Finite Group Databasebeta

← #15878483

Subgroups — #15878483

Order 3328.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic26C211yesmaximal, characteristic
2C2×#11718672C211yesmaximal, characteristic
3C2×#11718665C211yesmaximal, characteristic, complemented
4C22×#88050C211yesmaximal, characteristic, complemented
5#13115759C211yesmaximal, characteristic, complemented
6#13115655C211yesmaximal, characteristic, complemented
7#13115267C211yesmaximal, characteristic, complemented
8#13115257C211yesmaximal, characteristic, complemented
9#13115148C211yesmaximal, characteristic, complemented
10#13115143C211yesmaximal, characteristic, complemented
11#13114848C211yesmaximal, characteristic, complemented
12#13114770C211yesmaximal, characteristic, complemented
13#13114770C211yesmaximal, characteristic, complemented
14#13114669C211yesmaximal, characteristic, complemented
15C13×#2352C211yesmaximal, characteristic
16C23×Dic26C2211yescharacteristic
17C23×Dic26C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×C13×#117C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C2×D4×Dic13—21no—
22C2×#88178C2211yescharacteristic
23C2×#88178C2211yescharacteristic
24C22×#6099C2211yescharacteristic
25C23×#1055C2211yescharacteristic
26D4×Dic26—24no—
27D4×Dic26C418yescomplemented
28C2×#88142—21no—
29C2×#88132—21no—
30C2×#88132—21no—
31C2×#88123C2211yescharacteristic
32C2×C4×Dic26C2211yescharacteristic
33C13×#388—21no—
34C13×#387—21no—
35C13×#386—21no—
36C13×#382C2211yescharacteristic
37C13×#380C2211yescharacteristic
38C13×#380C2211yescharacteristic
39C4×C13×C4⋊C4C2211yescharacteristic
40C4×C13×C22⋊C4—21no—
41C2×C22⋊#1055C2211yescharacteristic
42C2×C22⋊#1055C2211yescharacteristic
43#11718672—24no—
44#11718665—24no—
45C2×#88050—24no—
46C2×#88050C2211yescharacteristic
47C2×#88050C2211yescharacteristic
48C2×#88050C2211yescharacteristic
49C2×#88050C2211yescharacteristic
50C2×#88050C2211yescharacteristic
51C2×#88050C2211yescharacteristic
52C2×#88050C2211yescharacteristic
53C2×#88050C2211yescharacteristic
54C2×#88050C2211yescharacteristic
55C2×#88050C2211yescharacteristic
56C2×#88050C2211yescharacteristic
57C2×#88050C2211yescharacteristic
58C2×C4⋊#1055C2211yescharacteristic
59C2×#88043C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63#11718121C2211yescharacteristic
64C22×D4×C13D411yescharacteristic
65C23×C4×C13—21no—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×Dic13—21no—
69C23×Dic13—21no—
70C22×Dic26—22no—
71C22×Dic26—22no—
72C22×Dic26—22no—
73C22×Dic26—22no—
74C22×Dic26—21no—
75C22×Dic26—21no—
76C22×Dic26—22no—
77C22×Dic26—22no—
78C22×Dic26—41no—
79C22×Dic26—41no—
80C22×Dic26—41no—
81C22×Dic26—41no—
82C22×Dic26C2×C414yes—
83C22×Dic26C2×C414yescomplemented
84C22×Dic26C2311yescharacteristic
85C22×Dic26C2311yescharacteristic
86C22×Dic26C2311yescharacteristic
87C4×D4×C13C2×C414yes—
88C4×D4×C13D414yes—
89C13×#117—22no—
90C13×#117—41no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—21no—
93C2×C13×C4⋊C4—41no—
94C2×C13×C4⋊C4D411yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C4⋊C4C2311yescharacteristic
97C2×C13×C4⋊C4C2311yescharacteristic
98C2×C13×C4⋊C4C2311yescharacteristic
99C2×C13×C22⋊C4—21no—
100C2×C13×C22⋊C4—21no—
101C2×C13×C22⋊C4—21no—
102C2×C13×C22⋊C4D411yescharacteristic
103C2×C13×C22⋊C4D411yescharacteristic
104C2×C42×C13—21no—
105C2×C42×C13—21no—
106C2×C42×C13C2311yescharacteristic
107C2×C22⋊Dic13—21no—
108C2×C22⋊Dic13—21no—
109D4×Dic13—28no—
110C2×C4⋊Dic13—21no—
111C2×C4⋊Dic13—21no—
112C2×C4⋊Dic13C2311yescharacteristic
113#88178—22no—
114#88178—22no—
115#88178C2×C414yes—
116#88178C2×C414yescomplemented
117C2×#6101—21no—
118C2×#6101—21no—
119C2×#6101—21no—
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#88142—28no—
132#88132—28no—
133#88132—28no—
134#88123—22no—
135#88123C2×C414yescomplemented
136C4×Dic26—22no—
137C4×Dic26C2×C414yescomplemented
138C13×#95—21no—
139C13×#95—21no—
140C13×#95—21no—
141C13×#95—21no—
142C13×#95—21no—
143C22⋊#1055—22no—
144C22⋊#1055—22no—
145#88050—22no—
146#88050—22no—
147#88050—22no—
148#88050—22no—
149#88050—22no—
150#88050—22no—
151#88050—22no—
152#88050—41no—
153#88050—41no—
154#88050—41no—
155#88050—41no—
156#88050D414yescomplemented
157C4⋊#1055—22no—
158#88043—22no—
159#22425—131nomaximal, Sylow
160C24×C13C2×D411yescharacteristic
161C24×C13C2×D411yescharacteristic
162C2×D4×C13—22no—
163C2×D4×C13—22no—
164C2×D4×C13C22⋊C414yes—
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—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—42no—
178C22×C4×C13—42no—
179C22×C4×C13—81no—
180C22×C4×C13C22×C412yes—
181C22×C4×C13C22×C412yes—
182C22×C4×C13C2×D412yes—
183C22×C4×C13C2×D412yes—
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2411yescharacteristic
189C22×Dic13—21no—
190C22×Dic13—24no—
191C22×Dic13—24no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13—21no—
195C22×Dic13—42no—
196C22×Dic13—42no—
197C22×Dic13—42no—
198C22×Dic13—42no—
199C2×Dic26—21no—
200C2×Dic26—21no—
201C2×Dic26—21no—
202C2×Dic26—21no—
203C2×Dic26—21no—
204C2×Dic26—21no—
205C2×Dic26—21no—
206C2×Dic26—21no—
207C2×Dic26—21no—
208C2×Dic26—21no—
209C2×Dic26—21no—
210C2×Dic26—28no—
211C2×Dic26—28no—
212C2×Dic26—24no—
213C2×Dic26—24no—
214C2×Dic26—21no—
215C2×Dic26—21no—
216C2×Dic26—44no—
217C2×Dic26—44no—
218C2×Dic26—44no—
219C2×Dic26—44no—
220C2×Dic26—44no—
221C2×Dic26—44no—
222C2×Dic26—42no—
223C2×Dic26—42no—
224C2×Dic26—42no—
225C2×Dic26—42no—
226C2×Dic26C22×C412yes—
227C2×Dic26C22×C412yes—
228C2×Dic26C22×C412yes—
229C2×Dic26C2×D412yes—
230C2×Dic26#4112yes—
231C13×C4⋊C4—21no—
232C13×C4⋊C4—21no—
233C13×C4⋊C4—21no—
234C13×C4⋊C4—21no—
235C13×C4⋊C4—21no—
236C13×C4⋊C4—21no—
237C13×C4⋊C4—21no—
238C13×C4⋊C4—42no—
239C13×C4⋊C4C22⋊C414yes—
240C13×C4⋊C4C2×D412yes—
241C13×C22⋊C4—42no—
242C13×C22⋊C4—42no—
243C13×C22⋊C4—81no—
244C13×C22⋊C4C22⋊C414yes—
245C13×C22⋊C4C22⋊C414yes—
246C42×C13—42no—
247C42×C13—81no—
248C42×C13C22×C412yes—
249C42×C13C2×D412yes—
250C22⋊Dic13—24no—
251C22⋊Dic13—24no—
252C4⋊Dic13—24no—
253C4⋊Dic13—24no—
254C4⋊Dic13—21no—
255C4⋊Dic13C22×C412yes—
256#6101—24no—
257#6101—24no—
258#6101—24no—
259C4×Dic13—24no—
260#6099—44no—
261C2×#1055—21no—
262C2×#1055—21no—
263C2×#1055—21no—
264C2×#1055—21no—
265C2×#1055—21no—
266C2×#1055—21no—
267C2×#1055—21no—
268C2×#1055—21no—
269C2×#1055—21no—
270C2×#1055—21no—
271C2×#1055—21no—
272C2×#1055—44no—
273C2×#1055C2×D412yes—
274C2×D4×Q8—131no—
275C2×#435—131no—
276C2×#419—131no—
277C22×#103—131no—
278#2352D1311yescharacteristic
279#1981—131no—
280#1960—131no—
281#1894—131no—
282#1892—131no—
283#1873—131no—
284#1872—131no—
285#1805—131no—
286#1787—131no—
287#1787—131no—
288#1763—131no—
289C23×C13—21no—
290C23×C13—21no—
291C23×C13—21no—
292C23×C13—21no—
293C23×C13—21no—
294C23×C13—21no—
295C23×C13—21no—
296C23×C13—21no—
297C23×C13—21no—
298C23×C13—21no—
299C23×C13C2×C22⋊C412yes—
300C23×C13C2×C22⋊C412yes—
301C23×C13#13712yes—
302C23×C13#13712yes—
303C23×C13C22×D411yescharacteristic
304D4×C13—28no—
305C2×C4×C13—21no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
310C2×C4×C13—21no—
311C2×C4×C13—21no—
312C2×C4×C13—21no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—22no—
317C2×C4×C13—22no—
318C2×C4×C13—22no—
319C2×C4×C13—22no—
320C2×C4×C13—22no—
321C2×C4×C13—22no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—41no—
329C2×C4×C13—41no—
330C2×C4×C13—41no—
331C2×C4×C13—41no—
332C2×C4×C13—41no—
333C2×C4×C13—84no—
334C2×C4×C13C2×C22⋊C412yes—
335C2×C4×C13C2×C22⋊C412yes—
336C2×C4×C13C2×C22⋊C412yes—
337C2×C4×C13C2×C22⋊C412yes—
338C2×C4×C13C23×C411yescharacteristic
339C2×C4×C13C22×D411yescharacteristic
340C2×C4×C13C22×D411yescharacteristic
341C2×C4×C13C2×#4111yescharacteristic
342C2×C4×C13H(5,𝔽2)11yescharacteristic
343C2×C4×C13H(5,𝔽2)11yescharacteristic
344C2×Dic13—22no—
345C2×Dic13—22no—
346C2×Dic13—22no—
347C2×Dic13—22no—
348C2×Dic13—22no—
349C2×Dic13—22no—
350C2×Dic13—48no—
351C2×Dic13—48no—
352C2×Dic13—41no—
353C2×Dic13—41no—
354C2×Dic13—41no—
355C2×Dic13—41no—
356C2×Dic13—41no—
357C2×Dic13—41no—
358Dic26—22no—
359Dic26—22no—
360Dic26—22no—
361Dic26—22no—
362Dic26—22no—
363Dic26—22no—
364Dic26—22no—
365Dic26—48no—
366Dic26—48no—
367Dic26—41no—
368Dic26—41no—
369Dic26—41no—
370Dic26—41no—
371Dic26C4×D414yes—
372#1055—22no—
373#1055—41no—
374#1055—41no—
375#1055—41no—
376C23×Q8—131no—
377C23×Q8—131no—
378C22×M16—131no—
379C23×C8—131no—
380D4×Q8—138no—
381D4×Q8—264no—
382C2×C4⋊Q8—131no—
383C2×C4⋊Q8—261no—
384C2×C22⋊Q8—131no—
385C2×C22⋊Q8—131no—
386C2×C22⋊Q8—261no—
387C2×C22⋊Q8—261no—
388C2×C4×Q8—131no—
389C2×C4×D4—261no—
390C2×C4×D4C2×D1311yescharacteristic
391C2×#117C2×D1311yescharacteristic
392C22×C4⋊C4C2×D1311yescharacteristic
393#435—264no—
394C2×C4⋊C8—131no—
395#419—264no—
396C2×#103—131no—
397C2×#103—131no—
398C2×#103—131no—
399C2×#103—131no—
400C2×#103—131no—
401C2×#103—131no—
402C2×#103—131no—
403C2×#103—131no—
404C2×#103—131no—
405C2×#103—131no—
406C2×#103—131no—
407C2×#103—131no—
408C2×#103—264no—
409C2×C22⋊C8—131no—
410C2×C22⋊C8—131no—
411C2×#97—131no—
412#388—21no—
413#387—21no—
414#386—21no—
415#382C2×D1311yescharacteristic
416#380C2×D1311yescharacteristic
417#380C2×D1311yescharacteristic
418C4×C4⋊C4C2×D1311yescharacteristic
419C4×C22⋊C4—21no—
420#340—131no—
421#340—131no—
422#340—131no—
423#340—131no—
424C22×C13—22no—
425C22×C13—22no—
426C22×C13—22no—
427C22×C13—22no—
428C22×C13—22no—
429C22×C13—22no—
430C22×C13—22no—
431C22×C13—22no—
432C22×C13—22no—
433C22×C13—41no—
434C22×C13—41no—
435C22×C13—41no—
436C22×C13—41no—
437C22×C13#41914yescomplemented
438C22×C13C22×C22⋊C411yescharacteristic
439C22×C13D4211yescharacteristic
440C22×C13#54611yescharacteristic
441C22×C13C2×#13711yescharacteristic
442C22×C13C2×#13711yescharacteristic
443C22×C13#57711yescharacteristic
444C22×C13#57811yescharacteristic
445C4×C13—22no—
446C4×C13—22no—
447C4×C13—22no—
448C4×C13—22no—
449C4×C13—42no—
450C4×C13—81no—
451C4×C13—81no—
452C4×C13—81no—
453C4×C13C2×C4×D411yescharacteristic
454C4×C13#51811yescharacteristic
455C4×C13D4211yescharacteristic
456C4×C13#54611yescharacteristic
457Dic13—24no—
458Dic13—42no—
459Dic13—42no—
460Dic13—42no—
461C22×Q8—134no—
462C22×Q8—134no—
463C22×Q8—131no—
464C22×Q8—131no—
465C22×Q8—131no—
466C22×Q8—262no—
467C22×Q8—262no—
468C22×Q8—262no—
469C22×Q8—262no—
470C22×Q8—262no—
471C22×Q8—262no—
472C22×Q8—261no—
473C22×Q8—261no—
474C22×Q8—521no—
475C22×Q8—521no—
476C22×Q8—521no—
477C22×Q8—521no—
478C22×D4C22⋊D1311yescharacteristic
479C23×C4—21no—
480C23×C4—261no—
481C23×C4—261no—
482C23×C4C22×D1311yescharacteristic
483C23×C4C22×D1311yescharacteristic
484C2×M16—262no—
485C2×M16—262no—
486C2×M16—521no—
487C22×C8—131no—
488C22×C8—131no—
489C22×C8—131no—
490C22×C8—131no—
491C22×C8—262no—
492C22×C8—262no—
493C22×C8—521no—
494C4⋊Q8—134no—
495C4⋊Q8—268no—
496C4⋊Q8—262no—
497C22⋊Q8—134no—
498C22⋊Q8—134no—
499C22⋊Q8—262no—
500C22⋊Q8—262no—
501C22⋊Q8—268no—
502C22⋊Q8—268no—
503C4×Q8—134no—
504C4×Q8—262no—
505C4×D4—268no—
506C4×D4C4×D1314yes—
507C4×D4D5214yes—
508#117—22no—
509#117—41no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—41no—
513C2×C4⋊C4—131no—
514C2×C4⋊C4—261no—
515C2×C4⋊C4—261no—
516C2×C4⋊C4—261no—
517C2×C4⋊C4—261no—
518C2×C4⋊C4—261no—
519C2×C4⋊C4C22⋊D1311yescharacteristic
520C2×C4⋊C4C22×D1311yescharacteristic
521C2×C4⋊C4C22×D1311yescharacteristic
522C2×C4⋊C4C22×D1311yescharacteristic
523C2×C4⋊C4C22×D1311yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—261no—
528C2×C22⋊C4—261no—
529C2×C22⋊C4C22⋊D1311yescharacteristic
530C2×C22⋊C4C22⋊D1311yescharacteristic
531C2×C42—21no—
532C2×C42—21no—
533C2×C42—261no—
534C2×C42C22×D1311yescharacteristic
535C4⋊C8—262no—
536#103—134no—
537#103—262no—
538#103—262no—
539#103—262no—
540#103—262no—
541#103—262no—
542#103—262no—
543#103—262no—
544#103—521no—
545#103—521no—
546#103—521no—
547#103—521no—
548C22⋊C8—262no—
549C22⋊C8—262no—
550#97—262no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556C2×C13—24no—
557C2×C13—42no—
558C2×C13D4×C22⋊C411yescharacteristic
559C2×C13C2×#41911yescharacteristic
560C2×C13#289811yescharacteristic
561C2×C13#326611yescharacteristic
562C2×C13#327011yescharacteristic
563C2×C13#331211yescharacteristic
564C2×C13#332011yescharacteristic
565C24C2×C22⋊D1311yescharacteristic
566C24C2×C22⋊D1311yescharacteristic
567C2×Q8—132no—
568C2×Q8—132no—
569C2×Q8—132no—
570C2×Q8—132no—
571C2×Q8—132no—
572C2×Q8—268no—
573C2×Q8—268no—
574C2×Q8—264no—
575C2×Q8—264no—
576C2×Q8—261no—
577C2×Q8—261no—
578C2×Q8—261no—
579C2×Q8—261no—
580C2×Q8—261no—
581C2×Q8—261no—
582C2×Q8—261no—
583C2×Q8—261no—
584C2×Q8—261no—
585C2×Q8—261no—
586C2×Q8—261no—
587C2×Q8—261no—
588C2×Q8—261no—
589C2×Q8—522no—
590C2×Q8—522no—
591C2×Q8—522no—
592C2×Q8—522no—
593C2×Q8—524no—
594C2×Q8—524no—
595C2×Q8—524no—
596C2×Q8—524no—
597C2×Q8—524no—
598C2×Q8—524no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4#610314yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—81no—
617C22×C4—261no—
618C22×C4—264no—
619C22×C4—264no—
620C22×C4—261no—
621C22×C4—261no—
622C22×C4—261no—
623C22×C4—522no—
624C22×C4—522no—
625C22×C4—522no—
626C22×C4—522no—
627C22×C4C2×C4×D1312yes—
628C22×C4C2×C4×D1312yes—
629C22×C4C2×D5212yes—
630C22×C4C2×D5212yes—
631C22×C4C2×C22⋊D1311yescharacteristic
632C22×C4C2×C22⋊D1311yescharacteristic
633C22×C4C2×C22⋊D1311yescharacteristic
634C22×C4C2×C22⋊D1311yescharacteristic
635C22×C4C23×D1311yescharacteristic
636M16—524no—
637C2×C8—132no—
638C2×C8—261no—
639C2×C8—261no—
640C2×C8—261no—
641C2×C8—261no—
642C2×C8—261no—
643C2×C8—261no—
644C2×C8—261no—
645C2×C8—261no—
646C2×C8—261no—
647C2×C8—261no—
648C2×C8—261no—
649C2×C8—524no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—42no—
658C4⋊C4—132no—
659C4⋊C4—264no—
660C4⋊C4—264no—
661C4⋊C4—264no—
662C4⋊C4—264no—
663C4⋊C4—264no—
664C4⋊C4—261no—
665C4⋊C4#610314yes—
666C4⋊C4D4×D1312yes—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—81no—
670C22⋊C4—264no—
671C22⋊C4—264no—
672C22⋊C4#610314yes—
673C22⋊C4#610314yes—
674C42—42no—
675C42—81no—
676C42—264no—
677C42C2×C4×D1312yes—
678C42C2×D5212yes—
679C13#2242511yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×#610312yes—
691C23C2×#610312yes—
692C23#8820512yes—
693C23#8820512yes—
694C23C22×C22⋊D1311yescharacteristic
695Q8—134no—
696Q8—262no—
697Q8—262no—
698Q8—262no—
699Q8—262no—
700Q8—262no—
701Q8—262no—
702Q8—262no—
703Q8—528no—
704Q8—528no—
705Q8—521no—
706Q8—521no—
707Q8—521no—
708Q8—521no—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—262no—
740C2×C4—262no—
741C2×C4—262no—
742C2×C4—262no—
743C2×C4—262no—
744C2×C4—262no—
745C2×C4—528no—
746C2×C4—528no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4—521no—
753C2×C4C2×#610312yes—
754C2×C4C2×#610312yes—
755C2×C4C2×#610312yes—
756C2×C4C2×#610312yes—
757C2×C4C22×C4×D1311yescharacteristic
758C2×C4C22×D5211yescharacteristic
759C2×C4C2×D4×D1311yescharacteristic
760C2×C4#8825111yescharacteristic
761C2×C4#41×D1311yescharacteristic
762C2×C4#8825611yescharacteristic
763C8—262no—
764C8—521no—
765C8—521no—
766C8—521no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1171866514yescomplemented
781C22C22×#610311yescharacteristic
782C22D4×C22⋊D1311yescharacteristic
783C22C2×#8820511yescharacteristic
784C22C2×#8820511yescharacteristic
785C22#1171953411yescharacteristic
786C22#1171954111yescharacteristic
787C22#1171954311yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—264no—
797C4—522no—
798C4—522no—
799C4—522no—
800C4C4×D4×D1311yescharacteristic
801C4#1171925011yescharacteristic
802C4D4×D5211yescharacteristic
803C4#1171925911yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×#610311yescharacteristic
807C2C2×#1171866511yescharacteristic
808C2#1312336611yescharacteristic
809C2#1312634211yescharacteristic
810C2#1312640211yescharacteristic
811C2#1312688111yescharacteristic
812C2#1312700111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2352C2
socleC23×C13C22×D4
prime radicalC22×D4×C13D4
cosocleC22×C4×C13C24
hypercenter#2352D13
hypocenterC13#22425
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. C2×#11718665C2semidirect
4. C22×#88050C2semidirect
5. #13115759C2semidirect
6. #13115655C2semidirect
7. #13115267C2semidirect
8. #13115257C2semidirect
9. #13115148C2semidirect
10. #13115143C2semidirect
11. #13114848C2semidirect
12. #13114770C2semidirect
13. #13114770C2semidirect
14. #13114669C2semidirect
27. D4×Dic26C4semidirect
83. C22×Dic26C2×C4semidirect
116. #88178C2×C4semidirect
135. #88123C2×C4semidirect
137. C4×Dic26C2×C4semidirect
156. #88050D4semidirect
437. C22×C13#419semidirect
679. C13#22425semidirect
780. C22#11718665semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic262
C2×#117186722
C2×#117186652
C22×#880502
#131157592
#131156552
#131152672
#131152572
#131151482
#131151432
#131148482
#131147702
#131146692
C13×#23522
#2242513