Finite Group Databasebeta

← #15925834

Subgroups — #15925834

Order 3328.

896 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic, complemented
2C2×#11718625C211yesmaximal, characteristic, complemented
3#13118549C211yesmaximal, characteristic, complemented
4#13116369C211yesmaximal, characteristic, complemented
5#13116338C211yesmaximal, characteristic, complemented
6#13116224C211yesmaximal, characteristic, complemented
7#13116174C211yesmaximal, characteristic, complemented
8#13115599C211yesmaximal, characteristic, complemented
9#13115407C211yesmaximal, characteristic, complemented
10#13115275C211yesmaximal, characteristic
11#13115159C211yesmaximal, characteristic
12#13115097C211yesmaximal, characteristic, complemented
13#13115029C211yesmaximal, characteristic, complemented
14#13115021C211yesmaximal, characteristic, complemented
15C13×#2361C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13—21no—
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C2×#88124C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#388—21no—
26C13×#386—21no—
27C13×#385—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718670—24no—
37#11718625—24no—
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718610—21no—
45#11718609—21no—
46#11718596C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4⋊#1055C2211yescharacteristic
51#11718315—21no—
52#11718308—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×C13—21no—
65C23×C4×C13C2311yescharacteristic
66C13×#121—22no—
67C13×#121Q814yes—
68C4×D4×C13—22no—
69C4×D4×C13—41no—
70C4×D4×C13—44no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
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×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88C2×C22⋊Dic13—21no—
89#88180—22no—
90#88180—41no—
91C2×C4⋊Dic13—21no—
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101—21no—
101C2×C4×Dic13—21no—
102C2×#6099—22no—
103C2×#6099—22no—
104C2×#6099—22no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88124—22no—
110#88124—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—22no—
126#88048—41no—
127#88047—22no—
128#88047D414yescomplemented
129C4⋊#1055—22no—
130C4⋊#1055—22no—
131#26366—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—42no—
141C2×D4×C13—42no—
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—42no—
153C22×C4×C13—42no—
154C22×C4×C13—81no—
155C22×C4×C13—81no—
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×Q812yes—
162C22×C4×C13#4112yes—
163C22×C4×C13C2411yescharacteristic
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4C2×D412yes—
175C13×C4⋊C4C2×Q812yes—
176C13×C22⋊C4—24no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—41no—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—42no—
181C13×C22⋊C4—81no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—42no—
187C22⋊Dic13—42no—
188C22⋊Dic13—81no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—42no—
197C4⋊Dic13—81no—
198C4⋊Dic13C2×D412yes—
199#6101—42no—
200#6101—42no—
201#6101—42no—
202#6101—81no—
203C4×Dic13—42no—
204#6099—28no—
205C2×#1055—21no—
206C2×#1055—21no—
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×#1055C2×D412yes—
216C2×#1055#4112yes—
217C2×#478—131no—
218C2×#428—131no—
219#2441—131no—
220#2361D1311yescharacteristic
221#2094—131no—
222#2088—131no—
223#2067—131no—
224#2059—131no—
225#1948—131no—
226#1918—131no—
227#1895—131no—
228#1875—131no—
229#1864—131no—
230#1853—131no—
231#1851—131no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—21no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—22no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13C22⋊Q812yes—
246C23×C13C22×D411yescharacteristic
247D4×C13—22no—
248D4×C13—22no—
249D4×C13—48no—
250D4×C13—41no—
251D4×C13—41no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
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—41no—
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—84no—
279C2×C4×C13—84no—
280C2×C4×C13C22⋊Q812yes—
281C2×C4×C13AGL(1,ℤ/8)12yes—
282C2×C4×C13C22×D411yescharacteristic
283C2×C4×C13C22×Q811yescharacteristic
284C2×C4×C13C2×#4111yescharacteristic
285C2×C4×C13C2×#4111yescharacteristic
286C2×C4×C13H(5,𝔽2)11yescharacteristic
287C2×C4×C132−1+411yescharacteristic
288C2×Dic13—22no—
289C2×Dic13—41no—
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—
300#1055—22no—
301#1055—22no—
302#1055—41no—
303#1055—41no—
304C22×M16—131no—
305C2×#125—131no—
306C2×#121C2×D1311yescharacteristic
307C2×C4×D4—21no—
308C2×C4×D4C2×D1311yescharacteristic
309C2×#117—131no—
310C22×C4⋊C4C2×D1311yescharacteristic
311#478—264no—
312#428—264no—
313C2×#107—131no—
314C2×#107—131no—
315C2×#106—131no—
316C2×#106—131no—
317C2×#106—131no—
318C2×#106—131no—
319C2×C4⋊C8—131no—
320C2×C4⋊C8—131no—
321C2×#102—131no—
322C2×#102—131no—
323C2×#102—131no—
324C2×#102—131no—
325C2×C22⋊C8—131no—
326#399—261no—
327#396—261no—
328#390C2×D1311yescharacteristic
329#389—131no—
330#389—131no—
331#389—261no—
332#389C2×D1311yescharacteristic
333#388—21no—
334#387—261no—
335#386—21no—
336#385—21no—
337#384—131no—
338#380—131no—
339C4×C4⋊C4C2×D1311yescharacteristic
340C4×C22⋊C4C2×D1311yescharacteristic
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#340—131no—
346#340—131no—
347#336—131no—
348#336—131no—
349C22×C13—22no—
350C22×C13—22no—
351C22×C13—22no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13—41no—
355C22×C13—41no—
356C22×C13—42no—
357C22×C13—42no—
358C22×C13—42no—
359C22×C13—81no—
360C22×C13—81no—
361C22×C13—81no—
362C22×C13—81no—
363C22×C13C2×C22⋊Q811yescharacteristic
364C22×C13D4211yescharacteristic
365C22×C13#54711yescharacteristic
366C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C13#57511yescharacteristic
368C22×C13#57711yescharacteristic
369C22×C13#57711yescharacteristic
370C4×C13—22no—
371C4×C13—22no—
372C4×C13—42no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—42no—
377C4×C13—81no—
378C4×C13#52511yescharacteristic
379C4×C13#53911yescharacteristic
380C4×C13D4×Q811yescharacteristic
381C4×C13#55411yescharacteristic
382Dic13—42no—
383Dic13—81no—
384Dic13—81no—
385Dic13—81no—
386C22×D4—21no—
387C22×D4C22×D1311yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4C22×D1311yescharacteristic
391C2×M16—262no—
392C2×M16—262no—
393C2×M16—262no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C22×C8—131no—
398#125—262no—
399#125—521no—
400#121—22no—
401#121Dic2614yes—
402C4×D4—22no—
403C4×D4—41no—
404C4×D4—44no—
405#117—262no—
406#117—521no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—131no—
415C2×C4⋊C4—261no—
416C2×C4⋊C4—261no—
417C2×C4⋊C4—261no—
418C2×C4⋊C4—261no—
419C2×C4⋊C4—261no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4C22×D1311yescharacteristic
422C2×C4⋊C4C22×D1311yescharacteristic
423C2×C4⋊C4C22×D1311yescharacteristic
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—261no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4C22⋊D1311yescharacteristic
431C2×C22⋊C4C22⋊D1311yescharacteristic
432C2×C42—21no—
433C2×C42—261no—
434C2×C42C22×D1311yescharacteristic
435C2×C42C22×D1311yescharacteristic
436#107—134no—
437#107—262no—
438#106—262no—
439#106—262no—
440#106—262no—
441#106—521no—
442C4⋊C8—262no—
443C4⋊C8—262no—
444#102—262no—
445#102—262no—
446#102—262no—
447#102—521no—
448C22⋊C8—262no—
449#95—21no—
450#95—21no—
451#95—261no—
452#95—261no—
453#95—261no—
454#95C22⋊D1311yescharacteristic
455#95C22⋊D1311yescharacteristic
456C2×C13—42no—
457C2×C13—82no—
458C2×C13#244911yescharacteristic
459C2×C13#307711yescharacteristic
460C2×C13#308411yescharacteristic
461C2×C13#327111yescharacteristic
462C2×C13#327211yescharacteristic
463C2×C13#334511yescharacteristic
464C2×C13#335111yescharacteristic
465C24—21no—
466C24C2×C22⋊D1311yescharacteristic
467C2×D4—24no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4C2×Dic2612yes—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—261no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4C2×Dic2612yes—
494C22×C4#612712yes—
495C22×C4C2×C22⋊D1311yescharacteristic
496C22×C4C2×C22⋊D1311yescharacteristic
497C22×C4C2×C22⋊D1311yescharacteristic
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C23×D1311yescharacteristic
501M16—268no—
502C2×C8—132no—
503C2×C8—132no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—132no—
521C4⋊C4—261no—
522C4⋊C4—261no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—522no—
529C4⋊C4—522no—
530C4⋊C4—522no—
531C4⋊C4—522no—
532C4⋊C4—1041no—
533C4⋊C4—1041no—
534C4⋊C4C2×Dic2612yes—
535C4⋊C4D4×D1312yes—
536C22⋊C4—24no—
537C22⋊C4—22no—
538C22⋊C4—41no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—522no—
543C22⋊C4—1041no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—42no—
549C42—522no—
550C13#2636611yescharacteristic, complemented, Sylow
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23#8817812yes—
565C23C22×C22⋊D1311yescharacteristic
566D4—22no—
567D4—22no—
568D4—48no—
569D4—41no—
570D4—41no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—262no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4#8817812yes—
612C2×C4#8818612yes—
613C2×C4C22×Dic2611yescharacteristic
614C2×C4C2×#612711yescharacteristic
615C2×C4C2×D4×D1311yescharacteristic
616C2×C4#8825111yescharacteristic
617C2×C4#41×D1311yescharacteristic
618C2×C4#8825711yescharacteristic
619C8—262no—
620C8—262no—
621C8—521no—
622C8—521no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C2×#8817811yescharacteristic
638C22C2×#8818611yescharacteristic
639C22D4×C22⋊D1311yescharacteristic
640C22#1171952711yescharacteristic
641C22#1171952911yescharacteristic
642C22#1171954111yescharacteristic
643C22#1171954211yescharacteristic
644C4—22no—
645C4—22no—
646C4—41no—
647C4—42no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—81no—
652C4—522no—
653C4—1041no—
654C4—1041no—
655C4—1041no—
656C4D4×Dic2611yescharacteristic
657C4#1171924411yescharacteristic
658C4#1171925211yescharacteristic
659C4#1171926911yescharacteristic
660C2—42no—
661C2—82no—
662C2#1311863911yescharacteristic
663C2#1312463311yescharacteristic
664C2#1312469811yescharacteristic
665C2#1312642211yescharacteristic
666C2#1312643211yescharacteristic
667C2#1312730611yescharacteristic
668C2#1312739011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2361C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2361D13
hypocenterC13#26366
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. C2×#11718670C2semidirect
2. C2×#11718625C2semidirect
3. #13118549C2semidirect
4. #13116369C2semidirect
5. #13116338C2semidirect
6. #13116224C2semidirect
7. #13116174C2semidirect
8. #13115599C2semidirect
9. #13115407C2semidirect
12. #13115097C2semidirect
13. #13115029C2semidirect
14. #13115021C2semidirect
128. #88047D4semidirect
550. C13#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×#117186252
#131185492
#131163692
#131163382
#131162242
#131161742
#131155992
#131154072
#131152752
#131151592
#131150972
#131150292
#131150212
C13×#23612
#2636613