Finite Group Databasebeta

← #15878393

Subgroups — #15878393

Order 3328.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719255C211yesmaximal, characteristic
2C2×#11718672C211yesmaximal, characteristic, complemented
3C2×#11718627C211yesmaximal, characteristic, complemented
4C22×#88049C211yesmaximal, characteristic, complemented
5#13115768C211yesmaximal, characteristic, complemented
6#13115650C211yesmaximal, characteristic, complemented
7#13115272C211yesmaximal, characteristic, complemented
8#13115257C211yesmaximal, characteristic, complemented
9#13115153C211yesmaximal, characteristic, complemented
10#13115143C211yesmaximal, characteristic, complemented
11#13114833C211yesmaximal, characteristic, complemented
12#13114774C211yesmaximal, characteristic, complemented
13#13114766C211yesmaximal, characteristic, complemented
14#13114664C211yesmaximal, characteristic, complemented
15D4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C23×D52C2211yescharacteristic
18C2×C4×D4×C13—21no—
19C2×C4×D4×C13C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic, complemented
22C2×#88191—21no—
23C2×#88184C2211yescharacteristic
24C2×#88178C2211yescharacteristic
25C22×#6099C2211yescharacteristic, complemented
26C23×#1055C2211yescharacteristic
27#11719255—24no—
28#11719255C418yescomplemented
29C2×#88148—21no—
30C2×#88138—21no—
31C2×C22⋊C4×D13—21no—
32C2×#88129C2211yescharacteristic
33C2×C4×D52C2211yescharacteristic
34C13×#389—21no—
35C13×#385—21no—
36C13×#385—21no—
37C13×#384C2211yescharacteristic, complemented
38C13×#380C2211yescharacteristic
39C13×#380C2211yescharacteristic, complemented
40C4×C13×C4⋊C4C2211yescharacteristic, complemented
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic, complemented
43#11718672—24no—
44C2×#88050C2211yescharacteristic, complemented
45C2×#88050C2211yescharacteristic, complemented
46C2×#88050C2211yescharacteristic, complemented
47C2×#88050C2211yescharacteristic, complemented
48#11718627—24no—
49C2×#88049—24no—
50C2×#88049C2211yescharacteristic
51C2×#88049C2211yescharacteristic
52C2×#88049C2211yescharacteristic
53C2×#88049C2211yescharacteristic
54C2×#88049C2211yescharacteristic
55C2×#88049C2211yescharacteristic
56C2×#88049C2211yescharacteristic
57C2×#88049C2211yescharacteristic
58C2×C4⋊#1055C2211yescharacteristic, complemented
59C2×#88043C2211yescharacteristic, complemented
60#11718121C2211yescharacteristic, complemented
61#11718121C2211yescharacteristic, complemented
62#11718121C2211yescharacteristic, complemented
63#11718121C2211yescharacteristic, complemented
64C24×D13—21no—
65C22×D4×C13D411yescharacteristic
66C23×C4×C13—21no—
67C23×C4×C13—21no—
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C22×C22⋊D13—21no—
71C22×C22⋊D13—21no—
72C2×#6127—22no—
73C2×#6127—22no—
74C2×#6127—22no—
75C2×#6127—41no—
76C2×#6127—41no—
77C2×#6127C2×C414yescomplemented
78C22×D52—22no—
79C22×D52—22no—
80C22×D52—21no—
81C22×D52—22no—
82C22×D52—41no—
83C22×D52—41no—
84C22×D52C2×C414yescomplemented
85C22×D52C2311yescharacteristic
86C22×D52C2311yescharacteristic
87C22×C4×D13—21no—
88C22×C4×D13—21no—
89C22×Dic26C2311yescharacteristic
90C4×D4×C13—44no—
91C4×D4×C13C2×C414yes—
92C4×D4×C13D414yes—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—21no—
96C2×C13×C4⋊C4—21no—
97C2×C13×C4⋊C4—21no—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4D411yescharacteristic
102C2×C13×C4⋊C4C2311yescharacteristic
103C2×C13×C4⋊C4C2311yescharacteristic
104C2×C13×C4⋊C4C2311yescharacteristic
105C2×C13×C4⋊C4C2311yescharacteristic
106C2×C13×C22⋊C4—21no—
107C2×C13×C22⋊C4—21no—
108C2×C13×C22⋊C4D411yescharacteristic
109C2×C13×C22⋊C4D411yescharacteristic
110C2×C42×C13—21no—
111C2×C42×C13C2311yescharacteristic
112C2×C22⋊Dic13—21no—
113#88191—28no—
114#88184—22no—
115#88184C2×C414yescomplemented
116C2×#6103—21no—
117C2×#6103—21no—
118C2×#6103—21no—
119C2×#6103—21no—
120C2×C4⋊Dic13C2311yescharacteristic
121#88178—22no—
122#88178C2×C414yescomplemented
123C2×#6101—21no—
124C2×#6099—22no—
125C2×#6099—22no—
126C2×#6099—41no—
127C22×#1055—22no—
128C22×#1055—22no—
129C22×#1055—41no—
130C22×#1055C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C22×#1055C2311yescharacteristic
133C22×#1055C2311yescharacteristic
134#88148—28no—
135#88138—28no—
136C22⋊C4×D13—28no—
137#88129—22no—
138#88129C2×C414yescomplemented
139C4×D52—22no—
140C4×D52C2×C414yescomplemented
141C13×#95—21no—
142C13×#95—21no—
143C13×#95—21no—
144C22⋊#1055—22no—
145C22⋊#1055—22no—
146#88050—22no—
147#88050—22no—
148#88050—41no—
149#88050—41no—
150#88049—22no—
151#88049—22no—
152#88049—22no—
153#88049—22no—
154#88049—22no—
155#88049—41no—
156#88049—41no—
157#88049D414yescomplemented
158C4⋊#1055—22no—
159#88043—22no—
160#22419—131nomaximal, Sylow
161C24×C13C2×D411yescharacteristic
162C24×C13C2×D411yescharacteristic
163C23×D13—21no—
164C23×D13—21no—
165C23×D13—24no—
166C23×D13—42no—
167C23×D13—42no—
168C23×D13—42no—
169C23×D13—42no—
170C23×D13—81no—
171C23×D13—81no—
172C2×D4×C13—22no—
173C2×D4×C13—22no—
174C2×D4×C13C22⋊C414yes—
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—42no—
188C22×C4×C13—42no—
189C22×C4×C13—42no—
190C22×C4×C13—42no—
191C22×C4×C13—81no—
192C22×C4×C13—81no—
193C22×C4×C13C22×C412yes—
194C22×C4×C13C22×C412yes—
195C22×C4×C13C2×D412yes—
196C22×C4×C13C2×D412yes—
197C22×C4×C13C2×D411yescharacteristic
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2411yescharacteristic
202C2×C22⋊D13—24no—
203C2×C22⋊D13—24no—
204C2×C22⋊D13—42no—
205C2×C22⋊D13—42no—
206C2×C22⋊D13—81no—
207C2×C22⋊D13—81no—
208C22×Dic13—21no—
209C22×Dic13—21no—
210#6127—28no—
211#6127—44no—
212#6127—44no—
213#6127—44no—
214C2×D52—21no—
215C2×D52—21no—
216C2×D52—21no—
217C2×D52—21no—
218C2×D52—21no—
219C2×D52—21no—
220C2×D52—21no—
221C2×D52—28no—
222C2×D52—24no—
223C2×D52—21no—
224C2×D52—44no—
225C2×D52—44no—
226C2×D52—44no—
227C2×D52—42no—
228C2×D52—42no—
229C2×D52C22×C412yes—
230C2×D52C22×C412yes—
231C2×D52C2×D412yes—
232C2×D52#4112yes—
233C2×C4×D13—24no—
234C2×C4×D13—24no—
235C2×C4×D13—42no—
236C2×C4×D13—42no—
237C2×C4×D13—81no—
238C2×C4×D13—81no—
239C2×Dic26—21no—
240C2×Dic26—21no—
241C2×Dic26—21no—
242C2×Dic26—21no—
243C2×Dic26—21no—
244C2×Dic26C22×C412yes—
245C13×C4⋊C4—21no—
246C13×C4⋊C4—21no—
247C13×C4⋊C4—21no—
248C13×C4⋊C4—21no—
249C13×C4⋊C4—21no—
250C13×C4⋊C4—21no—
251C13×C4⋊C4—21no—
252C13×C4⋊C4—42no—
253C13×C4⋊C4—42no—
254C13×C4⋊C4—42no—
255C13×C4⋊C4—81no—
256C13×C4⋊C4C22⋊C414yes—
257C13×C4⋊C4C2×D412yes—
258C13×C22⋊C4—42no—
259C13×C22⋊C4—42no—
260C13×C22⋊C4C22⋊C414yes—
261C13×C22⋊C4C22⋊C414yes—
262C42×C13—42no—
263C42×C13C22×C412yes—
264C42×C13C2×D412yes—
265C22⋊Dic13—24no—
266#6103—24no—
267#6103—24no—
268#6103—24no—
269#6103—24no—
270C4⋊Dic13—21no—
271C4⋊Dic13C22×C412yes—
272#6101—24no—
273#6099—44no—
274C2×#1055—21no—
275C2×#1055—21no—
276C2×#1055—21no—
277C2×#1055—21no—
278C2×#1055—21no—
279C2×#1055—21no—
280C2×#1055—21no—
281C2×#1055—21no—
282C2×#1055—21no—
283C2×#1055—21no—
284C2×#1055—21no—
285C2×#1055—44no—
286C2×#1055C2×D412yes—
287C2×#546—131no—
288C2×#435—131no—
289C2×#417—131no—
290C22×#102—131no—
291D4×C4⋊C4D1311yescharacteristic, complemented
292#1983—131no—
293#1959—131no—
294#1895—131no—
295#1892—131no—
296#1874—131no—
297#1872—131no—
298#1802—131no—
299#1788—131no—
300#1786—131no—
301#1762—131no—
302C23×C13—21no—
303C23×C13—21no—
304C23×C13—21no—
305C23×C13—21no—
306C23×C13—21no—
307C23×C13—21no—
308C23×C13—21no—
309C23×C13—21no—
310C23×C13—21no—
311C23×C13—21no—
312C23×C13C2×C22⋊C412yes—
313C23×C13C2×C22⋊C412yes—
314C23×C13AGL(1,ℤ/8)12yes—
315C23×C13#13712yes—
316C23×C13C22×D411yescharacteristic
317C22×D13—22no—
318C22×D13—22no—
319C22×D13—22no—
320C22×D13—22no—
321C22×D13—48no—
322C22×D13—41no—
323C22×D13—41no—
324C22×D13—41no—
325C22×D13—41no—
326C22×D13—41no—
327C22×D13—41no—
328C22×D13—41no—
329C22×D13—41no—
330C22×D13—41no—
331C22×D13—41no—
332C22×D13—48no—
333C22×D13—84no—
334C22×D13—84no—
335C22×D13—84no—
336C22×D13—84no—
337C22×D13—84no—
338D4×C13—28no—
339C2×C4×C13—21no—
340C2×C4×C13—21no—
341C2×C4×C13—21no—
342C2×C4×C13—21no—
343C2×C4×C13—21no—
344C2×C4×C13—21no—
345C2×C4×C13—21no—
346C2×C4×C13—21no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—84no—
368C2×C4×C13—84no—
369C2×C4×C13C2×C22⋊C412yes—
370C2×C4×C13C2×C22⋊C412yes—
371C2×C4×C13C2×C22⋊C412yes—
372C2×C4×C13C2×C22⋊C412yes—
373C2×C4×C13C23×C411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C2×C4×C13C22×D411yescharacteristic
376C2×C4×C13C2×#4111yescharacteristic
377C2×C4×C13H(5,𝔽2)11yescharacteristic
378C2×C4×C13H(5,𝔽2)11yescharacteristic
379C22⋊D13—48no—
380C22⋊D13—84no—
381C2×Dic13—22no—
382C2×Dic13—22no—
383C2×Dic13—41no—
384C2×Dic13—41no—
385C2×Dic13—41no—
386C2×Dic13—41no—
387D52—22no—
388D52—22no—
389D52—22no—
390D52—22no—
391D52—22no—
392D52—48no—
393D52—41no—
394D52—41no—
395D52C4×D414yescomplemented
396C4×D13—48no—
397C4×D13—84no—
398Dic26—22no—
399Dic26—22no—
400Dic26—41no—
401Dic26—41no—
402#1055—22no—
403#1055—41no—
404#1055—41no—
405#1055—41no—
406C22×#41—131no—
407C23×D4—131no—
408C22×M16—131no—
409C23×C8—131no—
410#546—138no—
411#546—264no—
412C2×#124—131no—
413C2×#123—261no—
414C2×C22⋊Q8—131no—
415C2×#121—131no—
416C2×#121—261no—
417C2×#120—261no—
418C2×C4×D4—21no—
419C2×C4×D4—131no—
420C2×C4×D4C2×D1311yescharacteristic
421C22×C4⋊C4C2×D1311yescharacteristic
422C22×C4⋊C4C2×D1311yescharacteristic, complemented
423C22×C22⋊C4—261no—
424#435—264no—
425C2×C4⋊C8—131no—
426#417—264no—
427C2×#103—131no—
428C2×#103—131no—
429C2×#103—131no—
430C2×#103—131no—
431C2×#102—131no—
432C2×#102—131no—
433C2×#102—131no—
434C2×#102—131no—
435C2×#102—131no—
436C2×#102—131no—
437C2×#102—131no—
438C2×#102—131no—
439C2×#102—264no—
440C2×C22⋊C8—131no—
441C2×C22⋊C8—131no—
442C2×#97—131no—
443#389—21no—
444#385—21no—
445#385—21no—
446#384C2×D1311yescharacteristic, complemented
447#380C2×D1311yescharacteristic
448#380C2×D1311yescharacteristic, complemented
449C4×C4⋊C4C2×D1311yescharacteristic, complemented
450#340—131no—
451#340—131no—
452#340—131no—
453#340—131no—
454C22×C13—22no—
455C22×C13—22no—
456C22×C13—22no—
457C22×C13—22no—
458C22×C13—22no—
459C22×C13—22no—
460C22×C13—22no—
461C22×C13—22no—
462C22×C13—22no—
463C22×C13—41no—
464C22×C13—41no—
465C22×C13—41no—
466C22×C13—41no—
467C22×C13#41714yescomplemented
468C22×C13C22×C22⋊C411yescharacteristic
469C22×C13D4211yescharacteristic
470C22×C13#54611yescharacteristic
471C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
472C22×C13C2×#13711yescharacteristic
473C22×C13#57611yescharacteristic
474C22×C13#57711yescharacteristic
475C2×D13—24no—
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C2×D13—42no—
480C2×D13—42no—
481C2×D13—42no—
482C2×D13—42no—
483C2×D13—42no—
484C2×D13—42no—
485C2×D13—816no—
486C2×D13—81no—
487C2×D13—81no—
488C2×D13—81no—
489C2×D13—81no—
490C4×C13—22no—
491C4×C13—22no—
492C4×C13—22no—
493C4×C13—22no—
494C4×C13—42no—
495C4×C13—81no—
496C4×C13—81no—
497C4×C13—81no—
498C4×C13C2×C4×D411yescharacteristic
499C4×C13#51811yescharacteristic
500C4×C13D4211yescharacteristic
501C4×C13#54611yescharacteristic
502Dic13—42no—
503Dic13—42no—
504C25—261no—
505C2×#41—134no—
506C2×#41—262no—
507C2×#41—262no—
508C2×#41—262no—
509C2×#41—521no—
510C2×#41—521no—
511C22×Q8—131no—
512C22×D4—134no—
513C22×D4—131no—
514C22×D4—131no—
515C22×D4—262no—
516C22×D4—262no—
517C22×D4—261no—
518C22×D4—261no—
519C22×D4—262no—
520C22×D4—261no—
521C22×D4—521no—
522C22×D4—521no—
523C22×D4C22⋊D1311yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—261no—
527C23×C4—261no—
528C23×C4C22×D1311yescharacteristic
529C23×C4C22×D1311yescharacteristic
530C2×M16—262no—
531C2×M16—262no—
532C2×M16—521no—
533C22×C8—131no—
534C22×C8—131no—
535C22×C8—131no—
536C22×C8—131no—
537C22×C8—262no—
538C22×C8—262no—
539C22×C8—521no—
540#124—134no—
541#124—262no—
542#123—268no—
543C22⋊Q8—134no—
544C22⋊Q8—262no—
545#121—134no—
546#121—262no—
547#121—268no—
548#120—268no—
549C4×D4—44no—
550C4×D4—134no—
551C4×D4—262no—
552C4×D4C4×D1314yes—
553C4×D4D5214yes—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—41no—
561C2×C4⋊C4—41no—
562C2×C4⋊C4—131no—
563C2×C4⋊C4—261no—
564C2×C4⋊C4C22⋊D1311yescharacteristic
565C2×C4⋊C4C22×D1311yescharacteristic
566C2×C4⋊C4C22×D1311yescharacteristic
567C2×C4⋊C4C22×D1311yescharacteristic
568C2×C4⋊C4C22×D1311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—261no—
572C2×C22⋊C4—261no—
573C2×C22⋊C4—261no—
574C2×C22⋊C4—261no—
575C2×C22⋊C4—261no—
576C2×C22⋊C4—268no—
577C2×C22⋊C4C22⋊D1311yescharacteristic
578C2×C22⋊C4C22⋊D1311yescharacteristic
579C2×C42—21no—
580C2×C42C22×D1311yescharacteristic
581C4⋊C8—262no—
582#103—262no—
583#103—262no—
584#103—521no—
585#103—521no—
586#102—134no—
587#102—262no—
588#102—262no—
589#102—262no—
590#102—262no—
591#102—262no—
592#102—521no—
593#102—521no—
594C22⋊C8—262no—
595C22⋊C8—262no—
596#97—262no—
597#95—21no—
598#95—21no—
599#95—21no—
600C2×C13—24no—
601C2×C13—42no—
602C2×C13D4×C22⋊C411yescharacteristic
603C2×C13C2×#41711yescharacteristic
604C2×C13#289711yescharacteristic
605C2×C13#326411yescharacteristic
606C2×C13#326611yescharacteristic
607C2×C13#330611yescharacteristic
608C2×C13#331411yescharacteristic
609D13—44no—
610D13—82no—
611C24—261no—
612C24—261no—
613C24—264no—
614C24—522no—
615C24—522no—
616C24—522no—
617C24—522no—
618C24—1041no—
619C24—1041no—
620C24C2×C22⋊D1311yescharacteristic
621C24C2×C22⋊D1311yescharacteristic
622#41—268no—
623#41—524no—
624#41—524no—
625#41—524no—
626C2×Q8—132no—
627C2×Q8—261no—
628C2×Q8—261no—
629C2×Q8—261no—
630C2×Q8—261no—
631C2×Q8—261no—
632C2×D4—22no—
633C2×D4—22no—
634C2×D4—132no—
635C2×D4—132no—
636C2×D4—132no—
637C2×D4—132no—
638C2×D4—268no—
639C2×D4—264no—
640C2×D4—264no—
641C2×D4—264no—
642C2×D4—261no—
643C2×D4—261no—
644C2×D4—261no—
645C2×D4—261no—
646C2×D4—261no—
647C2×D4—261no—
648C2×D4—261no—
649C2×D4—261no—
650C2×D4—524no—
651C2×D4—524no—
652C2×D4—524no—
653C2×D4—522no—
654C2×D4—522no—
655C2×D4—522no—
656C2×D4—522no—
657C2×D4—1041no—
658C2×D4—1041no—
659C2×D4#610314yes—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—81no—
677C22×C4—81no—
678C22×C4—261no—
679C22×C4—261no—
680C22×C4—264no—
681C22×C4—264no—
682C22×C4—522no—
683C22×C4—522no—
684C22×C4—1041no—
685C22×C4—1041no—
686C22×C4C2×C4×D1312yes—
687C22×C4C2×C4×D1312yes—
688C22×C4C2×D5212yes—
689C22×C4C2×D5212yes—
690C22×C4C2×C22⋊D1311yescharacteristic
691C22×C4C2×C22⋊D1311yescharacteristic
692C22×C4C2×C22⋊D1311yescharacteristic
693C22×C4C2×C22⋊D1311yescharacteristic
694C22×C4C23×D1311yescharacteristic
695M16—524no—
696C2×C8—132no—
697C2×C8—261no—
698C2×C8—261no—
699C2×C8—261no—
700C2×C8—261no—
701C2×C8—261no—
702C2×C8—261no—
703C2×C8—261no—
704C2×C8—261no—
705C2×C8—261no—
706C2×C8—261no—
707C2×C8—261no—
708C2×C8—524no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—42no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—81no—
720C4⋊C4—132no—
721C4⋊C4—264no—
722C4⋊C4—261no—
723C4⋊C4#610314yes—
724C4⋊C4D4×D1312yes—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—264no—
728C22⋊C4—264no—
729C22⋊C4—264no—
730C22⋊C4—264no—
731C22⋊C4—264no—
732C22⋊C4#610314yes—
733C22⋊C4#610314yes—
734C42—42no—
735C42C2×C4×D1312yes—
736C42C2×D5212yes—
737C13#2241911yescharacteristic, complemented, Sylow
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—262no—
749C23—262no—
750C23—262no—
751C23—262no—
752C23—528no—
753C23—521no—
754C23—521no—
755C23—521no—
756C23—521no—
757C23—521no—
758C23—521no—
759C23—521no—
760C23—521no—
761C23—521no—
762C23—521no—
763C23—528no—
764C23—1044no—
765C23—1044no—
766C23—1044no—
767C23—1044no—
768C23—1044no—
769C23C2×#610312yes—
770C23C2×#610312yes—
771C23#8818612yes—
772C23#8819612yes—
773C23C22×C22⋊D1311yescharacteristic
774Q8—262no—
775Q8—262no—
776Q8—521no—
777Q8—521no—
778D4—28no—
779D4—134no—
780D4—262no—
781D4—262no—
782D4—262no—
783D4—262no—
784D4—262no—
785D4—528no—
786D4—528no—
787D4—521no—
788D4—521no—
789D4—1044no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4—84no—
820C2×C4—262no—
821C2×C4—262no—
822C2×C4—528no—
823C2×C4—521no—
824C2×C4—521no—
825C2×C4—521no—
826C2×C4—521no—
827C2×C4—1044no—
828C2×C4C2×#610312yes—
829C2×C4C2×#610312yes—
830C2×C4C2×#610312yes—
831C2×C4C2×#610312yes—
832C2×C4C22×C4×D1311yescharacteristic
833C2×C4C22×D5211yescharacteristic
834C2×C4C2×D4×D1311yescharacteristic
835C2×C4#8825111yescharacteristic
836C2×C4#41×D1311yescharacteristic
837C2×C4#8825611yescharacteristic
838C8—262no—
839C8—521no—
840C8—521no—
841C8—521no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—264no—
856C22—522no—
857C22—522no—
858C22—522no—
859C22—522no—
860C22—522no—
861C22—522no—
862C22—522no—
863C22—522no—
864C22—522no—
865C22—10416no—
866C22—1041no—
867C22—1041no—
868C22—1041no—
869C22—1041no—
870C22#1171862714yescomplemented
871C22C22×#610311yescharacteristic
872C22C2×#8818611yescharacteristic
873C22D4×C22⋊D1311yescharacteristic
874C22C2×#8819611yescharacteristic
875C22#1171953411yescharacteristic
876C22#1171954011yescharacteristic
877C22#1171954211yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—522no—
887C4—522no—
888C4C4×D4×D1311yescharacteristic
889C4#1171925011yescharacteristic
890C4D4×D5211yescharacteristic
891C4#1171925911yescharacteristic
892C2—24no—
893C2—42no—
894C2—524no—
895C2—1042no—
896C2D4×#610311yescharacteristic
897C2C2×#1171862711yescharacteristic
898C2#1312335911yescharacteristic
899C2#1312631211yescharacteristic
900C2#1312634711yescharacteristic
901C2#1312679111yescharacteristic
902C2#1312691111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC2×#11719255C2
cosocleC22×C4×C13C24
hypercenterD4×C4⋊C4D13
hypocenterC13#22419
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718672C2semidirect
3. C2×#11718627C2semidirect
4. C22×#88049C2semidirect
5. #13115768C2semidirect
6. #13115650C2semidirect
7. #13115272C2semidirect
8. #13115257C2semidirect
9. #13115153C2semidirect
10. #13115143C2semidirect
11. #13114833C2semidirect
12. #13114774C2semidirect
13. #13114766C2semidirect
14. #13114664C2semidirect
15. D4×C13×C4⋊C4C2semidirect
21. C22×C13×C4⋊C4C22semidirect
25. C22×#6099C22semidirect
28. #11719255C4semidirect
37. C13×#384C22semidirect
39. C13×#380C22semidirect
40. C4×C13×C4⋊C4C22semidirect
42. C2×C22⋊#1055C22semidirect
44. C2×#88050C22semidirect
45. C2×#88050C22semidirect
46. C2×#88050C22semidirect
47. C2×#88050C22semidirect
58. C2×C4⋊#1055C22semidirect
59. C2×#88043C22semidirect
60. #11718121C22semidirect
61. #11718121C22semidirect
62. #11718121C22semidirect
63. #11718121C22semidirect
77. C2×#6127C2×C4semidirect
84. C22×D52C2×C4semidirect
115. #88184C2×C4semidirect
122. #88178C2×C4semidirect
138. #88129C2×C4semidirect
140. C4×D52C2×C4semidirect
157. #88049D4semidirect
291. D4×C4⋊C4D13semidirect
395. D52C4×D4semidirect
422. C22×C4⋊C4C2×D13semidirect
446. #384C2×D13semidirect
448. #380C2×D13semidirect
449. C4×C4⋊C4C2×D13semidirect
467. C22×C13#417semidirect
737. C13#22419semidirect
870. C22#11718627semidirect

Maximal subgroups

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

subgroupindex
C2×#117192552
C2×#117186722
C2×#117186272
C22×#880492
#131157682
#131156502
#131152722
#131152572
#131151532
#131151432
#131148332
#131147742
#131147662
#131146642
D4×C13×C4⋊C42
#2241913