Finite Group Databasebeta

← #15880209

Subgroups — #15880209

Order 3328.

1038 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718627C211yesmaximal, characteristic
2#13117667C211yesmaximal, characteristic
3#13115525C211yesmaximal, characteristic, complemented
4#13115511C211yesmaximal, characteristic, complemented
5#13115477C211yesmaximal, characteristic, complemented
6#13115470C211yesmaximal, characteristic, complemented
7#13115096C211yesmaximal, characteristic, complemented
8#13115082C211yesmaximal, characteristic, complemented
9#13114926C211yesmaximal, characteristic, complemented
10#13114867C211yesmaximal, characteristic, complemented
11#13114774C211yesmaximal, characteristic
12#13114664C211yesmaximal, characteristic, complemented
13C4×#88049C211yesmaximal, characteristic, complemented
14#13114620C211yesmaximal, characteristic, complemented
15C13×#2344C211yesmaximal, characteristic, complemented
16C22×#6127C2211yescharacteristic
17C2×C13×#117—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×#6099C2211yescharacteristic
20C2×C4×D52C2211yescharacteristic
21C2×C4×D52C2211yescharacteristic
22C13×#389C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#387—21no—
25C13×#387—21no—
26C13×#381—21no—
27C13×#380C2211yescharacteristic
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31#11718873C2211yescharacteristic
32C2×C22⋊#1055C2211yescharacteristic
33C2×#88050C2211yescharacteristic
34C2×#88050C2211yescharacteristic
35C2×#88050C2211yescharacteristic
36C2×#88050C2211yescharacteristic
37#11718627C418yescomplemented
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88049C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718617—21no—
45#11718617—21no—
46#11718590C2211yescharacteristic
47#11718590C2211yescharacteristic
48C2×#88043C2211yescharacteristic
49C2×C4×#1055C2211yescharacteristic
50#11718325—21no—
51D13×#95—21no—
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C2×#6127—22no—
64C2×#6127—22no—
65C2×#6127—22no—
66C2×#6127—41no—
67C2×#6127—41no—
68C2×#6127C2×C414yes—
69C22×D52C2311yescharacteristic
70C22×C4×D13—21no—
71C22×C4×D13—21no—
72C22×C4×D13—21no—
73C22×Dic26C2311yescharacteristic
74C13×#117—44no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4C2×C414yescomplemented
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C42×C13—21no—
88C2×C42×C13—21no—
89C2×C42×C13C2311yescharacteristic
90C2×C42×C13C2311yescharacteristic
91C2×C22⋊Dic13—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6099—41no—
97C2×#6099—41no—
98C2×#6099C2×C414yescomplemented
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C4×D52—22no—
104C4×D52—22no—
105C4×D52—41no—
106C4×D52—41no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—22no—
120#88050—41no—
121#88050—41no—
122#88050C2×C414yescomplemented
123#88050C2×C414yescomplemented
124#88049—22no—
125#88049—22no—
126#88049C2×C414yes—
127#88049C2×C414yes—
128#88048—41no—
129#88047—41no—
130#88043—41no—
131C4×#1055—41no—
132#22582—131nomaximal, Sylow
133C24×C13C2×D411yescharacteristic
134C23×D13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—24no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13C22×C412yes—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13#4112yes—
153C22×C4×C13C2411yescharacteristic
154C2×C22⋊D13—24no—
155C2×C22⋊D13—42no—
156C2×C22⋊D13—42no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160#6127—28no—
161#6127—44no—
162#6127—44no—
163#6127—44no—
164C2×D52—21no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52C22×C412yes—
168C2×D52#4112yes—
169C2×D52#4112yes—
170C2×C4×D13—24no—
171C2×C4×D13—42no—
172C2×C4×D13—42no—
173C2×C4×D13—42no—
174C2×C4×D13—42no—
175C2×C4×D13—42no—
176C2×C4×D13—42no—
177C2×C4×D13—81no—
178C2×C4×D13—81no—
179C2×Dic26—21no—
180C2×Dic26—21no—
181C2×Dic26—21no—
182C2×Dic26—21no—
183C2×Dic26—21no—
184C2×Dic26C22×C412yes—
185C13×C4⋊C4—24no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—42no—
193C13×C4⋊C4—42no—
194C13×C4⋊C4C22×C412yes—
195C13×C4⋊C4C22×C412yes—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—41no—
198C13×C22⋊C4—42no—
199C42×C13—21no—
200C42×C13—21no—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—42no—
204C42×C13—42no—
205C22⋊Dic13—81no—
206#6103—42no—
207#6103—42no—
208C4⋊Dic13—21no—
209C4⋊Dic13—21no—
210C4⋊Dic13—21no—
211C4⋊Dic13—21no—
212#6099—44no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055C22×C412yes—
224C2×#1055C22×C412yes—
225C2×#417—131no—
226#2344D1311yescharacteristic, complemented
227#2339—131no—
228#1935—131no—
229#1933—131no—
230#1928—131no—
231#1927—131no—
232#1864—131no—
233#1862—131no—
234#1824—131no—
235#1809—131no—
236#1788—131no—
237#1762—131no—
238C4×#102—131no—
239#1753—131no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13C4×D412yes—
247C23×C13C22×D411yescharacteristic
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254C22×D13—41no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—48no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13C4×D412yes—
286C2×C4×C13AGL(1,ℤ/8)12yes—
287C2×C4×C13C23×C411yescharacteristic
288C2×C4×C13C2×#4111yescharacteristic
289C2×C4×C13C2×#4111yescharacteristic
290C2×C4×C13C2×#4111yescharacteristic
291C2×C4×C13H(5,𝔽2)11yescharacteristic
292C2×C4×C13H(5,𝔽2)11yescharacteristic
293C22⋊D13—48no—
294C2×Dic13—22no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303D52—22no—
304D52—22no—
305D52—22no—
306D52#11714yescomplemented
307C4×D13—48no—
308C4×D13—84no—
309C4×D13—84no—
310Dic26—22no—
311Dic26—22no—
312Dic26—41no—
313Dic26—41no—
314#1055—22no—
315#1055—22no—
316#1055—41no—
317#1055—41no—
318C22×#41—131no—
319C22×M16—131no—
320C2×C4×D4—131no—
321C2×C4×D4—131no—
322C2×#117—21no—
323C22×C4⋊C4C2×D1311yescharacteristic
324C2×#107—131no—
325C2×#106—131no—
326#417—138no—
327C2×#103—131no—
328C2×#103—131no—
329C2×#103—131no—
330C2×#103—131no—
331C2×#102—131no—
332C2×#102—131no—
333C2×#102—131no—
334C2×#102—131no—
335C2×C22⋊C8—131no—
336C2×#97—131no—
337C2×C4×C8—131no—
338#391—131no—
339#391—131no—
340#389C2×D1311yescharacteristic
341#389C2×D1311yescharacteristic
342#387—21no—
343#387—21no—
344#386—261no—
345#386—261no—
346#381—21no—
347#381—261no—
348#380—131no—
349#380C2×D1311yescharacteristic
350C4×C4⋊C4C2×D1311yescharacteristic
351C4×C4⋊C4C2×D1311yescharacteristic
352C4×C22⋊C4C2×D1311yescharacteristic
353C2×#95—261no—
354#340—131no—
355#340—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360#336—131no—
361#336—131no—
362C22×C13—22no—
363C22×C13—22no—
364C22×C13—22no—
365C22×C13—41no—
366C22×C13—41no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13C2×C4×D411yescharacteristic
370C22×C13#54611yescharacteristic
371C22×C13#54611yescharacteristic
372C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C13#57511yescharacteristic
374C22×C13#57711yescharacteristic
375C22×C13#57811yescharacteristic
376C2×D13—24no—
377C2×D13—42no—
378C2×D13—42no—
379C2×D13—42no—
380C2×D13—42no—
381C2×D13—42no—
382C2×D13—42no—
383C4×C13—22no—
384C4×C13—22no—
385C4×C13—41no—
386C4×C13—42no—
387C4×C13—42no—
388C4×C13—41no—
389C4×C13—41no—
390C4×C13—81no—
391C4×C13—81no—
392C4×C13C2×#11711yescharacteristic
393C4×C13#51811yescharacteristic
394C4×C13#55111yescharacteristic
395C4×C13#55111yescharacteristic
396Dic13—42no—
397Dic13—81no—
398Dic13—81no—
399C2×#41—134no—
400C2×#41—262no—
401C2×#41—262no—
402C2×#41—262no—
403C2×#41—521no—
404C2×#41—521no—
405C22×Q8—131no—
406C22×D4—131no—
407C22×D4—261no—
408C23×C4—21no—
409C23×C4—261no—
410C23×C4—261no—
411C23×C4—261no—
412C23×C4C22×D1311yescharacteristic
413C2×M16—134no—
414C2×M16—521no—
415C2×M16—521no—
416C22×C8—131no—
417C22×C8—131no—
418C22×C8—131no—
419C22×C8—131no—
420C4×D4—262no—
421C4×D4—262no—
422C4×D4—521no—
423C4×D4—521no—
424#117—44no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—131no—
430C2×C4⋊C4—131no—
431C2×C4⋊C4C4×D1314yescomplemented
432C2×C4⋊C4C22×D1311yescharacteristic
433C2×C4⋊C4C22×D1311yescharacteristic
434C2×C4⋊C4C22×D1311yescharacteristic
435C2×C4⋊C4C22×D1311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—261no—
438C2×C22⋊C4—261no—
439C2×C22⋊C4—261no—
440C2×C22⋊C4C22⋊D1311yescharacteristic
441C2×C22⋊C4C22⋊D1311yescharacteristic
442C2×C42—21no—
443C2×C42—21no—
444C2×C42C22×D1311yescharacteristic
445C2×C42C22×D1311yescharacteristic
446#107—521no—
447#106—521no—
448#103—134no—
449#103—134no—
450#103—521no—
451#103—521no—
452#102—134no—
453#102—134no—
454#102—262no—
455#102—262no—
456C22⋊C8—262no—
457#97—521no—
458C4×C8—521no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—261no—
465#95—261no—
466#95—261no—
467#95—261no—
468#95—261no—
469#95C22⋊D1311yescharacteristic
470#95C22⋊D1311yescharacteristic
471C2×C13—42no—
472C2×C13#234211yescharacteristic
473C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
474C2×C13#294711yescharacteristic
475C2×C13#330611yescharacteristic
476C2×C13#331511yescharacteristic
477C2×C13#332311yescharacteristic
478C2×C13#333011yescharacteristic
479D13—44no—
480C24—261no—
481C24C2×C22⋊D1311yescharacteristic
482#41—268no—
483#41—524no—
484#41—524no—
485#41—524no—
486C2×Q8—132no—
487C2×Q8—261no—
488C2×Q8—261no—
489C2×Q8—261no—
490C2×Q8—261no—
491C2×Q8—261no—
492C2×D4—132no—
493C2×D4—132no—
494C2×D4—132no—
495C2×D4—264no—
496C2×D4—261no—
497C2×D4—261no—
498C2×D4—261no—
499C2×D4—522no—
500C2×D4—522no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—261no—
513C22×C4—264no—
514C22×C4—261no—
515C22×C4—261no—
516C22×C4—522no—
517C22×C4—522no—
518C22×C4—522no—
519C22×C4—522no—
520C22×C4—522no—
521C22×C4—522no—
522C22×C4—1041no—
523C22×C4—1041no—
524C22×C4C2×C4×D1312yes—
525C22×C4#612712yes—
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528C22×C4C2×C22⋊D1311yescharacteristic
529C22×C4C2×C22⋊D1311yescharacteristic
530C22×C4C2×C22⋊D1311yescharacteristic
531C22×C4C23×D1311yescharacteristic
532M16—524no—
533C2×C8—132no—
534C2×C8—132no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C4⋊C4—24no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4C2×C4×D1312yes—
559C4⋊C4C2×C4×D1312yes—
560C22⋊C4—22no—
561C22⋊C4—41no—
562C22⋊C4—42no—
563C22⋊C4—522no—
564C22⋊C4—522no—
565C22⋊C4—1041no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—42no—
572C13#2258211yescharacteristic, complemented, Sylow
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—262no—
580C23—262no—
581C23—262no—
582C23—521no—
583C23—521no—
584C23—521no—
585C23—521no—
586C23C4×C22⋊D1312yes—
587C23C22×C22⋊D1311yescharacteristic
588Q8—262no—
589Q8—262no—
590Q8—521no—
591Q8—521no—
592D4—134no—
593D4—262no—
594D4—262no—
595D4—262no—
596D4—528no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—48no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—262no—
628C2×C4—528no—
629C2×C4—521no—
630C2×C4—521no—
631C2×C4—521no—
632C2×C4—521no—
633C2×C4—521no—
634C2×C4—521no—
635C2×C4—521no—
636C2×C4—521no—
637C2×C4—1044no—
638C2×C4—1044no—
639C2×C4C4×C22⋊D1312yes—
640C2×C4#8818612yes—
641C2×C4C22×C4×D1311yescharacteristic
642C2×C4C2×#612711yescharacteristic
643C2×C4#41×D1311yescharacteristic
644C2×C4#41×D1311yescharacteristic
645C2×C4#8825611yescharacteristic
646C2×C4#8825611yescharacteristic
647C8—262no—
648C8—262no—
649C8—521no—
650C8—521no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—41no—
658C22—264no—
659C22—522no—
660C22—522no—
661C22—522no—
662C22—522no—
663C22—522no—
664C22—522no—
665C22C2×C4×C22⋊D1311yescharacteristic
666C22C2×#8818611yescharacteristic
667C22#1171952711yescharacteristic
668C22#1171953411yescharacteristic
669C22#1171953411yescharacteristic
670C22#1171954211yescharacteristic
671C22#1171954311yescharacteristic
672C4—22no—
673C4—22no—
674C4—41no—
675C4—42no—
676C4—42no—
677C4—41no—
678C4—41no—
679C4—81no—
680C4—81no—
681C4—522no—
682C4—1041no—
683C4—1041no—
684C4D13×#11711yescharacteristic
685C4#1171922611yescharacteristic
686C4#1171923211yescharacteristic
687C4#1171923211yescharacteristic
688C2—42no—
689C2—524no—
690C2#1311768611yescharacteristic
691C2C4×#8818611yescharacteristic
692C2#1312367911yescharacteristic
693C2#1312679111yescharacteristic
694C2#1312692611yescharacteristic
695C2#1312704611yescharacteristic
696C2#1312713511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#2344C2
socleC23×C13C22×D4
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#2344D13
hypocenterC13#22582
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2344

Complements

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

NH ≅ G/Ntype
3. #13115525C2semidirect
4. #13115511C2semidirect
5. #13115477C2semidirect
6. #13115470C2semidirect
7. #13115096C2semidirect
8. #13115082C2semidirect
9. #13114926C2semidirect
10. #13114867C2semidirect
12. #13114664C2semidirect
13. C4×#88049C2semidirect
14. #13114620C2semidirect
15. C13×#2344C2semidirect
37. #11718627C4semidirect
79. C2×C13×C4⋊C4C2×C4semidirect
98. C2×#6099C2×C4semidirect
122. #88050C2×C4semidirect
123. #88050C2×C4semidirect
226. #2344D13semidirect
306. D52#117semidirect
431. C2×C4⋊C4C4×D13semidirect
572. C13#22582semidirect

Maximal subgroups

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

subgroupindex
C2×#117186272
#131176672
#131155252
#131155112
#131154772
#131154702
#131150962
#131150822
#131149262
#131148672
#131147742
#131146642
C4×#880492
#131146202
C13×#23442
#2258213