Finite Group Databasebeta

← #15880659

Subgroups — #15880659

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718625C211yesmaximal, characteristic
2#13117731C211yesmaximal, characteristic
3#13117705C211yesmaximal, characteristic
4#13115573C211yesmaximal, characteristic, complemented
5#13115568C211yesmaximal, characteristic, complemented
6#13115426C211yesmaximal, characteristic, complemented
7#13115424C211yesmaximal, characteristic, complemented
8#13115417C211yesmaximal, characteristic, complemented
9#13115405C211yesmaximal, characteristic, complemented
10#13114932C211yesmaximal, characteristic
11#13114867C211yesmaximal, characteristic
12#13114732C211yesmaximal, characteristic, complemented
13#13114724C211yesmaximal, characteristic, complemented
14#13114622C211yesmaximal, characteristic
15C13×#1824C211yesmaximal, characteristic
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88180—21no—
18C2×#88180C2211yescharacteristic
19C22×#6099C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C13×#380C2211yescharacteristic
22#11718873C2211yescharacteristic
23#11718872—21no—
24C4×C22⋊Dic13C2211yescharacteristic
25C2×#88055C2211yescharacteristic
26C2×C8×Dic13C2211yescharacteristic
27#11718646C2211yescharacteristic
28#11718646C2211yescharacteristic
29#11718642—21no—
30#11718642—21no—
31C4⋊C4×Dic13C2211yescharacteristic
32C4⋊C4×Dic13C2211yescharacteristic
33C4⋊C4×Dic13C2211yescharacteristic
34C4⋊C4×Dic13C2211yescharacteristic
35#11718634C2211yescharacteristic
36#11718634C2211yescharacteristic
37#11718625C418yescomplemented
38C2×#88048C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44#11718605—21no—
45#11718605—21no—
46#11718312—21no—
47#11718310—21no—
48C13×#340C2211yescharacteristic
49C13×#340C2211yescharacteristic
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718142C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×C8×C13C2311yescharacteristic
63C22×C8×C13C2311yescharacteristic
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4C2×C414yes—
67C2×C13×C4⋊C4C2311yescharacteristic
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C22⋊C4—21no—
72C2×C22⋊Dic13—21no—
73C2×C22⋊Dic13—21no—
74C2×C22⋊Dic13D411yescharacteristic
75C2×C22⋊Dic13D411yescharacteristic
76#88180—22no—
77#88180—44no—
78#88180C2×C414yes—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13C2311yescharacteristic
82C2×C4⋊Dic13C2311yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
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×Dic13C2311yescharacteristic
93C2×C4×Dic13C2311yescharacteristic
94C2×#6099—22no—
95C2×#6099—22no—
96C2×#6099C2×C414yes—
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C13×C22⋊C8—22no—
100C13×#95—21no—
101#88071—21no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071D411yescharacteristic
111#88071D411yescharacteristic
112#88055—22no—
113C8×Dic13—22no—
114#88048—22no—
115#88048C2×C414yes—
116#88048C2×C414yes—
117#88047—22no—
118#88047C2×C414yes—
119#88047C2×C414yes—
120#22622—131nomaximal, Sylow
121C24×C13C2×D411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—24no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—42no—
132C22×C4×C13—42no—
133C22×C4×C13C22×C412yes—
134C22×C4×C13C2×D411yescharacteristic
135C22×C4×C13#4112yes—
136C22×C4×C13C2411yescharacteristic
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—21no—
141C22×Dic13C2×D411yescharacteristic
142C22×Dic13C2×D411yescharacteristic
143C22×Dic13C2×D411yescharacteristic
144C22×Dic13C2×D411yescharacteristic
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—21no—
148C2×C8×C13—21no—
149C2×C8×C13—21no—
150C2×C8×C13—21no—
151C13×C4⋊C4—24no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—21no—
156C13×C4⋊C4—21no—
157C13×C4⋊C4—21no—
158C13×C4⋊C4C22×C412yes—
159C13×C4⋊C4C22×C412yes—
160C13×C22⋊C4—81no—
161C22⋊Dic13—24no—
162C22⋊Dic13—22no—
163C22⋊Dic13—41no—
164C22⋊Dic13—42no—
165C4⋊Dic13—21no—
166C4⋊Dic13—21no—
167C4⋊Dic13—21no—
168C4⋊Dic13—21no—
169C4⋊Dic13—21no—
170C4⋊Dic13—21no—
171C4⋊Dic13—42no—
172C4⋊Dic13—42no—
173C4⋊Dic13C22×C412yes—
174C4⋊Dic13C22×C412yes—
175#6101—42no—
176#6101—42no—
177C4×Dic13—24no—
178C4×Dic13—21no—
179C4×Dic13—21no—
180C4×Dic13—21no—
181C4×Dic13—21no—
182C4×Dic13—42no—
183C4×Dic13—42no—
184C4×Dic13—81no—
185C4×Dic13—81no—
186#6099—28no—
187C2×#1055—21no—
188C2×#1055—21no—
189C2×#1055C22×C412yes—
190C2×#1055C22×C412yes—
191C2×#1055#4112yes—
192C2×#1055#4112yes—
193C2×#428—131no—
194#2347—131no—
195#2344—131no—
196#1943—131no—
197#1942—131no—
198#1921—131no—
199#1920—131no—
200#1919—131no—
201#1918—131no—
202#1825—131no—
203#1824D1311yescharacteristic
204#1809—131no—
205#1776—131no—
206C4×#106—131no—
207#1753—131no—
208C23×C13—21no—
209C23×C13—21no—
210C23×C13—21no—
211C23×C13—21no—
212C23×C13—21no—
213C23×C13—21no—
214C23×C13C4×D412yes—
215C23×C13C22×D411yescharacteristic
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—48no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13C4×D412yes—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×C4×C132−1+411yescharacteristic
241C2×C4×C132−1+411yescharacteristic
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—22no—
245C2×Dic13—22no—
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—41no—
256C2×Dic13—41no—
257C2×Dic13—41no—
258C2×Dic13—41no—
259C2×Dic13—41no—
260C2×Dic13—41no—
261C2×Dic13—41no—
262C2×Dic13—41no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13AGL(1,ℤ/8)12yes—
266C8×C13—41no—
267C8×C13—41no—
268#1055—22no—
269#1055#11714yescomplemented
270C22×M16—131no—
271C2×#117—131no—
272C2×#117—261no—
273C22×C4⋊C4C2×D1311yescharacteristic
274#428—138no—
275C2×#107—131no—
276C2×#107—131no—
277C2×#107—131no—
278C2×#106—131no—
279C2×#106—131no—
280C2×#106—131no—
281C2×C22⋊C8C2×D1311yescharacteristic
282C2×#97—131no—
283C2×C4×C8—131no—
284#389—131no—
285#389—131no—
286#389—131no—
287#389—131no—
288#388—261no—
289#388—261no—
290#387—261no—
291#387—261no—
292#383—261no—
293#381—261no—
294#380—131no—
295#380C2×D1311yescharacteristic
296C4×C4⋊C4—131no—
297C4×C4⋊C4—131no—
298C4×C4⋊C4—131no—
299C4×C4⋊C4—131no—
300C4×C4⋊C4—261no—
301C4×C22⋊C4—131no—
302#340—131no—
303#340—131no—
304#340—131no—
305#340—131no—
306#340—131no—
307#340—131no—
308#340C2×D1311yescharacteristic
309#340C2×D1311yescharacteristic
310#340C2×D1311yescharacteristic
311#340C2×D1311yescharacteristic
312#336—131no—
313#336—131no—
314C22×C13—22no—
315C22×C13—22no—
316C22×C13—22no—
317C22×C13—41no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13C2×C4×D411yescharacteristic
322C22×C13#54711yescharacteristic
323C22×C13#54711yescharacteristic
324C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
325C22×C13#57511yescharacteristic
326C22×C13#57711yescharacteristic
327C22×C13#57811yescharacteristic
328C4×C13—22no—
329C4×C13—42no—
330C4×C13—42no—
331C4×C13—81no—
332C4×C13—81no—
333C4×C13C2×#11711yescharacteristic
334C4×C13#51911yescharacteristic
335C4×C13#55211yescharacteristic
336C4×C13#55211yescharacteristic
337Dic13—22no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—42no—
342Dic13—42no—
343Dic13—81no—
344Dic13—81no—
345C23×C4—21no—
346C23×C4C22×D1311yescharacteristic
347C2×M16—134no—
348C2×M16—262no—
349C2×M16—262no—
350C22×C8—131no—
351C22×C8—131no—
352C22×C8C22×D1311yescharacteristic
353C22×C8C22×D1311yescharacteristic
354#117—134no—
355#117—262no—
356#117—524no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—131no—
360C2×C4⋊C4—131no—
361C2×C4⋊C4—131no—
362C2×C4⋊C4—131no—
363C2×C4⋊C4—261no—
364C2×C4⋊C4—261no—
365C2×C4⋊C4—261no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4C4×D1314yes—
368C2×C4⋊C4C22×D1311yescharacteristic
369C2×C4⋊C4C22×D1311yescharacteristic
370C2×C4⋊C4C22×D1311yescharacteristic
371C2×C4⋊C4C22×D1311yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—131no—
374C2×C22⋊C4—131no—
375C2×C22⋊C4—261no—
376C2×C22⋊C4—261no—
377C2×C42—131no—
378C2×C42—131no—
379C2×C42—261no—
380C2×C42—261no—
381C2×C42—261no—
382C2×C42—261no—
383C2×C42—261no—
384#107—134no—
385#107—134no—
386#107—262no—
387#106—134no—
388#106—134no—
389#106—262no—
390C22⋊C8—22no—
391#97—262no—
392C4×C8—262no—
393#95—21no—
394#95—131no—
395#95—131no—
396#95—261no—
397#95—261no—
398#95—261no—
399#95—261no—
400#95—261no—
401#95—261no—
402#95—261no—
403#95—261no—
404#95—261no—
405C2×C13—42no—
406C2×C13#234411yescharacteristic
407C2×C13C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C13#294711yescharacteristic
409C2×C13#334511yescharacteristic
410C2×C13#334911yescharacteristic
411C2×C13#335111yescharacteristic
412C2×C13#335311yescharacteristic
413C24D4×D1311yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—24no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—131no—
429C22×C4—261no—
430C22×C4—261no—
431C22×C4—261no—
432C22×C4—261no—
433C22×C4C2×C4×D1312yes—
434C22×C4D4×D1311yescharacteristic
435C22×C4#612912yes—
436C22×C4C23×D1311yescharacteristic
437M16—268no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—132no—
445C2×C8—132no—
446C2×C8—132no—
447C2×C8—132no—
448C2×C8—261no—
449C2×C8—261no—
450C4⋊C4—24no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—132no—
458C4⋊C4—132no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—522no—
466C4⋊C4—522no—
467C4⋊C4—522no—
468C4⋊C4—522no—
469C4⋊C4C2×C4×D1312yes—
470C4⋊C4C2×C4×D1312yes—
471C22⋊C4—81no—
472C22⋊C4—262no—
473C22⋊C4—264no—
474C22⋊C4—521no—
475C22⋊C4—522no—
476C42—264no—
477C42—261no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42—522no—
482C42—522no—
483C42—1041no—
484C42—1041no—
485C13#2262211yescharacteristic, complemented, Sylow
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23#8813512yes—
493C23C2×D4×D1311yescharacteristic
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—48no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—132no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—262no—
517C2×C4—262no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—261no—
525C2×C4—261no—
526C2×C4—261no—
527C2×C4—521no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4—521no—
531C2×C4—521no—
532C2×C4—521no—
533C2×C4—521no—
534C2×C4—521no—
535C2×C4—521no—
536C2×C4—521no—
537C2×C4#8813512yes—
538C2×C4C22×C4×D1311yescharacteristic
539C2×C4C2×#612911yescharacteristic
540C2×C4#41×D1311yescharacteristic
541C2×C4#41×D1311yescharacteristic
542C2×C4#8825711yescharacteristic
543C2×C4#8825711yescharacteristic
544C8—41no—
545C8—41no—
546C8—134no—
547C8—262no—
548C22—22no—
549C22—22no—
550C22—22no—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22C2×#8813511yescharacteristic
556C22#1171936011yescharacteristic
557C22#1171936011yescharacteristic
558C22#1171946711yescharacteristic
559C22#1171947111yescharacteristic
560C22D13×AGL(1,ℤ/8)11yescharacteristic
561C22#1171947811yescharacteristic
562C4—22no—
563C4—42no—
564C4—42no—
565C4—81no—
566C4—81no—
567C4—262no—
568C4—522no—
569C4—522no—
570C4—521no—
571C4—521no—
572C4—521no—
573C4—1041no—
574C4—1041no—
575C4#1171922111yescharacteristic
576C4D13×#11711yescharacteristic
577C4#1171935511yescharacteristic
578C4#1171935511yescharacteristic
579C2—42no—
580C2#1311770011yescharacteristic
581C2#1312364011yescharacteristic
582C2#1312367311yescharacteristic
583C2#1312729911yescharacteristic
584C2#1312735911yescharacteristic
585C2#1312740011yescharacteristic
586C2#1312741311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1824C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1824D13
hypocenterC13#22622
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #13115573C2semidirect
5. #13115568C2semidirect
6. #13115426C2semidirect
7. #13115424C2semidirect
8. #13115417C2semidirect
9. #13115405C2semidirect
12. #13114732C2semidirect
13. #13114724C2semidirect
37. #11718625C4semidirect
269. #1055#117semidirect
485. C13#22622semidirect

Maximal subgroups

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

subgroupindex
C2×#117186252
#131177312
#131177052
#131155732
#131155682
#131154262
#131154242
#131154172
#131154052
#131149322
#131148672
#131147322
#131147242
#131146222
C13×#18242
#2262213