Finite Group Databasebeta

← #15834137

Subgroups — #15834137

Order 3328.

598 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#13124905C211yesmaximal, characteristic
2#13123967C211yesmaximal, characteristic
3#13123934C211yesmaximal, characteristic, complemented
4#13113726C211yesmaximal, characteristic, complemented
5#13113725C211yesmaximal, characteristic, complemented
6#13113716C211yesmaximal, characteristic, complemented
7#13113711C211yesmaximal, characteristic, complemented
8#13113704C211yesmaximal, characteristic, complemented
9Q16×#1055C211yesmaximal, characteristic, complemented
10C8×#6107C211yesmaximal, characteristic, complemented
11#13113623C211yesmaximal, characteristic, complemented
12#13113289C211yesmaximal, characteristic, complemented
13#13113217C211yesmaximal, characteristic
14#13113121C211yesmaximal, characteristic, complemented
15C13×#1587C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×#6131C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718848C411yescharacteristic
22#11718843C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6106C2211yescharacteristic
25Q8×#1055C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718551C411yescharacteristic
28#11718549C411yescharacteristic
29#11718501—21no—
30#11718499—21no—
31#11718499C2211yescharacteristic
32#11718498—21no—
33#11718498C2211yescharacteristic
34#11718494C2211yescharacteristic
35#11718492C2211yescharacteristic
36#11718491—21no—
37#11718479C411yescharacteristic
38#11718476C411yescharacteristic
39#11718471C411yescharacteristic
40#11718452C411yescharacteristic
41#11718370—21no—
42#11718362—21no—
43C4×#6095C2211yescharacteristic
44#11718349—21no—
45#11718349C2211yescharacteristic
46#11718346—21no—
47#11718346C2211yescharacteristic
48#11718346C2211yescharacteristic
49C4×C8×D13C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718050C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6131C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71#88200C2×C411yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6106C2×C411yescharacteristic
76C2×#6095C2×C411yescharacteristic
77C2×#6094—21no—
78C2×#6094—21no—
79C2×#6094—21no—
80C2×C8×D13—21no—
81#88151C2×C411yescharacteristic
82#88150—21no—
83#88147—21no—
84#88147C2×C411yescharacteristic
85#88146—21no—
86#88146C2×C411yescharacteristic
87#88143—21no—
88#88142C2×C411yescharacteristic
89C4×D52—21no—
90C4×D52C2311yescharacteristic
91#88126—21no—
92C42×D13—21no—
93C42×D13C2311yescharacteristic
94C4×Dic26—21no—
95C4×Dic26C2311yescharacteristic
96C13×#107C2×C411yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×#103C2×C411yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#97—21no—
104C4×C8×C13—21no—
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88075C2×C411yescharacteristic
109#88075C2×C411yescharacteristic
110#88061C2×C411yescharacteristic
111#88060—21no—
112#88060—21no—
113#88060—21no—
114#88060C2×C411yescharacteristic
115#88060C2×C411yescharacteristic
116#88060D411yescharacteristic
117#88060D411yescharacteristic
118#88057C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88055—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054C2×C411yescharacteristic
125#88054C2×C411yescharacteristic
126#88054D411yescharacteristic
127#88054D411yescharacteristic
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13—21no—
131#88050C2×C411yescharacteristic
132#88049C2×C411yescharacteristic
133#88048C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18019—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147#6131—22no—
148#6131—41no—
149C2×D52—21no—
150C2×D52C22×C411yescharacteristic
151C2×C4×D13—21no—
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13C22×C411yescharacteristic
155C2×C4×D13C2×D411yescharacteristic
156C2×C4×D13#4111yescharacteristic
157C2×Dic26—21no—
158C2×Dic26C22×C411yescharacteristic
159C13×Q16—22no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C42×C13—21no—
172C42×C13—21no—
173C42×C13C2411yescharacteristic
174#6107—22no—
175#6106—41no—
176#6103—21no—
177#6103—21no—
178#6103—21no—
179#6103—21no—
180#6103—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13C22×C411yescharacteristic
184C4⋊Dic13C22×C411yescharacteristic
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×Dic13C22×C411yescharacteristic
194C4×Dic13C2×D411yescharacteristic
195C4×Dic13#4111yescharacteristic
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203#6095—41no—
204#6094—81no—
205#6094—81no—
206#6094—81no—
207C8×D13—24no—
208#3107—131no—
209#2991—131no—
210#2986—131no—
211#1590—131no—
212#1590—131no—
213#1588—131no—
214#1588—131no—
215#1587—131no—
216#1587D1311yescharacteristic, complemented
217C8×Q16—131no—
218C8×Q16—131no—
219#1574—131no—
220#1493—131no—
221#1476—131no—
222#1450—131no—
223C22×D13—21no—
224C22×D13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13#13112yes—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13C23×C411yescharacteristic
234C2×C4×C13C22×D411yescharacteristic
235C2×C4×C13C2×#4111yescharacteristic
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13C4×D411yescharacteristic
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242D52—21no—
243D52—21no—
244D52—42no—
245C4×D13—21no—
246C4×D13—21no—
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—22no—
250C4×D13—42no—
251C4×D13—41no—
252C4×D13—41no—
253C4×D13—42no—
254Dic26—21no—
255Dic26—21no—
256Dic26—42no—
257C8×C13—22no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—41no—
263C8×C13—41no—
264#1055—22no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#533—131no—
272C4×#41—131no—
273#485—131no—
274#485—131no—
275#475—131no—
276#474—131no—
277#462—131no—
278#461—131no—
279#452—131no—
280#452—131no—
281#446—131no—
282#446—261no—
283#446C2×D1311yescharacteristic
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—261no—
288C8×Q8C2×D1311yescharacteristic
289C4×Q16—131no—
290C4×Q16C2×D1311yescharacteristic
291C4×SD16—131no—
292C4×SD16—131no—
293#436—131no—
294#436—131no—
295#436—261no—
296#436—261no—
297#433—261no—
298#433—261no—
299#431—131no—
300#431—131no—
301#431—131no—
302#431—261no—
303#423—131no—
304#423—261no—
305C2×C4×C8—131no—
306#335—131no—
307#335—131no—
308#334—131no—
309#334C2×D1311yescharacteristic
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8C2×D1311yescharacteristic
315Q8⋊C8C2×D1311yescharacteristic
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322—131no—
319#322C2×D1311yescharacteristic
320C82—131no—
321C82—131no—
322C22×C13C2×C4×D411yescharacteristic
323C2×D13—21no—
324C2×D13—21no—
325C2×D13—21no—
326C2×D13—41no—
327C2×D13—41no—
328C2×D13—41no—
329C4×C13—22no—
330C4×C13—21no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13C2×#13111yescharacteristic
335C4×C13#56811yescharacteristic
336C4×C13#57711yescharacteristic
337C4×C13#57811yescharacteristic
338Dic13—21no—
339Dic13—21no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13#44312yes—
344C2×#41—131no—
345C2×Q16—131no—
346C2×Q16C4×D1311yescharacteristic
347C2×SD16—131no—
348C2×SD16—131no—
349C2×M16—261no—
350C2×M16—261no—
351C2×M16—261no—
352C22×C8—261no—
353C4⋊Q8—131no—
354C4⋊Q8—131no—
355#125—261no—
356C22⋊Q8—131no—
357C22⋊Q8—131no—
358C22⋊Q8—261no—
359C4×Q8—131no—
360C4×Q8—131no—
361C4×Q8—261no—
362C4×Q8C22×D1311yescharacteristic
363C4×Q8C22×D1311yescharacteristic
364C4×D4—131no—
365C4×D4—131no—
366C4×D4—261no—
367C4×D4—261no—
368#117—131no—
369#117—261no—
370#117—261no—
371C2×C42—131no—
372C2×C42—261no—
373#107—131no—
374#107C4×D1311yescharacteristic
375#106—131no—
376#106—131no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
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#103C4×D1311yescharacteristic
397#103C4×D1311yescharacteristic
398#102—131no—
399#102—131no—
400C22⋊C8—131no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—261no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—21no—
408#97—261no—
409C4×C8—21no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13#293311yescharacteristic
422C2×C13#294711yescharacteristic
423C2×C13C2×#44311yescharacteristic
424D13—41no—
425D13—81no—
426#41—262no—
427#41—521no—
428C2×Q8—131no—
429C2×Q8—261no—
430C2×Q8C2×C4×D1311yescharacteristic
431C2×Q8C2×C4×D1311yescharacteristic
432C2×D4—131no—
433C2×D4—261no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—261no—
438C22×C4—261no—
439C22×C4—261no—
440Q16—22no—
441Q16—262no—
442SD16—521no—
443SD16—521no—
444M16—1041no—
445M16—1041no—
446M16—1041no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—264no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8C2×C4×D1311yescharacteristic
459C2×C8C2×C4×D1311yescharacteristic
460C2×C8D4×D1311yescharacteristic
461C2×C8D4×D1311yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
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⋊C4C2×C4×D1311yescharacteristic
474C4⋊C4C2×C4×D1311yescharacteristic
475C22⋊C4—261no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—21no—
481C42—21no—
482C42—131no—
483C42—131no—
484C42—131no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42C23×D1311yescharacteristic
489C13#1801911yescharacteristic, complemented, Sylow
490C23—131no—
491C23—261no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—261no—
496Q8—261no—
497Q8—522no—
498Q8#8816112yes—
499D4—261no—
500D4—261no—
501D4—522no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—131no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—262no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—522no—
518C2×C4—522no—
519C2×C4—521no—
520C2×C4—521no—
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×D4×D1311yescharacteristic
523C2×C4#41×D1311yescharacteristic
524C8—22no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—262no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8—521no—
538C22—261no—
539C22—261no—
540C22—261no—
541C22—521no—
542C22—521no—
543C22—521no—
544C22C4×D4×D1311yescharacteristic
545C4—21no—
546C4—22no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—132no—
551C4—261no—
552C4—261no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4C2×#8816111yescharacteristic
557C4#1171945511yescharacteristic
558C4#1171948311yescharacteristic
559C4#1171948411yescharacteristic
560C2—521no—
561C2—1041no—
562C2#1312356211yescharacteristic
563C2#1312367811yescharacteristic
564C2D13×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1587C2
socleC22×C13C2×C4×D4
prime radicalC2×#6131C2×C4
cosocleC42×C13C24
hypercenter#1587D13
hypocenterC13#18019
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1587

Complements

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

NH ≅ G/Ntype
3. #13123934C2semidirect
4. #13113726C2semidirect
5. #13113725C2semidirect
6. #13113716C2semidirect
7. #13113711C2semidirect
8. #13113704C2semidirect
9. Q16×#1055C2semidirect
10. C8×#6107C2semidirect
11. #13113623C2semidirect
12. #13113289C2semidirect
14. #13113121C2semidirect
15. C13×#1587C2semidirect
216. #1587D13semidirect
489. C13#18019semidirect

Maximal subgroups

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

subgroupindex
#131249052
#131239672
#131239342
#131137262
#131137252
#131137162
#131137112
#131137042
Q16×#10552
C8×#61072
#131136232
#131132892
#131132172
#131131212
C13×#15872
#1801913