Finite Group Databasebeta

← #15863467

Subgroups — #15863467

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×Dic13C211yesmaximal, characteristic
2#13117238C211yesmaximal, characteristic
3#13117231C211yesmaximal, characteristic
4#13115003C211yesmaximal, characteristic, complemented
5#13115001C211yesmaximal, characteristic, complemented
6#13114968C211yesmaximal, characteristic, complemented
7#13114968C211yesmaximal, characteristic, complemented
8#13114869C211yesmaximal, characteristic
9#13114867C211yesmaximal, characteristic
10#13114867C211yesmaximal, characteristic
11#107×Dic13C211yesmaximal, characteristic, complemented
12#13114728C211yesmaximal, characteristic, complemented
13#106×Dic13C211yesmaximal, characteristic, complemented
14#13114724C211yesmaximal, characteristic, complemented
15C13×#1809C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C22×C4×Dic13C2211yescharacteristic
18C22×#6099C2211yescharacteristic
19C2×#88131—21no—
20C2×C13×#107C2211yescharacteristic
21C2×C13×#106C2211yescharacteristic
22C13×#380C2211yescharacteristic
23C13×#380C2211yescharacteristic
24#11718873C2211yescharacteristic
25#11718873C2211yescharacteristic
26M16×Dic13C418yescomplemented
27C2×#88058C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29C2×#88055C2211yescharacteristic
30C2×#88055C2211yescharacteristic
31C2×C8×Dic13C2211yescharacteristic
32C2×C8×Dic13C2211yescharacteristic
33#11718638C2211yescharacteristic
34#11718638C2211yescharacteristic
35#11718637C2211yescharacteristic
36#11718637C2211yescharacteristic
37C4⋊C4×Dic13C2211yescharacteristic
38C4⋊C4×Dic13C2211yescharacteristic
39C4⋊C4×Dic13C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718604—21no—
46#11718603—21no—
47C22⋊C4×Dic13—21no—
48#11718312—21no—
49#11718311—21no—
50#11718310—21no—
51#11718309—21no—
52C13×#340C2211yescharacteristic
53C13×#340C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×Dic13D411yescharacteristic
62C23×Dic13D411yescharacteristic
63C2×C13×M16—22no—
64C2×C13×M16—22no—
65C2×C13×M16C2×C414yes—
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C22⋊C4—21no—
73C2×C13×C22⋊C4—21no—
74C2×C22⋊Dic13—21no—
75C2×C22⋊Dic13—21no—
76C2×C4⋊Dic13C2311yescharacteristic
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×#6101—21no—
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×C4×Dic13—21no—
85C2×C4×Dic13—21no—
86C2×C4×Dic13—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13C2×C414yes—
89C2×C4×Dic13D411yescharacteristic
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13Q814yes—
92C2×C4×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×#6099—22no—
95C2×#6099—22no—
96C2×#6099C2×C414yes—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99#88131—44no—
100C13×#107—22no—
101C13×#106—22no—
102C13×#95—21no—
103C13×#95—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88058—22no—
115#88057—22no—
116#88055C2×C414yes—
117#88055C2×C414yes—
118C8×Dic13C2×C414yes—
119C8×Dic13C2×C414yes—
120#88048—22no—
121#88048—22no—
122#88047—22no—
123#88047—22no—
124#20819—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13C22×C412yes—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×Q812yes—
137C22×C4×C13C2411yescharacteristic
138C22×Dic13—22no—
139C22×Dic13—22no—
140C22×Dic13—21no—
141C22×Dic13—21no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—41no—
145C22×Dic13—41no—
146C22×Dic13C4⋊C414yes—
147C22×Dic13C4⋊C414yes—
148C22×Dic13C2×D411yescharacteristic
149C22×Dic13C2×D411yescharacteristic
150C22×Dic13C2×D411yescharacteristic
151C22×Dic13C2×D411yescharacteristic
152C13×M16—28no—
153C2×C8×C13—21no—
154C2×C8×C13—21no—
155C2×C8×C13C22×C412yes—
156C2×C8×C13C22×C412yes—
157C2×C8×C13#4112yes—
158C2×C8×C13#4112yes—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—42no—
169C22⋊Dic13—42no—
170C22⋊Dic13—42no—
171C4⋊Dic13—21no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179#6101—42no—
180#6101—42no—
181#6101—42no—
182#6101—42no—
183C4×Dic13—42no—
184C4×Dic13—42no—
185C4×Dic13—42no—
186C4×Dic13—42no—
187C4×Dic13C4⋊C414yes—
188C4×Dic13C4⋊C414yes—
189C4×Dic13C22×C412yes—
190C4×Dic13C22×C412yes—
191C4×Dic13C2×Q812yes—
192C4×Dic13C2×Q812yes—
193#6099—28no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055C22×C412yes—
197C2×#1055C22×C412yes—
198C2×#1055#4112yes—
199C2×#1055#4112yes—
200C2×C4×M16—131no—
201#2285—131no—
202#2283—131no—
203#1847—131no—
204#1847—131no—
205#1836—131no—
206#1836—131no—
207#1809—131no—
208#1809—131no—
209#1809—131no—
210#1809D1311yescharacteristic
211C4×#107—131no—
212C4×#107—131no—
213C4×#106—131no—
214C4×#106—131no—
215C23×C13—21no—
216C23×C13—21no—
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13C2×C4⋊C412yes—
222C23×C13C22×D411yescharacteristic
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13C2×C4⋊C412yes—
242C2×C4×C13C23×C411yescharacteristic
243C2×C4×C13C22×Q811yescharacteristic
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—28no—
255C2×Dic13—44no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13C2×C4⋊C412yes—
269C2×Dic13C2×C4⋊C412yes—
270C2×Dic13C2×C4⋊C412yes—
271C2×Dic13C2×C4⋊C412yes—
272C2×Dic13AGL(1,ℤ/8)12yes—
273C2×Dic13#13712yes—
274C8×C13—22no—
275C8×C13#11714yescomplemented
276#1055—22no—
277#1055#11714yescomplemented
278C22×M16—131no—
279C22×M16C2×D1311yescharacteristic
280C2×#117—261no—
281C22×C42—131no—
282C2×#107—131no—
283C2×#107—131no—
284C2×#107—131no—
285C2×#107C2×D1311yescharacteristic
286C2×#106—131no—
287C2×#106—131no—
288C2×#106—131no—
289C2×#106C2×D1311yescharacteristic
290C4×M16—138no—
291C2×#97—131no—
292C2×#97—131no—
293C2×C4×C8—131no—
294C2×C4×C8—131no—
295#384—131no—
296#384—131no—
297#383—261no—
298#382—131no—
299#382—131no—
300#382—261no—
301#381—261no—
302#380—131no—
303#380—131no—
304#380—261no—
305#380C2×D1311yescharacteristic
306#380C2×D1311yescharacteristic
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4—131no—
311C4×C4⋊C4—261no—
312C4×C22⋊C4—261no—
313#376—261no—
314#340—131no—
315#340—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340C2×D1311yescharacteristic
321#340C2×D1311yescharacteristic
322C22×C13—22no—
323C22×C13—22no—
324C22×C13—22no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13C22×C4⋊C411yescharacteristic
330C22×C13#53211yescharacteristic
331C22×C13#53211yescharacteristic
332C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
333C22×C13C2×#13711yescharacteristic
334C22×C13#57511yescharacteristic
335C22×C13#57511yescharacteristic
336C4×C13—22no—
337C4×C13—81no—
338C4×C13—81no—
339C4×C13—81no—
340C4×C13—81no—
341C4×C13C2×#11711yescharacteristic
342C4×C13C2×#11711yescharacteristic
343C4×C13#53311yescharacteristic
344C4×C13#53311yescharacteristic
345Dic13—22no—
346Dic13—22no—
347Dic13—22no—
348Dic13—81no—
349Dic13—81no—
350Dic13—81no—
351Dic13—81no—
352Dic13#42814yes—
353C23×C4—131no—
354C23×C4—131no—
355C23×C4C22×D1311yescharacteristic
356C2×M16—22no—
357C2×M16—22no—
358C2×M16—134no—
359C2×M16—262no—
360C2×M16—262no—
361C2×M16C4×D1314yes—
362C22×C8—131no—
363C22×C8—131no—
364C22×C8C22×D1311yescharacteristic
365C22×C8C22×D1311yescharacteristic
366#117—524no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—131no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—131no—
371C2×C4⋊C4—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4C22×D1311yescharacteristic
376C2×C4⋊C4C22×D1311yescharacteristic
377C2×C4⋊C4C22×D1311yescharacteristic
378C2×C4⋊C4C22×D1311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—261no—
382C2×C22⋊C4—261no—
383C2×C42—134no—
384C2×C42—131no—
385C2×C42—131no—
386C2×C42—134no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—261no—
390C2×C42—261no—
391C2×C42—261no—
392C2×C42—261no—
393#107—22no—
394#107—262no—
395#107—262no—
396#107—262no—
397#106—22no—
398#106—262no—
399#106—262no—
400#106—262no—
401#97—134no—
402#97—134no—
403C4×C8—134no—
404C4×C8—134no—
405#95—21no—
406#95—21no—
407#95—261no—
408#95—261no—
409#95—261no—
410#95—261no—
411#95—261no—
412#95—261no—
413#95—261no—
414#95—261no—
415#95—261no—
416#95—261no—
417C2×C13—42no—
418C2×C13#228511yescharacteristic
419C2×C13C2×#42811yescharacteristic
420C2×C13#291111yescharacteristic
421C2×C13#317111yescharacteristic
422C2×C13#317111yescharacteristic
423C2×C13#317211yescharacteristic
424C2×C13#317211yescharacteristic
425C24D4×D1311yescharacteristic
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—131no—
435C22×C4—134no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—134no—
440C22×C4—262no—
441C22×C4—262no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446C22×C4—521no—
447C22×C4—521no—
448C22×C4C2×C4×D1312yes—
449C22×C4D4×D1311yescharacteristic
450C22×C4Q8×D1312yes—
451C22×C4C23×D1311yescharacteristic
452M16—28no—
453M16—268no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—132no—
457C2×C8—132no—
458C2×C8—132no—
459C2×C8—132no—
460C2×C8—261no—
461C2×C8—261no—
462C2×C8C2×C4×D1312yes—
463C2×C8C2×C4×D1312yes—
464C2×C8#612912yes—
465C2×C8#612912yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4—522no—
483C4⋊C4—522no—
484C4⋊C4—522no—
485C4⋊C4—522no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—522no—
489C22⋊C4—522no—
490C42—134no—
491C42—134no—
492C42—132no—
493C42—132no—
494C42—132no—
495C42—132no—
496C42—522no—
497C42—522no—
498C42—522no—
499C42—522no—
500C13#2081911yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23C4⋊C4×D1312yes—
508C23C2×D4×D1311yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—132no—
528C2×C4—132no—
529C2×C4—132no—
530C2×C4—132no—
531C2×C4—132no—
532C2×C4—132no—
533C2×C4—268no—
534C2×C4—261no—
535C2×C4—261no—
536C2×C4—261no—
537C2×C4—261no—
538C2×C4—261no—
539C2×C4—261no—
540C2×C4—524no—
541C2×C4—521no—
542C2×C4—521no—
543C2×C4—521no—
544C2×C4—521no—
545C2×C4—521no—
546C2×C4—521no—
547C2×C4—521no—
548C2×C4—521no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4C4⋊C4×D1312yes—
554C2×C4C22×C4×D1311yescharacteristic
555C2×C4C2×#612911yescharacteristic
556C2×C4C2×#612911yescharacteristic
557C2×C4C2×Q8×D1311yescharacteristic
558C2×C4#41×D1311yescharacteristic
559C2×C4#41×D1311yescharacteristic
560C8—22no—
561C8—134no—
562C8—262no—
563C8#8813114yescomplemented
564C22—22no—
565C22—22no—
566C22—22no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22C2×C4⋊C4×D1311yescharacteristic
572C22#1171930111yescharacteristic
573C22#1171930111yescharacteristic
574C22D13×AGL(1,ℤ/8)11yescharacteristic
575C22#1171947811yescharacteristic
576C22D13×#13711yescharacteristic
577C22#1171948211yescharacteristic
578C4—22no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—134no—
584C4—262no—
585C4—262no—
586C4—262no—
587C4—1041no—
588C4—1041no—
589C4—1041no—
590C4—1041no—
591C4C2×#8813111yescharacteristic
592C4D13×#11711yescharacteristic
593C4#1171932711yescharacteristic
594C4#1171932711yescharacteristic
595C2—42no—
596C2#1311723811yescharacteristic
597C2D13×#42811yescharacteristic
598C2#1312342311yescharacteristic
599C2#1312542411yescharacteristic
600C2#1312542611yescharacteristic
601C2#1312543511yescharacteristic
602C2#1312543711yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1809C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1809D13
hypocenterC13#20819
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
4. #13115003C2semidirect
5. #13115001C2semidirect
6. #13114968C2semidirect
7. #13114968C2semidirect
11. #107×Dic13C2semidirect
12. #13114728C2semidirect
13. #106×Dic13C2semidirect
14. #13114724C2semidirect
26. M16×Dic13C4semidirect
275. C8×C13#117semidirect
277. #1055#117semidirect
500. C13#20819semidirect
563. C8#88131semidirect

Maximal subgroups

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

subgroupindex
C2×M16×Dic132
#131172382
#131172312
#131150032
#131150012
#131149682
#131148692
#131148672
#107×Dic132
#131147282
#106×Dic132
#131147242
C13×#18092
#2081913