Finite Group Databasebeta

← #15879237

Subgroups — #15879237

Order 3328.

1258 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718672C211yesmaximal, characteristic, complemented
2D4×C4⋊Dic13C211yesmaximal, characteristic, complemented
3#13115806C211yesmaximal, characteristic, complemented
4#13115794C211yesmaximal, characteristic, complemented
5#13115275C211yesmaximal, characteristic, complemented
6#13115265C211yesmaximal, characteristic, complemented
7#13115154C211yesmaximal, characteristic, complemented
8#13115154C211yesmaximal, characteristic, complemented
9#13114931C211yesmaximal, characteristic, complemented
10#13114926C211yesmaximal, characteristic, complemented
11#13114836C211yesmaximal, characteristic, complemented
12#13114661C211yesmaximal, characteristic, complemented
13#13114557C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C2×C13×#553C211yesmaximal, characteristic
16C13×#553—24no—
17C13×#553C418yescomplemented
18C2×C13×#126—21no—
19C2×C13×#125C2211yescharacteristic
20C2×C13×#123—21no—
21C2×C13×#121—21no—
22C2×C13×#121C2211yescharacteristic
23C2×C13×#121C2211yescharacteristic
24C2×C4×D4×C13—21no—
25C2×C4×D4×C13C2211yescharacteristic
26C2×C4×D4×C13C2211yescharacteristic
27C2×C13×#117C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C2×D4×Dic13—21no—
30C22×C4⋊Dic13C2211yescharacteristic
31C22×C4⋊Dic13C2211yescharacteristic
32C22×#6099C2211yescharacteristic
33C23×#1055C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38#11718873C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41C2×C22⋊#1055C2211yescharacteristic
42#11718672—24no—
43#11718646—21no—
44#11718611—21no—
45#11718611—21no—
46#11718596C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C2×#88043C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×D4×C13—21no—
63C22×D4×C13—21no—
64C22×D4×C13D411yescharacteristic
65C22×D4×C13C2311yescharacteristic
66C23×C4×C13—21no—
67C23×C4×C13—21no—
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×Dic13—21no—
71C23×Dic13—21no—
72C13×#126—28no—
73C13×#125—22no—
74C13×#125C2×C414yescomplemented
75C13×#123—28no—
76C13×#121—28no—
77C13×#121—22no—
78C13×#121—22no—
79C13×#121C2×C414yescomplemented
80C13×#121C2×C414yescomplemented
81C4×D4×C13—28no—
82C4×D4×C13—22no—
83C4×D4×C13C2×C414yes—
84C4×D4×C13C2×C414yescomplemented
85C4×D4×C13D414yes—
86C13×#117—22no—
87C13×#117C2×C414yescomplemented
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4C2×C414yescomplemented
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4D411yescharacteristic
102C2×C13×C22⋊C4D411yescharacteristic
103C2×C42×C13—21no—
104C2×C42×C13C2311yescharacteristic
105C2×C22⋊Dic13—21no—
106C2×C22⋊Dic13—21no—
107D4×Dic13—44no—
108C2×C4⋊Dic13—22no—
109C2×C4⋊Dic13—22no—
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13—21no—
112C2×C4⋊Dic13—21no—
113C2×C4⋊Dic13—21no—
114C2×C4⋊Dic13—41no—
115C2×C4⋊Dic13—41no—
116C2×C4⋊Dic13C2311yescharacteristic
117C2×C4⋊Dic13C2311yescharacteristic
118C2×C4⋊Dic13C2311yescharacteristic
119C2×C4⋊Dic13C2311yescharacteristic
120C2×C4×Dic13—21no—
121C2×#6099—22no—
122C2×#6099—22no—
123C2×#6099—41no—
124C22×#1055—22no—
125C22×#1055—22no—
126C22×#1055—41no—
127C22×#1055C2311yescharacteristic
128C22×#1055C2311yescharacteristic
129C22×#1055C2311yescharacteristic
130C22×#1055C2311yescharacteristic
131#88072—22no—
132#88072—22no—
133#88072—41no—
134#88072—41no—
135#88071—21no—
136#88071—21no—
137#88071—21no—
138C22⋊#1055—22no—
139C22⋊#1055—22no—
140C4⋊#1055—22no—
141#88043—22no—
142#22493—131nomaximal, Sylow
143C24×C13—21no—
144C24×C13C2×D411yescharacteristic
145C24×C13C2×D411yescharacteristic
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—24no—
149C2×D4×C13—24no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—42no—
156C2×D4×C13—42no—
157C2×D4×C13—81no—
158C2×D4×C13—81no—
159C2×D4×C13C22⋊C414yes—
160C2×D4×C13C22×C412yes—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—24no—
173C22×C4×C13—24no—
174C22×C4×C13—81no—
175C22×C4×C13—81no—
176C22×C4×C13—81no—
177C22×C4×C13—81no—
178C22×C4×C13C22×C412yes—
179C22×C4×C13C22×C412yes—
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D412yes—
185C22×C4×C13C2×D412yes—
186C22×C4×C13C2411yescharacteristic
187C22×Dic13—21no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—42no—
192C22×Dic13—42no—
193C22×Dic13—42no—
194C22×Dic13—42no—
195C22×Dic13—81no—
196C22×Dic13—81no—
197C13×C4⋊C4—24no—
198C13×C4⋊C4—24no—
199C13×C4⋊C4—24no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4—21no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4C22⋊C414yes—
204C13×C4⋊C4C22×C412yes—
205C13×C4⋊C4C22×C412yes—
206C13×C4⋊C4C22×C412yes—
207C13×C22⋊C4—24no—
208C13×C22⋊C4—24no—
209C13×C22⋊C4—24no—
210C13×C22⋊C4—24no—
211C13×C22⋊C4C22⋊C414yes—
212C13×C22⋊C4C22⋊C414yes—
213C42×C13—24no—
214C42×C13C22×C412yes—
215C42×C13C2×D412yes—
216C22⋊Dic13—42no—
217C22⋊Dic13—42no—
218C4⋊Dic13—21no—
219C4⋊Dic13—21no—
220C4⋊Dic13—21no—
221C4⋊Dic13—21no—
222C4⋊Dic13—21no—
223C4⋊Dic13—21no—
224C4⋊Dic13—21no—
225C4⋊Dic13—42no—
226C4⋊Dic13—42no—
227C4⋊Dic13—42no—
228C4⋊Dic13—81no—
229C4⋊Dic13#4112yes—
230C4×Dic13—42no—
231#6099—44no—
232C2×#1055—21no—
233C2×#1055—21no—
234C2×#1055—21no—
235C2×#1055—21no—
236C2×#1055—21no—
237C2×#1055—21no—
238C2×#1055—21no—
239C2×#1055—21no—
240C2×#1055—21no—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—44no—
244C2×#1055#4112yes—
245C2×#553D1311yescharacteristic
246C2×#435—131no—
247D4×C4⋊C4—131no—
248#1992—131no—
249#1989—131no—
250#1895—131no—
251#1893—131no—
252#1874—131no—
253#1874—131no—
254#1825—131no—
255#1824—131no—
256#1802—131no—
257#1762—131no—
258#1736—131no—
259C2×#340—131no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—22no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—41no—
276C23×C13—41no—
277C23×C13C2×C22⋊C412yes—
278C23×C13C2×C22⋊C412yes—
279C23×C13AGL(1,ℤ/8)12yes—
280C23×C13#13712yes—
281C23×C13C22×D411yescharacteristic
282D4×C13—28no—
283D4×C13—22no—
284D4×C13—22no—
285D4×C13—48no—
286D4×C13—41no—
287D4×C13—41no—
288D4×C13—84no—
289C2×C4×C13—21no—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—21no—
294C2×C4×C13—21no—
295C2×C4×C13—21no—
296C2×C4×C13—21no—
297C2×C4×C13—22no—
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—41no—
309C2×C4×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—41no—
313C2×C4×C13—41no—
314C2×C4×C13—84no—
315C2×C4×C13—84no—
316C2×C4×C13C2×C22⋊C412yes—
317C2×C4×C13C2×C22⋊C412yes—
318C2×C4×C13C2×C22⋊C412yes—
319C2×C4×C13C2×C22⋊C412yes—
320C2×C4×C13C23×C411yescharacteristic
321C2×C4×C13C22×D411yescharacteristic
322C2×C4×C13C2×#4111yescharacteristic
323C2×C4×C13C2×#4111yescharacteristic
324C2×C4×C13H(5,𝔽2)11yescharacteristic
325C2×C4×C132−1+411yescharacteristic
326C2×Dic13—22no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—84no—
339C2×Dic13—84no—
340#1055—22no—
341#1055—41no—
342#1055—41no—
343#1055—41no—
344C22×M16—131no—
345C23×C8—131no—
346#553—24no—
347#553Dic1318yescomplemented
348C2×#126—21no—
349C2×#125C2×D1311yescharacteristic
350C2×#123—21no—
351C2×#121—21no—
352C2×#121C2×D1311yescharacteristic
353C2×#121C2×D1311yescharacteristic
354C2×C4×D4—21no—
355C2×C4×D4—261no—
356C2×C4×D4C2×D1311yescharacteristic
357C2×C4×D4C2×D1311yescharacteristic
358C2×#117C2×D1311yescharacteristic
359C22×C4⋊C4—131no—
360C22×C4⋊C4—131no—
361C22×C4⋊C4C2×D1311yescharacteristic
362#435—264no—
363C2×C4⋊C8—131no—
364C2×#102—131no—
365C2×#102—131no—
366C2×#102—131no—
367C2×#102—131no—
368C2×C22⋊C8—131no—
369C2×C22⋊C8—131no—
370C2×#97—131no—
371#389—261no—
372#385—261no—
373#385—261no—
374#384—131no—
375#380—131no—
376#380—131no—
377C4×C4⋊C4—131no—
378#340—131no—
379#340—131no—
380#340—131no—
381#340—131no—
382#340—131no—
383#340—131no—
384#340—131no—
385#340—131no—
386#340—131no—
387#340—131no—
388#340—131no—
389#340—131no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—22no—
399C22×C13—41no—
400C22×C13—41no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—42no—
406C22×C13—81no—
407C22×C13—81no—
408C22×C13—81no—
409C22×C13—81no—
410C22×C13#41714yes—
411C22×C13C22×C22⋊C411yescharacteristic
412C22×C13#54611yescharacteristic
413C22×C13#54711yescharacteristic
414C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C13C2×#13711yescharacteristic
416C22×C13#57611yescharacteristic
417C22×C13#57711yescharacteristic
418C4×C13—22no—
419C4×C13—22no—
420C4×C13—22no—
421C4×C13—22no—
422C4×C13—42no—
423C4×C13—42no—
424C4×C13—42no—
425C4×C13C4×#4111yescharacteristic
426C4×C13#52011yescharacteristic
427C4×C13#54611yescharacteristic
428C4×C13#54711yescharacteristic
429Dic13—42no—
430Dic13—81no—
431Dic13—81no—
432Dic13—81no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4C22⋊D1311yescharacteristic
436C22×D4C22×D1311yescharacteristic
437C23×C4—21no—
438C23×C4—21no—
439C23×C4—261no—
440C23×C4—261no—
441C23×C4C22×D1311yescharacteristic
442C23×C4C22×D1311yescharacteristic
443C2×M16—262no—
444C2×M16—262no—
445C2×M16—521no—
446C22×C8—131no—
447C22×C8—131no—
448C22×C8—131no—
449C22×C8—131no—
450C22×C8—262no—
451C22×C8—262no—
452C22×C8—521no—
453#126—28no—
454#125—22no—
455#125C2×Dic1314yescomplemented
456#123—28no—
457#121—28no—
458#121—22no—
459#121—22no—
460#121C2×Dic1314yescomplemented
461#121C2×Dic1314yescomplemented
462C4×D4—28no—
463C4×D4—22no—
464C4×D4—524no—
465C4×D4C2×Dic1314yes—
466C4×D4C2×Dic1314yescomplemented
467C4×D4C22⋊D1314yes—
468#117—22no—
469#117C2×Dic1314yescomplemented
470C2×C4⋊C4—21no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—131no—
475C2×C4⋊C4—131no—
476C2×C4⋊C4—131no—
477C2×C4⋊C4—131no—
478C2×C4⋊C4—262no—
479C2×C4⋊C4—262no—
480C2×C4⋊C4—261no—
481C2×C4⋊C4—261no—
482C2×C4⋊C4—261no—
483C2×C4⋊C4—261no—
484C2×C4⋊C4—521no—
485C2×C4⋊C4—521no—
486C2×C4⋊C4C2×Dic1314yescomplemented
487C2×C4⋊C4C22⋊D1311yescharacteristic
488C2×C4⋊C4C22×D1311yescharacteristic
489C2×C4⋊C4C22×D1311yescharacteristic
490C2×C4⋊C4C22×D1311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—261no—
496C2×C22⋊C4—261no—
497C2×C22⋊C4C22⋊D1311yescharacteristic
498C2×C22⋊C4C22⋊D1311yescharacteristic
499C2×C42—21no—
500C2×C42—261no—
501C2×C42C22×D1311yescharacteristic
502C4⋊C8—262no—
503#102—262no—
504#102—262no—
505#102—521no—
506#102—521no—
507C22⋊C8—262no—
508C22⋊C8—262no—
509#97—262no—
510#95—261no—
511#95—261no—
512#95—261no—
513C2×C13—24no—
514C2×C13—42no—
515C2×C13—82no—
516C2×C13#233911yescharacteristic
517C2×C13C2×#41711yescharacteristic
518C2×C13#289711yescharacteristic
519C2×C13#331811yescharacteristic
520C2×C13#332011yescharacteristic
521C2×C13#334511yescharacteristic
522C2×C13#334611yescharacteristic
523C24—21no—
524C24C2×C22⋊D1311yescharacteristic
525C24C2×C22⋊D1311yescharacteristic
526C2×D4—22no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—42no—
536C2×D4—42no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4C22⋊Dic1314yes—
540C2×D4C22×Dic1312yes—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—81no—
555C22×C4—81no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—522no—
563C22×C4—522no—
564C22×C4—522no—
565C22×C4—522no—
566C22×C4—1041no—
567C22×C4—1041no—
568C22×C4C22×Dic1312yes—
569C22×C4C22×Dic1312yes—
570C22×C4C2×C22⋊D1311yescharacteristic
571C22×C4C2×C22⋊D1311yescharacteristic
572C22×C4C2×C22⋊D1311yescharacteristic
573C22×C4C2×C22⋊D1311yescharacteristic
574C22×C4C2×C22⋊D1312yes—
575C22×C4C2×C22⋊D1312yes—
576C22×C4C23×D1311yescharacteristic
577M16—524no—
578C2×C8—132no—
579C2×C8—261no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8—261no—
584C2×C8—261no—
585C2×C8—261no—
586C2×C8—261no—
587C2×C8—261no—
588C2×C8—261no—
589C2×C8—261no—
590C2×C8—524no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—132no—
598C4⋊C4—261no—
599C4⋊C4—261no—
600C4⋊C4—261no—
601C4⋊C4—261no—
602C4⋊C4—261no—
603C4⋊C4—261no—
604C4⋊C4—261no—
605C4⋊C4—522no—
606C4⋊C4—522no—
607C4⋊C4—522no—
608C4⋊C4—1041no—
609C4⋊C4C22⋊Dic1314yes—
610C4⋊C4C22×Dic1312yes—
611C4⋊C4C22×Dic1312yes—
612C4⋊C4C22×Dic1312yes—
613C22⋊C4—24no—
614C22⋊C4—24no—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—522no—
618C22⋊C4—522no—
619C22⋊C4C22⋊Dic1314yes—
620C22⋊C4C22⋊Dic1314yes—
621C42—24no—
622C42—522no—
623C42C22×Dic1312yes—
624C42C2×C22⋊D1312yes—
625C13#2249311yescharacteristic, complemented, Sylow
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23#8820312yes—
644C23#8820512yes—
645C23C2×C22⋊Dic1312yes—
646C23C2×C22⋊Dic1312yes—
647C23C22×C22⋊D1311yescharacteristic
648D4—28no—
649D4—22no—
650D4—22no—
651D4—48no—
652D4—41no—
653D4—41no—
654D4—84no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—84no—
681C2×C4—84no—
682C2×C4—262no—
683C2×C4—521no—
684C2×C4—521no—
685C2×C4—521no—
686C2×C4—521no—
687C2×C4—521no—
688C2×C4—521no—
689C2×C4—521no—
690C2×C4—521no—
691C2×C4—521no—
692C2×C4—521no—
693C2×C4—521no—
694C2×C4—1044no—
695C2×C4—1044no—
696C2×C4C2×C22⋊Dic1312yes—
697C2×C4C2×C22⋊Dic1312yes—
698C2×C4C2×C22⋊Dic1312yes—
699C2×C4C2×C22⋊Dic1312yes—
700C2×C4#41×D1311yescharacteristic
701C2×C4#41×D1311yescharacteristic
702C2×C4#8825611yescharacteristic
703C2×C4#8825711yescharacteristic
704C2×C4C23×Dic1311yescharacteristic
705C2×C4C22×C22⋊D1311yescharacteristic
706C8—262no—
707C8—521no—
708C8—521no—
709C8—521no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22#1171889314yes—
731C22C2×#8820311yescharacteristic
732C22C2×#8820511yescharacteristic
733C22#1171952911yescharacteristic
734C22#1171953411yescharacteristic
735C22#1171954011yescharacteristic
736C22#1171954111yescharacteristic
737C22C22×C22⋊Dic1311yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—522no—
746C4—1041no—
747C4—1041no—
748C4—1041no—
749C4#1171952911yescharacteristic
750C4#41×Dic1311yescharacteristic
751C4#1171953211yescharacteristic
752C4#1171953411yescharacteristic
753C2—24no—
754C2—42no—
755C2—82no—
756C2#1311766611yescharacteristic
757C2C2×#1171889311yescharacteristic
758C2#1312336211yescharacteristic
759C2#1312697111yescharacteristic
760C2#1312700111yescharacteristic
761C2#1312730011yescharacteristic
762C2#1312732111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#553C2
socleC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenterC2×#553D13
hypocenterC13#22493
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#11718672C2semidirect
2. D4×C4⋊Dic13C2semidirect
3. #13115806C2semidirect
4. #13115794C2semidirect
5. #13115275C2semidirect
6. #13115265C2semidirect
7. #13115154C2semidirect
8. #13115154C2semidirect
9. #13114931C2semidirect
10. #13114926C2semidirect
11. #13114836C2semidirect
12. #13114661C2semidirect
13. #13114557C2semidirect
14. C2×#11718121C2semidirect
17. C13×#553C4semidirect
74. C13×#125C2×C4semidirect
79. C13×#121C2×C4semidirect
80. C13×#121C2×C4semidirect
84. C4×D4×C13C2×C4semidirect
87. C13×#117C2×C4semidirect
92. C2×C13×C4⋊C4C2×C4semidirect
347. #553Dic13semidirect
455. #125C2×Dic13semidirect
460. #121C2×Dic13semidirect
461. #121C2×Dic13semidirect
466. C4×D4C2×Dic13semidirect
469. #117C2×Dic13semidirect
486. C2×C4⋊C4C2×Dic13semidirect
625. C13#22493semidirect

Maximal subgroups

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

subgroupindex
C2×#117186722
D4×C4⋊Dic132
#131158062
#131157942
#131152752
#131152652
#131151542
#131149312
#131149262
#131148362
#131146612
#131145572
C2×#117181212
C2×C13×#5532
#2249313