C211yesmaximal, characteristic
6C2×#11718596C211yesmaximal, characteristic, complemented
7#13113101C211yesmaximal, characteristic, complemented
8#13113101C211yesmaximal, characteristic, complemented
9#13113093C211yesmaximal, characteristic, complemented
10#13113089C211yesmaximal, characteristic, complemented
11#13113081C211yesmaximal, characteristic
12#13113081C211yesmaximal, characteristic
13#13113070C211yesmaximal, characteristic, complemented
14#13113063C211yesmaximal, characteristic, complemented
15C2×C13×#388C211yesmaximal, characteristic
16C24×Dic13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C22⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C22⋊Dic13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×C4⋊Dic13C2211yescharacteristic
29C22×C4⋊Dic13C2211yescharacteristic
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×C4⋊Dic13C2211yescharacteristic
33C22×C4⋊Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C13×#388C418yescomplemented
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×#88071C2211yescharacteristic
39C2×#88071C2211yescharacteristic
40C2×#88071C2211yescharacteristic
41C2×#88071C2211yescharacteristic
42C2×#88071C2211yescharacteristic
43C2×#88071C2211yescharacteristic
44C2×#88071C2211yescharacteristic
45C2×#88071C2211yescharacteristic
46C2×#88071C2211yescharacteristic
47C2×#88071C2211yescharacteristic
48C2×#88071C2211yescharacteristic
49C2×#88071C2211yescharacteristic
50C2×#88071C2211yescharacteristic
51C2×#88071C2211yescharacteristic
52#11718646—24no—
53#11718612—24no—
54#11718611—24no—
55#11718611—24no—
56#11718611—24no—
57#11718596—24no—
58C25×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—22no—
66C23×Dic13—22no—
67C23×Dic13—22no—
68C23×Dic13—41no—
69C23×Dic13—41no—
70C23×Dic13—41no—
71C23×Dic13—41no—
72C23×Dic13C2311yescharacteristic
73C23×Dic13C2311yescharacteristic
74C23×Dic13C2311yescharacteristic
75C23×Dic13C2311yescharacteristic
76C23×Dic13C2311yescharacteristic
77C23×Dic13C2311yescharacteristic
78C23×Dic13C2311yescharacteristic
79C23×Dic13C2311yescharacteristic
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4C2×C414yescomplemented
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4C2×C414yes—
88C2×C13×C22⋊C4C2×C414yes—
89C2×C13×C22⋊C4C2×C414yes—
90C2×C13×C22⋊C4D414yes—
91C2×C13×C22⋊C4Q814yes—
92C2×C42×C13—22no—
93C2×C42×C13—22no—
94C2×C42×C13C2×C414yescomplemented
95C2×C22⋊Dic13—22no—
96C2×C22⋊Dic13—22no—
97C2×C22⋊Dic13—22no—
98C2×C22⋊Dic13—22no—
99C2×C22⋊Dic13—22no—
100C2×C22⋊Dic13—41no—
101C2×C22⋊Dic13—41no—
102C2×C22⋊Dic13—41no—
103C2×C22⋊Dic13—41no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—22no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—22no—
111C2×C4⋊Dic13—22no—
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—22no—
114C2×C4⋊Dic13—22no—
115C2×C4⋊Dic13—22no—
116C2×C4⋊Dic13—22no—
117C2×C4⋊Dic13—22no—
118C2×C4⋊Dic13—41no—
119C2×C4⋊Dic13—41no—
120C2×C4⋊Dic13—41no—
121C2×C4⋊Dic13—41no—
122C2×C4⋊Dic13—41no—
123C2×C4⋊Dic13—41no—
124C2×C4⋊Dic13—41no—
125C2×C4⋊Dic13—41no—
126C2×C4⋊Dic13—41no—
127C2×C4⋊Dic13—41no—
128C2×C4⋊Dic13—41no—
129C2×C4⋊Dic13—41no—
130C2×C4⋊Dic13D414yes—
131C2×C4×Dic13—22no—
132C2×C4×Dic13—22no—
133C2×C4×Dic13—41no—
134C13×#95C2×C414yescomplemented
135C13×#95C2×C414yescomplemented
136#88071—22no—
137#88071—22no—
138#88071—22no—
139#88071—22no—
140#88071—22no—
141#88071—22no—
142#88071—22no—
143#88071—22no—
144#88071—22no—
145#88071—22no—
146#88071—41no—
147#88071—41no—
148#88071—41no—
149#88071D414yes—
150#14405—131nomaximal, Sylow
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13C22×C412yes—
164C24×C13C2×D412yes—
165C24×C13C2×Q812yes—
166C24×C13C2411yescharacteristic
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
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—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13C22×C412yes—
196C22×C4×C13C22×C412yes—
197C22×C4×C13C22×C412yes—
198C22×C4×C13C22×C412yes—
199C22×C4×C13C22×C412yes—
200C22×C4×C13C22×C412yes—
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13C2×D412yes—
204C22×C4×C13C2×D412yes—
205C22×C4×C13C2×Q812yes—
206C22×C4×C13C2×Q812yes—
207C22×C4×C13#4112yes—
208C22×C4×C13#4112yes—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—21no—
212C22×Dic13—21no—
213C22×Dic13—21no—
214C22×Dic13—21no—
215C22×Dic13—21no—
216C22×Dic13—21no—
217C22×Dic13—21no—
218C22×Dic13—21no—
219C22×Dic13—21no—
220C22×Dic13—21no—
221C22×Dic13—21no—
222C22×Dic13—21no—
223C22×Dic13—21no—
224C22×Dic13—21no—
225C22×Dic13—21no—
226C22×Dic13—21no—
227C22×Dic13—21no—
228C22×Dic13—21no—
229C22×Dic13—21no—
230C22×Dic13—21no—
231C22×Dic13—21no—
232C22×Dic13—21no—
233C22×Dic13—21no—
234C22×Dic13—21no—
235C22×Dic13—21no—
236C22×Dic13—21no—
237C22×Dic13—21no—
238C22×Dic13—21no—
239C22×Dic13—21no—
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—44no—
262C22×Dic13—44no—
263C22×Dic13—44no—
264C22×Dic13—44no—
265C22×Dic13—44no—
266C22×Dic13—44no—
267C22×Dic13—44no—
268C22×Dic13C2×D412yes—
269C22×Dic13C2×D412yes—
270C22×Dic13C2×D412yes—
271C22×Dic13C2×D412yes—
272C13×C4⋊C4—28no—
273C13×C22⋊C4—28no—
274C13×C22⋊C4—28no—
275C13×C22⋊C4C4⋊C4116yescomplemented
276C42×C13—28no—
277C22⋊Dic13—44no—
278C22⋊Dic13—44no—
279C22⋊Dic13—44no—
280C4⋊Dic13—44no—
281C4⋊Dic13—44no—
282C4⋊Dic13—44no—
283C4⋊Dic13—44no—
284C4⋊Dic13—44no—
285C4⋊Dic13—44no—
286C4⋊Dic13—44no—
287C4⋊Dic13—44no—
288C4⋊Dic13—44no—
289C4×Dic13—44no—
290C2×#389—131no—
291C2×#388—131no—
292C2×#388D1311yescharacteristic
293C2×#385—131no—
294C2×#385—131no—
295C2×#385—131no—
296C2×#384—131no—
297#1444—131no—
298#1444—131no—
299#1442—131no—
300#1441—131no—
301#1439—131no—
302#1439—131no—
303#1436—131no—
304#1434—131no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13C2×C4⋊C414yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×Q811yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13H(5,𝔽2)11yescharacteristic
348C23×C13H(5,𝔽2)11yescharacteristic
349C23×C13H(5,𝔽2)11yescharacteristic
350C23×C13H(5,𝔽2)11yescharacteristic
351C23×C132−1+411yescharacteristic
352C23×C132−1+411yescharacteristic
353C23×C132−1+411yescharacteristic
354C23×C132−1+411yescharacteristic
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13C2×C4⋊C414yes—
394C2×C4×C13C2×C4⋊C414yes—
395C2×C4×C13C4×D414yes—
396C2×C4×C13C4×D414yes—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—22no—
402C2×Dic13—22no—
403C2×Dic13—22no—
404C2×Dic13—22no—
405C2×Dic13—22no—
406C2×Dic13—22no—
407C2×Dic13—22no—
408C2×Dic13—22no—
409C2×Dic13—416no—
410C2×Dic13—41no—
411C2×Dic13—41no—
412C2×Dic13—41no—
413C2×Dic13—41no—
414C2×Dic13—41no—
415C2×Dic13—41no—
416C2×Dic13—41no—
417C2×Dic13—41no—
418C2×Dic13—41no—
419C2×Dic13—41no—
420C2×Dic13—41no—
421C2×Dic13—41no—
422C2×Dic13—41no—
423C2×Dic13—41no—
424C2×Dic13—41no—
425C2×Dic13—41no—
426C2×Dic13—41no—
427C2×Dic13—41no—
428C2×Dic13—41no—
429C2×Dic13—41no—
430C2×Dic13—41no—
431C2×Dic13—41no—
432C2×Dic13—41no—
433C2×Dic13—41no—
434C2×Dic13—41no—
435C2×Dic13—41no—
436C2×Dic13—41no—
437C2×Dic13—41no—
438C2×Dic13—41no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13—41no—
445C2×Dic13—41no—
446C2×Dic13—41no—
447C2×Dic13—41no—
448C2×Dic13—41no—
449C2×Dic13—41no—
450C2×Dic13—41no—
451C2×Dic13—41no—
452C2×Dic13—41no—
453C2×Dic13—41no—
454C24×C4—131no—
455C22×C4⋊C4—131no—
456C22×C4⋊C4—131no—
457C22×C4⋊C4—131no—
458C22×C4⋊C4—131no—
459C22×C4⋊C4—131no—
460C22×C4⋊C4—131no—
461C22×C4⋊C4—131no—
462C22×C4⋊C4—131no—
463C22×C4⋊C4—131no—
464C22×C4⋊C4C2×D1311yescharacteristic
465C22×C22⋊C4—131no—
466C22×C22⋊C4—131no—
467C22×C22⋊C4—131no—
468C22×C22⋊C4C2×D1311yescharacteristic
469C22×C22⋊C4C2×D1311yescharacteristic
470C22×C22⋊C4C2×D1311yescharacteristic
471C22×C42—131no—
472C22×C42C2×D1311yescharacteristic
473#389—264no—
474#388—264no—
475#388Dic1318yescomplemented
476#385—264no—
477#385—264no—
478#385—264no—
479#384—264no—
480C2×#95—131no—
481C2×#95—131no—
482C2×#95—131no—
483C2×#95—131no—
484C2×#95—131no—
485C2×#95—131no—
486C2×#95—131no—
487C2×#95—131no—
488C2×#95—131no—
489C2×#95—131no—
490C2×#95—131no—
491C2×#95—131no—
492C2×#95—131no—
493C2×#95—131no—
494C2×#95C2×D1311yescharacteristic
495C2×#95C2×D1311yescharacteristic
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13C22×C4⋊C411yescharacteristic
512C22×C13C2×C4×D411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13#52011yescharacteristic
515C22×C13#52011yescharacteristic
516C22×C13#52011yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13#53411yescharacteristic
519C22×C13#53511yescharacteristic
520C22×C13#53511yescharacteristic
521C22×C13#53611yescharacteristic
522C22×C13#53611yescharacteristic
523C22×C13#53611yescharacteristic
524C22×C13#53911yescharacteristic
525C22×C13#53911yescharacteristic
526C22×C13#54211yescharacteristic
527C22×C13#54211yescharacteristic
528C22×C13#54411yescharacteristic
529C22×C13#54411yescharacteristic
530C22×C13D4211yescharacteristic
531C22×C13D4211yescharacteristic
532C22×C13D4211yescharacteristic
533C22×C13#54711yescharacteristic
534C22×C13#54711yescharacteristic
535C22×C13#54711yescharacteristic
536C22×C13#54811yescharacteristic
537C22×C13D4×Q811yescharacteristic
538C22×C13D4×Q811yescharacteristic
539C22×C13#55311yescharacteristic
540C22×C13#55411yescharacteristic
541C22×C13#55411yescharacteristic
542C22×C13#56011yescharacteristic
543C22×C13#56311yescharacteristic
544C22×C13#56311yescharacteristic
545C22×C13#56311yescharacteristic
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—24no—
549C4×C13—24no—
550C4×C13—42no—
551C4×C13—42no—
552Dic13—42no—
553Dic13—42no—
554Dic13—42no—
555Dic13—42no—
556Dic13—81no—
557Dic13—81no—
558Dic13—81no—
559Dic13—81no—
560C25C22×D1311yescharacteristic
561C23×C4—131no—
562C23×C4—131no—
563C23×C4—131no—
564C23×C4—131no—
565C23×C4—131no—
566C23×C4—131no—
567C23×C4—131no—
568C23×C4—131no—
569C23×C4—262no—
570C23×C4—262no—
571C23×C4—262no—
572C23×C4—521no—
573C23×C4—521no—
574C23×C4—521no—
575C23×C4—521no—
576C23×C4C22×D1311yescharacteristic
577C23×C4C22×D1311yescharacteristic
578C23×C4C22×D1311yescharacteristic
579C23×C4C22×D1311yescharacteristic
580C23×C4C22×D1311yescharacteristic
581C23×C4C22×D1311yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—134no—
585C2×C4⋊C4—262no—
586C2×C4⋊C4—262no—
587C2×C4⋊C4—262no—
588C2×C4⋊C4—262no—
589C2×C4⋊C4—262no—
590C2×C4⋊C4—262no—
591C2×C4⋊C4—262no—
592C2×C4⋊C4—262no—
593C2×C4⋊C4—262no—
594C2×C4⋊C4—262no—
595C2×C4⋊C4—262no—
596C2×C4⋊C4—262no—
597C2×C4⋊C4—262no—
598C2×C4⋊C4—262no—
599C2×C4⋊C4—521no—
600C2×C4⋊C4—521no—
601C2×C4⋊C4—521no—
602C2×C4⋊C4—521no—
603C2×C4⋊C4—521no—
604C2×C4⋊C4—521no—
605C2×C4⋊C4—521no—
606C2×C4⋊C4—521no—
607C2×C4⋊C4—521no—
608C2×C4⋊C4—521no—
609C2×C4⋊C4—521no—
610C2×C4⋊C4—521no—
611C2×C4⋊C4C2×Dic1314yescomplemented
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—262no—
617C2×C22⋊C4—262no—
618C2×C22⋊C4—262no—
619C2×C22⋊C4—262no—
620C2×C22⋊C4—262no—
621C2×C22⋊C4—521no—
622C2×C22⋊C4—521no—
623C2×C22⋊C4—521no—
624C2×C22⋊C4—521no—
625C2×C22⋊C4Dic2614yes—
626C2×C22⋊C4D5214yes—
627C2×C22⋊C4C2×Dic1314yes—
628C2×C22⋊C4C2×Dic1314yes—
629C2×C22⋊C4C2×Dic1314yes—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—262no—
633C2×C42—262no—
634C2×C42—521no—
635C2×C42C2×Dic1314yescomplemented
636#95—134no—
637#95—262no—
638#95—262no—
639#95—262no—
640#95—262no—
641#95—262no—
642#95—262no—
643#95—262no—
644#95—262no—
645#95—262no—
646#95—262no—
647#95—521no—
648#95—521no—
649#95—521no—
650#95C2×Dic1314yescomplemented
651#95C2×Dic1314yescomplemented
652C2×C13—44no—
653C2×C13#231711yescharacteristic
654C2×C13#232211yescharacteristic
655C2×C13#232611yescharacteristic
656C2×C13D4×C4⋊C411yescharacteristic
657C2×C13D4×C4⋊C411yescharacteristic
658C2×C13#236111yescharacteristic
659C2×C13#238311yescharacteristic
660C2×C13#266911yescharacteristic
661C2×C13#267411yescharacteristic
662C2×C13#267711yescharacteristic
663C2×C13#268011yescharacteristic
664C2×C13#271811yescharacteristic
665C2×C13#272011yescharacteristic
666C2×C13#272911yescharacteristic
667C2×C13#279011yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C2×Dic2612yes—
681C24C2×D5212yes—
682C24C22×Dic1312yes—
683C24C23×D1311yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—132no—
713C22×C4—132no—
714C22×C4—132no—
715C22×C4—132no—
716C22×C4—261no—
717C22×C4—261no—
718C22×C4—261no—
719C22×C4—261no—
720C22×C4—261no—
721C22×C4—261no—
722C22×C4—261no—
723C22×C4—261no—
724C22×C4—261no—
725C22×C4—261no—
726C22×C4—261no—
727C22×C4—261no—
728C22×C4—261no—
729C22×C4—261no—
730C22×C4—261no—
731C22×C4—261no—
732C22×C4—261no—
733C22×C4—261no—
734C22×C4—261no—
735C22×C4—261no—
736C22×C4—261no—
737C22×C4—261no—
738C22×C4—261no—
739C22×C4—261no—
740C22×C4—261no—
741C22×C4—261no—
742C22×C4—261no—
743C22×C4—261no—
744C22×C4—261no—
745C22×C4—261no—
746C22×C4—261no—
747C22×C4—261no—
748C22×C4—261no—
749C22×C4—261no—
750C22×C4—261no—
751C22×C4—261no—
752C22×C4—261no—
753C22×C4—261no—
754C22×C4—261no—
755C22×C4—261no—
756C22×C4—261no—
757C22×C4—261no—
758C22×C4—261no—
759C22×C4—261no—
760C22×C4—261no—
761C22×C4—261no—
762C22×C4—261no—
763C22×C4—261no—
764C22×C4—261no—
765C22×C4—261no—
766C22×C4—261no—
767C22×C4—261no—
768C22×C4—524no—
769C22×C4—524no—
770C22×C4—524no—
771C22×C4—524no—
772C22×C4—524no—
773C22×C4—524no—
774C22×C4—524no—
775C22×C4C2×Dic2612yes—
776C22×C4C2×Dic2612yes—
777C22×C4C2×D5212yes—
778C22×C4C2×D5212yes—
779C22×C4D4×D1312yes—
780C22×C4D4×D1312yes—
781C22×C4#612912yes—
782C22×C4#612912yes—
783C22×C4C22×Dic1312yes—
784C22×C4C22×Dic1312yes—
785C22×C4C22×Dic1312yes—
786C22×C4C22×Dic1312yes—
787C22×C4C22×Dic1312yes—
788C22×C4C22×Dic1312yes—
789C4⋊C4—28no—
790C4⋊C4—524no—
791C4⋊C4—524no—
792C4⋊C4—524no—
793C4⋊C4—524no—
794C4⋊C4—524no—
795C4⋊C4—524no—
796C4⋊C4—524no—
797C4⋊C4—524no—
798C4⋊C4—524no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—524no—
802C22⋊C4—524no—
803C22⋊C4—524no—
804C22⋊C4C4⋊Dic13116yescomplemented
805C42—28no—
806C42—524no—
807C13#1440511yescharacteristic, complemented, Sylow
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊Dic1314yes—
843C23C22×Dic2611yescharacteristic
844C23C22×D5211yescharacteristic
845C23C2×D4×D1311yescharacteristic
846C23C2×D4×D1311yescharacteristic
847C23C2×#612911yescharacteristic
848C23C2×#612911yescharacteristic
849C23#8825611yescharacteristic
850C23#8825611yescharacteristic
851C23#8825611yescharacteristic
852C23#8825611yescharacteristic
853C23#8825711yescharacteristic
854C23#8825711yescharacteristic
855C23#8825711yescharacteristic
856C23#8825711yescharacteristic
857C23C23×Dic1311yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—262no—
897C2×C4—262no—
898C2×C4—262no—
899C2×C4—262no—
900C2×C4—262no—
901C2×C4—262no—
902C2×C4—262no—
903C2×C4—262no—
904C2×C4—262no—
905C2×C4—262no—
906C2×C4—262no—
907C2×C4—262no—
908C2×C4—5216no—
909C2×C4—521no—
910C2×C4—521no—
911C2×C4—521no—
912C2×C4—521no—
913C2×C4—521no—
914C2×C4—521no—
915C2×C4—521no—
916C2×C4—521no—
917C2×C4—521no—
918C2×C4—521no—
919C2×C4—521no—
920C2×C4—521no—
921C2×C4—521no—
922C2×C4—521no—
923C2×C4—521no—
924C2×C4—521no—
925C2×C4—521no—
926C2×C4—521no—
927C2×C4—521no—
928C2×C4—521no—
929C2×C4—521no—
930C2×C4—521no—
931C2×C4—521no—
932C2×C4—521no—
933C2×C4—521no—
934C2×C4—521no—
935C2×C4—521no—
936C2×C4—521no—
937C2×C4—521no—
938C2×C4—521no—
939C2×C4—521no—
940C2×C4—521no—
941C2×C4—521no—
942C2×C4—521no—
943C2×C4—521no—
944C2×C4—521no—
945C2×C4—521no—
946C2×C4—521no—
947C2×C4—521no—
948C2×C4—521no—
949C2×C4—521no—
950C2×C4—521no—
951C2×C4—521no—
952C2×C4—521no—
953C2×C4C2×C4⋊Dic1314yes—
954C2×C4C2×C4⋊Dic1314yes—
955C2×C4D4×Dic1314yes—
956C2×C4D4×Dic1314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22#1171922411yescharacteristic
973C22#1171922411yescharacteristic
974C22#1171923011yescharacteristic
975C22#1171923111yescharacteristic
976C22D4×Dic2611yescharacteristic
977C22D4×Dic2611yescharacteristic
978C22#1171924811yescharacteristic
979C22#1171924811yescharacteristic
980C22D4×D5211yescharacteristic
981C22D4×D5211yescharacteristic
982C22#1171926011yescharacteristic
983C22#1171926011yescharacteristic
984C22#1171930311yescharacteristic
985C22#1171931411yescharacteristic
986C22#1171931611yescharacteristic
987C22#1171932311yescharacteristic
988C22#1171935311yescharacteristic
989C22#1171935811yescharacteristic
990C22#1171937011yescharacteristic
991C22#1171937011yescharacteristic
992C22#1171937911yescharacteristic
993C22#1171938011yescharacteristic
994C22#1171938711yescharacteristic
995C22#1171938711yescharacteristic
996C22#1171941611yescharacteristic
997C22#1171941711yescharacteristic
998C22#1171941711yescharacteristic
999C22#1171941711yescharacteristic
1000C22C22×C4⋊Dic1311yescharacteristic
1001C22C2×D4×Dic1311yescharacteristic
1002C22C2×D4×Dic1311yescharacteristic
1003C22#1171953211yescharacteristic
1004C22#1171953211yescharacteristic
1005C22#1171953211yescharacteristic
1006C22#1171953211yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—522no—
1014C4—522no—
1015C4—522no—
1016C4—522no—
1017C4—1041no—
1018C4—1041no—
1019C4—1041no—
1020C4—1041no—
1021C2—44no—
1022C2#1311745911yescharacteristic
1023C2#1311750811yescharacteristic
1024C2#1311754911yescharacteristic
1025C2D4×C4⋊Dic1311yescharacteristic
1026C2D4×C4⋊Dic1311yescharacteristic
1027C2#1311785611yescharacteristic
1028C2#1311802811yescharacteristic
1029C2#1312105111yescharacteristic
1030C2#1312111511yescharacteristic
1031C2#1312114811yescharacteristic
1032C2#1312117411yescharacteristic
1033C2#1312168411yescharacteristic
1034C2#1312171311yescharacteristic
1035C2#1312181911yescharacteristic
1036C2#1312260611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#388C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#388D13
hypocenterC13#14405
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. C2×#11718646C2semidirect
6. C2×#11718596C2semidirect
7. #13113101C2semidirect
8. #13113101C2semidirect
9. #13113093C2semidirect
10. #13113089C2semidirect
13. #13113070C2semidirect
14. #13113063C2semidirect
35. C13×#388C4semidirect
82. C2×C13×C4⋊C4C2×C4semidirect
94. C2×C42×C13C2×C4semidirect
134. C13×#95C2×C4semidirect
135. C13×#95C2×C4semidirect
275. C13×C22⋊C4C4⋊C4semidirect
475. #388Dic13semidirect
611. C2×C4⋊C4C2×Dic13semidirect
635. C2×C42C2×Dic13semidirect
650. #95C2×Dic13semidirect
651. #95C2×Dic13semidirect
804. C22⋊C4C4⋊Dic13semidirect
807. C13#14405semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117186122
C2×#117186112
C2×#117185962
#131131012
#131130932
#131130892
#131130812
#131130702
#131130632
C2×C13×#3882
#1440513