Finite Group Databasebeta

← #15833993

Subgroups — #15833993

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124903C211yesmaximal, characteristic
2#13123844C211yesmaximal, characteristic
3#13123778C211yesmaximal, characteristic, complemented
4#13113742C211yesmaximal, characteristic, complemented
5#13113734C211yesmaximal, characteristic, complemented
6#13113706C211yesmaximal, characteristic, complemented
7#13113694C211yesmaximal, characteristic, complemented
8#13113686C211yesmaximal, characteristic, complemented
9#13113672C211yesmaximal, characteristic, complemented
10#13113645C211yesmaximal, characteristic, complemented
11#13113618C211yesmaximal, characteristic, complemented
12#13113307C211yesmaximal, characteristic, complemented
13#13113220C211yesmaximal, characteristic
14#13113130C211yesmaximal, characteristic, complemented
15C8×C13×SD16C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×#6129C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C8×D4×C13C2211yescharacteristic
21#11718834C411yescharacteristic
22#11718823C411yescharacteristic
23#11718772—21no—
24C2×#88055—21no—
25C4×#6107C2211yescharacteristic
26#11718685C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718528C411yescharacteristic
30#11718515C411yescharacteristic
31#11718500—21no—
32#11718496C2211yescharacteristic
33D13×C4⋊C8C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718475C411yescharacteristic
38#11718454C411yescharacteristic
39#11718444C411yescharacteristic
40#11718420C411yescharacteristic
41#11718391—21no—
42#11718380—21no—
43C4×Dic52C2211yescharacteristic
44#11718350—21no—
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48#11718340—21no—
49#11718340C2211yescharacteristic
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
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×#6094D411yescharacteristic
82C2×#6094D411yescharacteristic
83C2×C8×D13—21no—
84#88151C2×C411yescharacteristic
85#88150—21no—
86#88146C2×C411yescharacteristic
87#88143—21no—
88#88142C2×C411yescharacteristic
89#88141C2×C411yescharacteristic
90#88135—21no—
91#88131—21no—
92#88126—21no—
93C42×D13C2311yescharacteristic
94C4×Dic26—21no—
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×#106C2×C411yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#102C2×C411yescharacteristic
103C13×C22⋊C8—21no—
104C4×C8×C13—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88075C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110C22⋊#1055—21no—
111#88060—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#88055—21no—
121#88055—21no—
122#88055D411yescharacteristic
123#88055D411yescharacteristic
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054C2×C411yescharacteristic
131#88054C2×C411yescharacteristic
132C8×Dic13—21no—
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#18009—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—41no—
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—41no—
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—41no—
206#6094—22no—
207#6094—41no—
208C8×D13—42no—
209#3107—131no—
210#2970—131no—
211#2962—131no—
212#1593—131no—
213#1591—131no—
214#1587—131no—
215#1585—131no—
216#1584—131no—
217#1582—131no—
218SD16⋊C8—131no—
219C8×SD16D1311yescharacteristic, complemented
220#1573—131no—
221#1497—131no—
222#1477—131no—
223#1453—131no—
224C23×C13—21no—
225C22×D13C4×D411yescharacteristic
226Q8×C13—21no—
227Q8×C13—21no—
228D4×C13—21no—
229D4×C13#13112yes—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13C23×C411yescharacteristic
236C2×C4×C13C22×D411yescharacteristic
237C2×C4×C13C2×#4111yescharacteristic
238C22⋊D13—42no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—42no—
244C2×Dic13—81no—
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C4×D411yescharacteristic
247C2×Dic13C4×D411yescharacteristic
248C4×D13—21no—
249C4×D13—21no—
250C4×D13—21no—
251C4×D13—21no—
252C4×D13—41no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—21no—
257Dic26—81no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13#13712yes—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272#533—131no—
273C4×#41—131no—
274#485—131no—
275#485—131no—
276#475—131no—
277#474—131no—
278#462—131no—
279#461—131no—
280#452—131no—
281#452—131no—
282#446—131no—
283#446—131no—
284#446—131no—
285#446—131no—
286#446—261no—
287#446—261no—
288C8×Q8—131no—
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16C2×D1311yescharacteristic
294#435—261no—
295#435—261no—
296C8×D4—131no—
297C8×D4C2×D1311yescharacteristic
298#432—131no—
299#432—261no—
300#431—131no—
301#431—131no—
302#424—261no—
303C2×C4⋊C8—131no—
304#405—261no—
305C4×M16—131no—
306C2×#97—261no—
307#335—131no—
308#335—131no—
309#334—131no—
310#334C2×D1311yescharacteristic
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8C2×D1311yescharacteristic
317D4⋊C8—131no—
318D4⋊C8C2×D1311yescharacteristic
319#322—131no—
320#322—131no—
321#322—131no—
322C82C2×D1311yescharacteristic
323C22×C13—22no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13C2×C4×D411yescharacteristic
327C2×D13—21no—
328C2×D13—21no—
329C2×D13—21no—
330C4×C13—21no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13C2×#13111yescharacteristic
335C4×C13#56811yescharacteristic
336C4×C13C2×#13711yescharacteristic
337C4×C13#57511yescharacteristic
338Dic13—21no—
339Dic13—21no—
340Dic13—21no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C2×#41—131no—
346C2×Q16—131no—
347C2×Q16—131no—
348C2×SD16—131no—
349C2×SD16C4×D1311yescharacteristic
350C2×M16—131no—
351C2×M16—131no—
352C22×C8—21no—
353C22×C8—261no—
354C22×C8—261no—
355C4⋊Q8—131no—
356C4⋊Q8—131no—
357#125—261no—
358C22⋊Q8—131no—
359C22⋊Q8—131no—
360C22⋊Q8—261no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—261no—
365C4×Q8C22×D1311yescharacteristic
366C4×D4—131no—
367C4×D4—261no—
368C4×D4—261no—
369C4×D4C22×D1311yescharacteristic
370#117—131no—
371#117—261no—
372#117—261no—
373C2×C42—131no—
374C2×C42—261no—
375#107—131no—
376#107—131no—
377#106—131no—
378#106C4×D1311yescharacteristic
379C4⋊C8—21no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8C22×D1311yescharacteristic
392C4⋊C8C22×D1311yescharacteristic
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103C4×D1311yescharacteristic
399#102—131no—
400#102C4×D1311yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—131no—
408#97—131no—
409#97—261no—
410#97—261no—
411#97—261no—
412#97—261no—
413#97—261no—
414C4×C8—21no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—42no—
423C2×C13#293311yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295711yescharacteristic
426D13—41no—
427#41—262no—
428#41—521no—
429C2×Q8—131no—
430C2×Q8—131no—
431C2×Q8—261no—
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—261no—
434C2×D4C2×C4×D1311yescharacteristic
435C22×C4—21no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—131no—
439C22×C4—261no—
440C22×C4—261no—
441Q16—521no—
442Q16—521no—
443SD16—22no—
444SD16—262no—
445M16—262no—
446M16—521no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—522no—
459C2×C8—522no—
460C2×C8C2×C4×D1311yescharacteristic
461C2×C8C2×C4×D1311yescharacteristic
462C2×C8D4×D1311yescharacteristic
463C2×C8D4×D1311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—131no—
466C4⋊C4—131no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
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—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—21no—
483C42—131no—
484C42—131no—
485C42—131no—
486C42—261no—
487C42—261no—
488C42—261no—
489C42—261no—
490C42C23×D1311yescharacteristic
491C13#1800911yescharacteristic, complemented, Sylow
492C23—21no—
493C23—131no—
494Q8—21no—
495Q8—21no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—1041no—
501D4—21no—
502D4—522no—
503D4#8815512yes—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—131no—
510C2×C4—131no—
511C2×C4—131no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—521no—
521C2×C4—522no—
522C2×C4—1041no—
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C2×D4×D1311yescharacteristic
525C2×C4#41×D1311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8#8816912yes—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—261no—
544C22—261no—
545C22—261no—
546C22C4×D4×D1311yescharacteristic
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—261no—
552C4—261no—
553C4—261no—
554C4—521no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4C2×#8815511yescharacteristic
559C4#1171945511yescharacteristic
560C4C2×#8816911yescharacteristic
561C4#1171947311yescharacteristic
562C2—42no—
563C2—521no—
564C2#1312355611yescharacteristic
565C2C4×#8816911yescharacteristic
566C2#1312374811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC8×C13×SD16C2
socleC22×C13C2×C4×D4
prime radicalC2×#6129C2×C4
cosocleC42×C13C24
hypercenterC8×SD16D13
hypocenterC13#18009
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×SD16

Complements

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

NH ≅ G/Ntype
3. #13123778C2semidirect
4. #13113742C2semidirect
5. #13113734C2semidirect
6. #13113706C2semidirect
7. #13113694C2semidirect
8. #13113686C2semidirect
9. #13113672C2semidirect
10. #13113645C2semidirect
11. #13113618C2semidirect
12. #13113307C2semidirect
14. #13113130C2semidirect
15. C8×C13×SD16C2semidirect
219. C8×SD16D13semidirect
491. C13#18009semidirect

Maximal subgroups

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

subgroupindex
#131249032
#131238442
#131237782
#131137422
#131137342
#131137062
#131136942
#131136862
#131136722
#131136452
#131136182
#131133072
#131132202
#131131302
C8×C13×SD162
#1800913