Finite Group Databasebeta

← #15834140

Subgroups — #15834140

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#13124903C211yesmaximal, characteristic
2#13123964C211yesmaximal, characteristic
3#13123934C211yesmaximal, characteristic, complemented
4#13113729C211yesmaximal, characteristic, complemented
5#13113715C211yesmaximal, characteristic, complemented
6#13113712C211yesmaximal, characteristic, complemented
7#13113706C211yesmaximal, characteristic, complemented
8#13113705C211yesmaximal, characteristic, complemented
9C8×Dic52C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113623C211yesmaximal, characteristic, complemented
12#13113289C211yesmaximal, characteristic, complemented
13#13113215C211yesmaximal, characteristic
14#13113118C211yesmaximal, characteristic, complemented
15C13×#1590C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×#6129C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C4×C13×SD16C2211yescharacteristic
20C13×#436C2211yescharacteristic
21#11718834C411yescharacteristic
22#11718823C411yescharacteristic
23#11718789—21no—
24#11718779—21no—
25C4×#6107C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28#11718673C2211yescharacteristic
29#11718528C411yescharacteristic
30#11718515C411yescharacteristic
31#11718501—21no—
32#11718498C2211yescharacteristic
33#11718494C2211yescharacteristic
34#11718492C2211yescharacteristic
35#11718491—21no—
36#11718491C2211yescharacteristic
37#11718475C411yescharacteristic
38#11718454C411yescharacteristic
39#11718444C411yescharacteristic
40#11718420C411yescharacteristic
41#11718390—21no—
42#11718379—21no—
43#11718370—21no—
44#11718362—21no—
45C4×Dic52C2211yescharacteristic
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
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#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×#6129C2×C411yescharacteristic
68C2×C13×SD16C2×C411yescharacteristic
69C2×C13×M16—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—
79C2×#6099—21no—
80C2×Dic52C2×C411yescharacteristic
81C2×#6094—21no—
82C2×C8×D13—21no—
83#88151C2×C411yescharacteristic
84#88150—21no—
85#88146C2×C411yescharacteristic
86#88143—21no—
87#88142C2×C411yescharacteristic
88#88141C2×C411yescharacteristic
89#88135—21no—
90#88131—21no—
91#88126—21no—
92C42×D13C2311yescharacteristic
93C4×Dic26—21no—
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×#106C2×C411yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×#103C2×C411yescharacteristic
101C13×#102C2×C411yescharacteristic
102C13×C22⋊C8—21no—
103C13×#97—21no—
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107#88075C2×C411yescharacteristic
108#88072C2×C411yescharacteristic
109C22⋊#1055—21no—
110#88060—21no—
111#88060C2×C411yescharacteristic
112#88060C2×C411yescharacteristic
113#88060D411yescharacteristic
114#88060D411yescharacteristic
115#88058C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88056C2×C411yescharacteristic
118#88055—21no—
119#88054—21no—
120#88054—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—
131C8×Dic13—21no—
132C8×Dic13—21no—
133#88050C2×C411yescharacteristic
134#88050C2×C411yescharacteristic
135#88048C2×C411yescharacteristic
136#88047C2×C411yescharacteristic
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18019—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—41no—
160C13×M16—81no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
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—41no—
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
197#6099—81no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205Dic52—22no—
206#6094—81no—
207C8×D13—24no—
208#3107—131no—
209#2991—131no—
210#2986—131no—
211#1590—131no—
212#1590D1311yescharacteristic, complemented
213#1588—131no—
214#1588—131no—
215#1587—131no—
216#1587—131no—
217C8×Q16—131no—
218C8×Q16—131no—
219#1574—131no—
220#1493—131no—
221#1476—131no—
222#1450—131no—
223C23×C13—21no—
224C22×D13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227D4×C13—21no—
228D4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13C23×C411yescharacteristic
235C2×C4×C13C22×D411yescharacteristic
236C2×C4×C13C2×#4111yescharacteristic
237C22⋊D13—42no—
238C2×Dic13—21no—
239C2×Dic13—21no—
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—42no—
243C2×Dic13—42no—
244C2×Dic13C4×D411yescharacteristic
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C4×D411yescharacteristic
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—21no—
250C4×D13—21no—
251C4×D13—22no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—42no—
256Dic26#13112yes—
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—131no—
288C8×Q8—261no—
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16C2×D1311yescharacteristic
293#436—131no—
294#436—261no—
295#436—261no—
296#436C2×D1311yescharacteristic
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⋊C8—131no—
315Q8⋊C8C2×D1311yescharacteristic
316D4⋊C8—131no—
317D4⋊C8C2×D1311yescharacteristic
318#322—131no—
319#322—131no—
320C82—131no—
321C82C2×D1311yescharacteristic
322C22×C13—41no—
323C22×C13—41no—
324C22×C13—41no—
325C22×C13C2×C4×D411yescharacteristic
326C2×D13—21no—
327C2×D13—21no—
328C2×D13—21no—
329C4×C13—21no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13C2×#13111yescharacteristic
334C4×C13#56811yescharacteristic
335C4×C13#57711yescharacteristic
336C4×C13#57811yescharacteristic
337Dic13—22no—
338Dic13—21no—
339Dic13—21no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13#44312yes—
344C2×#41—131no—
345C2×Q16—131no—
346C2×Q16—131no—
347C2×SD16—131no—
348C2×SD16C4×D1311yescharacteristic
349C2×M16—21no—
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—131no—
362C4×Q8—261no—
363C4×Q8C22×D1311yescharacteristic
364C4×D4—131no—
365C4×D4—261no—
366C4×D4—261no—
367C4×D4C22×D1311yescharacteristic
368#117—131no—
369#117—261no—
370#117—261no—
371C2×C42—131no—
372C2×C42—261no—
373#107—131no—
374#107—131no—
375#106—131no—
376#106C4×D1311yescharacteristic
377C4⋊C8—21no—
378C4⋊C8—131no—
379C4⋊C8—131no—
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⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103C4×D1311yescharacteristic
398#102—131no—
399#102C4×D1311yescharacteristic
400C22⋊C8—21no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—131no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—21no—
408#97—261no—
409C4×C8—131no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—261no—
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—81no—
422C2×C13#293311yescharacteristic
423C2×C13#294711yescharacteristic
424C2×C13C2×#44311yescharacteristic
425D13—41no—
426#41—262no—
427#41—521no—
428C2×Q8—131no—
429C2×Q8—131no—
430C2×Q8—261no—
431C2×Q8C2×C4×D1311yescharacteristic
432C2×D4—261no—
433C2×D4C2×C4×D1311yescharacteristic
434C22×C4—21no—
435C22×C4—131no—
436C22×C4—131no—
437C22×C4—131no—
438C22×C4—261no—
439C22×C4—261no—
440Q16—262no—
441Q16—262no—
442SD16—41no—
443SD16—521no—
444M16—81no—
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—131no—
464C4⋊C4—131no—
465C4⋊C4—261no—
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—21no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C42—21no—
481C42—131no—
482C42—131no—
483C42—131no—
484C42—261no—
485C42—261no—
486C42—261no—
487C42—261no—
488C42C23×D1311yescharacteristic
489C13#1801911yescharacteristic, complemented, Sylow
490C23—21no—
491C23—131no—
492Q8—21no—
493Q8—21no—
494Q8—132no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—522no—
499D4—21no—
500D4—21no—
501D4—522no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—131no—
508C2×C4—131no—
509C2×C4—131no—
510C2×C4—262no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—522no—
520C2×C4—522no—
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—41no—
539C22—41no—
540C22—41no—
541C22—261no—
542C22—261no—
543C22—261no—
544C22C4×D4×D1311yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—132no—
550C4—261no—
551C4—261no—
552C4—262no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4#1171945011yescharacteristic
557C4D13×#13111yescharacteristic
558C4#1171946711yescharacteristic
559C4#1171947611yescharacteristic
560C2—81no—
561C2—521no—
562C2#1312356511yescharacteristic
563C2#1312367211yescharacteristic
564C2D13×#44311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1590C2
socleC22×C13C2×C4×D4
prime radicalC2×#6129C2×C4
cosocleC42×C13C24
hypercenter#1590D13
hypocenterC13#18019
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1590

Complements

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

NH ≅ G/Ntype
3. #13123934C2semidirect
4. #13113729C2semidirect
5. #13113715C2semidirect
6. #13113712C2semidirect
7. #13113706C2semidirect
8. #13113705C2semidirect
9. C8×Dic52C2semidirect
10. #13113640C2semidirect
11. #13113623C2semidirect
12. #13113289C2semidirect
14. #13113118C2semidirect
15. C13×#1590C2semidirect
212. #1590D13semidirect
489. C13#18019semidirect

Maximal subgroups

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

subgroupindex
#131249032
#131239642
#131239342
#131137292
#131137152
#131137122
#131137062
#131137052
C8×Dic522
#131136402
#131136232
#131132892
#131132152
#131131182
C13×#15902
#1801913