Finite Group Databasebeta

← #15834782

Subgroups — #15834782

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125436C211yesmaximal, characteristic
2#13123834C211yesmaximal, characteristic
3#13123785C211yesmaximal, characteristic, complemented
4#13113741C211yesmaximal, characteristic, complemented
5#13113730C211yesmaximal, characteristic, complemented
6#13113711C211yesmaximal, characteristic, complemented
7#13113710C211yesmaximal, characteristic, complemented
8#13113683C211yesmaximal, characteristic, complemented
9#13113675C211yesmaximal, characteristic, complemented
10#13113652C211yesmaximal, characteristic, complemented
11#13113633C211yesmaximal, characteristic, complemented
12#13113589C211yesmaximal, characteristic, complemented
13#13113250C211yesmaximal, characteristic
14#13113139C211yesmaximal, characteristic, complemented
15C13×#1485C211yesmaximal, characteristic, complemented
16C13×#533C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C4×C13×M16C2211yescharacteristic
20#11718750C411yescharacteristic
21#11718747C411yescharacteristic
22#11718743C411yescharacteristic
23#11718741C411yescharacteristic
24#11718713C411yescharacteristic
25#11718713C411yescharacteristic
26#11718710C411yescharacteristic
27#11718710C411yescharacteristic
28C4×#6107C2211yescharacteristic
29C4×#6107C2211yescharacteristic
30C4×#6106C2211yescharacteristic
31C4×#6106C2211yescharacteristic
32#11718685—21no—
33#11718685—21no—
34#11718685C2211yescharacteristic
35#11718685C2211yescharacteristic
36Q8×#1055C2211yescharacteristic
37Q8×#1055C2211yescharacteristic
38#11718660—21no—
39#11718658—21no—
40C2×C4⋊#1055C2211yescharacteristic
41C4×#6099C2211yescharacteristic
42C4×#6099C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718495C2211yescharacteristic
45#11718492C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718390—21no—
48#11718389—21no—
49#11718351—21no—
50#11718350—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×Q8⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×M16—21no—
68C13×C4⋊Q8C2×C411yescharacteristic
69C13×C4⋊Q8C2×C411yescharacteristic
70C13×#125—21no—
71C13×C22⋊Q8—21no—
72C13×C22⋊Q8C2×C411yescharacteristic
73C13×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C13—21no—
75C4×Q8×C13C2311yescharacteristic
76C4×Q8×C13C2311yescharacteristic
77C13×#117—21no—
78C2×C42×C13C2311yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82C2×#6106C2×C411yescharacteristic
83#88184C2×C411yescharacteristic
84#88183—21no—
85C4×C22⋊D13—21no—
86#88178C2×C411yescharacteristic
87C2×#6099C2×C411yescharacteristic
88C2×#6099C2×C411yescharacteristic
89C2×#6099D411yescharacteristic
90C2×#6099D411yescharacteristic
91C22×#1055—21no—
92C2×#6094—21no—
93C2×C8×D13—21no—
94#88130—21no—
95#88129C2×C411yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98#88124C2×C411yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C22⋊C8—21no—
103C13×#97—21no—
104C4×C8×C13—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109#88075C2×C411yescharacteristic
110#88075C2×C411yescharacteristic
111#88060—21no—
112#88060—21no—
113#88055—21no—
114#88054—21no—
115#88054—21no—
116C8×Dic13—21no—
117#88050C2×C411yescharacteristic
118#88050C2×C411yescharacteristic
119#88049C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88048C2×C411yescharacteristic
122#88048C2×C411yescharacteristic
123#88047C2×C411yescharacteristic
124#88047C2×C411yescharacteristic
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055—21no—
130C4⋊#1055C2311yescharacteristic
131C4⋊#1055C2311yescharacteristic
132#88043—21no—
133#88043—21no—
134#88043C2×C411yescharacteristic
135#88043C2×C411yescharacteristic
136#88043D411yescharacteristic
137#88043D411yescharacteristic
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18077—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C2×C22⋊D13—21no—
152C2×D52C22×C411yescharacteristic
153C2×C4×D13—21no—
154C2×Dic26C22×C411yescharacteristic
155C13×M16—42no—
156C2×C8×C13—21no—
157C2×C8×C13—21no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4C22×C411yescharacteristic
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C22⋊C4—21no—
170C13×C22⋊C4—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13C22×C411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C42×C13#4111yescharacteristic
176C42×C13C2411yescharacteristic
177C22⋊Dic13—21no—
178#6107—22no—
179#6107—41no—
180#6106—22no—
181#6106—41no—
182#6103—21no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193#6099—22no—
194#6099—22no—
195#6099—41no—
196#6099—41no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—42no—
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#6094—42no—
209C8×D13—42no—
210#3172—131no—
211#2969—131no—
212#2962—131no—
213#1592—131no—
214#1591—131no—
215#1588—131no—
216#1587—131no—
217#1584—131no—
218#1582—131no—
219#1579—131no—
220C8×SD16—131no—
221#1565—131no—
222#1485D1311yescharacteristic, complemented
223#1483—131no—
224#1455—131no—
225C23×C13C4×D411yescharacteristic
226C22×D13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231Q8×C13—81no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—41no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C22⋊D13—81no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251D52—21no—
252D52—21no—
253C4×D13—41no—
254C4×D13—41no—
255Dic26—21no—
256Dic26—21no—
257C8×C13—22no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—41no—
268#1055—41no—
269#1055#13112yes—
270#1055#13712yes—
271#533C2×D1311yescharacteristic
272#529—131no—
273#501—131no—
274#497—131no—
275#491—131no—
276#489—131no—
277#470—131no—
278#470—131no—
279#468—131no—
280#468—131no—
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293#436—131no—
294#436—261no—
295#435—261no—
296C8×D4—131no—
297#433—261no—
298#431C2×D1311yescharacteristic
299#424—261no—
300C2×C4⋊C8—131no—
301#405—261no—
302#405—261no—
303C4×M16—131no—
304C4×M16—131no—
305C4×M16C2×D1311yescharacteristic
306#335—131no—
307#335—131no—
308#334—131no—
309#334—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8C2×D1311yescharacteristic
313Q8⋊C8C2×D1311yescharacteristic
314Q8⋊C8C2×D1311yescharacteristic
315Q8⋊C8C2×D1311yescharacteristic
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322—131no—
319#322—131no—
320#322—131no—
321C82—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13C2×C4×D411yescharacteristic
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13C2×#13111yescharacteristic
338C4×C13#56811yescharacteristic
339C4×C13C2×#13711yescharacteristic
340C4×C13#57511yescharacteristic
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C2×M16—21no—
349C2×M16—131no—
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—131no—
353C2×M16—261no—
354C22×C8—261no—
355C22×C8—261no—
356C4⋊Q8C4×D1311yescharacteristic
357C4⋊Q8C4×D1311yescharacteristic
358#126—261no—
359#125—21no—
360#125—131no—
361#124—131no—
362#123—261no—
363C22⋊Q8—21no—
364C22⋊Q8—131no—
365C22⋊Q8C4×D1311yescharacteristic
366C22⋊Q8C4×D1311yescharacteristic
367#121—131no—
368C4×Q8—21no—
369C4×Q8—131no—
370C4×Q8C22×D1311yescharacteristic
371C4×Q8C22×D1311yescharacteristic
372C4×D4—131no—
373C4×D4—261no—
374#117—21no—
375#117—261no—
376C2×C42C22×D1311yescharacteristic
377#107—131no—
378#107—131no—
379#106—131no—
380#106—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400C22⋊C8—21no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403#97—21no—
404#97—131no—
405#97—131no—
406#97—131no—
407#97—131no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—21no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—41no—
422C2×C13#293511yescharacteristic
423C2×C13C4×#13711yescharacteristic
424C2×C13#295611yescharacteristic
425D13—81no—
426C2×Q8—21no—
427C2×Q8—131no—
428C2×Q8C2×C4×D1311yescharacteristic
429C2×Q8C2×C4×D1311yescharacteristic
430C2×D4—131no—
431C2×D4—261no—
432C22×C4—261no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4D4×D1311yescharacteristic
435C22×C4#612911yescharacteristic
436Q16—262no—
437Q16—521no—
438SD16—262no—
439SD16—521no—
440M16—42no—
441M16—262no—
442M16—262no—
443M16—522no—
444M16—521no—
445M16—521no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—522no—
461C2×C8—522no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—131no—
470C4⋊C4—131no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4C2×C4×D1311yescharacteristic
476C4⋊C4C2×C4×D1311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—21no—
485C42—21no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42D4×D1311yescharacteristic
489C42#612911yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1807711yescharacteristic, complemented, Sylow
492C23—261no—
493C23#8813511yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—81no—
499Q8—261no—
500Q8—261no—
501D4—261no—
502D4—261no—
503D4—1041no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4#8813511yescharacteristic
519C2×C4#8813511yescharacteristic
520C2×C4#8813511yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4C2×#612911yescharacteristic
524C8—22no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—132no—
529C8—132no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8—521no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—521no—
542C22—521no—
543C22—521no—
544C22C2×#8813511yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4D13×#13111yescharacteristic
557C4#1171945511yescharacteristic
558C4D13×#13711yescharacteristic
559C4#1171948211yescharacteristic
560C2—41no—
561C2—1041no—
562C2#1312357611yescharacteristic
563C2#1312365111yescharacteristic
564C2#1312374211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1485C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1485D13
hypocenterC13#18077
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
3. #13123785C2semidirect
4. #13113741C2semidirect
5. #13113730C2semidirect
6. #13113711C2semidirect
7. #13113710C2semidirect
8. #13113683C2semidirect
9. #13113675C2semidirect
10. #13113652C2semidirect
11. #13113633C2semidirect
12. #13113589C2semidirect
14. #13113139C2semidirect
15. C13×#1485C2semidirect
222. #1485D13semidirect
491. C13#18077semidirect

Maximal subgroups

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

subgroupindex
#131254362
#131238342
#131237852
#131137412
#131137302
#131137112
#131137102
#131136832
#131136752
#131136522
#131136332
#131135892
#131132502
#131131392
C13×#14852
#1807713