Finite Group Databasebeta

← #15832614

Subgroups — #15832614

Order 3328.

626 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#13123918C211yesmaximal, characteristic
2#13123915C211yesmaximal, characteristic
3C4×Q16×D13C211yesmaximal, characteristic
4#13113709C211yesmaximal, characteristic, complemented
5#13113708C211yesmaximal, characteristic, complemented
6#13113706C211yesmaximal, characteristic, complemented
7#13113689C211yesmaximal, characteristic, complemented
8#13113686C211yesmaximal, characteristic, complemented
9#13113684C211yesmaximal, characteristic, complemented
10#13113683C211yesmaximal, characteristic, complemented
11#13113581C211yesmaximal, characteristic
12#13113229C211yesmaximal, characteristic
13#13113229C211yesmaximal, characteristic
14#13113127C211yesmaximal, characteristic
15C13×#1587C211yesmaximal, characteristic, complemented
16C2×Q16×D13C411yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C4×Q8×D13C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C8×Q8×C13C2211yescharacteristic
21C4×C13×Q16C2211yescharacteristic
22Q16×Dic13C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27D13×#107C411yescharacteristic
28#11718534C411yescharacteristic
29#11718496—21no—
30#11718494—21no—
31#11718494C2211yescharacteristic
32#11718494C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718491—21no—
35#11718491C2211yescharacteristic
36#11718489—21no—
37D13×#103C411yescharacteristic
38D13×#103C411yescharacteristic
39#11718451C411yescharacteristic
40#11718451C411yescharacteristic
41#11718366—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44#11718346—21no—
45#11718346C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×Q8×D13C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71C4×Q8×C13C2311yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76Q16×D13—24no—
77C2×Dic52C2×C411yescharacteristic
78C2×C8×D13C2×C411yescharacteristic
79C2×C8×D13C2×C411yescharacteristic
80C4⋊C4×D13—21no—
81C4⋊C4×D13—21no—
82C4⋊C4×D13C2×C411yescharacteristic
83C4⋊C4×D13C2×C411yescharacteristic
84#88141—21no—
85#88141—21no—
86#88141C2×C411yescharacteristic
87#88141C2×C411yescharacteristic
88C42×D13—21no—
89C42×D13—21no—
90C42×D13C2311yescharacteristic
91C4×Dic26—21no—
92C4×Dic26—21no—
93C4×Dic26C2311yescharacteristic
94C4×Dic26C2311yescharacteristic
95C13×#107C2×C411yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×#103C2×C411yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#97—21no—
103C4×C8×C13—21no—
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109#88060—21no—
110#88060—21no—
111#88060—21no—
112#88060D411yescharacteristic
113#88060D411yescharacteristic
114#88058C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88055—21no—
118#88055—21no—
119#88054—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054D411yescharacteristic
125#88054D411yescharacteristic
126C8×Dic13—21no—
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13C2×C411yescharacteristic
131C8×Dic13C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88050C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135#88047C2×C411yescharacteristic
136C4⋊#1055—21no—
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17880—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148Q8×D13—22no—
149Q8×D13—22no—
150Q8×D13—22no—
151Q8×D13M1614yes—
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13C22×C411yescharacteristic
157C2×C4×D13C2×D411yescharacteristic
158C2×C4×D13#4111yescharacteristic
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26C22×C411yescharacteristic
162C2×Dic26C22×C411yescharacteristic
163C13×Q16—22no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13C22×C411yescharacteristic
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C42×C13—21no—
176C42×C13—21no—
177C42×C13C2411yescharacteristic
178#6107—22no—
179#6107—22no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13C22×C411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13#4111yescharacteristic
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206Dic52—22no—
207C8×D13—22no—
208C8×D13—22no—
209#2983—131no—
210#2982—131no—
211C2×C4×Q16—131no—
212#1587—131no—
213#1587—131no—
214#1587—131no—
215#1587D1311yescharacteristic, complemented
216#1584—131no—
217#1584—131no—
218#1584—131no—
219#1584—131no—
220#1564—131no—
221#1479—131no—
222#1479—131no—
223#1452—131no—
224C22×D13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13C2×M1612yes—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242C2×Dic13C4×D411yescharacteristic
243C4×D13—24no—
244C4×D13—21no—
245C4×D13—21no—
246C4×D13—41no—
247C4×D13—42no—
248C4×D13—81no—
249C4×D13—81no—
250C4×D13C2×M1612yes—
251C4×D13#13112yes—
252Dic26—21no—
253Dic26—24no—
254Dic26—21no—
255Dic26—21no—
256Dic26—42no—
257Dic26C2×M1612yes—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272C22×Q16—131no—
273C2×C4×Q8—131no—
274C2×C4×Q8—131no—
275#446—131no—
276#446—131no—
277#446—131no—
278#446—261no—
279#446—261no—
280#446C2×D1311yescharacteristic
281C8×Q8—131no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—261no—
285C8×Q8—261no—
286C8×Q8C2×D1311yescharacteristic
287C4×Q16—131no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×Q16—131no—
292C4×Q16—131no—
293C4×Q16—131no—
294C4×Q16C2×D1311yescharacteristic
295#432—261no—
296#432—261no—
297#431—131no—
298#431—131no—
299#431—131no—
300#431—131no—
301#431—261no—
302#431—261no—
303C2×#107—131no—
304C2×#103—131no—
305C2×#103—131no—
306C2×C4×C8—131no—
307#335—131no—
308#335—131no—
309#334—131no—
310#334C2×D1311yescharacteristic
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8C2×D1311yescharacteristic
318Q8⋊C8C2×D1311yescharacteristic
319#322—131no—
320#322—131no—
321#322—131no—
322#322C2×D1311yescharacteristic
323C22×C13C2×C4×D411yescharacteristic
324C2×D13—21no—
325C2×D13—21no—
326C2×D13#43512yes—
327C4×C13—22no—
328C4×C13—21no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13C22×M1611yescharacteristic
333C4×C13C2×#13111yescharacteristic
334C4×C13#57811yescharacteristic
335C4×C13#57811yescharacteristic
336Dic13—22no—
337Dic13—21no—
338Dic13—21no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13#43512yes—
343C22×Q8—131no—
344C22×Q8—131no—
345C2×Q16—131no—
346C2×Q16—131no—
347C2×Q16—131no—
348C2×Q16—264no—
349C2×Q16C4×D1311yescharacteristic
350C22×C8—131no—
351C22×C8—131no—
352C4×Q8—131no—
353C4×Q8—131no—
354C4×Q8—131no—
355C4×Q8—131no—
356C4×Q8—131no—
357C4×Q8—131no—
358C4×Q8—261no—
359C4×Q8—261no—
360C4×Q8—261no—
361C4×Q8—261no—
362C4×Q8C22×D1311yescharacteristic
363C4×Q8C22×D1311yescharacteristic
364C2×C4⋊C4—131no—
365C2×C4⋊C4—131no—
366C2×C4⋊C4—261no—
367C2×C4⋊C4—261no—
368C2×C42—131no—
369C2×C42—261no—
370C2×C42—261no—
371#107—131no—
372#107—131no—
373#107—131no—
374#107C4×D1311yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—21no—
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#103C4×D1311yescharacteristic
397#103C4×D1311yescharacteristic
398C22⋊C8—131no—
399C22⋊C8—131no—
400C22⋊C8—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—261no—
405#97—261no—
406#97—261no—
407C4×C8—21no—
408C4×C8—131no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13C2×#43511yescharacteristic
422C2×C13#295011yescharacteristic
423C2×C13#295711yescharacteristic
424D13—22no—
425C2×Q8—134no—
426C2×Q8—131no—
427C2×Q8—131no—
428C2×Q8—261no—
429C2×Q8—261no—
430C2×Q8—262no—
431C2×Q8—262no—
432C2×Q8—262no—
433C2×Q8C2×C4×D1311yescharacteristic
434C2×Q8C2×C4×D1311yescharacteristic
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—261no—
439C22×C4—261no—
440C22×C4—261no—
441C22×C4—261no—
442Q16—22no—
443Q16—262no—
444Q16—262no—
445Q16—262no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—262no—
454C2×C8—262no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8C2×C4×D1311yescharacteristic
459C2×C8C2×C4×D1311yescharacteristic
460C2×C8D4×D1311yescharacteristic
461C2×C8D4×D1311yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—131no—
465C4⋊C4—131no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4C2×C4×D1311yescharacteristic
475C4⋊C4C2×C4×D1311yescharacteristic
476C42—21no—
477C42—21no—
478C42—131no—
479C42—131no—
480C42—131no—
481C42—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42C23×D1311yescharacteristic
488C13#1788011yescharacteristic, complemented, Sylow
489C23—131no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—132no—
494Q8—264no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—522no—
499Q8M16×D1312yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—131no—
505C2×C4—132no—
506C2×C4—132no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—264no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—521no—
517C2×C4—522no—
518C2×C4—1041no—
519C2×C4—1041no—
520C2×C4C22×C4×D1311yescharacteristic
521C2×C4C2×D4×D1311yescharacteristic
522C2×C4#41×D1311yescharacteristic
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—521no—
535C8—521no—
536C8—521no—
537C22—132no—
538C22—261no—
539C22—261no—
540C22C4×D4×D1311yescharacteristic
541C4—21no—
542C4—22no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—132no—
547C4—261no—
548C4—261no—
549C4—262no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4C2×M16×D1311yescharacteristic
554C4D13×#13111yescharacteristic
555C4#1171948411yescharacteristic
556C4#1171948411yescharacteristic
557C2—262no—
558C2D13×#43511yescharacteristic
559C2#1312370111yescharacteristic
560C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1587C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1587D13
hypocenterC13#17880
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
4. #13113709C2semidirect
5. #13113708C2semidirect
6. #13113706C2semidirect
7. #13113689C2semidirect
8. #13113686C2semidirect
9. #13113684C2semidirect
10. #13113683C2semidirect
15. C13×#1587C2semidirect
215. #1587D13semidirect
488. C13#17880semidirect

Maximal subgroups

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

subgroupindex
#131239182
#131239152
C4×Q16×D132
#131137092
#131137082
#131137062
#131136892
#131136862
#131136842
#131136832
#131135812
#131132292
#131131272
C13×#15872
#1788013