Finite Group Databasebeta

← #15870518

Subgroups — #15870518

Order 3328.

948 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic
2#13117391C211yesmaximal, characteristic, complemented
3C4×D4×Dic13C211yesmaximal, characteristic
4#13115791C211yesmaximal, characteristic, complemented
5#13115602C211yesmaximal, characteristic, complemented
6#13115426C211yesmaximal, characteristic, complemented
7#13115412C211yesmaximal, characteristic, complemented
8#13115095C211yesmaximal, characteristic
9#13115081C211yesmaximal, characteristic
10#13114728C211yesmaximal, characteristic, complemented
11#13114724C211yesmaximal, characteristic, complemented
12C4⋊C8×Dic13C211yesmaximal, characteristic, complemented
13#102×Dic13C211yesmaximal, characteristic
14#102×Dic13C211yesmaximal, characteristic
15C13×#1804C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×D4×Dic13C2211yescharacteristic
18C2×D4×Dic13C2211yescharacteristic
19C22×C4×Dic13—21no—
20C2×#88124C2211yescharacteristic
21C2×C13×C4⋊C8C2211yescharacteristic
22C2×C13×#102C2211yescharacteristic
23C2×C13×#102C2211yescharacteristic
24C13×#382C2211yescharacteristic
25C2×#88072C2211yescharacteristic
26C2×#88072C2211yescharacteristic
27C4×C22⋊Dic13—21no—
28C2×C8×Dic13C2211yescharacteristic
29C2×C8×Dic13C2211yescharacteristic
30#11718670C418yescomplemented
31C4⋊C4×Dic13C2211yescharacteristic
32C4⋊C4×Dic13C2211yescharacteristic
33C4⋊C4×Dic13C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35#11718634C2211yescharacteristic
36#11718634C2211yescharacteristic
37C2×#88048C2211yescharacteristic
38C2×#88048C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40C2×#88047C2211yescharacteristic
41C22⋊C4×Dic13—21no—
42C22⋊C4×Dic13—21no—
43C4×C4⋊Dic13C2211yescharacteristic
44C42×Dic13C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46#11718313—21no—
47#11718313—21no—
48#11718310—21no—
49#11718310—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×Dic13—21no—
63C23×Dic13—21no—
64C22×C8×C13C2311yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C4×D4×C13—22no—
67C4×D4×C13C2×C414yes—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C42×C13C2311yescharacteristic
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13—21no—
75D4×Dic13—22no—
76D4×Dic13—22no—
77D4×Dic13—22no—
78D4×Dic13Q814yes—
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13—21no—
91C2×C4×Dic13—21no—
92C2×C4×Dic13—44no—
93C2×C4×Dic13D411yescharacteristic
94C2×C4×Dic13D411yescharacteristic
95C2×C4×Dic13D411yescharacteristic
96C2×C4×Dic13D411yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101#88124—22no—
102#88124C2×C414yescomplemented
103C13×C4⋊C8—22no—
104C13×#102—22no—
105C13×#102—22no—
106C13×#95—21no—
107C13×#95—21no—
108#88072C2×C414yes—
109#88072C2×C414yes—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117C8×Dic13—22no—
118C8×Dic13—22no—
119#88048—22no—
120#88048C2×C414yescomplemented
121#88047—22no—
122#88047C2×C414yescomplemented
123C4⋊#1055C2×C414yescomplemented
124C4×#478—131nomaximal, Sylow
125C24×C13—21no—
126C2×D4×C13—21no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13C22×C412yes—
130C2×D4×C13C2×Q812yes—
131C2×D4×C13#4112yes—
132C22×C4×C13—21no—
133C22×C4×C13—24no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—42no—
137C22×C4×C13—42no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2411yescharacteristic
141C22×Dic13—24no—
142C22×Dic13—21no—
143C22×Dic13—21no—
144C22×Dic13—21no—
145C22×Dic13—21no—
146C22×Dic13—24no—
147C22×Dic13—42no—
148C22×Dic13—42no—
149C22×Dic13—42no—
150C22×Dic13—42no—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4C22×C412yes—
167C13×C22⋊C4—24no—
168C42×C13C22×C412yes—
169C42×C13#4112yes—
170C22⋊Dic13—24no—
171C22⋊Dic13—24no—
172C4⋊Dic13—21no—
173C4⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13C22×C412yes—
177C4⋊Dic13C22×C412yes—
178C4⋊Dic13C2×Q812yes—
179C4⋊Dic13#4112yes—
180#6101—24no—
181#6101—24no—
182#6101—42no—
183#6101—42no—
184C4×Dic13—21no—
185C4×Dic13—21no—
186C4×Dic13—22no—
187C4×Dic13—22no—
188C4×Dic13—22no—
189C4×Dic13—41no—
190C4×Dic13—42no—
191C4×Dic13—42no—
192C4×Dic13—42no—
193C4×Dic13—42no—
194C4×Dic13—42no—
195C4×Dic13C2×Q812yes—
196C4×Dic13#4112yes—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055C22×C412yes—
202C2×#1055C22×C412yes—
203C2×#478—131no—
204C4×#125—131no—
205C42×D4—131no—
206#1989—131no—
207#1949—131no—
208#1921—131no—
209#1919—131no—
210#1864—131no—
211#1862—131no—
212#1804D1311yescharacteristic
213C4×#107—131no—
214C4×#106—131no—
215C4×C4⋊C8—131no—
216C4×#102—131no—
217C4×#102—131no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13C22×D411yescharacteristic
226D4×C13—22no—
227D4×C13—22no—
228D4×C13—22no—
229D4×C13C4×Q814yes—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—22no—
235C2×C4×C13—48no—
236C2×C4×C13—41no—
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—41no—
244C2×C4×C13C4×D412yes—
245C2×C4×C13C4×D412yes—
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×Q811yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×C4×C13C2×#4111yescharacteristic
250C2×C4×C13C2×#4111yescharacteristic
251C2×C4×C13C2×#4111yescharacteristic
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—22no—
257C2×Dic13—22no—
258C2×Dic13—22no—
259C2×Dic13—21no—
260C2×Dic13—22no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—48no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—48no—
273C2×Dic13C22⋊Q812yes—
274C2×Dic13C22⋊Q812yes—
275C2×Dic13#13512yes—
276C2×Dic13#13512yes—
277C2×Dic13AGL(1,ℤ/8)12yes—
278C8×C13—41no—
279C8×C13—41no—
280#1055—22no—
281#1055—22no—
282C2×#125—131no—
283C2×C4×D4—131no—
284C2×C4×D4—131no—
285C2×C4×D4C2×D1311yescharacteristic
286C22×C42—261no—
287#478—138no—
288C2×#107—131no—
289C2×#107—131no—
290C2×#106—131no—
291C2×#106—131no—
292C2×C4⋊C8—131no—
293C2×C4⋊C8C2×D1311yescharacteristic
294C2×#102—131no—
295C2×#102—131no—
296C2×#102C2×D1311yescharacteristic
297C2×#102C2×D1311yescharacteristic
298C2×C4×C8—131no—
299C2×C4×C8—131no—
300#389—131no—
301#389—131no—
302#387—261no—
303#387—261no—
304#382C2×D1311yescharacteristic
305C4×C4⋊C4—131no—
306C4×C4⋊C4—131no—
307C4×C4⋊C4—131no—
308C4×C4⋊C4—131no—
309C4×C4⋊C4—131no—
310C4×C4⋊C4—261no—
311C4×C4⋊C4—261no—
312C4×C22⋊C4—261no—
313C4×C22⋊C4—261no—
314C4×C22⋊C4—261no—
315C43—131no—
316#340—131no—
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340C2×D1311yescharacteristic
323#340C2×D1311yescharacteristic
324#336—131no—
325#336—131no—
326C22×C13—24no—
327C22×C13—42no—
328C22×C13—42no—
329C22×C13—42no—
330C22×C13—42no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13C2×C4×D411yescharacteristic
334C22×C13C2×C22⋊Q811yescharacteristic
335C22×C13#52511yescharacteristic
336C22×C13C2×#13511yescharacteristic
337C22×C13C2×#13511yescharacteristic
338C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C13#57511yescharacteristic
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—81no—
344C4×C13—81no—
345C4×C13C2×C4×Q811yescharacteristic
346C4×C13C4×#4111yescharacteristic
347C4×C13#52911yescharacteristic
348C4×C13#53311yescharacteristic
349Dic13—22no—
350Dic13—22no—
351Dic13—42no—
352Dic13—41no—
353Dic13—42no—
354Dic13—42no—
355Dic13—42no—
356Dic13#47814yescomplemented
357C22×D4C22×D1311yescharacteristic
358C23×C4—21no—
359C23×C4—261no—
360C23×C4—261no—
361C22×C8—131no—
362C22×C8—131no—
363C22×C8C22×D1311yescharacteristic
364C22×C8C22×D1311yescharacteristic
365#125—134no—
366#125—262no—
367C4×D4—22no—
368C4×D4—134no—
369C4×D4—262no—
370C4×D4—262no—
371C4×D4—262no—
372C4×D4C4×D1314yes—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—131no—
375C2×C4⋊C4—131no—
376C2×C4⋊C4—131no—
377C2×C4⋊C4—261no—
378C2×C4⋊C4—261no—
379C2×C4⋊C4—261no—
380C2×C4⋊C4—261no—
381C2×C4⋊C4C22×D1311yescharacteristic
382C2×C4⋊C4C22×D1311yescharacteristic
383C2×C4⋊C4C22×D1311yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—261no—
386C2×C22⋊C4—261no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—261no—
394C2×C42—261no—
395C2×C42—261no—
396C2×C42—261no—
397C2×C42—261no—
398C2×C42—524no—
399C2×C42C22×D1311yescharacteristic
400#107—134no—
401#107—262no—
402#106—134no—
403#106—262no—
404C4⋊C8—22no—
405C4⋊C8—134no—
406#102—22no—
407#102—22no—
408#102—134no—
409#102—134no—
410C4×C8—262no—
411C4×C8—262no—
412#95—21no—
413#95—21no—
414#95—261no—
415#95—261no—
416#95—261no—
417#95—261no—
418#95—261no—
419#95—261no—
420#95—261no—
421C2×C13—44no—
422C2×C13C4×C22⋊Q811yescharacteristic
423C2×C13C4×#13511yescharacteristic
424C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
425C2×C13C2×#47811yescharacteristic
426C2×C13#307611yescharacteristic
427C2×C13#310211yescharacteristic
428C2×C13#310511yescharacteristic
429C24—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4C2×C4×D1312yes—
434C2×D4#612912yes—
435C2×D4Q8×D1312yes—
436C22×C4—21no—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—264no—
447C22×C4—264no—
448C22×C4—261no—
449C22×C4—261no—
450C22×C4—261no—
451C22×C4—261no—
452C22×C4—522no—
453C22×C4—522no—
454C22×C4—522no—
455C22×C4—522no—
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458C22×C4C23×D1311yescharacteristic
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—132no—
466C2×C8—132no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—132no—
477C4⋊C4—132no—
478C4⋊C4—132no—
479C4⋊C4—132no—
480C4⋊C4—264no—
481C4⋊C4—264no—
482C4⋊C4—261no—
483C4⋊C4—261no—
484C4⋊C4—261no—
485C4⋊C4—261no—
486C4⋊C4—522no—
487C4⋊C4—522no—
488C4⋊C4C2×C4×D1312yes—
489C22⋊C4—24no—
490C22⋊C4—264no—
491C22⋊C4—264no—
492C42—132no—
493C42—132no—
494C42—262no—
495C42—262no—
496C42—262no—
497C42—261no—
498C42—261no—
499C42—521no—
500C42—522no—
501C42—522no—
502C42—522no—
503C42—522no—
504C42—522no—
505C42C2×C4×D1312yes—
506C42#612912yes—
507C13C4×#47811yescharacteristic, complemented, Sylow
508C23—22no—
509C23—22no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23C2×D4×D1311yescharacteristic
516D4—22no—
517D4—22no—
518D4—22no—
519D4#8814114yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—48no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—132no—
535C2×C4—132no—
536C2×C4—132no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—261no—
540C2×C4—261no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—262no—
544C2×C4—262no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—262no—
549C2×C4—262no—
550C2×C4—528no—
551C2×C4—528no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4#8813512yes—
561C2×C4#8813512yes—
562C2×C4C22×C4×D1311yescharacteristic
563C2×C4C2×#612911yescharacteristic
564C2×C4C2×#612911yescharacteristic
565C2×C4C2×Q8×D1311yescharacteristic
566C2×C4#41×D1311yescharacteristic
567C2×C4#41×D1311yescharacteristic
568C8—41no—
569C8—41no—
570C8—262no—
571C8—262no—
572C22—24no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22C2×#8813511yescharacteristic
580C22#1171931111yescharacteristic
581C22D13×C22⋊Q811yescharacteristic
582C22D13×#13511yescharacteristic
583C22D13×#13511yescharacteristic
584C22D13×AGL(1,ℤ/8)11yescharacteristic
585C22#1171947811yescharacteristic
586C4—22no—
587C4—22no—
588C4—42no—
589C4—81no—
590C4—81no—
591C4—134no—
592C4—262no—
593C4—262no—
594C4—522no—
595C4—522no—
596C4—522no—
597C4—522no—
598C4—521no—
599C4C2×#8814111yescharacteristic
600C4#1171922711yescharacteristic
601C4#1171930511yescharacteristic
602C4#1171932711yescharacteristic
603C2—44no—
604C2#1311736411yescharacteristic
605C2#1312360411yescharacteristic
606C2#1312364011yescharacteristic
607C2D13×#47811yescharacteristic
608C2#1312462111yescharacteristic
609C2#1312485111yescharacteristic
610C2#1312488211yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1804C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
cosocleC22×C4×C13C24
hypercenter#1804D13
hypocenterC13C4×#478
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. #13117391C2semidirect
4. #13115791C2semidirect
5. #13115602C2semidirect
6. #13115426C2semidirect
7. #13115412C2semidirect
10. #13114728C2semidirect
11. #13114724C2semidirect
12. C4⋊C8×Dic13C2semidirect
30. #11718670C4semidirect
102. #88124C2×C4semidirect
120. #88048C2×C4semidirect
122. #88047C2×C4semidirect
123. C4⋊#1055C2×C4semidirect
356. Dic13#478semidirect
507. C13C4×#478semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
#131173912
C4×D4×Dic132
#131157912
#131156022
#131154262
#131154122
#131150952
#131150812
#131147282
#131147242
C4⋊C8×Dic132
#102×Dic132
C13×#18042
C4×#47813