Finite Group Databasebeta

← #16804985

Subgroups — #16804985

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131365C211yesmaximal, characteristic, complemented
2D4×C4⋊#261C211yesmaximal, characteristic
3#13131017C211yesmaximal, characteristic, complemented
4#13130948C211yesmaximal, characteristic, complemented
5#13130941C212yesmaximal, complemented
6#13130900C212yesmaximal, complemented
7#13130801C212yesmaximal
8#13130633C211yesmaximal, characteristic, complemented
9#13130607C212yesmaximal
10C4×#88115C211yesmaximal, characteristic
11D13×#474C211yesmaximal, characteristic
12C2×Q8×#261—21no—
13C2×D4×#261C2212yes—
14C22×C4⋊#261—21no—
15D13×C4⋊Q8C2211yescharacteristic
16C4×D4×D13C2211yescharacteristic
17(C2×#261)⋊Q8—21no—
18C2×#88115C2211yescharacteristic
19C2×#88115C2211yescharacteristic
20#11719136—21no—
21C2×#88101C2212yes—
22C2×#88100C2212yes—
23#11719083C2212yes—
24#11719083C2212yes—
25#11719082—22no—
26C4⋊C4×#261C2212yes—
27#11719070—22no—
28#11719059C2211yescharacteristic
29C4×C4⋊#261C2211yescharacteristic
30C4×C4⋊#261C2211yescharacteristic
31C4×D13⋊C8C2211yescharacteristic
32C13×#474C411yescharacteristic, complemented
33#11718748C411yescharacteristic, complemented
34#11718668C411yescharacteristic, complemented
35#11718551C412yescomplemented
36D13×#107C2212yes—
37#11718507C411yescharacteristic, complemented
38D13×C4⋊C8C2211yescharacteristic
39D13×#102C2212yes—
40#11718420C412yescomplemented
41#11718265C2212yes—
42(C2×#261)⋊C8C2212yes—
43#11718246C2212yes—
44#11718246C2212yes—
45#11718246C2211yescharacteristic
46#11718246C2211yescharacteristic
47C23×#261—22no—
48C2×Q8×D13—21no—
49C2×D4×D13C2311yescharacteristic
50C22×C4×D13—21no—
51C2×C22⋊#261—22no—
52Q8×#261—44no—
53D4×#261—24no—
54D4×#261—42no—
55C2×C4⋊#261—22no—
56C2×C4⋊#261—22no—
57C2×C4⋊#261—21no—
58C2×C4⋊#261—21no—
59C2×C4⋊#261—44no—
60C2×C4⋊#261D411yescharacteristic
61C2×C4⋊#261D411yescharacteristic
62C2×C4⋊#261C2312yes—
63C2×C4⋊#261C2311yescharacteristic
64C2×C4⋊#261C2311yescharacteristic
65C2×C4×#261—22no—
66C2×C4×#261—21no—
67C2×C4×#261C2312yes—
68C2×D13⋊C8C2311yescharacteristic
69C2×D13⋊C8C2311yescharacteristic
70C13×C4⋊Q8C2×C411yescharacteristic, complemented
71C4×D4×C13C2×C411yescharacteristic
72#88198—21no—
73D4×Dic13C2×C411yescharacteristic
74C4×C22⋊D13—21no—
75C2×C8×D13C2312yes—
76#88147C2×C411yescharacteristic
77C4⋊C4×D13—21no—
78C4⋊C4×D13C2312yes—
79C4⋊C4×D13C2311yescharacteristic
80#88142—21no—
81#88142C2×C412yescomplemented
82#88135—21no—
83C22⋊C4×D13—21no—
84C4×D52C2×C411yescharacteristic
85C42×D13C2311yescharacteristic
86#88123C2×C411yescharacteristic, complemented
87#88115—22no—
88#88115Q814yescomplemented
89(C2×#261)⋊C4—22no—
90(C2×#261)⋊C4—22no—
91(C2×#261)⋊C4—22no—
92(C2×#261)⋊C4—21no—
93(C2×#261)⋊C4D412yes—
94C4×#1057—21no—
95C4×#1057—21no—
96#88101—42no—
97#88100—42no—
98C13×#107C2×C412yescomplemented
99C13×C4⋊C8C2×C411yescharacteristic, complemented
100C13×#102C2×C412yes—
101#88072C2×C412yes—
102#88061C2×C412yes—
103#88058C2×C412yescomplemented
104#88054C2×C412yescomplemented
105#88049C2×C412yes—
106#88047C2×C412yescomplemented
107#88047C2×C412yescomplemented
108C4⋊#1055C2×C411yescharacteristic, complemented
109#22968—131nomaximal, Sylow
110C23×D13—21no—
111C22×#261—21no—
112C22×#261—21no—
113C22×#261—22no—
114C22×#261—44no—
115C22×#261—44no—
116C22×#261—82no—
117C22×#261C2×D412yes—
118C22×#261C2×D412yes—
119C2×Q8×C13—21no—
120C2×D4×C13C22×C411yescharacteristic
121C22×C4×C13—21no—
122C2×C22⋊D13—21no—
123C22×Dic13—21no—
124Q8×D13—42no—
125Q8×D13—42no—
126D4×D13—21no—
127D4×D13—21no—
128D4×D13C2×Q812yes—
129D4×D13#4112yes—
130C2×D52C22×C411yescharacteristic
131C2×C4×D13—21no—
132C2×C4×D13—22no—
133C2×C4×D13—21no—
134C2×C4×D13—21no—
135C2×C4×D13—42no—
136C2×C4×D13—42no—
137C2×C4×D13C2×D411yescharacteristic
138C2×C4×D13C2×D411yescharacteristic
139C2×C4×D13C2411yescharacteristic
140C2×Dic26—21no—
141C2×Dic26—22no—
142C22⋊#261—44no—
143C2×#1057—21no—
144C2×#1057—21no—
145C4⋊#261—22no—
146C4⋊#261—22no—
147C4⋊#261—21no—
148C4⋊#261—22no—
149C4⋊#261—21no—
150C4⋊#261—22no—
151C4⋊#261—21no—
152C4⋊#261—44no—
153C4⋊#261—44no—
154C4⋊#261—42no—
155C4⋊#261—81no—
156C4⋊#261C2×Q812yes—
157C4×#261—22no—
158C4×#261—22no—
159C4×#261—44no—
160C4×#261—42no—
161D13⋊C8—21no—
162D13⋊C8—21no—
163D13⋊C8—21no—
164D13⋊C8C2×Q812yes—
165C2×C8×C13C22×C412yes—
166C13×C4⋊C4—21no—
167C13×C4⋊C4C22×C412yes—
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C22⋊C4—21no—
170C42×C13C22×C411yescharacteristic
171C22⋊Dic13—21no—
172#6103—21no—
173#6103—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13C22×C412yes—
176C4⋊Dic13C22×C411yescharacteristic
177#6101—22no—
178#6101—21no—
179#6101—22no—
180C4×Dic13C22×C411yescharacteristic
181C4×Dic13#4111yescharacteristic
182C4×Dic13#4111yescharacteristic
183C2×#1055C22×C412yes—
184C8×D13—22no—
185C8×D13—22no—
186C2×#474—131no—
187#2365—131no—
188D4×C4⋊C4—131no—
189#1990—131no—
190#1948—131no—
191#1943—132no—
192#1921—132no—
193#1864—132no—
194#1770—131no—
195#1762—132no—
196C4×#102—131no—
197C23×C13—21no—
198C22×D13—21no—
199C22×D13—22no—
200C22×D13—22no—
201C22×D13—41no—
202C22×D13—41no—
203C22×D13—41no—
204C22×D13—41no—
205C22×D13C22×D411yescharacteristic
206C2×#261—22no—
207C2×#261—22no—
208C2×#261—22no—
209C2×#261—22no—
210C2×#261—22no—
211C2×#261—22no—
212C2×#261—22no—
213C2×#261—41no—
214C2×#261—41no—
215C2×#261—42no—
216C2×#261—41no—
217C2×#261—41no—
218C2×#261—42no—
219C2×#261—42no—
220C2×#261—41no—
221C2×#261—88no—
222Q8×C13—42no—
223D4×C13—21no—
224D4×C13C4×Q812yescomplemented
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—42no—
228C2×C4×C13C4×D411yescharacteristic
229C2×C4×C13C4×D411yescharacteristic
230C2×C4×C13C23×C411yescharacteristic
231C22⋊D13—22no—
232C22⋊D13—22no—
233C2×Dic13—22no—
234C2×Dic13—21no—
235C2×Dic13—42no—
236C2×Dic13C4×D411yescharacteristic
237C2×Dic13C4×D411yescharacteristic
238C2×Dic13C2×#4111yescharacteristic
239D52—21no—
240D52C4×Q812yescomplemented
241C4×D13—21no—
242C4×D13—21no—
243C4×D13—42no—
244C4×D13—41no—
245C4×D13—41no—
246C4×D13—42no—
247C4×D13—42no—
248C4×D13—42no—
249C4×D13AGL(1,ℤ/8)12yes—
250C4×D13AGL(1,ℤ/8)12yes—
251C4×D13C22×Q811yescharacteristic
252C4×D13C2×#4111yescharacteristic
253C4×D13H(5,𝔽2)11yescharacteristic
254C4×D132−1+411yescharacteristic
255Dic26—42no—
256Dic26—44no—
257#1057—22no—
258#1057—41no—
259C8×C13—22no—
260#1055—22no—
261C2×C4⋊Q8—131no—
262C2×C4×Q8—261no—
263C2×C4×D4—131no—
264C2×C4×D4—132no—
265C22×C4⋊C4—261no—
266#474—131no—
267#474—131no—
268#474—132no—
269#474—131no—
270#474—132no—
271#474#26111yescharacteristic, complemented
272C2×#107—132no—
273C2×#106—132no—
274C2×C4⋊C8—131no—
275C2×#102—131no—
276C2×#102—132no—
277C2×#102—131no—
278C2×#97—132no—
279C2×C4×C8—131no—
280#391—261no—
281#389—132no—
282#389—132no—
283#387—262no—
284#385—262no—
285#384—131no—
286#380—261no—
287C4×C4⋊C4—131no—
288C4×C4⋊C4—132no—
289C4×C4⋊C4—131no—
290#340—132no—
291#340—131no—
292#340—131no—
293#340—132no—
294#340—132no—
295#336—132no—
296C22×C13—22no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13C2×C4×D411yescharacteristic
300C2×D13—22no—
301C2×D13—41no—
302C2×D13—41no—
303C2×D13—42no—
304C2×D13—42no—
305C2×D13—42no—
306C2×D13—42no—
307C2×D13#54611yescharacteristic
308C2×D13D4×Q811yescharacteristic
309C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
310C2×D13C2×AGL(1,ℤ/8)11yescharacteristic
311C2×D13#57711yescharacteristic
312C2×D13#57811yescharacteristic
313#261—42no—
314#261—42no—
315#261—42no—
316#261—81no—
317#261—82no—
318C4×C13—21no—
319C4×C13—42no—
320C4×C13—41no—
321C4×C13#44212yes—
322C4×C13C2×C4×Q811yescharacteristic
323C4×C13#52011yescharacteristic
324Dic13—21no—
325Dic13—42no—
326Dic13—41no—
327Dic13#44212yes—
328Dic13#55211yescharacteristic
329Dic13#55411yescharacteristic
330C22×Q8—261no—
331C22×D4—131no—
332C23×C4—261no—
333C23×C4—262no—
334C22×C8—131no—
335C22×C8—132no—
336C22×C8—131no—
337C4⋊Q8—132no—
338C4⋊Q8—131no—
339C4⋊Q8—261no—
340C4⋊Q8—261no—
341C4⋊Q8C2×#26111yescharacteristic, complemented
342C4×Q8—524no—
343C4×D4—131no—
344C4×D4—131no—
345C4×D4—131no—
346C4×D4—261no—
347C4×D4—261no—
348C4×D4—264no—
349C4×D4—522no—
350C4×D4C2×#26111yescharacteristic
351C2×C4⋊C4—131no—
352C2×C4⋊C4—131no—
353C2×C4⋊C4—132no—
354C2×C4⋊C4—131no—
355C2×C4⋊C4—131no—
356C2×C4⋊C4—132no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—261no—
359C2×C4⋊C4—261no—
360C2×C4⋊C4—262no—
361C2×C4⋊C4—262no—
362C2×C4⋊C4—261no—
363C2×C4⋊C4—524no—
364C2×C22⋊C4—261no—
365C2×C22⋊C4—262no—
366C2×C42—131no—
367C2×C42—132no—
368C2×C42—262no—
369C2×C42—261no—
370#107—132no—
371#107—132no—
372#107—132no—
373#107C2×#26112yescomplemented
374#106—522no—
375C4⋊C8—132no—
376C4⋊C8—131no—
377C4⋊C8C2×#26111yescharacteristic, complemented
378#102—134no—
379#102—132no—
380#102—132no—
381#102—132no—
382#102—262no—
383#102C2×#26112yes—
384#97—522no—
385C4×C8—261no—
386C4×C8—261no—
387#95—132no—
388#95—261no—
389#95—262no—
390#95—262no—
391#95—262no—
392C2×C13—42no—
393C2×C13#236011yescharacteristic
394C2×C13C2×#44211yescharacteristic
395C2×C13#294711yescharacteristic
396D13—42no—
397D13#332411yescharacteristic
398D13#333011yescharacteristic
399D13#338411yescharacteristic
400D13#338611yescharacteristic
401C24—261no—
402C2×Q8—21no—
403C2×Q8—262no—
404C2×Q8—261no—
405C2×Q8—522no—
406C2×Q8—522no—
407C2×D4—132no—
408C2×D4—132no—
409C2×D4—131no—
410C2×D4—261no—
411C2×D4—261no—
412C2×D4—261no—
413C2×D4C22×#26111yescharacteristic
414C22×C4—21no—
415C22×C4—131no—
416C22×C4—131no—
417C22×C4—131no—
418C22×C4—132no—
419C22×C4—132no—
420C22×C4—261no—
421C22×C4—262no—
422C22×C4—261no—
423C22×C4—261no—
424C22×C4—261no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4—262no—
428C22×C4—522no—
429C22×C4—522no—
430C22×C4—524no—
431C22×C4—524no—
432C22×C4—1042no—
433C2×C8—132no—
434C2×C8—132no—
435C2×C8—262no—
436C2×C8—262no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8—261no—
441C2×C8—261no—
442C2×C8C22×#26112yes—
443C4⋊C4—21no—
444C4⋊C4—132no—
445C4⋊C4—132no—
446C4⋊C4—131no—
447C4⋊C4—261no—
448C4⋊C4—262no—
449C4⋊C4—262no—
450C4⋊C4—262no—
451C4⋊C4—262no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—262no—
456C4⋊C4—262no—
457C4⋊C4—261no—
458C4⋊C4—522no—
459C4⋊C4—524no—
460C4⋊C4—524no—
461C4⋊C4—1041no—
462C4⋊C4C22×#26112yes—
463C4⋊C4C22×#26111yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—261no—
466C22⋊C4—261no—
467C22⋊C4—261no—
468C22⋊C4—524no—
469C42—131no—
470C42—131no—
471C42—131no—
472C42—262no—
473C42—262no—
474C42—522no—
475C42—524no—
476C42C22×#26111yescharacteristic
477C13#2296811yescharacteristic, complemented, Sylow
478C23—21no—
479C23—131no—
480C23—262no—
481C23—262no—
482C23—261no—
483C23—521no—
484C23—521no—
485C23—521no—
486C23—521no—
487Q8—42no—
488Q8—524no—
489Q8—522no—
490D4—21no—
491D4—132no—
492D4—262no—
493D4—262no—
494D4—261no—
495D4Q8×#26112yescomplemented
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—42no—
499C2×C4—131no—
500C2×C4—131no—
501C2×C4—132no—
502C2×C4—132no—
503C2×C4—131no—
504C2×C4—131no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—131no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—262no—
511C2×C4—262no—
512C2×C4—262no—
513C2×C4—262no—
514C2×C4—262no—
515C2×C4—262no—
516C2×C4—262no—
517C2×C4—261no—
518C2×C4—262no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—521no—
526C2×C4—521no—
527C2×C4—522no—
528C2×C4—521no—
529C2×C4—522no—
530C2×C4—521no—
531C2×C4—522no—
532C2×C4—522no—
533C2×C4—521no—
534C2×C4—1048no—
535C2×C4D4×#26111yescharacteristic
536C2×C4D4×#26111yescharacteristic
537C2×C4C23×#26111yescharacteristic
538C8—22no—
539C8—262no—
540C8—262no—
541C8—521no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—131no—
546C22—131no—
547C22—131no—
548C22—131no—
549C22—131no—
550C22—131no—
551C22—262no—
552C22—522no—
553C22—522no—
554C22—522no—
555C22—522no—
556C22—521no—
557C22—521no—
558C22C2×D4×#26111yescharacteristic
559C4—21no—
560C4—41no—
561C4—42no—
562C4—132no—
563C4—131no—
564C4—131no—
565C4—261no—
566C4—522no—
567C4—522no—
568C4—522no—
569C4—521no—
570C4—522no—
571C4—1041no—
572C4—1042no—
573C4#1171910212yes—
574C4C2×Q8×#26111yescharacteristic
575C4#1171963111yescharacteristic
576C2—42no—
577C2—131no—
578C2—131no—
579C2—131no—
580C2—131no—
581C2—522no—
582C2#1313136011yescharacteristic
583C2C2×#1171910211yescharacteristic
584C2#1313159411yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC2×C4×C13C23×C4
FrattiniC2×C4C23×#261
FittingC13×#474C4
socleC22×C13C2×C4×D4
prime radicalC2×D4×D13C23
cosocleC2×C4×D13C24
hypercenter#474#261
hypocenterC13#22968
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #13131365C2semidirect
3. #13131017C2semidirect
4. #13130948C2semidirect
5. #13130941C2semidirect
6. #13130900C2semidirect
8. #13130633C2semidirect
32. C13×#474C4semidirect
33. #11718748C4semidirect
34. #11718668C4semidirect
35. #11718551C4semidirect
37. #11718507C4semidirect
40. #11718420C4semidirect
70. C13×C4⋊Q8C2×C4semidirect
81. #88142C2×C4semidirect
86. #88123C2×C4semidirect
88. #88115Q8semidirect
98. C13×#107C2×C4semidirect
99. C13×C4⋊C8C2×C4semidirect
103. #88058C2×C4semidirect
104. #88054C2×C4semidirect
106. #88047C2×C4semidirect
107. #88047C2×C4semidirect
108. C4⋊#1055C2×C4semidirect
224. D4×C13C4×Q8semidirect
240. D52C4×Q8semidirect
271. #474#261semidirect
341. C4⋊Q8C2×#261semidirect
373. #107C2×#261semidirect
377. C4⋊C8C2×#261semidirect
477. C13#22968semidirect
495. D4Q8×#261semidirect

Maximal subgroups

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

subgroupindex
#131313652
D4×C4⋊#2612
#131310172
#131309482
#131309412
#131309002
#131308012
#131306332
#131306072
C4×#881152
D13×#4742
#2296813