Finite Group Databasebeta

← #15834116

Subgroups — #15834116

Order 3328.

600 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#13124918C211yesmaximal, characteristic
2#13123998C211yesmaximal, characteristic
3#13123923C211yesmaximal, characteristic, complemented
4#13113734C211yesmaximal, characteristic, complemented
5#13113728C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113709C211yesmaximal, characteristic, complemented
8#13113709C211yesmaximal, characteristic, complemented
9#13113695C211yesmaximal, characteristic, complemented
10C8×Dic52C211yesmaximal, characteristic, complemented
11C8×#6095C211yesmaximal, characteristic, complemented
12#13113621C211yesmaximal, characteristic, complemented
13#13113297C211yesmaximal, characteristic
14C2×#11718048C211yesmaximal, characteristic, complemented
15C13×#1450C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C2×C4×C8×C13C2211yescharacteristic
21#11718587C2211yescharacteristic
22C2×C4⋊#1055C2211yescharacteristic
23#11718506C411yescharacteristic
24#11718506C411yescharacteristic
25#11718501—21no—
26#11718500—21no—
27#11718490C411yescharacteristic
28#11718490C411yescharacteristic
29#11718489—21no—
30#11718489—21no—
31#11718400C411yescharacteristic
32#11718399C411yescharacteristic
33#11718397C411yescharacteristic
34#11718391—21no—
35#11718386—21no—
36#11718382C411yescharacteristic
37#11718380—21no—
38#11718379—21no—
39C4×Dic52C2211yescharacteristic
40C4×Dic52C2211yescharacteristic
41C4×#6095C2211yescharacteristic
42C4×#6095C2211yescharacteristic
43#11718349C2211yescharacteristic
44C8×D52C2211yescharacteristic
45#11718340C2211yescharacteristic
46#11718340C2211yescharacteristic
47#11718340C2211yescharacteristic
48C8×Dic26C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C82×C13C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718051C2211yescharacteristic
56#11718051C2211yescharacteristic
57#11718050C2211yescharacteristic
58#11718050C2211yescharacteristic
59#11718049C2211yescharacteristic
60#11718049C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718048C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C22×C8×C13—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—
77C22×#1055—21no—
78C2×Dic52C2×C411yescharacteristic
79C2×Dic52C2×C411yescharacteristic
80C2×#6095C2×C411yescharacteristic
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×C8×D13—21no—
84#88130—21no—
85#88129C2×C411yescharacteristic
86C4×D52C2311yescharacteristic
87#88126—21no—
88#88124C2×C411yescharacteristic
89C4×Dic26—21no—
90C4×Dic26—21no—
91C4×Dic26C2×C411yescharacteristic
92C4×Dic26C2×C411yescharacteristic
93C4×Dic26C2311yescharacteristic
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×C4⋊C8C2×C411yescharacteristic
97C13×C4⋊C8C2×C411yescharacteristic
98C13×C4⋊C8D411yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×C22⋊C8C2×C411yescharacteristic
101C13×C22⋊C8C2×C411yescharacteristic
102C13×C22⋊C8D411yescharacteristic
103C13×C22⋊C8D411yescharacteristic
104C4×C8×C13—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111C22⋊#1055—21no—
112#88061C2×C411yescharacteristic
113#88061C2×C411yescharacteristic
114#88060—21no—
115#88060—21no—
116#88058C2×C411yescharacteristic
117#88058C2×C411yescharacteristic
118#88057C2×C411yescharacteristic
119#88057C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88056C2×C411yescharacteristic
124#88056C2×C411yescharacteristic
125#88056C2×C411yescharacteristic
126#88055—21no—
127#88055—21no—
128#88055—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134#88054—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142C4⋊#1055C2311yescharacteristic
143#88043—21no—
144#18017—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—22no—
154C2×Dic26—21no—
155C2×Dic26—41no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C2×C8×C13—24no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C42×C13C22×C411yescharacteristic
171C42×C13C2×D411yescharacteristic
172C42×C13#4111yescharacteristic
173C42×C13C2411yescharacteristic
174C22⋊Dic13—21no—
175#6103—21no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—81no—
202Dic52—22no—
203Dic52—41no—
204#6095—22no—
205#6095—41no—
206#6094—81no—
207C8×D13—81no—
208#3108—131no—
209#2994—131no—
210#2984—131no—
211#1591—131no—
212#1590—131no—
213#1588—131no—
214#1587—131no—
215#1587—131no—
216#1585—131no—
217C8×Q16—131no—
218C8×SD16—131no—
219#1573—131no—
220#1494—131no—
221C2×Q8⋊C8—131no—
222#1450D1311yescharacteristic, complemented
223C23×C13C4×D411yescharacteristic
224C22×D13—21no—
225C2×C4×C13—22no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13C4×D411yescharacteristic
231C2×C4×C13C4×D411yescharacteristic
232C2×C4×C13C4×D411yescharacteristic
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C22⋊D13—42no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246D52—21no—
247D52—21no—
248C4×D13—41no—
249C4×D13—41no—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—42no—
256Dic26#13112yes—
257C8×C13—22no—
258C8×C13—22no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—21no—
265C8×C13—21no—
266C8×C13—21no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#529—131no—
272C2×C4×Q8—131no—
273#483—131no—
274#480—131no—
275#479—131no—
276#479—131no—
277#464—131no—
278#464—131no—
279#451—131no—
280#448—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#435—261no—
295C8×D4—131no—
296C8×D4—261no—
297#433—261no—
298#432—131no—
299#432—261no—
300#431—261no—
301#431C2×D1311yescharacteristic
302#431C2×D1311yescharacteristic
303#424—261no—
304C2×C4⋊C8—131no—
305C2×C4×C8C2×D1311yescharacteristic
306#335—131no—
307#335—131no—
308#334—131no—
309#334—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322C2×D1311yescharacteristic
319#322C2×D1311yescharacteristic
320C82C2×D1311yescharacteristic
321C82C2×D1311yescharacteristic
322C22×C13—21no—
323C22×C13—21no—
324C22×C13#44312yes—
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×C13C2×#13111yescharacteristic
334C4×C13#56811yescharacteristic
335C4×C13#57711yescharacteristic
336C4×C13#57811yescharacteristic
337Dic13—22no—
338Dic13—41no—
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C22×Q8—131no—
345C2×Q16—131no—
346C2×Q16—131no—
347C2×SD16—131no—
348C2×SD16—131no—
349C2×M16—261no—
350C22×C8—21no—
351C22×C8—261no—
352C22×C8—261no—
353#126—261no—
354#125—131no—
355#124—131no—
356#123—261no—
357C22⋊Q8—131no—
358#121—131no—
359C4×Q8—131no—
360C4×Q8—131no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—261no—
365C4×Q8—261no—
366C4×D4—131no—
367C4×D4—261no—
368#117—261no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—261no—
371C2×C42—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⋊C8C4×D1311yescharacteristic
389C4⋊C8C4×D1311yescharacteristic
390C4⋊C8D5211yescharacteristic
391C4⋊C8D5211yescharacteristic
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—261no—
401C22⋊C8—261no—
402C22⋊C8—261no—
403C22⋊C8C4×D1311yescharacteristic
404C22⋊C8C4×D1311yescharacteristic
405C22⋊C8D5211yescharacteristic
406C22⋊C8D5211yescharacteristic
407#97—261no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—21no—
412C4×C8—261no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8C22×D1311yescharacteristic
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—22no—
422C2×C13#293311yescharacteristic
423C2×C13#294711yescharacteristic
424C2×C13C2×#44311yescharacteristic
425D13—81no—
426C2×Q8—131no—
427C2×Q8—131no—
428C2×Q8—131no—
429C2×Q8—262no—
430C2×Q8—261no—
431C2×Q8—521no—
432C2×D4—131no—
433C2×D4—261no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4C2×C4×D1311yescharacteristic
438C22×C4C2×D5211yescharacteristic
439C22×C4#612711yescharacteristic
440Q16—262no—
441Q16—521no—
442SD16—262no—
443SD16—521no—
444M16—1041no—
445C2×C8—24no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—261no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—1041no—
453C2×C8—1041no—
454C2×C8C2×C4×D1311yescharacteristic
455C2×C8C2×C4×D1311yescharacteristic
456C2×C8C2×C4×D1311yescharacteristic
457C2×C8C2×C4×D1311yescharacteristic
458C2×C8C2×D5211yescharacteristic
459C2×C8C2×D5211yescharacteristic
460C2×C8C2×D5211yescharacteristic
461C2×C8C2×D5211yescharacteristic
462C4⋊C4—131no—
463C4⋊C4—131no—
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⋊C4—261no—
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—261no—
481C42—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42C2×C4×D1311yescharacteristic
486C42C2×D5211yescharacteristic
487C42#612711yescharacteristic
488C42C23×D1311yescharacteristic
489C13#1801711yescharacteristic, complemented, Sylow
490C23—261no—
491C23C4×D5211yescharacteristic
492Q8—132no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—522no—
499D4—261no—
500D4—261no—
501D4—522no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—522no—
515C2×C4—522no—
516C2×C4—521no—
517C2×C4—521no—
518C2×C4C4×D5211yescharacteristic
519C2×C4C4×D5211yescharacteristic
520C2×C4C4×D5211yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C22×D5211yescharacteristic
523C2×C4C2×#612711yescharacteristic
524C8—22no—
525C8—22no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—21no—
534C8—521no—
535C8—521no—
536C8—521no—
537C8—521no—
538C22—21no—
539C22—21no—
540C22—521no—
541C22—521no—
542C22—521no—
543C22#1171836112yes—
544C22C2×C4×D5211yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—262no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4D13×#13111yescharacteristic
557C4#1171945511yescharacteristic
558C4#1171945611yescharacteristic
559C4#1171945811yescharacteristic
560C2—22no—
561C2—1041no—
562C2#1312356411yescharacteristic
563C2#1312368111yescharacteristic
564C2C2×#1171836111yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1450C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1450D13
hypocenterC13#18017
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1450

Complements

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

NH ≅ G/Ntype
3. #13123923C2semidirect
4. #13113734C2semidirect
5. #13113728C2semidirect
6. #13113716C2semidirect
7. #13113709C2semidirect
8. #13113709C2semidirect
9. #13113695C2semidirect
10. C8×Dic52C2semidirect
11. C8×#6095C2semidirect
12. #13113621C2semidirect
14. C2×#11718048C2semidirect
15. C13×#1450C2semidirect
222. #1450D13semidirect
489. C13#18017semidirect

Maximal subgroups

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

subgroupindex
#131249182
#131239982
#131239232
#131137342
#131137282
#131137162
#131137092
#131136952
C8×Dic522
C8×#60952
#131136212
#131132972
C2×#117180482
C13×#14502
#1801713