Finite Group Databasebeta

← #15925990

Subgroups — #15925990

Order 3328.

900 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718669C211yesmaximal, characteristic
2C2×C4×#6105C211yesmaximal, characteristic
3#13118675C211yesmaximal, characteristic, complemented
4#13116380C211yesmaximal, characteristic, complemented
5#13116313C211yesmaximal, characteristic, complemented
6#13116214C211yesmaximal, characteristic, complemented
7#13116169C211yesmaximal, characteristic, complemented
8#13115561C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic
11#13115170C211yesmaximal, characteristic
12#13115103C211yesmaximal, characteristic, complemented
13#13115097C211yesmaximal, characteristic
14#13115097C211yesmaximal, characteristic
15D4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4—21no—
20C22×#6105C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#385—21no—
26C13×#385—21no—
27C13×#384C2211yescharacteristic
28C13×#380—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C4×#6105—24no—
34#11718669—24no—
35#11718642—21no—
36#11718640—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
44C2×#88048C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718318—21no—
52#11718307—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C22×Dic26—21no—
66C22×Dic26C2311yescharacteristic
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—41no—
72C4×D4×C13—41no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—44no—
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C42×C13C2311yescharacteristic
89C2×#6105—22no—
90C2×#6105—22no—
91C2×#6105Q814yescomplemented
92C2×C4⋊Dic13—21no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88123—22no—
105#88123—41no—
106C4×Dic26—22no—
107C4×Dic26—41no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112#88072—22no—
113#88072—22no—
114#88072D414yes—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88050—22no—
122#88050—22no—
123#88050—41no—
124#88048—22no—
125#88048—22no—
126#88048—22no—
127#88048—22no—
128#88048—41no—
129C4⋊#1055—22no—
130C4×#1055—22no—
131#26376—131nomaximal, Sylow
132C24×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13C2×D412yes—
137C2×D4×C13C2×Q812yes—
138C2×D4×C13#4112yes—
139C22×C4×C13—24no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—81no—
150C22×C4×C13—81no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26—42no—
168C2×Dic26—42no—
169C2×Dic26—81no—
170C2×Dic26C2×Q812yes—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—41no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4—42no—
180C13×C4⋊C4—81no—
181C13×C4⋊C4SD1614yescomplemented
182C13×C4⋊C4#4112yes—
183C13×C22⋊C4—24no—
184C13×C22⋊C4—42no—
185C13×C22⋊C4—42no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191C42×C13—21no—
192#6105—28no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—42no—
199C4⋊Dic13C2×D412yes—
200#6101—42no—
201#6101—81no—
202#6101—81no—
203C4×Dic13—42no—
204C2×#1055—21no—
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×#1055C2×D412yes—
215C2×#1055C2×Q812yes—
216C2×#476—131no—
217C2×C4×SD16—131no—
218#2451—131no—
219D4×C4⋊C4D1311yescharacteristic
220#2096—131no—
221#2084—131no—
222#2066—131no—
223#2058—131no—
224#1941—131no—
225#1916—131no—
226#1877—131no—
227#1877—131no—
228#1865—131no—
229#1864—131no—
230#1864—131no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13C22×D411yescharacteristic
239D4×C13—22no—
240D4×C13—22no—
241D4×C13—22no—
242D4×C13C22⋊Q814yes—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—48no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—84no—
269C2×C4×C13—84no—
270C2×C4×C13C2×SD1612yes—
271C2×C4×C13C2×SD1612yes—
272C2×C4×C13C2×SD1612yes—
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C22×Q811yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13C2×#4111yescharacteristic
277C2×C4×C13H(5,𝔽2)11yescharacteristic
278C2×C4×C132−1+411yescharacteristic
279C2×Dic13—22no—
280C2×Dic13—22no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291Dic26—22no—
292Dic26—22no—
293Dic26—41no—
294Dic26—41no—
295Dic26—84no—
296#1055—22no—
297#1055—22no—
298#1055—41no—
299#1055—41no—
300C22×SD16—131no—
301C2×C4⋊Q8—131no—
302C2×C4×Q8—131no—
303C2×C4×D4C2×D1311yescharacteristic
304C2×C4×D4C2×D1311yescharacteristic
305C2×C4×D4C2×D1311yescharacteristic
306C22×C4⋊C4—21no—
307#476—264no—
308C4×SD16—264no—
309C2×#106—131no—
310C2×#106—131no—
311C2×#106—131no—
312C2×#106—131no—
313C2×#106—131no—
314C2×C4⋊C8—131no—
315C2×#103—131no—
316C2×#103—131no—
317C2×#103—131no—
318C2×#102—131no—
319C2×#102—131no—
320C2×#102—131no—
321C2×C4×C8—131no—
322#398—261no—
323#395—261no—
324#391—131no—
325#391—131no—
326#391—261no—
327#389—131no—
328#389—131no—
329#389C2×D1311yescharacteristic
330#389C2×D1311yescharacteristic
331#387—261no—
332#385—21no—
333#385—21no—
334#384C2×D1311yescharacteristic
335#380—21no—
336C4×C4⋊C4C2×D1311yescharacteristic
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#336—131no—
342#336—131no—
343#336—131no—
344#336—131no—
345C22×C13—24no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—42no—
352C22×C13#52511yescharacteristic
353C22×C13D4211yescharacteristic
354C22×C13D4×Q811yescharacteristic
355C22×C13C22×SD1611yescharacteristic
356C22×C13#57511yescharacteristic
357C22×C13#57711yescharacteristic
358C22×C13#57711yescharacteristic
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—22no—
362C4×C13—42no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—41no—
366C4×C13—81no—
367C4×C13—81no—
368C4×C13C2×C22⋊Q811yescharacteristic
369C4×C13#53911yescharacteristic
370C4×C13#54711yescharacteristic
371C4×C13#55411yescharacteristic
372Dic13—42no—
373Dic13—42no—
374Dic13—81no—
375Dic13—81no—
376C22×Q8—131no—
377C22×Q8—261no—
378C22×D4C22×D1311yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—21no—
382C2×SD16—134no—
383C2×SD16—262no—
384C2×SD16—262no—
385C22×C8—131no—
386C22×C8—131no—
387C22×C8—131no—
388C22×C8—131no—
389C4⋊Q8—262no—
390C4⋊Q8—521no—
391C4×Q8—262no—
392C4×Q8—521no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—41no—
398C4×D4—41no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—44no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4—261no—
410C2×C4⋊C4—261no—
411C2×C4⋊C4C22⋊D1311yescharacteristic
412C2×C4⋊C4C22⋊D1311yescharacteristic
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C42—261no—
420C2×C42C22×D1311yescharacteristic
421C2×C42C22×D1311yescharacteristic
422C2×C42C22×D1311yescharacteristic
423#106—262no—
424#106—262no—
425#106—262no—
426#106—262no—
427#106—521no—
428C4⋊C8—262no—
429#103—262no—
430#103—262no—
431#103—521no—
432#102—134no—
433#102—262no—
434#102—262no—
435C4×C8—262no—
436#95—21no—
437#95—21no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95—261no—
442#95—261no—
443#95—261no—
444#95C22⋊D1311yescharacteristic
445#95C22⋊D1311yescharacteristic
446C2×C13—44no—
447C2×C13#244911yescharacteristic
448C2×C13#310111yescharacteristic
449C2×C13#312511yescharacteristic
450C2×C13#326711yescharacteristic
451C2×C13D4×SD1611yescharacteristic
452C2×C13Q8×SD1611yescharacteristic
453C2×C13#338811yescharacteristic
454C24—21no—
455C2×Q8—132no—
456C2×Q8—261no—
457C2×Q8—261no—
458C2×Q8—261no—
459C2×Q8—261no—
460C2×Q8—261no—
461C2×Q8—522no—
462C2×Q8—522no—
463C2×Q8—1041no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4#612712yes—
468C2×D4D4×D1312yes—
469C2×D4Q8×D1312yes—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—42no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—81no—
481C22×C4—81no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C23×D1311yescharacteristic
493SD16—268no—
494C2×C8—132no—
495C2×C8—132no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—42no—
513C4⋊C4—42no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—132no—
517C4⋊C4—261no—
518C4⋊C4—261no—
519C4⋊C4—261no—
520C4⋊C4—261no—
521C4⋊C4—261no—
522C4⋊C4—522no—
523C4⋊C4—522no—
524C4⋊C4—1041no—
525C4⋊C4—1041no—
526C4⋊C4#610514yescomplemented
527C4⋊C4#612712yes—
528C22⋊C4—24no—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—21no—
537C42—522no—
538C13#2637611yescharacteristic, complemented, Sylow
539C23—22no—
540C23—22no—
541C23—22no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C22×C22⋊D1311yescharacteristic
547Q8—262no—
548Q8—262no—
549Q8—521no—
550Q8—521no—
551Q8—1044no—
552D4—22no—
553D4—22no—
554D4—22no—
555D4#8815014yes—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—48no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—84no—
582C2×C4—84no—
583C2×C4—262no—
584C2×C4—262no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4—521no—
594C2×C4—521no—
595C2×C4C2×#610512yes—
596C2×C4C2×#610512yes—
597C2×C4C2×#610512yes—
598C2×C4C2×#612711yescharacteristic
599C2×C4C2×#612711yescharacteristic
600C2×C4C2×D4×D1311yescharacteristic
601C2×C4#8825111yescharacteristic
602C2×C4C2×Q8×D1311yescharacteristic
603C2×C4#8825411yescharacteristic
604C8—262no—
605C8—262no—
606C8—521no—
607C8—521no—
608C22—24no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22#1171949611yescharacteristic
616C22C22×#610511yescharacteristic
617C22D4×C22⋊D1311yescharacteristic
618C22Q8×C22⋊D1311yescharacteristic
619C22#1171952711yescharacteristic
620C22#1171954111yescharacteristic
621C22#1171954211yescharacteristic
622C4—22no—
623C4—22no—
624C4—22no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—522no—
632C4—522no—
633C4—1041no—
634C4—1041no—
635C4#1171921211yescharacteristic
636C4C2×#8815011yescharacteristic
637C4#1171921611yescharacteristic
638C4#1171922011yescharacteristic
639C2—44no—
640C2#1311864511yescharacteristic
641C2#1312484411yescharacteristic
642C2#1312511311yescharacteristic
643C2#1312636211yescharacteristic
644C2D4×#610511yescharacteristic
645C2Q8×#610511yescharacteristic
646C2#1312778111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterD4×C4⋊C4D13
hypocenterC13#26376
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13118675C2semidirect
4. #13116380C2semidirect
5. #13116313C2semidirect
6. #13116214C2semidirect
7. #13116169C2semidirect
8. #13115561C2semidirect
9. #13115395C2semidirect
12. #13115103C2semidirect
91. C2×#6105Q8semidirect
181. C13×C4⋊C4SD16semidirect
526. C4⋊C4#6105semidirect
538. C13#26376semidirect

Maximal subgroups

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

subgroupindex
C2×#117186692
C2×C4×#61052
#131186752
#131163802
#131163132
#131162142
#131161692
#131155612
#131153952
#131151702
#131151032
#131150972
D4×C13×C4⋊C42
#2637613