Finite Group Databasebeta

← #15833570

Subgroups — #15833570

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125443C211yesmaximal, characteristic
2#13123985C211yesmaximal, characteristic
3#13123933C211yesmaximal, characteristic, complemented
4#13113742C211yesmaximal, characteristic, complemented
5#13113735C211yesmaximal, characteristic, complemented
6#13113730C211yesmaximal, characteristic, complemented
7#13113729C211yesmaximal, characteristic, complemented
8#13113652C211yesmaximal, characteristic, complemented
9#13113645C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113639C211yesmaximal, characteristic, complemented
12#13113604C211yesmaximal, characteristic, complemented
13#13113292C211yesmaximal, characteristic, complemented
14C8×#6099C211yesmaximal, characteristic, complemented
15C13×#1494C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C2×C4×C8×C13C2211yescharacteristic
20#11718730C411yescharacteristic
21#11718726C411yescharacteristic
22#11718721C411yescharacteristic
23#11718716C411yescharacteristic
24#11718713C411yescharacteristic
25#11718713C411yescharacteristic
26#11718703C411yescharacteristic
27#11718703C411yescharacteristic
28C4×#6107C2211yescharacteristic
29C4×#6107C2211yescharacteristic
30#11718685C2211yescharacteristic
31Q8×#1055C2211yescharacteristic
32C4×#6105C2211yescharacteristic
33C4×#6105C2211yescharacteristic
34#11718673—21no—
35#11718673C2211yescharacteristic
36#11718672—21no—
37D4×#1055C2211yescharacteristic
38#11718661—21no—
39#11718660—21no—
40#11718586C2211yescharacteristic
41#11718585C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718492C2211yescharacteristic
44#11718492C2211yescharacteristic
45#11718491C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718381—21no—
48#11718381—21no—
49#11718362—21no—
50#11718362—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718048C2211yescharacteristic
60#11718048C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×C8×C13—21no—
68C13×#126—21no—
69C13×#125C2×C411yescharacteristic
70C13×#124C2×C411yescharacteristic
71C13×#123—21no—
72C13×C22⋊Q8C2×C411yescharacteristic
73C13×#121C2×C411yescharacteristic
74C4×Q8×C13C2311yescharacteristic
75C4×D4×C13—21no—
76C4×D4×C13C2311yescharacteristic
77C13×#117—21no—
78C2×C42×C13C2311yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6105C2×C411yescharacteristic
82C2×#6105C2×C411yescharacteristic
83#88180—21no—
84#88178—21no—
85#88178C2×C411yescharacteristic
86#88178C2×C411yescharacteristic
87C2×#6099—21no—
88C2×#6099—21no—
89C2×#6099C2×C411yescharacteristic
90C2×#6099C2×C411yescharacteristic
91C22×#1055—21no—
92#88124—21no—
93#88123C2×C411yescharacteristic
94#88123C2×C411yescharacteristic
95C4×Dic26—21no—
96C4×Dic26C2311yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C22⋊C8—21no—
101C13×#97—21no—
102C4×C8×C13—21no—
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105#88075C2×C411yescharacteristic
106#88075C2×C411yescharacteristic
107#88072C2×C411yescharacteristic
108#88072C2×C411yescharacteristic
109C22⋊#1055—21no—
110C22⋊#1055—21no—
111C22⋊#1055D411yescharacteristic
112C22⋊#1055D411yescharacteristic
113#88055—21no—
114#88055—21no—
115#88054—21no—
116#88054—21no—
117#88054—21no—
118#88054—21no—
119C8×Dic13—21no—
120C8×Dic13—21no—
121#88050C2×C411yescharacteristic
122#88050C2×C411yescharacteristic
123#88050C2×C411yescharacteristic
124#88050C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055D411yescharacteristic
133C4⋊#1055D411yescharacteristic
134C4⋊#1055C2311yescharacteristic
135C4⋊#1055C2311yescharacteristic
136#88043—21no—
137#88043C2×C411yescharacteristic
138#88043C2×C411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17969—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×Dic26—21no—
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C2×C8×C13—21no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—42no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4C22×C411yescharacteristic
165C13×C4⋊C4C22×C411yescharacteristic
166C13×C22⋊C4—21no—
167C13×C22⋊C4—21no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C13×C22⋊C4—21no—
171C42×C13—21no—
172C42×C13C22×C411yescharacteristic
173C42×C13C2×D411yescharacteristic
174C42×C13#4111yescharacteristic
175C42×C13C2411yescharacteristic
176C22⋊Dic13—21no—
177C22⋊Dic13—21no—
178#6107—22no—
179#6107—22no—
180#6105—22no—
181#6105—22no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22×C411yescharacteristic
186C4⋊Dic13C22×C411yescharacteristic
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193#6099—22no—
194#6099—22no—
195#6099—81no—
196#6099—81no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—81no—
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#3172—131no—
209#2993—131no—
210#2985—131no—
211#1593—131no—
212#1592—131no—
213#1591—131no—
214#1590—131no—
215#1579—131no—
216SD16⋊C8—131no—
217C8×Q16—131no—
218C8×SD16—131no—
219#1569—131no—
220#1494D1311yescharacteristic
221#1493—131no—
222C8×M16—131no—
223C23×C13—21no—
224C23×C13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227D4×C13—21no—
228D4×C13—21no—
229D4×C13—81no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—81no—
255C8×C13—22no—
256C8×C13—41no—
257C8×C13—41no—
258C8×C13—41no—
259#1055—21no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—41no—
266#1055—41no—
267#1055#13112yes—
268#1055#13112yes—
269#533—131no—
270#529C2×D1311yescharacteristic
271#501—131no—
272#497—131no—
273#491—131no—
274#489—131no—
275#470—131no—
276#470—131no—
277#468—131no—
278#468—131no—
279#446—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C4×Q16—131no—
288C4×Q16—131no—
289C4×SD16—131no—
290C4×SD16—131no—
291#436—131no—
292#436—261no—
293#435—261no—
294C8×D4—131no—
295#433—261no—
296#433—261no—
297#433—261no—
298#432C2×D1311yescharacteristic
299#431—131no—
300#424—261no—
301#423—131no—
302C4×M16—131no—
303C2×C4×C8C2×D1311yescharacteristic
304#335—131no—
305#335—131no—
306#334—131no—
307#334—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8C2×D1311yescharacteristic
313Q8⋊C8C2×D1311yescharacteristic
314D4⋊C8C2×D1311yescharacteristic
315D4⋊C8C2×D1311yescharacteristic
316#322—131no—
317#322—131no—
318C82—131no—
319C82—131no—
320C22×C13—21no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13C2×C4×D411yescharacteristic
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13C2×#13111yescharacteristic
335C4×C13C2×#13111yescharacteristic
336C4×C13#57711yescharacteristic
337C4×C13#57811yescharacteristic
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342C2×Q16—131no—
343C2×Q16—131no—
344C2×SD16—131no—
345C2×SD16—131no—
346C2×M16—131no—
347C2×M16—131no—
348C2×M16—261no—
349C2×M16—261no—
350C22×C8—21no—
351C22×C8—261no—
352C4⋊Q8—131no—
353C4⋊Q8—131no—
354#126—21no—
355#125—261no—
356#125C4×D1311yescharacteristic
357#124C4×D1311yescharacteristic
358#123—21no—
359C22⋊Q8—131no—
360C22⋊Q8—131no—
361C22⋊Q8—261no—
362C22⋊Q8C4×D1311yescharacteristic
363#121C4×D1311yescharacteristic
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—261no—
367C4×Q8C22×D1311yescharacteristic
368C4×D4—21no—
369C4×D4C22×D1311yescharacteristic
370#117—21no—
371#117—261no—
372C2×C42C22×D1311yescharacteristic
373#107—131no—
374#107—131no—
375#106—131no—
376#106—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390#103—131no—
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#102—131no—
397#102—131no—
398C22⋊C8—21no—
399C22⋊C8—131no—
400C22⋊C8—131no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—131no—
405#97—131no—
406#97—261no—
407#97—261no—
408#97—261no—
409C4×C8—21no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C2×C13—41no—
420C2×C13—81no—
421C2×C13#293111yescharacteristic
422C2×C13#294711yescharacteristic
423C2×C13#295611yescharacteristic
424C2×Q8—131no—
425C2×Q8—131no—
426C2×Q8—261no—
427C2×Q8C2×C4×D1311yescharacteristic
428C2×D4—21no—
429C2×D4C2×C4×D1311yescharacteristic
430C22×C4—21no—
431C22×C4C2×C4×D1311yescharacteristic
432C22×C4D4×D1311yescharacteristic
433C22×C4#612911yescharacteristic
434Q16—262no—
435Q16—262no—
436SD16—262no—
437SD16—262no—
438M16—262no—
439M16—262no—
440M16—1041no—
441M16—1041no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—1041no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—131no—
463C4⋊C4—131no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—21no—
481C42—261no—
482C42—261no—
483C42C2×C4×D1311yescharacteristic
484C42D4×D1311yescharacteristic
485C42#612911yescharacteristic
486C42C23×D1311yescharacteristic
487C13#1796911yescharacteristic, complemented, Sylow
488C23—21no—
489C23#8813511yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—261no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—1041no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4#8813511yescharacteristic
515C2×C4#8813511yescharacteristic
516C2×C4#8813511yescharacteristic
517C2×C4C22×C4×D1311yescharacteristic
518C2×C4C2×D4×D1311yescharacteristic
519C2×C4C2×#612911yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—132no—
525C8—132no—
526C8—261no—
527C8—261no—
528C8—261no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—521no—
533C8—521no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22C2×#8813511yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—521no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4D13×#13111yescharacteristic
553C4D13×#13111yescharacteristic
554C4#1171947511yescharacteristic
555C4#1171947611yescharacteristic
556C2—41no—
557C2—81no—
558C2#1312354411yescharacteristic
559C2#1312368211yescharacteristic
560C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1494C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#1494D13
hypocenterC13#17969
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #13123933C2semidirect
4. #13113742C2semidirect
5. #13113735C2semidirect
6. #13113730C2semidirect
7. #13113729C2semidirect
8. #13113652C2semidirect
9. #13113645C2semidirect
10. #13113640C2semidirect
11. #13113639C2semidirect
12. #13113604C2semidirect
13. #13113292C2semidirect
14. C8×#6099C2semidirect
487. C13#17969semidirect

Maximal subgroups

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

subgroupindex
#131254432
#131239852
#131239332
#131137422
#131137352
#131137302
#131137292
#131136522
#131136452
#131136402
#131136392
#131136042
#131132922
C8×#60992
C13×#14942
#1796913