Finite Group Databasebeta

← #15832992

Subgroups — #15832992

Order 3328.

596 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124918C211yesmaximal, characteristic
2#13123981C211yesmaximal, characteristic
3#13123916C211yesmaximal, characteristic, complemented
4#13113713C211yesmaximal, characteristic, complemented
5#13113706C211yesmaximal, characteristic, complemented
6#13113685C211yesmaximal, characteristic, complemented
7#13113678C211yesmaximal, characteristic, complemented
8#13113654C211yesmaximal, characteristic, complemented
9#13113647C211yesmaximal, characteristic, complemented
10#13113642C211yesmaximal, characteristic, complemented
11#13113635C211yesmaximal, characteristic, complemented
12#13113264C211yesmaximal, characteristic, complemented
13#13113242C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1574C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#423C2211yescharacteristic
21#11718789—21no—
22#11718788—21no—
23#11718586C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718506C411yescharacteristic
26#11718506C411yescharacteristic
27#11718501—21no—
28#11718500—21no—
29#11718499C2211yescharacteristic
30#11718495C2211yescharacteristic
31#11718492C2211yescharacteristic
32#11718491C2211yescharacteristic
33#11718491C2211yescharacteristic
34#11718491C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718490C411yescharacteristic
38#11718490C411yescharacteristic
39#11718400C411yescharacteristic
40#11718399C411yescharacteristic
41#11718397C411yescharacteristic
42#11718382C411yescharacteristic
43#11718379—21no—
44#11718379—21no—
45C4×Dic52C2211yescharacteristic
46C4×Dic52C2211yescharacteristic
47C4×#6095C2211yescharacteristic
48C4×#6095C2211yescharacteristic
49C8×Dic26—21no—
50C8×Dic26—21no—
51C13×#335C2211yescharacteristic
52C13×#335C2211yescharacteristic
53C13×#334C2211yescharacteristic
54C13×#334C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718076C2211yescharacteristic
60#11718076C2211yescharacteristic
61#11718075C2211yescharacteristic
62#11718075C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C2×C13×M16—21no—
69C2×C42×C13C2311yescharacteristic
70#88184C2×C411yescharacteristic
71#88183—21no—
72C4×C22⋊D13—21no—
73C2×C4⋊Dic13C2×C411yescharacteristic
74#88178C2×C411yescharacteristic
75C2×#6101—21no—
76C2×C4×Dic13—21no—
77C2×Dic52C2×C411yescharacteristic
78C2×Dic52C2×C411yescharacteristic
79C2×#6095C2×C411yescharacteristic
80C2×#6095C2×C411yescharacteristic
81C2×#6094—21no—
82C2×C8×D13—21no—
83#88130—21no—
84#88129C2×C411yescharacteristic
85C4×D52C2311yescharacteristic
86#88126—21no—
87#88124C2×C411yescharacteristic
88C4×Dic26—21no—
89C4×Dic26—21no—
90C4×Dic26C2×C411yescharacteristic
91C4×Dic26C2×C411yescharacteristic
92C4×Dic26C2311yescharacteristic
93C4×Dic26C2311yescharacteristic
94C4×Dic26C2311yescharacteristic
95C13×C4⋊C8—21no—
96C13×C4⋊C8C2×C411yescharacteristic
97C13×C4⋊C8C2×C411yescharacteristic
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C22⋊C8—21no—
103C13×C22⋊C8C2×C411yescharacteristic
104C13×C22⋊C8C2×C411yescharacteristic
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C22⋊#1055—21no—
109C22⋊#1055D411yescharacteristic
110C22⋊#1055D411yescharacteristic
111#88061C2×C411yescharacteristic
112#88061C2×C411yescharacteristic
113#88060—21no—
114#88060—21no—
115#88058C2×C411yescharacteristic
116#88058C2×C411yescharacteristic
117#88057C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88055—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132C8×Dic13—21no—
133C8×Dic13—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C4⋊#1055—21no—
138C4⋊#1055D411yescharacteristic
139C4⋊#1055D411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17919—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C2×C22⋊D13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C2×D52C22×C411yescharacteristic
152C2×C4×D13—21no—
153C2×Dic26—21no—
154C2×Dic26—22no—
155C2×Dic26—22no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C13×M16—81no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C22×C411yescharacteristic
167C2×C8×C13C22×C411yescharacteristic
168C42×C13C22×C411yescharacteristic
169C42×C13C2×D411yescharacteristic
170C42×C13#4111yescharacteristic
171C42×C13C2411yescharacteristic
172C22⋊Dic13—21no—
173#6103—21no—
174#6103—21no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13C22×C411yescharacteristic
179C4⋊Dic13C22×C411yescharacteristic
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182#6101—21no—
183#6101—21no—
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—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055C2×D411yescharacteristic
198C2×#1055C2×D411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201Dic52—22no—
202Dic52—22no—
203#6095—22no—
204#6095—22no—
205#6094—81no—
206C8×D13—81no—
207#3108—131no—
208#2993—131no—
209#2982—131no—
210#1588—131no—
211#1587—131no—
212#1584—131no—
213#1583—131no—
214#1579—131no—
215SD16⋊C8—131no—
216C8×Q16—131no—
217C8×SD16—131no—
218#1574D1311yescharacteristic, complemented
219#1487—131no—
220#1482—131no—
221#1454—131no—
222C23×C13C4×D411yescharacteristic
223C22×D13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—41no—
229C2×C4×C13C4×D411yescharacteristic
230C2×C4×C13C4×D411yescharacteristic
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C23×C411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×C4×C13C2×#4111yescharacteristic
235C22⋊D13—81no—
236C2×Dic13—24no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—81no—
245D52—21no—
246D52—21no—
247C4×D13—41no—
248C4×D13—41no—
249Dic26—24no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26#13112yes—
255Dic26#13112yes—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#1055—41no—
270#529—131no—
271C2×C4×Q8—131no—
272#483—131no—
273#480—131no—
274#479—131no—
275#479—131no—
276#464—131no—
277#464—131no—
278#451—131no—
279#448—131no—
280#446—131no—
281C8×Q8—131no—
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—261no—
287C8×Q8—261no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16—131no—
292#436—131no—
293#436—261no—
294#435—261no—
295C8×D4—131no—
296#433—261no—
297#431—131no—
298#431—131no—
299#431—261no—
300#431—261no—
301#431C2×D1311yescharacteristic
302#431C2×D1311yescharacteristic
303#424—261no—
304#423C2×D1311yescharacteristic
305#335C2×D1311yescharacteristic
306#335C2×D1311yescharacteristic
307#334C2×D1311yescharacteristic
308#334C2×D1311yescharacteristic
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315D4⋊C8—131no—
316D4⋊C8—131no—
317#322—131no—
318#322—131no—
319#322—131no—
320C82—131no—
321C22×C13—21no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13C2×C4×D411yescharacteristic
325C2×D13—41no—
326C2×D13—41no—
327C2×D13—41no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13C2×#13111yescharacteristic
333C4×C13C2×#13111yescharacteristic
334C4×C13#57711yescharacteristic
335C4×C13#57811yescharacteristic
336Dic13—22no—
337Dic13—22no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343C22×Q8—131no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C2×M16—21no—
349C2×M16—261no—
350C22×C8—261no—
351#126—261no—
352#125—131no—
353#124—131no—
354#123—261no—
355C22⋊Q8—131no—
356#121—131no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—131no—
360C4×Q8—131no—
361C4×Q8—131no—
362C4×Q8—261no—
363C4×Q8—261no—
364C4×D4—131no—
365C4×D4—261no—
366#117—261no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—261no—
369C2×C42—261no—
370C2×C42C22×D1311yescharacteristic
371#107—131no—
372#107—131no—
373#106—131no—
374#106—131no—
375C4⋊C8—21no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—261no—
379C4⋊C8—261no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8C4×D1311yescharacteristic
386C4⋊C8C4×D1311yescharacteristic
387C4⋊C8C22×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#102—131no—
398#102—131no—
399C22⋊C8—21no—
400C22⋊C8—131no—
401C22⋊C8—131no—
402C22⋊C8—261no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C4×D1311yescharacteristic
406C22⋊C8C4×D1311yescharacteristic
407#97—261no—
408C4×C8—21no—
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
420C2×C13—41no—
421C2×C13#292911yescharacteristic
422C2×C13#294711yescharacteristic
423C2×C13#295711yescharacteristic
424D13—81no—
425C2×Q8—131no—
426C2×Q8—131no—
427C2×Q8—131no—
428C2×Q8—262no—
429C2×Q8—262no—
430C2×Q8—261no—
431C2×D4—131no—
432C2×D4—261no—
433C22×C4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4D4×D1311yescharacteristic
438C22×C4#613111yescharacteristic
439Q16—262no—
440Q16—262no—
441SD16—262no—
442SD16—262no—
443M16—81no—
444M16—1041no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—1041no—
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C2×C8C2×C4×D1311yescharacteristic
459C2×C8C2×C4×D1311yescharacteristic
460C4⋊C4—131no—
461C4⋊C4—131no—
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⋊C4—261no—
472C4⋊C4—261no—
473C22⋊C4—261no—
474C22⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—261no—
479C42—261no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42C2×C4×D1311yescharacteristic
484C42D4×D1311yescharacteristic
485C42#613111yescharacteristic
486C42C23×D1311yescharacteristic
487C13#1791911yescharacteristic, complemented, Sylow
488C23—261no—
489C23#8814711yescharacteristic
490Q8—132no—
491Q8—132no—
492Q8—264no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—261no—
497D4—261no—
498D4—261no—
499D4—1041no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—264no—
506C2×C4—261no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—521no—
514C2×C4—521no—
515C2×C4—1041no—
516C2×C4#8814711yescharacteristic
517C2×C4#8814711yescharacteristic
518C2×C4#8814711yescharacteristic
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C2×D4×D1311yescharacteristic
521C2×C4C2×#613111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—521no—
535C8—521no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—521no—
540C22—521no—
541C22—521no—
542C22C2×#8814711yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—262no—
548C4—262no—
549C4—521no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4D13×#13111yescharacteristic
555C4D13×#13111yescharacteristic
556C4#1171948011yescharacteristic
557C4#1171948411yescharacteristic
558C2—41no—
559C2—1041no—
560C2#1312352911yescharacteristic
561C2#1312367711yescharacteristic
562C2#1312375211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1574C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1574D13
hypocenterC13#17919
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #13123916C2semidirect
4. #13113713C2semidirect
5. #13113706C2semidirect
6. #13113685C2semidirect
7. #13113678C2semidirect
8. #13113654C2semidirect
9. #13113647C2semidirect
10. #13113642C2semidirect
11. #13113635C2semidirect
12. #13113264C2semidirect
14. #13113136C2semidirect
15. C13×#1574C2semidirect
218. #1574D13semidirect
487. C13#17919semidirect

Maximal subgroups

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

subgroupindex
#131249182
#131239812
#131239162
#131137132
#131137062
#131136852
#131136782
#131136542
#131136472
#131136422
#131136352
#131132642
#131132422
#131131362
C13×#15742
#1791913