Finite Group Databasebeta

← #15834110

Subgroups — #15834110

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#13123992C211yesmaximal, characteristic
3#13123926C211yesmaximal, characteristic, complemented
4#13113732C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113713C211yesmaximal, characteristic, complemented
7#13113706C211yesmaximal, characteristic, complemented
8#13113706C211yesmaximal, characteristic, complemented
9#13113692C211yesmaximal, characteristic, complemented
10#13113642C211yesmaximal, characteristic, complemented
11#13113635C211yesmaximal, characteristic, complemented
12#13113294C211yesmaximal, characteristic
13C2×#11718076C211yesmaximal, characteristic, complemented
14#13113120C211yesmaximal, characteristic, complemented
15C13×#1573C211yesmaximal, characteristic, complemented
16#11719184C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C2×C13×C4⋊C8C2211yescharacteristic
21#11718772—21no—
22C8×C22⋊D13—21no—
23#11718586C2211yescharacteristic
24C2×C4×#1055C2211yescharacteristic
25#11718506C411yescharacteristic
26#11718506C411yescharacteristic
27#11718501—21no—
28#11718500—21no—
29#11718499C2211yescharacteristic
30#11718495C2211yescharacteristic
31#11718492C2211yescharacteristic
32#11718492C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718491C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718491C2211yescharacteristic
37#11718490C411yescharacteristic
38#11718490C411yescharacteristic
39#11718400C411yescharacteristic
40#11718399C411yescharacteristic
41#11718397C411yescharacteristic
42#11718382C411yescharacteristic
43#11718380—21no—
44#11718379—21no—
45#11718362—21no—
46#11718362—21no—
47C4×Dic52C2211yescharacteristic
48C4×Dic52C2211yescharacteristic
49C4×#6095C2211yescharacteristic
50C4×#6095C2211yescharacteristic
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#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
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⋊C8—21no—
97C13×C4⋊C8C2×C411yescharacteristic
98C13×C4⋊C8C2×C411yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8C2×C411yescharacteristic
105C13×C22⋊C8C2×C411yescharacteristic
106C13×#97—21no—
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
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#88055—21no—
127#88055—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C4⋊#1055D411yescharacteristic
138C4⋊#1055D411yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
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—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—81no—
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—24no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055C2×D411yescharacteristic
199C2×#1055C2×D411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
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#1573D1311yescharacteristic, complemented
220#1494—131no—
221C2×Q8⋊C8—131no—
222#1450—131no—
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—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265#1055—22no—
266#1055—22no—
267#1055—21no—
268#1055—21no—
269#1055—21no—
270#1055—21no—
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—261no—
299#432C2×D1311yescharacteristic
300#431—131no—
301#431—261no—
302#431C2×D1311yescharacteristic
303#424—261no—
304C2×C4⋊C8C2×D1311yescharacteristic
305C2×C4×C8—131no—
306#335C2×D1311yescharacteristic
307#335C2×D1311yescharacteristic
308#334C2×D1311yescharacteristic
309#334C2×D1311yescharacteristic
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#322—131no—
319#322—131no—
320C82—131no—
321C82—131no—
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—21no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—261no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8C4×D1311yescharacteristic
387C4⋊C8C4×D1311yescharacteristic
388C4⋊C8C22×D1311yescharacteristic
389C4⋊C8C22×D1311yescharacteristic
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—131no—
402C22⋊C8—131no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C4×D1311yescharacteristic
406C22⋊C8C4×D1311yescharacteristic
407#97—21no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
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×C4D4×D1311yescharacteristic
439C22×C4#613111yescharacteristic
440Q16—262no—
441Q16—521no—
442SD16—262no—
443SD16—521no—
444M16—1041no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—81no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—264no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—1041no—
458C2×C8C2×C4×D1311yescharacteristic
459C2×C8C2×C4×D1311yescharacteristic
460C2×C8C2×C4×D1311yescharacteristic
461C2×C8C2×C4×D1311yescharacteristic
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
486C42D4×D1311yescharacteristic
487C42#613111yescharacteristic
488C42C23×D1311yescharacteristic
489C13#1801711yescharacteristic, complemented, Sylow
490C23—261no—
491C23#8814711yescharacteristic
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×C4#8814711yescharacteristic
519C2×C4#8814711yescharacteristic
520C2×C4#8814711yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4C2×#613111yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—262no—
533C8—262no—
534C8—261no—
535C8—261no—
536C8—261no—
537C8—261no—
538C22—21no—
539C22—21no—
540C22—521no—
541C22—521no—
542C22—521no—
543C22#1171855612yes—
544C22C2×#8814711yescharacteristic
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#1171948011yescharacteristic
559C4#1171948411yescharacteristic
560C2—22no—
561C2—1041no—
562C2#1312356011yescharacteristic
563C2#1312367711yescharacteristic
564C2C2×#1171855611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1573C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1573D13
hypocenterC13#18017
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #13123926C2semidirect
4. #13113732C2semidirect
5. #13113725C2semidirect
6. #13113713C2semidirect
7. #13113706C2semidirect
8. #13113706C2semidirect
9. #13113692C2semidirect
10. #13113642C2semidirect
11. #13113635C2semidirect
13. C2×#11718076C2semidirect
14. #13113120C2semidirect
15. C13×#1573C2semidirect
219. #1573D13semidirect
489. C13#18017semidirect

Maximal subgroups

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

subgroupindex
#131249182
#131239922
#131239262
#131137322
#131137252
#131137132
#131137062
#131136922
#131136422
#131136352
#131132942
C2×#117180762
#131131202
C13×#15732
#1801713