Finite Group Databasebeta

← #15925699

Subgroups — #15925699

Order 3328.

904 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718668C211yesmaximal, characteristic, complemented
2C2×#11718656C211yesmaximal, characteristic, complemented
3#13118538C211yesmaximal, characteristic, complemented
4#13116369C211yesmaximal, characteristic, complemented
5#13116338C211yesmaximal, characteristic, complemented
6#13116210C211yesmaximal, characteristic, complemented
7#13116169C211yesmaximal, characteristic, complemented
8#13115594C211yesmaximal, characteristic, complemented
9#13115428C211yesmaximal, characteristic, complemented
10#13115275C211yesmaximal, characteristic
11#13115154C211yesmaximal, characteristic
12#13115083C211yesmaximal, characteristic, complemented
13#13115035C211yesmaximal, characteristic, complemented
14#13115021C211yesmaximal, characteristic, complemented
15C13×#2363C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×#88132—21no—
22C2×#88123C2211yescharacteristic
23C13×#390—21no—
24C13×#390C2211yescharacteristic
25C13×#389C2211yescharacteristic
26C13×#388—21no—
27C13×#386—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4—21no—
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718873C2211yescharacteristic
36C2×C22⋊#1055C2211yescharacteristic
37#11718668—24no—
38#11718656—24no—
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718611—21no—
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718322—21no—
52#11718317—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C23×C4×C13—21no—
64C23×C4×C13C2311yescharacteristic
65C23×Dic13—21no—
66C22×Dic26—21no—
67C13×#121—22no—
68C13×#121Q814yescomplemented
69C4×D4×C13—22no—
70C4×D4×C13—41no—
71C13×#117—22no—
72C13×#117—41no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13—21no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13—41no—
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×C4⋊Dic13C2311yescharacteristic
99C2×#6101—21no—
100C2×#6101—21no—
101C2×#6099—22no—
102C2×#6099—22no—
103C2×#6099—22no—
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108#88132—44no—
109#88123—22no—
110#88123—41no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95D411yescharacteristic
114C13×#95D411yescharacteristic
115#88072—22no—
116#88072—22no—
117#88072—22no—
118#88072—41no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122C22⋊#1055—22no—
123#88048—22no—
124#88048—22no—
125#88048—41no—
126#88047—22no—
127#88047—22no—
128#88047D414yescomplemented
129C4⋊#1055—22no—
130C4⋊#1055—22no—
131#26357—131nomaximal, Sylow
132C24×C13—21no—
133C24×C13C2×D411yescharacteristic
134C2×D4×C13—24no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—21no—
140C2×D4×C13—81no—
141C2×D4×C13—81no—
142C2×D4×C13C2×Q812yes—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13—81no—
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×Q812yes—
159C22×C4×C13#4112yes—
160C22×C4×C13C2411yescharacteristic
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—42no—
166C22×Dic13—42no—
167C22×Dic13—81no—
168C2×Dic26—42no—
169C2×Dic26—42no—
170C2×Dic26—81no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—81no—
176C13×C4⋊C4C2×D412yes—
177C13×C4⋊C4C2×Q812yes—
178C13×C22⋊C4—24no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—42no—
182C13×C22⋊C4—42no—
183C13×C22⋊C4—42no—
184C13×C22⋊C4—81no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—42no—
190C42×C13—81no—
191C22⋊Dic13—42no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13—42no—
200C4⋊Dic13—42no—
201C4⋊Dic13—42no—
202C4⋊Dic13—81no—
203C4⋊Dic13C2×D412yes—
204#6101—42no—
205#6101—42no—
206#6099—28no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055C2×D412yes—
218C2×#1055#4112yes—
219C2×#474—131no—
220C2×#428—131no—
221#2440—131no—
222#2363D1311yescharacteristic
223#2094—131no—
224#2088—131no—
225#2065—131no—
226#2058—131no—
227#1947—131no—
228#1921—131no—
229#1895—131no—
230#1874—131no—
231#1862—131no—
232#1854—131no—
233#1851—131no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—22no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13C22⋊Q812yes—
248C23×C13C22×D411yescharacteristic
249D4×C13—22no—
250D4×C13—22no—
251D4×C13—41no—
252D4×C13—41no—
253D4×C13—84no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
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—22no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—84no—
280C2×C4×C13C22⋊Q812yes—
281C2×C4×C13AGL(1,ℤ/8)12yes—
282C2×C4×C13#13712yes—
283C2×C4×C13C22×D411yescharacteristic
284C2×C4×C13C22×Q811yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13C2×#4111yescharacteristic
287C2×C4×C13H(5,𝔽2)11yescharacteristic
288C2×C4×C132−1+411yescharacteristic
289C2×Dic13—22no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295C2×Dic13—41no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—84no—
302Dic26—84no—
303#1055—22no—
304#1055—22no—
305#1055—41no—
306#1055—41no—
307C22×M16—131no—
308C2×C4⋊Q8—131no—
309C2×C22⋊Q8—261no—
310C2×#121C2×D1311yescharacteristic
311C2×C4×D4C2×D1311yescharacteristic
312C2×#117C2×D1311yescharacteristic
313C22×C4⋊C4—131no—
314#474—264no—
315#428—264no—
316C2×#107—131no—
317C2×#107—131no—
318C2×#107—131no—
319C2×#106—131no—
320C2×#106—131no—
321C2×#106—131no—
322C2×C4⋊C8—131no—
323C2×C4⋊C8—131no—
324C2×#102—131no—
325C2×#102—131no—
326C2×#102—131no—
327C2×#102—131no—
328C2×C22⋊C8—131no—
329#398—261no—
330#395—261no—
331#390—21no—
332#390C2×D1311yescharacteristic
333#389—131no—
334#389—131no—
335#389C2×D1311yescharacteristic
336#388—21no—
337#386—21no—
338#385—261no—
339#384—131no—
340#380—131no—
341C4×C4⋊C4C2×D1311yescharacteristic
342C4×C22⋊C4—21no—
343C4×C22⋊C4C2×D1311yescharacteristic
344#340—131no—
345#340—131no—
346#340—131no—
347#340—131no—
348#340—131no—
349#340—131no—
350#336—131no—
351#336—131no—
352C22×C13—22no—
353C22×C13—22no—
354C22×C13—22no—
355C22×C13—41no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—41no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13—42no—
362C22×C13—81no—
363C22×C13—81no—
364C22×C13—81no—
365C22×C13—81no—
366C22×C13C2×C22⋊Q811yescharacteristic
367C22×C13D4211yescharacteristic
368C22×C13#54711yescharacteristic
369C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C13C2×#13711yescharacteristic
371C22×C13#57611yescharacteristic
372C22×C13#57711yescharacteristic
373C4×C13—22no—
374C4×C13—22no—
375C4×C13—22no—
376C4×C13—42no—
377C4×C13—41no—
378C4×C13—42no—
379C4×C13—41no—
380C4×C13—81no—
381C4×C13#52511yescharacteristic
382C4×C13#53911yescharacteristic
383C4×C13D4×Q811yescharacteristic
384C4×C13#55411yescharacteristic
385Dic13—42no—
386Dic13—81no—
387Dic13—81no—
388Dic13—81no—
389C22×Q8—261no—
390C22×D4—21no—
391C22×D4C22×D1311yescharacteristic
392C23×C4—21no—
393C23×C4—261no—
394C23×C4C22×D1311yescharacteristic
395C2×M16—262no—
396C2×M16—262no—
397C2×M16—262no—
398C22×C8—131no—
399C22×C8—131no—
400C22×C8—131no—
401C22×C8—131no—
402C4⋊Q8—262no—
403C4⋊Q8—521no—
404C22⋊Q8—524no—
405#121—22no—
406#121Dic2614yescomplemented
407C4×D4—22no—
408C4×D4—41no—
409#117—22no—
410#117—41no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—262no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—521no—
424C2×C4⋊C4C22×D1311yescharacteristic
425C2×C4⋊C4C22×D1311yescharacteristic
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—261no—
433C2×C22⋊C4C22⋊D1311yescharacteristic
434C2×C22⋊C4C22⋊D1311yescharacteristic
435C2×C42—21no—
436C2×C42—21no—
437C2×C42C22×D1311yescharacteristic
438C2×C42C22×D1311yescharacteristic
439#107—134no—
440#107—262no—
441#107—262no—
442#106—262no—
443#106—262no—
444#106—521no—
445C4⋊C8—262no—
446C4⋊C8—262no—
447#102—262no—
448#102—262no—
449#102—262no—
450#102—521no—
451C22⋊C8—262no—
452#95—21no—
453#95—21no—
454#95—261no—
455#95—261no—
456#95—261no—
457#95C22⋊D1311yescharacteristic
458#95C22⋊D1311yescharacteristic
459C2×C13—42no—
460C2×C13—82no—
461C2×C13#244911yescharacteristic
462C2×C13#307911yescharacteristic
463C2×C13#308111yescharacteristic
464C2×C13#326411yescharacteristic
465C2×C13#327811yescharacteristic
466C2×C13#334611yescharacteristic
467C2×C13#335411yescharacteristic
468C24—21no—
469C24C2×C22⋊D1311yescharacteristic
470C2×Q8—522no—
471C2×Q8—522no—
472C2×Q8—1041no—
473C2×D4—24no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—81no—
480C2×D4—81no—
481C2×D4C2×Dic2612yes—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—261no—
493C22×C4—261no—
494C22×C4—261no—
495C22×C4—261no—
496C22×C4—522no—
497C22×C4—522no—
498C22×C4—1041no—
499C22×C4C2×Dic2612yes—
500C22×C4#612712yes—
501C22×C4C2×C22⋊D1311yescharacteristic
502C22×C4C2×C22⋊D1311yescharacteristic
503C22×C4C2×C22⋊D1311yescharacteristic
504C22×C4C2×C22⋊D1311yescharacteristic
505C22×C4C2×C22⋊D1311yescharacteristic
506C22×C4C23×D1311yescharacteristic
507M16—268no—
508C2×C8—132no—
509C2×C8—132no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C2×C8—261no—
516C2×C8—261no—
517C2×C8—261no—
518C2×C8—261no—
519C2×C8—261no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—81no—
525C4⋊C4—132no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—261no—
529C4⋊C4—261no—
530C4⋊C4—261no—
531C4⋊C4—261no—
532C4⋊C4—261no—
533C4⋊C4—522no—
534C4⋊C4—522no—
535C4⋊C4—522no—
536C4⋊C4—522no—
537C4⋊C4—522no—
538C4⋊C4—1041no—
539C4⋊C4C2×Dic2612yes—
540C4⋊C4D4×D1312yes—
541C22⋊C4—24no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—522no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—42no—
554C42—81no—
555C13#2635711yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23#8817812yes—
570C23C22×C22⋊D1311yescharacteristic
571Q8—1044no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576D4—84no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—84no—
603C2×C4—262no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—1044no—
616C2×C4#8817812yes—
617C2×C4#8820312yes—
618C2×C4#8820512yes—
619C2×C4C22×Dic2611yescharacteristic
620C2×C4C2×#612711yescharacteristic
621C2×C4C2×D4×D1311yescharacteristic
622C2×C4#8825111yescharacteristic
623C2×C4#41×D1311yescharacteristic
624C2×C4#8825711yescharacteristic
625C8—262no—
626C8—262no—
627C8—521no—
628C8—521no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C2×#8817811yescharacteristic
644C22D4×C22⋊D1311yescharacteristic
645C22C2×#8820311yescharacteristic
646C22C2×#8820511yescharacteristic
647C22#1171952911yescharacteristic
648C22#1171954011yescharacteristic
649C22#1171954111yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—81no—
658C4—522no—
659C4—1041no—
660C4—1041no—
661C4—1041no—
662C4D4×Dic2611yescharacteristic
663C4#1171924411yescharacteristic
664C4#1171925211yescharacteristic
665C4#1171926911yescharacteristic
666C2—42no—
667C2—82no—
668C2#1311863911yescharacteristic
669C2#1312465111yescharacteristic
670C2#1312466711yescharacteristic
671C2#1312631711yescharacteristic
672C2#1312650211yescharacteristic
673C2#1312732111yescharacteristic
674C2#1312742511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2363C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2363D13
hypocenterC13#26357
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. C2×#11718668C2semidirect
2. C2×#11718656C2semidirect
3. #13118538C2semidirect
4. #13116369C2semidirect
5. #13116338C2semidirect
6. #13116210C2semidirect
7. #13116169C2semidirect
8. #13115594C2semidirect
9. #13115428C2semidirect
12. #13115083C2semidirect
13. #13115035C2semidirect
14. #13115021C2semidirect
68. C13×#121Q8semidirect
128. #88047D4semidirect
406. #121Dic26semidirect
555. C13#26357semidirect

Maximal subgroups

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

subgroupindex
C2×#117186682
C2×#117186562
#131185382
#131163692
#131163382
#131162102
#131161692
#131155942
#131154282
#131152752
#131151542
#131150832
#131150352
#131150212
C13×#23632
#2635713