Finite Group Databasebeta

← #15828794

Subgroups — #15828794

Order 3328.

1738 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D13C211yesmaximal, characteristic
2C2×#11718868C211yesmaximal, characteristic, complemented
3#13113172C214yesmaximal, complemented
4#13113165C212yesmaximal, complemented
5#13113162C212yesmaximal, complemented
6#13113152C214yesmaximal, complemented
7C2×C13×#407C211yesmaximal, characteristic, complemented
8C24×C4×C13C2211yescharacteristic
9C23×C22⋊D13C411yescharacteristic
10C23×C4×D13C411yescharacteristic
11C22×C13×M16—21no—
12C22×C22⋊Dic13C411yescharacteristic
13C2×C4×C22⋊D13—21no—
14C2×C4×C22⋊D13—21no—
15C2×C4×C22⋊D13—21no—
16C2×C4×C22⋊D13—21no—
17C2×C4×C22⋊D13—21no—
18C2×C4×C22⋊D13—21no—
19C2×C4×C22⋊D13—21no—
20C2×C4×C22⋊D13—21no—
21C2×C4×C22⋊D13C412yes—
22C2×C4×C22⋊D13C412yes—
23C2×C4×C22⋊D13C2212yes—
24C2×C4×C22⋊D13C2212yes—
25C22×#6103C2211yescharacteristic
26C22×#6101C2211yescharacteristic
27C22×C4×Dic13C411yescharacteristic
28C22×#6099—21no—
29C13×#407—21no—
30C13×#407—21no—
31C13×#407C2212yes—
32C13×#407C2212yescomplemented
33C2×C13×C22⋊C8—21no—
34C2×C13×C22⋊C8C2212yescomplemented
35#11718868—21no—
36#11718868—21no—
37#11718868C2212yes—
38#11718868C2212yescomplemented
39C2×C22⋊#1055—21no—
40C2×C22⋊#1055C2212yescomplemented
41#11718061C2218yescomplemented
42#11718060C2218yescomplemented
43C25×C13C2×C411yescharacteristic
44C24×D13C2×C411yescharacteristic
45C23×C4×C13—44no—
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13D411yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C22×C22⋊D13—21no—
62C22×C22⋊D13—21no—
63C22×C22⋊D13—21no—
64C22×C22⋊D13—28no—
65C22×C22⋊D13C2×C412yes—
66C22×C22⋊D13C2×C412yes—
67C23×Dic13C2×C411yescharacteristic
68C23×Dic13C2×C411yescharacteristic
69C23×Dic13C2×C411yescharacteristic
70C22×C4×D13—21no—
71C22×C4×D13—21no—
72C22×C4×D13—21no—
73C22×C4×D13—21no—
74C22×C4×D13—44no—
75C22×C4×D13C2×C412yes—
76C22×C4×D13C2×C412yes—
77C2×C13×M16—22no—
78C2×C13×M16—22no—
79C2×C13×M16—44no—
80C22×C8×C13—22no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13C2×C412yes—
86C2×C22⋊Dic13C2×C412yes—
87C4×C22⋊D13—22no—
88C4×C22⋊D13—22no—
89C4×C22⋊D13—22no—
90C4×C22⋊D13—22no—
91C4×C22⋊D13—22no—
92C4×C22⋊D13—22no—
93C4×C22⋊D13—22no—
94C4×C22⋊D13—22no—
95C4×C22⋊D13—22no—
96C4×C22⋊D13—22no—
97C4×C22⋊D13—22no—
98C4×C22⋊D13—22no—
99C4×C22⋊D13—22no—
100C4×C22⋊D13—22no—
101C4×C22⋊D13—22no—
102C4×C22⋊D13—22no—
103C2×#6103—21no—
104C2×#6103—21no—
105C2×#6103—21no—
106C2×#6103—21no—
107C2×#6103C2×C412yes—
108C2×#6103C2312yes—
109C2×#6101—21no—
110C2×#6101—21no—
111C2×#6101—21no—
112C2×#6101—21no—
113C2×#6101C2×C412yes—
114C2×#6101C2312yes—
115C2×C4×Dic13—21no—
116C2×C4×Dic13—21no—
117C2×C4×Dic13—21no—
118C2×C4×Dic13—21no—
119C2×C4×Dic13C2×C412yes—
120C2×C4×Dic13C2×C412yes—
121C2×#6099—22no—
122C2×#6099—22no—
123C2×#6099—44no—
124C22×#1055—22no—
125C13×C22⋊C8—22no—
126C13×C22⋊C8—22no—
127C13×C22⋊C8—22no—
128C13×C22⋊C8C2314yes—
129C22⋊#1055—22no—
130C22⋊#1055—22no—
131C22⋊#1055—22no—
132C22⋊#1055C2314yes—
133#17362—131nomaximal, Sylow
134C24×C13—24no—
135C24×C13—42no—
136C24×C13—42no—
137C24×C13C22⋊C411yescharacteristic
138C24×C13C22⋊C411yescharacteristic
139C24×C13C22⋊C411yescharacteristic
140C24×C13C22⋊C411yescharacteristic
141C24×C13C22×C411yescharacteristic
142C24×C13C22×C411yescharacteristic
143C24×C13C22×C411yescharacteristic
144C23×D13—21no—
145C23×D13—21no—
146C23×D13—24no—
147C23×D13—42no—
148C23×D13—42no—
149C23×D13C22×C412yes—
150C22×C4×C13—24no—
151C22×C4×C13—24no—
152C22×C4×C13—24no—
153C22×C4×C13—42no—
154C22×C4×C13—42no—
155C22×C4×C13—42no—
156C22×C4×C13—42no—
157C22×C4×C13—42no—
158C22×C4×C13—42no—
159C22×C4×C13—42no—
160C22×C4×C13—42no—
161C22×C4×C13—42no—
162C22×C4×C13—42no—
163C22×C4×C13—42no—
164C22×C4×C13C22⋊C411yescharacteristic
165C22×C4×C13C22⋊C411yescharacteristic
166C22×C4×C13C22⋊C411yescharacteristic
167C22×C4×C13C22⋊C411yescharacteristic
168C22×C4×C13C22⋊C411yescharacteristic
169C22×C4×C13C22⋊C411yescharacteristic
170C22×C4×C13C22⋊C411yescharacteristic
171C22×C4×C13C22⋊C411yescharacteristic
172C22×C4×C13C22⋊C411yescharacteristic
173C22×C4×C13C22⋊C411yescharacteristic
174C22×C4×C13C22⋊C411yescharacteristic
175C22×C4×C13C22⋊C411yescharacteristic
176C22×C4×C13C22×C411yescharacteristic
177C22×C4×C13C22×C411yescharacteristic
178C22×C4×C13C22×C411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2×D411yescharacteristic
191C22×C4×C13C2411yescharacteristic
192C2×C22⋊D13—28no—
193C2×C22⋊D13—28no—
194C2×C22⋊D13—28no—
195C2×C22⋊D13—28no—
196C2×C22⋊D13—22no—
197C2×C22⋊D13—22no—
198C2×C22⋊D13—22no—
199C2×C22⋊D13—22no—
200C2×C22⋊D13—24no—
201C2×C22⋊D13—24no—
202C2×C22⋊D13—24no—
203C2×C22⋊D13M1618yescomplemented
204C22×Dic13—21no—
205C22×Dic13—21no—
206C22×Dic13—24no—
207C22×Dic13—21no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210C22×Dic13—21no—
211C22×Dic13—42no—
212C22×Dic13—42no—
213C22×Dic13C22×C412yes—
214C22×Dic13C22×C412yes—
215C22×Dic13C22×C412yes—
216C2×C4×D13—22no—
217C2×C4×D13—22no—
218C2×C4×D13—22no—
219C2×C4×D13—22no—
220C2×C4×D13—44no—
221C2×C4×D13—44no—
222C2×C4×D13—44no—
223C2×C4×D13—44no—
224C2×C4×D13—44no—
225C2×C4×D13—44no—
226C13×M16—44no—
227C13×M16—44no—
228C2×C8×C13—24no—
229C2×C8×C13—44no—
230C22⋊Dic13—22no—
231C22⋊Dic13—22no—
232C22⋊Dic13—22no—
233C22⋊Dic13—22no—
234#6103—22no—
235#6103—22no—
236#6103—22no—
237#6103—22no—
238#6101—22no—
239#6101—22no—
240#6101—22no—
241#6101—22no—
242C4×Dic13—22no—
243C4×Dic13—22no—
244C4×Dic13—22no—
245C4×Dic13—22no—
246#6099—44no—
247#6099—44no—
248C2×#1055—24no—
249C2×#1055—44no—
250C22×C4×D4—131no—
251C2×#407—131no—
252C2×#407D1311yescharacteristic, complemented
253#1465—134no—
254#1463—132no—
255#1462—132no—
256#1459—134no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—22no—
268C23×C13—22no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13—416no—
278C23×C13C2×C22⋊C411yescharacteristic
279C23×C13C2×C22⋊C411yescharacteristic
280C23×C13C2×C22⋊C411yescharacteristic
281C23×C13C2×C22⋊C411yescharacteristic
282C23×C13C2×C22⋊C411yescharacteristic
283C23×C13C2×C22⋊C411yescharacteristic
284C23×C13C2×M1614yes—
285C23×C13C23×C411yescharacteristic
286C22×D13—24no—
287C22×D13—24no—
288C22×D13—22no—
289C22×D13—22no—
290C22×D13—42no—
291C22×D13—416no—
292C22×D13—42no—
293C22×D13—42no—
294C22×D13—42no—
295C22×D13—42no—
296C22×D13—42no—
297C22×D13C2×M1614yescomplemented
298C2×C4×C13—22no—
299C2×C4×C13—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
305C2×C4×C13—22no—
306C2×C4×C13—22no—
307C2×C4×C13—22no—
308C2×C4×C13—22no—
309C2×C4×C13—22no—
310C2×C4×C13—22no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13#9914yes—
326C2×C4×C13C2×C22⋊C411yescharacteristic
327C2×C4×C13C2×C22⋊C411yescharacteristic
328C2×C4×C13C2×C22⋊C411yescharacteristic
329C2×C4×C13C2×C22⋊C411yescharacteristic
330C2×C4×C13C2×C22⋊C411yescharacteristic
331C2×C4×C13C2×C22⋊C411yescharacteristic
332C2×C4×C13C22×D411yescharacteristic
333C2×C4×C13C22×D411yescharacteristic
334C22⋊D13—28no—
335C22⋊D13—28no—
336C22⋊D13—28no—
337C22⋊D13—28no—
338C2×Dic13—24no—
339C2×Dic13—24no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—42no—
348C2×Dic13—42no—
349C2×Dic13—42no—
350C2×Dic13C2×M1614yescomplemented
351C4×D13—44no—
352C4×D13—44no—
353C4×D13—44no—
354C4×D13—44no—
355C8×C13—44no—
356#1055—44no—
357C23×D4—131no—
358C24×C4—131no—
359C24×C4C2×D1311yescharacteristic
360C22×M16—21no—
361C22×M16—261no—
362C2×C4×D4—132no—
363C2×C4×D4—132no—
364C2×C4×D4—132no—
365C2×C4×D4—132no—
366C2×C4×D4—261no—
367C2×C4×D4—261no—
368C2×C4×D4—261no—
369C2×C4×D4—261no—
370C2×C4×D4—261no—
371C2×C4×D4—261no—
372C2×C4×D4—261no—
373C2×C4×D4—261no—
374C22×C4⋊C4—131no—
375C22×C22⋊C4—131no—
376C22×C22⋊C4—131no—
377C22×C42—131no—
378#407—21no—
379#407—21no—
380#407—132no—
381#407—132no—
382#407—261no—
383#407—261no—
384#407C2×D1312yes—
385#407C2×D1312yescomplemented
386C2×C22⋊C8—21no—
387C2×C22⋊C8—132no—
388C2×C22⋊C8—261no—
389C2×C22⋊C8C2×D1312yescomplemented
390#324—138no—
391#323—138no—
392C22×C13—28no—
393C22×C13—21no—
394C22×C13—21no—
395C22×C13—21no—
396C22×C13—21no—
397C22×C13—21no—
398C22×C13—21no—
399C22×C13—21no—
400C22×C13—21no—
401C22×C13—21no—
402C22×C13—21no—
403C22×C13—21no—
404C22×C13—21no—
405C22×C13—21no—
406C22×C13—21no—
407C22×C13—21no—
408C22×C13—21no—
409C22×C13—44no—
410C22×C13—44no—
411C22×C13—44no—
412C22×C13—44no—
413C22×C13—44no—
414C22×C13—44no—
415C22×C13#40712yes—
416C22×C13#40712yes—
417C22×C13C2×#9912yes—
418C22×C13#41312yes—
419C22×C13C22×C22⋊C411yescharacteristic
420C22×C13C22×M1612yes—
421C2×D13—24no—
422C2×D13—44no—
423C2×D13—48no—
424C2×D13—48no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—44no—
428C4×C13—21no—
429C4×C13—21no—
430C4×C13—21no—
431C4×C13—21no—
432C4×C13—21no—
433C4×C13—21no—
434C4×C13C2×#9912yes—
435C4×C13C2×#9912yes—
436Dic13—24no—
437Dic13—42no—
438Dic13—42no—
439C25—131no—
440C25C4×D1311yescharacteristic
441C22×D4—132no—
442C22×D4—132no—
443C22×D4—268no—
444C22×D4—261no—
445C22×D4—261no—
446C22×D4—261no—
447C22×D4—261no—
448C23×C4—44no—
449C23×C4—131no—
450C23×C4—131no—
451C23×C4—131no—
452C23×C4—132no—
453C23×C4—132no—
454C23×C4—261no—
455C23×C4—261no—
456C23×C4—261no—
457C23×C4—261no—
458C23×C4—524no—
459C23×C4C4×D1311yescharacteristic
460C23×C4C4×D1311yescharacteristic
461C23×C4C4×D1311yescharacteristic
462C23×C4D5211yescharacteristic
463C23×C4D5211yescharacteristic
464C23×C4D5211yescharacteristic
465C23×C4D5211yescharacteristic
466C23×C4C22⋊D1311yescharacteristic
467C23×C4C22⋊D1311yescharacteristic
468C23×C4C22⋊D1311yescharacteristic
469C23×C4C22⋊D1311yescharacteristic
470C23×C4C22×D1311yescharacteristic
471C23×C4C22×D1311yescharacteristic
472C23×C4C22×D1311yescharacteristic
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—44no—
476C2×M16—262no—
477C2×M16—262no—
478C2×M16—524no—
479C22×C8—22no—
480C22×C8—262no—
481C4×D4—262no—
482C4×D4—262no—
483C4×D4—262no—
484C4×D4—262no—
485C4×D4—262no—
486C4×D4—262no—
487C4×D4—262no—
488C4×D4—262no—
489C4×D4—262no—
490C4×D4—262no—
491C4×D4—262no—
492C4×D4—262no—
493C4×D4—262no—
494C4×D4—262no—
495C4×D4—262no—
496C4×D4—262no—
497C2×C4⋊C4—132no—
498C2×C4⋊C4—132no—
499C2×C4⋊C4—261no—
500C2×C4⋊C4—261no—
501C2×C4⋊C4—261no—
502C2×C4⋊C4—261no—
503C2×C22⋊C4—132no—
504C2×C22⋊C4—132no—
505C2×C22⋊C4—132no—
506C2×C22⋊C4—132no—
507C2×C22⋊C4—261no—
508C2×C22⋊C4—261no—
509C2×C22⋊C4—261no—
510C2×C22⋊C4—261no—
511C2×C22⋊C4—261no—
512C2×C22⋊C4—261no—
513C2×C22⋊C4—261no—
514C2×C22⋊C4—261no—
515C2×C42—132no—
516C2×C42—132no—
517C2×C42—261no—
518C2×C42—261no—
519C2×C42—261no—
520C2×C42—261no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C22⋊C8—134no—
525C22⋊C8—262no—
526C22⋊C8—262no—
527C22⋊C8—262no—
528C22⋊C8C22×D1314yes—
529C2×C13—22no—
530C2×C13—22no—
531C2×C13—22no—
532C2×C13—22no—
533C2×C13—22no—
534C2×C13—41no—
535C2×C13—41no—
536C2×C13C2×#40711yescharacteristic
537C2×C13C22×#9911yescharacteristic
538C2×C13C2×#41311yescharacteristic
539D13—44no—
540C24—24no—
541C24—42no—
542C24—42no—
543C24—132no—
544C24—264no—
545C24—261no—
546C24—261no—
547C24—522no—
548C24—522no—
549C24#610311yescharacteristic
550C24#610311yescharacteristic
551C24#610311yescharacteristic
552C24#610311yescharacteristic
553C24C2×C4×D1311yescharacteristic
554C24C2×C4×D1311yescharacteristic
555C24C2×C4×D1311yescharacteristic
556C2×D4—138no—
557C2×D4—264no—
558C2×D4—264no—
559C2×D4—268no—
560C2×D4—268no—
561C2×D4—268no—
562C2×D4—268no—
563C2×D4—264no—
564C2×D4—262no—
565C2×D4—262no—
566C2×D4—262no—
567C2×D4—262no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—132no—
583C22×C4—132no—
584C22×C4—132no—
585C22×C4—264no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—524no—
597C22×C4—524no—
598C22×C4—524no—
599C22×C4—524no—
600C22×C4—524no—
601C22×C4—524no—
602C22×C4—522no—
603C22×C4—522no—
604C22×C4#610311yescharacteristic
605C22×C4#610311yescharacteristic
606C22×C4#610311yescharacteristic
607C22×C4#610311yescharacteristic
608C22×C4#610311yescharacteristic
609C22×C4#610311yescharacteristic
610C22×C4#610311yescharacteristic
611C22×C4#610311yescharacteristic
612C22×C4#610311yescharacteristic
613C22×C4#610311yescharacteristic
614C22×C4#610311yescharacteristic
615C22×C4#610311yescharacteristic
616C22×C4C2×C4×D1311yescharacteristic
617C22×C4C2×C4×D1311yescharacteristic
618C22×C4C2×C4×D1311yescharacteristic
619C22×C4C2×D5211yescharacteristic
620C22×C4C2×D5211yescharacteristic
621C22×C4C2×D5211yescharacteristic
622C22×C4C2×D5211yescharacteristic
623C22×C4C2×D5211yescharacteristic
624C22×C4C2×D5211yescharacteristic
625C22×C4C2×C22⋊D1311yescharacteristic
626C22×C4C2×C22⋊D1311yescharacteristic
627C22×C4C2×C22⋊D1311yescharacteristic
628C22×C4C2×C22⋊D1311yescharacteristic
629C22×C4C2×C22⋊D1311yescharacteristic
630C22×C4C2×C22⋊D1311yescharacteristic
631C22×C4C23×D1311yescharacteristic
632M16—44no—
633M16—44no—
634M16—524no—
635M16—524no—
636C2×C8—24no—
637C2×C8—44no—
638C2×C8—264no—
639C2×C8—524no—
640C4⋊C4—262no—
641C4⋊C4—262no—
642C4⋊C4—262no—
643C4⋊C4—262no—
644C22⋊C4—262no—
645C22⋊C4—262no—
646C22⋊C4—262no—
647C22⋊C4—262no—
648C22⋊C4—262no—
649C22⋊C4—262no—
650C22⋊C4—262no—
651C22⋊C4—262no—
652C42—262no—
653C42—262no—
654C42—262no—
655C42—262no—
656C13#1736211yescharacteristic, complemented, Sylow
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—416no—
678C23—134no—
679C23—264no—
680C23—264no—
681C23—262no—
682C23—262no—
683C23—522no—
684C23—522no—
685C23—522no—
686C23—5216no—
687C23—522no—
688C23—522no—
689C23—522no—
690C23M16×D1314yes—
691C23C2×#610311yescharacteristic
692C23C2×#610311yescharacteristic
693C23C2×#610311yescharacteristic
694C23C2×#610311yescharacteristic
695C23C2×#610311yescharacteristic
696C23C2×#610311yescharacteristic
697C23C22×C4×D1311yescharacteristic
698D4—268no—
699D4—268no—
700D4—268no—
701D4—268no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—134no—
730C2×C4—264no—
731C2×C4—264no—
732C2×C4—262no—
733C2×C4—262no—
734C2×C4—262no—
735C2×C4—262no—
736C2×C4—524no—
737C2×C4—524no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—524no—
743C2×C4—524no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4#8804614yes—
747C2×C4C2×#610311yescharacteristic
748C2×C4C2×#610311yescharacteristic
749C2×C4C2×#610311yescharacteristic
750C2×C4C2×#610311yescharacteristic
751C2×C4C2×#610311yescharacteristic
752C2×C4C2×#610311yescharacteristic
753C2×C4C22×D5211yescharacteristic
754C2×C4C22×C22⋊D1311yescharacteristic
755C8—44no—
756C8—524no—
757C22—28no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—264no—
781C22—524no—
782C22—524no—
783C22—528no—
784C22—528no—
785C22—522no—
786C22—522no—
787C22C2×#8804612yes—
788C22#1171878712yes—
789C22#1171878712yes—
790C22#1171879312yes—
791C22C2×M16×D1312yes—
792C22C22×#610311yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—264no—
800C4—522no—
801C4—522no—
802C4C2×#8804612yes—
803C4C2×#8804612yes—
804C2—22no—
805C2—22no—
806C2—22no—
807C2—22no—
808C2—22no—
809C2—41no—
810C2—41no—
811C2—524no—
812C2C2×#1171878711yescharacteristic
813C2C22×#8804611yescharacteristic
814C2C2×#1171879311yescharacteristic
subgroupG/H
centerC2×C4C2×#6103
commutatorC23×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#407C2
socleC22×C13C22×C22⋊C4
prime radicalC23×C22⋊D13C4
cosocleC22×C4×C13C24
hypercenterC2×#407D13
hypocenterC13#17362
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#11718868C2semidirect
3. #13113172C2semidirect
4. #13113165C2semidirect
5. #13113162C2semidirect
6. #13113152C2semidirect
7. C2×C13×#407C2semidirect
32. C13×#407C22semidirect
34. C2×C13×C22⋊C8C22semidirect
38. #11718868C22semidirect
40. C2×C22⋊#1055C22semidirect
41. #11718061C22semidirect
42. #11718060C22semidirect
203. C2×C22⋊D13M16semidirect
252. C2×#407D13semidirect
297. C22×D13C2×M16semidirect
350. C2×Dic13C2×M16semidirect
385. #407C2×D13semidirect
389. C2×C22⋊C8C2×D13semidirect
656. C13#17362semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D132
C2×#117188682
#131131722
#131131652
#131131622
#131131522
C2×C13×#4072
#1736213