Finite Group Databasebeta

← #15899000

Subgroups — #15899000

Order 3328.

1150 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic, complemented
2C2×#11718669C211yesmaximal, characteristic, complemented
3C2×#11718668C211yesmaximal, characteristic, complemented
4#13116174C212yesmaximal, complemented
5#13115982C212yesmaximal, complemented
6#13115788C211yesmaximal, characteristic, complemented
7#13115784C211yesmaximal, characteristic, complemented
8#13115159C212yesmaximal
9#13115033C212yesmaximal, complemented
10#13114816C211yesmaximal, characteristic, complemented
11C4×C13×#121C211yesmaximal, characteristic
12C2×C13×#121C2211yescharacteristic
13C2×C4×D4×C13—21no—
14C2×C4×D4×C13C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C2×#88180C2212yes—
17C2×#88178—21no—
18C2×#88178—21no—
19#11719175—24no—
20#11719175—24no—
21C2×#88124C2212yes—
22C2×#88123C2211yescharacteristic
23C2×#88123C2211yescharacteristic
24C2×C4×Dic26—21no—
25C2×C4×Dic26—21no—
26C13×#390C2211yescharacteristic
27C13×#389C2211yescharacteristic
28C13×#388—21no—
29C13×#386—21no—
30C13×#380C2211yescharacteristic
31C4×C13×C4⋊C4C2211yescharacteristic
32C4×C13×C22⋊C4—21no—
33C2×#88072C2212yes—
34C2×#88072C2212yes—
35C2×C22⋊#1055C2212yes—
36#11718669—24no—
37#11718668—24no—
38C2×#88048C2212yes—
39C2×#88047C2212yes—
40C2×C4⋊#1055C2211yescharacteristic
41C2×C4⋊#1055C2211yescharacteristic
42#11718121C2212yes—
43#11718121C2212yes—
44#11718121C2212yes—
45#11718121C2212yes—
46#11718116C2212yes—
47C22×D4×C13—21no—
48C22×D4×C13C2311yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13D411yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C22×Dic26—21no—
54C22×Dic26—21no—
55C13×#121—22no—
56C13×#121Q814yescomplemented
57C4×D4×C13—22no—
58C4×D4×C13—22no—
59C4×D4×C13—44no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4C2311yescharacteristic
62C2×C13×C4⋊C4C2311yescharacteristic
63C2×C13×C4⋊C4C2311yescharacteristic
64C2×C13×C22⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C13×C22⋊C4—21no—
68C2×C13×C22⋊C4—21no—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—21no—
72C2×C42×C13D411yescharacteristic
73C2×C42×C13D411yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C42×C13C2311yescharacteristic
76C2×C22⋊Dic13—22no—
77#88180—24no—
78#88180—24no—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2312yes—
82C2×C4⋊Dic13C2312yes—
83#88178—28no—
84#88178—28no—
85C2×#6101—22no—
86C2×#6101—22no—
87C2×C4×Dic13—22no—
88C22×#1055C2312yes—
89C22×#1055C2312yes—
90#88124—24no—
91#88124—24no—
92#88123—22no—
93#88123—22no—
94#88123D414yescomplemented
95#88123D414yescomplemented
96C4×Dic26—28no—
97C4×Dic26—28no—
98C13×#95—21no—
99C13×#95—21no—
100C13×#95—21no—
101#88072—24no—
102#88072—24no—
103C22⋊#1055—24no—
104#88048—24no—
105#88047—24no—
106C4⋊#1055—22no—
107C4⋊#1055—22no—
108#24300—131nomaximal, Sylow
109C24×C13—21no—
110C24×C13C2×D411yescharacteristic
111C2×D4×C13—24no—
112C2×D4×C13—21no—
113C2×D4×C13—21no—
114C2×D4×C13—21no—
115C2×D4×C13—21no—
116C2×D4×C13—21no—
117C2×D4×C13—42no—
118C2×D4×C13—42no—
119C2×D4×C13C2×Q812yes—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—41no—
132C22×C4×C13—41no—
133C22×C4×C13—42no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×Q812yes—
142C22×C4×C13#4112yes—
143C22×C4×C13C2411yescharacteristic
144C22×Dic13—22no—
145C22×Dic13—22no—
146C2×Dic26—24no—
147C2×Dic26—24no—
148C2×Dic26—42no—
149C2×Dic26—42no—
150C2×Dic26—42no—
151C2×Dic26—42no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—42no—
158C13×C4⋊C4C2×Q812yes—
159C13×C22⋊C4—24no—
160C13×C22⋊C4—42no—
161C13×C22⋊C4—42no—
162C13×C22⋊C4—42no—
163C13×C22⋊C4—42no—
164C42×C13—22no—
165C42×C13—22no—
166C42×C13—21no—
167C42×C13—21no—
168C42×C13—42no—
169C42×C13C2×D412yes—
170C42×C13C2×D412yes—
171C22⋊Dic13—28no—
172C4⋊Dic13—24no—
173C4⋊Dic13—24no—
174C4⋊Dic13—22no—
175C4⋊Dic13—22no—
176C4⋊Dic13C2×D414yes—
177C4⋊Dic13C2×D414yes—
178#6101—28no—
179#6101—28no—
180C4×Dic13—28no—
181C2×#1055—22no—
182C2×#1055—22no—
183C2×#1055—22no—
184C2×#1055—22no—
185C2×#1055—22no—
186C2×#1055—22no—
187C2×#533—131no—
188C2×#476—131no—
189C2×#474—131no—
190C4×#121D1311yescharacteristic
191#2059—132no—
192#2025—132no—
193#1988—131no—
194#1987—131no—
195#1875—132no—
196#1854—132no—
197#1797—131no—
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—21no—
202C23×C13—21no—
203C23×C13—21no—
204C23×C13—22no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13C22⋊Q812yes—
212C23×C13C22×D411yescharacteristic
213D4×C13—22no—
214D4×C13—22no—
215D4×C13—48no—
216D4×C13—41no—
217D4×C13—41no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—44no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13—44no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—84no—
244C2×C4×C13#12012yes—
245C2×C4×C13#12012yes—
246C2×C4×C13C22⋊Q812yes—
247C2×C4×C13#13512yes—
248C2×C4×C13AGL(1,ℤ/8)12yes—
249C2×C4×C13C22×D411yescharacteristic
250C2×C4×C13C22×D411yescharacteristic
251C2×C4×C13C22×Q811yescharacteristic
252C2×C4×C13C2×#4111yescharacteristic
253C2×C4×C132−1+411yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×Dic13—24no—
256C2×Dic13—24no—
257C2×Dic13—42no—
258C2×Dic13—42no—
259C2×Dic13—42no—
260C2×Dic13—42no—
261Dic26—48no—
262Dic26—48no—
263#1055—42no—
264#1055—42no—
265#533—264no—
266#533—264no—
267C2×C4⋊Q8—131no—
268C2×C4⋊Q8—131no—
269C2×#125—132no—
270C2×C22⋊Q8—261no—
271C2×C22⋊Q8—261no—
272C2×#121C2×D1311yescharacteristic
273C2×C4×Q8—261no—
274C2×C4×Q8—261no—
275C2×C4×D4—21no—
276C2×C4×D4C2×D1311yescharacteristic
277C2×#117—132no—
278C22×C42C2×D1311yescharacteristic
279#476—264no—
280#474—264no—
281C2×#107—132no—
282C2×#106—132no—
283C2×C4⋊C8—131no—
284C2×C4⋊C8—131no—
285C2×#102—132no—
286C2×#102—132no—
287C2×C22⋊C8—132no—
288#390C2×D1311yescharacteristic
289#389C2×D1311yescharacteristic
290#388—21no—
291#386—21no—
292#380C2×D1311yescharacteristic
293C4×C4⋊C4C2×D1311yescharacteristic
294C4×C22⋊C4—21no—
295#340—132no—
296#340—132no—
297#340—132no—
298#340—132no—
299#336—132no—
300C22×C13—22no—
301C22×C13—22no—
302C22×C13—22no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—41no—
306C22×C13—41no—
307C22×C13—42no—
308C22×C13—42no—
309C22×C13—42no—
310C22×C13—81no—
311C22×C13—81no—
312C22×C13—81no—
313C22×C13—81no—
314C22×C13C2×#12011yescharacteristic
315C22×C13C2×C22⋊Q811yescharacteristic
316C22×C13#53611yescharacteristic
317C22×C13C2×#13511yescharacteristic
318C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C13#57511yescharacteristic
320C22×C13#57511yescharacteristic
321C4×C13—22no—
322C4×C13—22no—
323C4×C13—42no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—81no—
327C4×C13—81no—
328C4×C13#44914yes—
329C4×C13#54811yescharacteristic
330C4×C13#54811yescharacteristic
331C4×C13D4×Q811yescharacteristic
332C4×C13D4×Q811yescharacteristic
333Dic13—44no—
334Dic13—44no—
335C22×Q8—261no—
336C22×Q8—261no—
337C22×D4—21no—
338C22×D4C22×D1311yescharacteristic
339C23×C4—21no—
340C23×C4C22⋊D1311yescharacteristic
341C23×C4C22⋊D1311yescharacteristic
342C23×C4C22×D1311yescharacteristic
343C22×C8—132no—
344C22×C8—132no—
345C4⋊Q8—134no—
346C4⋊Q8—134no—
347C4⋊Q8—262no—
348C4⋊Q8—262no—
349#125—264no—
350#125—264no—
351C22⋊Q8—268no—
352C22⋊Q8—268no—
353#121—22no—
354#121Dic2614yescomplemented
355C4×Q8—268no—
356C4×Q8—268no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4—44no—
360#117—264no—
361#117—264no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—132no—
364C2×C4⋊C4—132no—
365C2×C4⋊C4—262no—
366C2×C4⋊C4—262no—
367C2×C4⋊C4—261no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—262no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—21no—
381C2×C42—262no—
382C2×C42C22⋊D1311yescharacteristic
383C2×C42C22⋊D1311yescharacteristic
384C2×C42C22×D1311yescharacteristic
385C2×C42C22×D1311yescharacteristic
386#107—264no—
387#106—264no—
388C4⋊C8—262no—
389C4⋊C8—262no—
390#102—264no—
391#102—264no—
392C22⋊C8—264no—
393#95—21no—
394#95—21no—
395#95—21no—
396C2×C13—42no—
397C2×C13—82no—
398C2×C13#240911yescharacteristic
399C2×C13C2×#44911yescharacteristic
400C2×C13#300511yescharacteristic
401C2×C13#307611yescharacteristic
402C2×C13#307711yescharacteristic
403C2×C13#323311yescharacteristic
404C2×C13#323511yescharacteristic
405C24—21no—
406C24C2×C22⋊D1311yescharacteristic
407C2×Q8—264no—
408C2×Q8—264no—
409C2×Q8—522no—
410C2×Q8—522no—
411C2×Q8—522no—
412C2×Q8—522no—
413C2×D4—24no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4C2×Dic2612yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—262no—
439C22×C4—262no—
440C22×C4C2×Dic2612yes—
441C22×C4#612712yes—
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C2×C22⋊D1311yescharacteristic
444C22×C4C2×C22⋊D1311yescharacteristic
445C22×C4C2×C22⋊D1311yescharacteristic
446C22×C4C2×C22⋊D1311yescharacteristic
447C22×C4C23×D1311yescharacteristic
448C2×C8—262no—
449C2×C8—262no—
450C2×C8—262no—
451C2×C8—262no—
452C2×C8—262no—
453C2×C8—262no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—42no—
460C4⋊C4—134no—
461C4⋊C4—134no—
462C4⋊C4—268no—
463C4⋊C4—268no—
464C4⋊C4—264no—
465C4⋊C4—264no—
466C4⋊C4—262no—
467C4⋊C4—262no—
468C4⋊C4C2×Dic2612yes—
469C22⋊C4—24no—
470C22⋊C4—42no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—42no—
474C22⋊C4—268no—
475C42—22no—
476C42—22no—
477C42—21no—
478C42—21no—
479C42—42no—
480C42—268no—
481C42D4×D1312yes—
482C42D4×D1312yes—
483C13#2430011yescharacteristic, complemented, Sylow
484C23—21no—
485C23—21no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23#8817812yes—
498C23C22×C22⋊D1311yescharacteristic
499Q8—528no—
500Q8—528no—
501D4—22no—
502D4—22no—
503D4—48no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—84no—
532C2×C4—264no—
533C2×C4—264no—
534C2×C4—522no—
535C2×C4—522no—
536C2×C4—522no—
537C2×C4—522no—
538C2×C4#8817812yes—
539C2×C4#8818612yes—
540C2×C4#8819112yes—
541C2×C4#8819112yes—
542C2×C4#8820412yes—
543C2×C4C22×Dic2611yescharacteristic
544C2×C4C2×#612711yescharacteristic
545C2×C4C2×D4×D1311yescharacteristic
546C2×C4C2×D4×D1311yescharacteristic
547C2×C4#8825711yescharacteristic
548C2×C4#8825711yescharacteristic
549C8—522no—
550C8—522no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C2×#8817811yescharacteristic
566C22C2×#8818611yescharacteristic
567C22C2×#8819111yescharacteristic
568C22C2×#8820411yescharacteristic
569C22#1171952711yescharacteristic
570C22#1171952711yescharacteristic
571C22#1171953011yescharacteristic
572C4—22no—
573C4—22no—
574C4—42no—
575C4—41no—
576C4—41no—
577C4—81no—
578C4—81no—
579C4—524no—
580C4—524no—
581C4#1171869814yes—
582C4D4×Dic2611yescharacteristic
583C4D4×Dic2611yescharacteristic
584C4#1171925711yescharacteristic
585C4#1171925711yescharacteristic
586C2—42no—
587C2—82no—
588C2#1311820111yescharacteristic
589C2C2×#1171869811yescharacteristic
590C2#1312407611yescharacteristic
591C2#1312462411yescharacteristic
592C2#1312463311yescharacteristic
593C2#1312601111yescharacteristic
594C2#1312603011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC4×C13×#121C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenterC4×#121D13
hypocenterC13#24300
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
2. C2×#11718669C2semidirect
3. C2×#11718668C2semidirect
4. #13116174C2semidirect
5. #13115982C2semidirect
6. #13115788C2semidirect
7. #13115784C2semidirect
9. #13115033C2semidirect
10. #13114816C2semidirect
56. C13×#121Q8semidirect
94. #88123D4semidirect
95. #88123D4semidirect
354. #121Dic26semidirect
483. C13#24300semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
C2×#117186692
C2×#117186682
#131161742
#131159822
#131157882
#131157842
#131151592
#131150332
#131148162
C4×C13×#1212
#2430013