Finite Group Databasebeta

← #15832950

Subgroups — #15832950

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124903C211yesmaximal, characteristic
2C8×#6129C211yesmaximal, characteristic
3#13123765C211yesmaximal, characteristic, complemented
4#13113689C211yesmaximal, characteristic, complemented
5#13113685C211yesmaximal, characteristic, complemented
6#13113673C211yesmaximal, characteristic, complemented
7#13113669C211yesmaximal, characteristic, complemented
8#13113656C211yesmaximal, characteristic, complemented
9#13113653C211yesmaximal, characteristic, complemented
10#13113648C211yesmaximal, characteristic, complemented
11#13113626C211yesmaximal, characteristic, complemented
12#13113272C211yesmaximal, characteristic
13#13113255C211yesmaximal, characteristic, complemented
14#13113124C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×#6129C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718834C411yescharacteristic
22#11718823C411yescharacteristic
23C8×C22⋊D13—21no—
24C2×C8×Dic13—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718528C411yescharacteristic
30#11718515C411yescharacteristic
31#11718500—21no—
32#11718498C2211yescharacteristic
33#11718494C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718475C411yescharacteristic
38#11718454C411yescharacteristic
39#11718444C411yescharacteristic
40#11718420C411yescharacteristic
41#11718386—21no—
42#11718379—21no—
43C4×Dic52C2211yescharacteristic
44#11718350—21no—
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48C8×Dic26—21no—
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66#11718046C2211yescharacteristic
67C2×#6129C2×C411yescharacteristic
68C2×C13×SD16C2×C411yescharacteristic
69C22×C8×C13—21no—
70C4×Q8×C13C2311yescharacteristic
71C4×D4×C13C2311yescharacteristic
72#88200C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75D4×Dic13C2×C411yescharacteristic
76C2×#6105C2×C411yescharacteristic
77C4×C22⋊D13—21no—
78C2×C4×Dic13—21no—
79C22×#1055—21no—
80C2×Dic52C2×C411yescharacteristic
81C2×#6094—21no—
82C2×#6094—21no—
83C2×C8×D13D411yescharacteristic
84C2×C8×D13D411yescharacteristic
85#88151C2×C411yescharacteristic
86#88150—21no—
87#88146C2×C411yescharacteristic
88#88143—21no—
89#88142C2×C411yescharacteristic
90#88141C2×C411yescharacteristic
91#88135—21no—
92#88131—21no—
93#88126—21no—
94C42×D13C2311yescharacteristic
95C4×Dic26—21no—
96C4×Dic26C2311yescharacteristic
97C4×Dic26C2311yescharacteristic
98C13×#106C2×C411yescharacteristic
99C13×C4⋊C8—21no—
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#102C2×C411yescharacteristic
104C13×C22⋊C8—21no—
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109#88075C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111C22⋊#1055—21no—
112#88060—21no—
113#88060C2×C411yescharacteristic
114#88060C2×C411yescharacteristic
115#88058C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88056C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054C2×C411yescharacteristic
126#88054C2×C411yescharacteristic
127C8×Dic13—21no—
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131C8×Dic13D411yescharacteristic
132C8×Dic13D411yescharacteristic
133#88050C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17916—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13C22×C411yescharacteristic
147C22×C4×C13—21no—
148C2×C22⋊D13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151#6129—22no—
152#6129—22no—
153C2×C4×D13C22×C411yescharacteristic
154C2×C4×D13C2×D411yescharacteristic
155C2×C4×D13#4111yescharacteristic
156C2×Dic26—21no—
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C13×SD16—22no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—42no—
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C42×C13—21no—
173C42×C13C2411yescharacteristic
174C22⋊Dic13—21no—
175#6107—22no—
176#6105—22no—
177#6103—21no—
178#6103—21no—
179#6103—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13C22×C411yescharacteristic
182C4⋊Dic13C22×C411yescharacteristic
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×Dic13C22×C411yescharacteristic
195C4×Dic13C2×D411yescharacteristic
196C4×Dic13#4111yescharacteristic
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—42no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205Dic52—22no—
206#6094—42no—
207#6094—42no—
208C8×D13—22no—
209C8×D13—41no—
210#3107—131no—
211C8×#41—131no—
212#2960—131no—
213#1584—131no—
214#1584—131no—
215#1582—131no—
216#1582—131no—
217#1579—131no—
218#1579—131no—
219SD16⋊C8—131no—
220SD16⋊C8D1311yescharacteristic, complemented
221#1574—131no—
222#1489—131no—
223#1485—131no—
224#1451—131no—
225C23×C13—21no—
226C22×D13C4×D411yescharacteristic
227Q8×C13—21no—
228Q8×C13—21no—
229D4×C13—21no—
230D4×C13#13112yes—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—41no—
235C2×C4×C13—41no—
236C2×C4×C13C23×C411yescharacteristic
237C2×C4×C13C22×D411yescharacteristic
238C2×C4×C13C2×#4111yescharacteristic
239C22⋊D13—24no—
240C2×Dic13—24no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—21no—
245C2×Dic13—42no—
246C2×Dic13C4×D411yescharacteristic
247C2×Dic13C4×D411yescharacteristic
248C2×Dic13C4×D411yescharacteristic
249C4×D13—21no—
250C4×D13—21no—
251C4×D13—21no—
252C4×D13—21no—
253C4×D13—22no—
254Dic26—21no—
255Dic26—21no—
256Dic26—21no—
257Dic26—42no—
258Dic26#13112yes—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272#1055#13712yes—
273#533—131no—
274C4×#41—131no—
275#485—131no—
276#485—131no—
277#475—131no—
278#474—131no—
279#462—131no—
280#461—131no—
281#452—131no—
282#452—131no—
283#446—131no—
284#446—131no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—261no—
290C8×Q8C2×D1311yescharacteristic
291C4×Q16—131no—
292C4×Q16—131no—
293C4×SD16—131no—
294C4×SD16C2×D1311yescharacteristic
295C8×D4—131no—
296C8×D4—261no—
297C8×D4—261no—
298C8×D4C2×D1311yescharacteristic
299#431—131no—
300#431—131no—
301#431—261no—
302#424—261no—
303#423—131no—
304#405—261no—
305C4×M16—131no—
306C2×C4×C8—131no—
307C2×C4×C8—261no—
308#335—131no—
309#335C2×D1311yescharacteristic
310#334—131no—
311#334—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8C2×D1311yescharacteristic
318D4⋊C8—131no—
319D4⋊C8C2×D1311yescharacteristic
320#322—131no—
321#322—131no—
322#322—131no—
323#322C2×D1311yescharacteristic
324C22×C13—22no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13C2×C4×D411yescharacteristic
328C2×D13—21no—
329C2×D13—21no—
330C2×D13—21no—
331C4×C13—21no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13C2×#13111yescharacteristic
336C4×C13C2×#13111yescharacteristic
337C4×C13C2×#13711yescharacteristic
338C4×C13#57511yescharacteristic
339Dic13—22no—
340Dic13—21no—
341Dic13—21no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345Dic13#44412yes—
346C2×#41—131no—
347C2×Q16—131no—
348C2×Q16—131no—
349C2×SD16—131no—
350C2×SD16C4×D1311yescharacteristic
351C2×M16—261no—
352C2×M16—261no—
353C22×C8—21no—
354C22×C8—131no—
355C22×C8—131no—
356C22×C8—261no—
357C4⋊Q8—131no—
358C4⋊Q8—131no—
359#125—261no—
360C22⋊Q8—131no—
361C22⋊Q8—131no—
362C22⋊Q8—261no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—261no—
367C4×Q8C22×D1311yescharacteristic
368C4×D4—131no—
369C4×D4—261no—
370C4×D4—261no—
371C4×D4C22×D1311yescharacteristic
372#117—131no—
373#117—261no—
374#117—261no—
375C2×C42—131no—
376C2×C42—261no—
377#107—131no—
378#107—131no—
379#106—131no—
380#106C4×D1311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—131no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8C22×D1311yescharacteristic
393C4⋊C8C22×D1311yescharacteristic
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103—131no—
399#103C4×D1311yescharacteristic
400#102—131no—
401#102C4×D1311yescharacteristic
402C22⋊C8—21no—
403C22⋊C8—131no—
404C22⋊C8—131no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—261no—
408#97—261no—
409#97—261no—
410C4×C8—21no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C4×C8C22×D1311yescharacteristic
423C2×C13—42no—
424C2×C13#292911yescharacteristic
425C2×C13C4×#13711yescharacteristic
426C2×C13C2×#44411yescharacteristic
427D13—41no—
428#41—262no—
429#41—262no—
430C2×Q8—131no—
431C2×Q8—131no—
432C2×Q8—261no—
433C2×Q8C2×C4×D1311yescharacteristic
434C2×D4—261no—
435C2×D4C2×C4×D1311yescharacteristic
436C22×C4—21no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—261no—
441C22×C4—261no—
442Q16—262no—
443Q16—262no—
444SD16—22no—
445SD16—262no—
446M16—522no—
447M16—522no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—42no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—262no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—261no—
460C2×C8—521no—
461C2×C8—522no—
462C2×C8C2×C4×D1311yescharacteristic
463C2×C8C2×C4×D1311yescharacteristic
464C2×C8D4×D1311yescharacteristic
465C2×C8D4×D1311yescharacteristic
466C4⋊C4—21no—
467C4⋊C4—131no—
468C4⋊C4—131no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4C2×C4×D1311yescharacteristic
478C4⋊C4C2×C4×D1311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—21no—
485C42—131no—
486C42—131no—
487C42—131no—
488C42—261no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42C23×D1311yescharacteristic
493C13#1791611yescharacteristic, complemented, Sylow
494C23—21no—
495C23—131no—
496Q8—21no—
497Q8—21no—
498Q8—132no—
499Q8—261no—
500Q8—261no—
501Q8—261no—
502Q8—522no—
503D4—21no—
504D4—264no—
505D4#8815512yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—131no—
512C2×C4—131no—
513C2×C4—131no—
514C2×C4—262no—
515C2×C4—264no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—261no—
524C2×C4—522no—
525C2×C4C22×C4×D1311yescharacteristic
526C2×C4C2×D4×D1311yescharacteristic
527C2×C4#41×D1311yescharacteristic
528C8—21no—
529C8—21no—
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—132no—
536C8—261no—
537C8—261no—
538C8—261no—
539C8—521no—
540C8—521no—
541C8—521no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—261no—
546C22—261no—
547C22—261no—
548C22C4×D4×D1311yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—132no—
554C4—261no—
555C4—261no—
556C4—262no—
557C4—521no—
558C4—521no—
559C4—521no—
560C4C2×#8815511yescharacteristic
561C4D13×#13111yescharacteristic
562C4#1171947811yescharacteristic
563C4D13×#13711yescharacteristic
564C2—42no—
565C2—521no—
566C2#1312352511yescharacteristic
567C2#1312365811yescharacteristic
568C2D13×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×SD16⋊C8C2
socleC22×C13C2×C4×D4
prime radicalC2×#6129C2×C4
cosocleC42×C13C24
hypercenterSD16⋊C8D13
hypocenterC13#17916
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ SD16⋊C8

Complements

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

NH ≅ G/Ntype
3. #13123765C2semidirect
4. #13113689C2semidirect
5. #13113685C2semidirect
6. #13113673C2semidirect
7. #13113669C2semidirect
8. #13113656C2semidirect
9. #13113653C2semidirect
10. #13113648C2semidirect
11. #13113626C2semidirect
13. #13113255C2semidirect
14. #13113124C2semidirect
15. C13×SD16⋊C8C2semidirect
220. SD16⋊C8D13semidirect
493. C13#17916semidirect

Maximal subgroups

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

subgroupindex
#131249032
C8×#61292
#131237652
#131136892
#131136852
#131136732
#131136692
#131136562
#131136532
#131136482
#131136262
#131132722
#131132552
#131131242
C13×SD16⋊C82
#1791613