Finite Group Databasebeta

← #15784519

Subgroups — #15784519

Order 3328.

2390 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718618C211yesmaximal, characteristic
2C2×#11718874C211yesmaximal, characteristic
3C2×#11718617C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic13C211yesmaximal, characteristic, complemented
6C2×#11718327C211yesmaximal, characteristic, complemented
7#13113074C211yesmaximal, characteristic, complemented
8#13113073C211yesmaximal, characteristic, complemented
9#13113073C211yesmaximal, characteristic, complemented
10#13113072C211yesmaximal, characteristic, complemented
11#13113069C211yesmaximal, characteristic, complemented
12#13113067C211yesmaximal, characteristic, complemented
13C4×#88071C211yesmaximal, characteristic, complemented
14#95×Dic13C211yesmaximal, characteristic, complemented
15C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C23×C22⋊D13C2211yescharacteristic
18C23×C4×D13C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C42×C13C2211yescharacteristic
22C22×C42×C13C2211yescharacteristic
23C22×C22⋊Dic13C2211yescharacteristic
24C22×C22⋊Dic13C2211yescharacteristic
25C22×C22⋊Dic13C2211yescharacteristic
26C22×#6103C2211yescharacteristic
27C22×#6103C2211yescharacteristic
28C22×#6103C2211yescharacteristic
29C22×#6103C2211yescharacteristic
30C22×#6103C2211yescharacteristic
31C22×#6101C2211yescharacteristic
32C22×C4×Dic13C2211yescharacteristic
33C22×C4×Dic13C2211yescharacteristic
34C22×C4×Dic13C2211yescharacteristic
35C22×C4×Dic13C2211yescharacteristic
36C22×C4×Dic13C2211yescharacteristic
37C4×C13×C22⋊C4—24no—
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40#11718874C418yescomplemented
41C4×C22⋊Dic13—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
54#11718618C418yescomplemented
55#11718617C418yescomplemented
56C4×#6103—24no—
57#11718327—24no—
58C25×C13C2311yescharacteristic
59C24×D13C2311yescharacteristic
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—41no—
65C23×C4×C13—41no—
66C23×C4×C13C2×C414yescomplemented
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C22×C22⋊D13—41no—
74C22×C22⋊D13—41no—
75C22×C22⋊D13—41no—
76C22×C22⋊D13—41no—
77C22×C22⋊D13C2×C414yes—
78C22×C22⋊D13C2×C414yes—
79C22×C22⋊D13C2×C414yes—
80C23×Dic13C2311yescharacteristic
81C23×Dic13C2311yescharacteristic
82C23×Dic13C2311yescharacteristic
83C23×Dic13C2311yescharacteristic
84C23×Dic13C2311yescharacteristic
85C23×Dic13C2311yescharacteristic
86C23×Dic13C2311yescharacteristic
87C22×C4×D13—22no—
88C22×C4×D13—22no—
89C22×C4×D13—22no—
90C22×C4×D13—22no—
91C22×C4×D13—41no—
92C22×C4×D13—41no—
93C22×C4×D13C2×C414yescomplemented
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4C2×C414yes—
99C2×C13×C22⋊C4C2×C414yescomplemented
100C2×C42×C13—22no—
101C2×C42×C13—22no—
102C2×C42×C13—22no—
103C2×C42×C13—22no—
104C2×C42×C13—41no—
105C2×C42×C13—41no—
106C2×C22⋊Dic13—22no—
107C2×C22⋊Dic13—22no—
108C2×C22⋊Dic13—22no—
109C2×C22⋊Dic13—22no—
110C2×C22⋊Dic13—41no—
111C2×C22⋊Dic13—41no—
112C2×C22⋊Dic13C2×C414yes—
113C2×C22⋊Dic13C2×C414yescomplemented
114C2×C22⋊Dic13C2×C414yescomplemented
115C2×#6103—22no—
116C2×#6103—22no—
117C2×#6103—22no—
118C2×#6103—22no—
119C2×#6103—22no—
120C2×#6103—22no—
121C2×#6103—22no—
122C2×#6103—22no—
123C2×#6103—41no—
124C2×#6103—41no—
125C2×#6103C2×C414yes—
126C2×#6103C2×C414yes—
127C2×#6103C2×C414yescomplemented
128C2×#6103C2×C414yescomplemented
129C2×#6103C2×C414yescomplemented
130C2×#6101—41no—
131C2×#6101—41no—
132C2×#6101C2×C414yescomplemented
133C2×C4×Dic13—22no—
134C2×C4×Dic13—22no—
135C2×C4×Dic13—22no—
136C2×C4×Dic13—22no—
137C2×C4×Dic13—22no—
138C2×C4×Dic13—22no—
139C2×C4×Dic13—22no—
140C2×C4×Dic13—22no—
141C2×C4×Dic13—41no—
142C2×C4×Dic13—41no—
143C2×C4×Dic13—41no—
144C2×C4×Dic13—41no—
145C2×C4×Dic13—41no—
146C2×C4×Dic13—41no—
147C2×C4×Dic13C2×C414yescomplemented
148C13×#95—22no—
149C13×#95D414yescomplemented
150#88071—22no—
151#88071—22no—
152#88071—22no—
153#88071—22no—
154#88071—22no—
155#88071—41no—
156#88071—41no—
157#88071C2×C414yescomplemented
158#88071C2×C414yescomplemented
159#88071C2×C414yescomplemented
160#88071C2×C414yescomplemented
161#88071D414yescomplemented
162#13824—131nomaximal, Sylow
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×C13C22×C412yes—
176C24×C13C22×C412yes—
177C24×C13C22×C412yes—
178C24×C13C2411yescharacteristic
179C23×D13—21no—
180C23×D13—21no—
181C23×D13—21no—
182C23×D13—21no—
183C23×D13—21no—
184C23×D13—21no—
185C23×D13—21no—
186C23×D13—21no—
187C23×D13—21no—
188C23×D13—21no—
189C23×D13—21no—
190C23×D13—21no—
191C23×D13C22×C412yes—
192C23×D13C22×C412yes—
193C23×D13C22×C412yes—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
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—21no—
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—28no—
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×C13C22×C412yes—
235C22×C4×C13C2×D412yes—
236C22×C4×C13C2×D412yes—
237C22×C4×C13C2×D412yes—
238C22×C4×C13C2×D412yes—
239C22×C4×C13#4112yes—
240C22×C4×C13#4112yes—
241C22×C4×C13#4112yes—
242C22×C4×C13#4112yes—
243C2×C22⋊D13—44no—
244C2×C22⋊D13—44no—
245C2×C22⋊D13—44no—
246C2×C22⋊D13—44no—
247C2×C22⋊D13—44no—
248C2×C22⋊D13—44no—
249C2×C22⋊D13C42116yescomplemented
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×Dic13C22×C412yes—
287C22×Dic13C22×C412yes—
288C22×Dic13C22×C412yes—
289C22×Dic13C22×C412yes—
290C22×Dic13C22×C412yes—
291C22×Dic13C22×C412yes—
292C22×Dic13C22×C412yes—
293C22×Dic13C22×C412yes—
294C22×Dic13C22×C412yes—
295C22×Dic13C2×D412yes—
296C22×Dic13C2×D412yes—
297C22×Dic13#4112yes—
298C22×Dic13#4112yes—
299C2×C4×D13—28no—
300C2×C4×D13—28no—
301C2×C4×D13—44no—
302C2×C4×D13—44no—
303C2×C4×D13—44no—
304C2×C4×D13—44no—
305C2×C4×D13—44no—
306C13×C22⋊C4—28no—
307C13×C22⋊C4—28no—
308C42×C13—44no—
309C42×C13—44no—
310C22⋊Dic13—28no—
311C22⋊Dic13—28no—
312C22⋊Dic13—44no—
313#6103—28no—
314#6103—28no—
315#6103—28no—
316#6103—28no—
317#6103—44no—
318#6101—44no—
319C4×Dic13—44no—
320C4×Dic13—44no—
321C4×Dic13—44no—
322C4×Dic13—44no—
323C4×Dic13—44no—
324C2×#390—131no—
325C2×#386—131no—
326C2×#386—131no—
327C2×C4×C22⋊C4—131no—
328C2×C4×C22⋊C4—131no—
329C2×C4×C22⋊C4—131no—
330C2×C4×C22⋊C4D1311yescharacteristic, complemented
331#1437—131no—
332#1437—131no—
333#1437—131no—
334#1437—131no—
335#1436—131no—
336#1436—131no—
337C4×#95—131no—
338C4×#95—131no—
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—22no—
356C23×C13—22no—
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×C13C2×C4214yes—
374C23×C13C23×C411yescharacteristic
375C23×C13C23×C411yescharacteristic
376C23×C13C23×C411yescharacteristic
377C23×C13C22×D411yescharacteristic
378C23×C13C22×D411yescharacteristic
379C23×C13C2×#4111yescharacteristic
380C23×C13C2×#4111yescharacteristic
381C23×C13C2×#4111yescharacteristic
382C23×C13C2×#4111yescharacteristic
383C23×C13C2×#4111yescharacteristic
384C23×C13C2×#4111yescharacteristic
385C23×C13H(5,𝔽2)11yescharacteristic
386C23×C13H(5,𝔽2)11yescharacteristic
387C23×C13H(5,𝔽2)11yescharacteristic
388C23×C13H(5,𝔽2)11yescharacteristic
389C22×D13—22no—
390C22×D13—22no—
391C22×D13—22no—
392C22×D13—22no—
393C22×D13—22no—
394C22×D13—22no—
395C22×D13—22no—
396C22×D13—22no—
397C22×D13—22no—
398C22×D13—22no—
399C22×D13—22no—
400C22×D13—22no—
401C22×D13—22no—
402C22×D13—22no—
403C22×D13—22no—
404C22×D13—22no—
405C22×D13—22no—
406C22×D13—22no—
407C22×D13—41no—
408C22×D13—41no—
409C22×D13—41no—
410C22×D13—41no—
411C22×D13—41no—
412C22×D13—41no—
413C22×D13—41no—
414C22×D13—41no—
415C22×D13—41no—
416C22×D13—41no—
417C22×D13—41no—
418C22×D13—41no—
419C22×D13—41no—
420C22×D13—41no—
421C22×D13—41no—
422C22×D13—41no—
423C22×D13C2×C4214yes—
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—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—22no—
452C2×C4×C13—22no—
453C2×C4×C13—22no—
454C2×C4×C13—416no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13C4×D414yes—
464C2×C4×C13C4×D414yes—
465C2×C4×C13C4×D414yes—
466C2×C4×C13C4×D414yes—
467C22⋊D13—416no—
468C2×Dic13—22no—
469C2×Dic13—22no—
470C2×Dic13—22no—
471C2×Dic13—22no—
472C2×Dic13—22no—
473C2×Dic13—22no—
474C2×Dic13—22no—
475C2×Dic13—22no—
476C2×Dic13—22no—
477C2×Dic13—22no—
478C2×Dic13—22no—
479C2×Dic13—22no—
480C2×Dic13—22no—
481C2×Dic13—22no—
482C2×Dic13—22no—
483C2×Dic13—22no—
484C2×Dic13—22no—
485C2×Dic13—22no—
486C2×Dic13—22no—
487C2×Dic13—22no—
488C2×Dic13—22no—
489C2×Dic13—22no—
490C2×Dic13—22no—
491C2×Dic13—22no—
492C2×Dic13—22no—
493C2×Dic13—22no—
494C2×Dic13—22no—
495C2×Dic13—22no—
496C2×Dic13—22no—
497C2×Dic13—22no—
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—
508C2×Dic13—41no—
509C2×Dic13—41no—
510C2×Dic13—41no—
511C2×Dic13—41no—
512C2×Dic13—41no—
513C2×Dic13—41no—
514C2×Dic13C2×C4214yes—
515C2×Dic13C4×D414yes—
516C2×Dic13C4×D414yes—
517C4×D13—416no—
518C23×D4—131no—
519C24×C4—131no—
520C24×C4C2×D1311yescharacteristic
521C22×C4⋊C4—131no—
522C22×C22⋊C4—131no—
523C22×C22⋊C4—131no—
524C22×C22⋊C4—131no—
525C22×C22⋊C4—131no—
526C22×C22⋊C4—131no—
527C22×C22⋊C4—131no—
528C22×C22⋊C4—131no—
529C22×C22⋊C4—131no—
530C22×C22⋊C4C2×D1311yescharacteristic
531C22×C22⋊C4C2×D1311yescharacteristic
532C22×C42—131no—
533C22×C42—131no—
534C22×C42—131no—
535C22×C42—131no—
536C22×C42—131no—
537C22×C42C2×D1311yescharacteristic
538C22×C42C2×D1311yescharacteristic
539#390—138no—
540#386—138no—
541#386—138no—
542C4×C22⋊C4—24no—
543C4×C22⋊C4—264no—
544C4×C22⋊C4—264no—
545C4×C22⋊C4—264no—
546C2×#95—131no—
547C2×#95—131no—
548C2×#95—131no—
549C2×#95—131no—
550C2×#95—131no—
551C2×#95—131no—
552C2×#95—131no—
553C2×#95—131no—
554C2×#95—131no—
555C2×#95—131no—
556C2×#95—131no—
557C2×#95—131no—
558C2×#95C2×D1311yescharacteristic
559C2×#95C2×D1311yescharacteristic
560C22×C13—24no—
561C22×C13—24no—
562C22×C13—24no—
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—42no—
573C22×C13—42no—
574C22×C13—42no—
575C22×C13C22×C4211yescharacteristic
576C22×C13C2×C4×D411yescharacteristic
577C22×C13C2×C4×D411yescharacteristic
578C22×C13C2×C4×D411yescharacteristic
579C22×C13C2×C4×D411yescharacteristic
580C22×C13C2×C4×D411yescharacteristic
581C22×C13C2×C4×D411yescharacteristic
582C22×C13C4×#4111yescharacteristic
583C22×C13C4×#4111yescharacteristic
584C22×C13C4×#4111yescharacteristic
585C22×C13C4×#4111yescharacteristic
586C22×C13C4×#4111yescharacteristic
587C22×C13C4×#4111yescharacteristic
588C22×C13#51811yescharacteristic
589C22×C13#51811yescharacteristic
590C22×C13#51811yescharacteristic
591C22×C13#51811yescharacteristic
592C22×C13#51811yescharacteristic
593C22×C13#51811yescharacteristic
594C22×C13D4211yescharacteristic
595C22×C13#54611yescharacteristic
596C22×C13#54611yescharacteristic
597C22×C13#54611yescharacteristic
598C22×C13#54611yescharacteristic
599C22×C13#55011yescharacteristic
600C22×C13#55011yescharacteristic
601C22×C13#55111yescharacteristic
602C22×C13#55111yescharacteristic
603C22×C13#55311yescharacteristic
604C22×C13#55311yescharacteristic
605C22×C13#55311yescharacteristic
606C22×C13#55311yescharacteristic
607C22×C13#55511yescharacteristic
608C22×C13#55511yescharacteristic
609C22×C13#55911yescharacteristic
610C2×D13—24no—
611C2×D13—24no—
612C2×D13—24no—
613C2×D13—42no—
614C2×D13—42no—
615C2×D13—42no—
616C2×D13—42no—
617C2×D13—42no—
618C2×D13—42no—
619C2×D13—42no—
620C2×D13—42no—
621C2×D13—42no—
622C2×D13—42no—
623C2×D13—42no—
624C2×D13—42no—
625C4×C13—24no—
626C4×C13—24no—
627C4×C13—24no—
628C4×C13—24no—
629C4×C13—42no—
630C4×C13—42no—
631Dic13—24no—
632Dic13—24no—
633Dic13—24no—
634Dic13—42no—
635Dic13—42no—
636Dic13—42no—
637Dic13—42no—
638C25—131no—
639C25C22×D1311yescharacteristic
640C22×D4—134no—
641C22×D4—134no—
642C22×D4—134no—
643C22×D4—521no—
644C22×D4—521no—
645C22×D4—521no—
646C22×D4—521no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—22no—
650C23×C4—22no—
651C23×C4—41no—
652C23×C4—41no—
653C23×C4—131no—
654C23×C4—131no—
655C23×C4—131no—
656C23×C4—131no—
657C23×C4—131no—
658C23×C4—131no—
659C23×C4—131no—
660C23×C4—134no—
661C23×C4—262no—
662C23×C4—262no—
663C23×C4—262no—
664C23×C4—262no—
665C23×C4—521no—
666C23×C4—521no—
667C23×C4C4×D1314yescomplemented
668C23×C4C22×D1311yescharacteristic
669C23×C4C22×D1311yescharacteristic
670C23×C4C22×D1311yescharacteristic
671C23×C4C22×D1311yescharacteristic
672C23×C4C22×D1311yescharacteristic
673C23×C4C22×D1311yescharacteristic
674C2×C4⋊C4—134no—
675C2×C4⋊C4—521no—
676C2×C4⋊C4—521no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—134no—
682C2×C22⋊C4—134no—
683C2×C22⋊C4—134no—
684C2×C22⋊C4—134no—
685C2×C22⋊C4—134no—
686C2×C22⋊C4—134no—
687C2×C22⋊C4—134no—
688C2×C22⋊C4—134no—
689C2×C22⋊C4—262no—
690C2×C22⋊C4—262no—
691C2×C22⋊C4—262no—
692C2×C22⋊C4—262no—
693C2×C22⋊C4—262no—
694C2×C22⋊C4—262no—
695C2×C22⋊C4—262no—
696C2×C22⋊C4—262no—
697C2×C22⋊C4—262no—
698C2×C22⋊C4—262no—
699C2×C22⋊C4—262no—
700C2×C22⋊C4—262no—
701C2×C22⋊C4—521no—
702C2×C22⋊C4—521no—
703C2×C22⋊C4—521no—
704C2×C22⋊C4—521no—
705C2×C22⋊C4C4×D1314yes—
706C2×C22⋊C4C4×D1314yescomplemented
707C2×C42—22no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—22no—
711C2×C42—41no—
712C2×C42—41no—
713C2×C42—134no—
714C2×C42—262no—
715C2×C42—262no—
716C2×C42—262no—
717C2×C42—262no—
718C2×C42—262no—
719C2×C42—262no—
720C2×C42—262no—
721C2×C42—262no—
722C2×C42—521no—
723C2×C42—521no—
724C2×C42—521no—
725C2×C42—521no—
726C2×C42—521no—
727C2×C42—521no—
728#95—22no—
729#95—134no—
730#95—134no—
731#95—134no—
732#95—134no—
733#95—134no—
734#95—262no—
735#95—262no—
736#95—262no—
737#95—262no—
738#95—262no—
739#95—521no—
740#95—521no—
741#95C22⋊D1314yescomplemented
742C2×C13—44no—
743C2×C13C42×D411yescharacteristic
744C2×C13C42×D411yescharacteristic
745C2×C13#227311yescharacteristic
746C2×C13#235811yescharacteristic
747C2×C13#235811yescharacteristic
748C2×C13#236311yescharacteristic
749C2×C13#236311yescharacteristic
750C2×C13#236311yescharacteristic
751C2×C13#236311yescharacteristic
752C2×C13#236411yescharacteristic
753C2×C13#236411yescharacteristic
754C2×C13#236611yescharacteristic
755C2×C13#237211yescharacteristic
756C2×C13#237411yescharacteristic
757C2×C13#237411yescharacteristic
758D13—44no—
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—132no—
772C24—132no—
773C24—132no—
774C24—261no—
775C24—261no—
776C24—261no—
777C24—261no—
778C24—261no—
779C24—261no—
780C24—261no—
781C24—261no—
782C24—261no—
783C24—261no—
784C24—261no—
785C24—261no—
786C24C2×C4×D1312yes—
787C24C2×C4×D1312yes—
788C24C2×C4×D1312yes—
789C24C23×D1311yescharacteristic
790C2×D4—1316no—
791C2×D4—524no—
792C2×D4—524no—
793C2×D4—524no—
794C2×D4—524no—
795C2×D4—524no—
796C2×D4—524no—
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—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—28no—
826C22×C4—28no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—132no—
833C22×C4—132no—
834C22×C4—132no—
835C22×C4—132no—
836C22×C4—132no—
837C22×C4—132no—
838C22×C4—132no—
839C22×C4—132no—
840C22×C4—132no—
841C22×C4—132no—
842C22×C4—132no—
843C22×C4—132no—
844C22×C4—132no—
845C22×C4—268no—
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×C4—261no—
872C22×C4—261no—
873C22×C4—261no—
874C22×C4—261no—
875C22×C4—261no—
876C22×C4—261no—
877C22×C4—261no—
878C22×C4—261no—
879C22×C4—261no—
880C22×C4—261no—
881C22×C4—261no—
882C22×C4—268no—
883C22×C4—524no—
884C22×C4—524no—
885C22×C4—524no—
886C22×C4—524no—
887C22×C4—524no—
888C22×C4C2×C4×D1312yes—
889C22×C4C2×C4×D1312yes—
890C22×C4C2×C4×D1312yes—
891C22×C4C2×C4×D1312yes—
892C22×C4C2×C4×D1312yes—
893C22×C4C2×C4×D1312yes—
894C22×C4#612712yes—
895C22×C4#612712yes—
896C22×C4#612712yes—
897C22×C4D4×D1312yes—
898C22×C4#612912yes—
899C22×C4C2×C22⋊D1312yes—
900C22×C4C2×C22⋊D1312yes—
901C22×C4C2×C22⋊D1312yes—
902C4⋊C4—524no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—268no—
906C22⋊C4—268no—
907C22⋊C4—268no—
908C22⋊C4—268no—
909C22⋊C4—268no—
910C22⋊C4—268no—
911C22⋊C4—524no—
912C22⋊C4—524no—
913C42—44no—
914C42—44no—
915C42—524no—
916C42—524no—
917C42—524no—
918C42—524no—
919C42—524no—
920C13#1382411yescharacteristic, complemented, Sylow
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
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—134no—
956C23—262no—
957C23—262no—
958C23—262no—
959C23—262no—
960C23—262no—
961C23—262no—
962C23—262no—
963C23—262no—
964C23—262no—
965C23—262no—
966C23—262no—
967C23—262no—
968C23—262no—
969C23—262no—
970C23—262no—
971C23—262no—
972C23—262no—
973C23—262no—
974C23—521no—
975C23—521no—
976C23—521no—
977C23—521no—
978C23—521no—
979C23—521no—
980C23—521no—
981C23—521no—
982C23—521no—
983C23—521no—
984C23—521no—
985C23—521no—
986C23—521no—
987C23—521no—
988C23—521no—
989C23—521no—
990C23C42×D1314yes—
991C23C22×C4×D1311yescharacteristic
992C23C22×C4×D1311yescharacteristic
993C23C22×C4×D1311yescharacteristic
994C23C2×#612711yescharacteristic
995C23C2×#612711yescharacteristic
996C23C2×#612711yescharacteristic
997C23C2×D4×D1311yescharacteristic
998C23C2×#612911yescharacteristic
999C23#8825111yescharacteristic
1000C23#8825111yescharacteristic
1001C23#41×D1311yescharacteristic
1002C23#41×D1311yescharacteristic
1003C23#8825611yescharacteristic
1004C23#8825611yescharacteristic
1005C23C22×C22⋊D1311yescharacteristic
1006D4—5216no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—416no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—134no—
1047C2×C4—134no—
1048C2×C4—134no—
1049C2×C4—262no—
1050C2×C4—262no—
1051C2×C4—262no—
1052C2×C4—262no—
1053C2×C4—262no—
1054C2×C4—262no—
1055C2×C4—262no—
1056C2×C4—262no—
1057C2×C4—262no—
1058C2×C4—262no—
1059C2×C4—262no—
1060C2×C4—262no—
1061C2×C4—262no—
1062C2×C4—262no—
1063C2×C4—262no—
1064C2×C4—262no—
1065C2×C4—262no—
1066C2×C4—262no—
1067C2×C4—262no—
1068C2×C4—262no—
1069C2×C4—262no—
1070C2×C4—262no—
1071C2×C4—262no—
1072C2×C4—262no—
1073C2×C4—262no—
1074C2×C4—262no—
1075C2×C4—262no—
1076C2×C4—262no—
1077C2×C4—262no—
1078C2×C4—262no—
1079C2×C4—5216no—
1080C2×C4—521no—
1081C2×C4—521no—
1082C2×C4—521no—
1083C2×C4—521no—
1084C2×C4—521no—
1085C2×C4—521no—
1086C2×C4—521no—
1087C2×C4—521no—
1088C2×C4—521no—
1089C2×C4—521no—
1090C2×C4—521no—
1091C2×C4—521no—
1092C2×C4—521no—
1093C2×C4—521no—
1094C2×C4—521no—
1095C2×C4—521no—
1096C2×C4#8813514yes—
1097C2×C4C4×C22⋊D1314yes—
1098C2×C4C4×C22⋊D1314yes—
1099C2×C4C4×C22⋊D1314yes—
1100C22—24no—
1101C22—24no—
1102C22—24no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—264no—
1116C22—264no—
1117C22—264no—
1118C22—522no—
1119C22—522no—
1120C22—522no—
1121C22—522no—
1122C22—522no—
1123C22—522no—
1124C22—522no—
1125C22—522no—
1126C22—522no—
1127C22—522no—
1128C22—522no—
1129C22—522no—
1130C22C2×C42×D1311yescharacteristic
1131C22C4×#612711yescharacteristic
1132C22C4×#612711yescharacteristic
1133C22C4×#612711yescharacteristic
1134C22C2×#8813511yescharacteristic
1135C22#1171919111yescharacteristic
1136C22#1171919511yescharacteristic
1137C22#1171920011yescharacteristic
1138C22#1171922611yescharacteristic
1139C22#1171922711yescharacteristic
1140C22#1171923511yescharacteristic
1141C22#1171923711yescharacteristic
1142C22C4×#612911yescharacteristic
1143C22C4×#612911yescharacteristic
1144C22#1171924511yescharacteristic
1145C22C4×D4×D1311yescharacteristic
1146C22C4×D4×D1311yescharacteristic
1147C22#1171925011yescharacteristic
1148C22#1171925011yescharacteristic
1149C22#1171925011yescharacteristic
1150C22#1171925011yescharacteristic
1151C22#1171925511yescharacteristic
1152C22#1171925811yescharacteristic
1153C22#1171926111yescharacteristic
1154C22#1171926311yescharacteristic
1155C22#1171926411yescharacteristic
1156C22#1171926811yescharacteristic
1157C22#1171927011yescharacteristic
1158C22C2×C4×C22⋊D1311yescharacteristic
1159C22C2×C4×C22⋊D1311yescharacteristic
1160C22C2×C4×C22⋊D1311yescharacteristic
1161C22D4×C22⋊D1311yescharacteristic
1162C22#1171951111yescharacteristic
1163C22#1171953411yescharacteristic
1164C22#1171953911yescharacteristic
1165C4—24no—
1166C4—24no—
1167C4—24no—
1168C4—24no—
1169C4—42no—
1170C4—42no—
1171C4—264no—
1172C4—264no—
1173C4—264no—
1174C4—522no—
1175C4—522no—
1176C4—522no—
1177C4—522no—
1178C2—44no—
1179C2—524no—
1180C2C4×#8813511yescharacteristic
1181C2C42×C22⋊D1311yescharacteristic
1182C2#1311718811yescharacteristic
1183C2#1311781311yescharacteristic
1184C2#1311781511yescharacteristic
1185C2#1311787011yescharacteristic
1186C2#1311787211yescharacteristic
1187C2#1311787411yescharacteristic
1188C2#1311787511yescharacteristic
1189C2#1311788111yescharacteristic
1190C2#1311788711yescharacteristic
1191C2#1311789811yescharacteristic
1192C2#1311794411yescharacteristic
1193C2#1311796711yescharacteristic
1194C2#1311797011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC22×C13C22×C42
FittingC2×C4×C13×C22⋊C4C2
socle, cosocleC24×C13C24
prime radicalC23×C22⋊D13C22
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#13824
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×C4×#6103C2semidirect
5. C2×C4×C22⋊Dic13C2semidirect
6. C2×#11718327C2semidirect
7. #13113074C2semidirect
8. #13113073C2semidirect
9. #13113073C2semidirect
10. #13113072C2semidirect
11. #13113069C2semidirect
12. #13113067C2semidirect
13. C4×#88071C2semidirect
14. #95×Dic13C2semidirect
15. C2×C4×C13×C22⋊C4C2semidirect
40. #11718874C4semidirect
54. #11718618C4semidirect
55. #11718617C4semidirect
66. C23×C4×C13C2×C4semidirect
93. C22×C4×D13C2×C4semidirect
99. C2×C13×C22⋊C4C2×C4semidirect
113. C2×C22⋊Dic13C2×C4semidirect
114. C2×C22⋊Dic13C2×C4semidirect
127. C2×#6103C2×C4semidirect
128. C2×#6103C2×C4semidirect
129. C2×#6103C2×C4semidirect
132. C2×#6101C2×C4semidirect
147. C2×C4×Dic13C2×C4semidirect
149. C13×#95D4semidirect
157. #88071C2×C4semidirect
158. #88071C2×C4semidirect
159. #88071C2×C4semidirect
160. #88071C2×C4semidirect
161. #88071D4semidirect
249. C2×C22⋊D13C42semidirect
330. C2×C4×C22⋊C4D13semidirect
667. C23×C4C4×D13semidirect
706. C2×C22⋊C4C4×D13semidirect
741. #95C22⋊D13semidirect
920. C13#13824semidirect

Maximal subgroups

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

subgroupindex
C2×#117186182
C2×#117188742
C2×#117186172
C2×C4×#61032
C2×C4×C22⋊Dic132
C2×#117183272
#131130742
#131130732
#131130722
#131130692
#131130672
C4×#880712
#95×Dic132
C2×C4×C13×C22⋊C42
#1382413