Finite Group Databasebeta

← #15833857

Subgroups — #15833857

Order 3328.

602 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124873C211yesmaximal, characteristic
2#13123788C211yesmaximal, characteristic
3#13123784C211yesmaximal, characteristic
4#13113730C211yesmaximal, characteristic, complemented
5#13113687C211yesmaximal, characteristic, complemented
6#13113685C211yesmaximal, characteristic, complemented
7#13113684C211yesmaximal, characteristic, complemented
8#13113684C211yesmaximal, characteristic, complemented
9C8×Dic52C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113609C211yesmaximal, characteristic
12#13113289C211yesmaximal, characteristic
13D13×Q8⋊C8C211yesmaximal, characteristic
14C8×#6094C211yesmaximal, characteristic
15C13×#1591C211yesmaximal, characteristic, complemented
16#11719283C2211yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C4×C13×Q16C2211yescharacteristic
21#11718847C411yescharacteristic
22#11718843C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718545C411yescharacteristic
28#11718536C411yescharacteristic
29#11718500—21no—
30#11718498—21no—
31#11718498C2211yescharacteristic
32D13×C4⋊C8C2211yescharacteristic
33#11718492—21no—
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718470C411yescharacteristic
38#11718469C411yescharacteristic
39#11718455C411yescharacteristic
40#11718454C411yescharacteristic
41#11718369—21no—
42#11718368—21no—
43#11718362—21no—
44#11718362—21no—
45C4×Dic52C2211yescharacteristic
46C4×#6094C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C82×C13C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718047C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71#88200C2×C411yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73#88198C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76C2×Dic52C2×C411yescharacteristic
77C2×#6094—21no—
78C2×#6094D411yescharacteristic
79C2×#6094D411yescharacteristic
80C2×C8×D13—21no—
81C2×C8×D13—21no—
82#88151C2×C411yescharacteristic
83#88150—21no—
84C4⋊C4×D13—21no—
85C4⋊C4×D13C2×C411yescharacteristic
86#88143—21no—
87#88142C2×C411yescharacteristic
88#88141—21no—
89#88141C2×C411yescharacteristic
90#88126—21no—
91C42×D13—21no—
92C42×D13C2311yescharacteristic
93C4×Dic26—21no—
94C4×Dic26—21no—
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×#107C2×C411yescharacteristic
98C13×C4⋊C8—21no—
99C13×C4⋊C8—21no—
100C13×C4⋊C8C2311yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#97—21no—
105C13×#97—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C4×C8×C13C2311yescharacteristic
109#88075C2×C411yescharacteristic
110#88075C2×C411yescharacteristic
111#88060C2×C411yescharacteristic
112#88060C2×C411yescharacteristic
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88055—21no—
117#88055D411yescharacteristic
118#88055D411yescharacteristic
119#88054—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—
131#88050C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135C4⋊#1055—21no—
136C4⋊#1055—21no—
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055—21no—
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17998—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×Q8×C13C22×C411yescharacteristic
147Q8×D13—22no—
148Q8×D13—41no—
149C2×C4×D13—21no—
150C2×C4×D13—21no—
151C2×C4×D13C22×C411yescharacteristic
152C2×C4×D13C2×D411yescharacteristic
153C2×C4×D13#4111yescharacteristic
154C2×Dic26—21no—
155C2×Dic26—21no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C13×Q16—41no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C4⋊C4C22×C411yescharacteristic
170C42×C13—21no—
171C42×C13—21no—
172C42×C13C2411yescharacteristic
173#6107—22no—
174#6107—41no—
175#6103—21no—
176#6103—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13C22×C411yescharacteristic
180C4⋊Dic13C22×C411yescharacteristic
181#6101—21no—
182#6101—21no—
183#6101—21no—
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189C4×Dic13—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
203Dic52—22no—
204#6094—22no—
205#6094—42no—
206#6094Q1614yescomplemented
207C8×D13—42no—
208C8×D13—42no—
209#3104—131no—
210Q8×M16—131no—
211#2962—131no—
212#1591—131no—
213#1591D1311yescharacteristic, complemented
214#1584—131no—
215#1584—131no—
216#1584—131no—
217#1584—131no—
218C8×Q16—131no—
219C8×Q16—131no—
220#1571—131no—
221#1493—131no—
222C2×Q8⋊C8—131no—
223C8×M16—131no—
224C22×D13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
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×Dic13—21no—
240C2×Dic13C4×D411yescharacteristic
241C2×Dic13C4×D411yescharacteristic
242C2×Dic13C4×D411yescharacteristic
243C4×D13—21no—
244C4×D13—21no—
245C4×D13—41no—
246C4×D13—42no—
247C4×D13—81no—
248C4×D13C2×Q1612yes—
249C4×D13#13512yes—
250Dic26—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—42no—
254Dic26—81no—
255Dic26#13112yes—
256C8×C13—22no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13C2×Q1612yes—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—41no—
267#1055—41no—
268#1055—41no—
269#1055C2×Q1612yes—
270#533—131no—
271C2×C4×Q8—131no—
272#484—131no—
273#484—131no—
274#477—131no—
275#477—131no—
276#462—131no—
277#462—131no—
278#451—131no—
279#451—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284#446—261no—
285#446—261no—
286#446C2×D1311yescharacteristic
287#446C2×D1311yescharacteristic
288C8×Q8—131no—
289C8×Q8—131no—
290C8×Q8—131no—
291C8×Q8—131no—
292C4×Q16—131no—
293C4×Q16—131no—
294C4×Q16—131no—
295C4×Q16C2×D1311yescharacteristic
296#431—131no—
297#424—261no—
298#423—131no—
299#423—261no—
300C2×C4⋊C8—131no—
301#405—261no—
302C4×M16—131no—
303C4×M16—261no—
304C2×C4×C8—131no—
305#335—131no—
306#335—131no—
307#335—131no—
308#335C2×D1311yescharacteristic
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8C2×D1311yescharacteristic
316Q8⋊C8C2×D1311yescharacteristic
317#322—131no—
318#322—131no—
319C82—131no—
320C82C2×D1311yescharacteristic
321C22×C13C2×C4×D411yescharacteristic
322C2×D13—21no—
323C2×D13—21no—
324C2×D13C4×Q1612yes—
325C4×C13—21no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13C2×#13111yescharacteristic
331C4×C13#56811yescharacteristic
332C4×C13C22×Q1611yescharacteristic
333C4×C13C2×#13511yescharacteristic
334Dic13—22no—
335Dic13—21no—
336Dic13—21no—
337Dic13—41no—
338Dic13—41no—
339Dic13—41no—
340Dic13C4×Q1612yes—
341C22×Q8—131no—
342C2×Q16—131no—
343C2×Q16—131no—
344C2×Q16—131no—
345C2×Q16C4×D1311yescharacteristic
346C2×M16—131no—
347C2×M16—131no—
348C2×M16—261no—
349C22×C8—261no—
350C22×C8—261no—
351C4⋊Q8—131no—
352C4⋊Q8—131no—
353#125—261no—
354C22⋊Q8—131no—
355C22⋊Q8—131no—
356C22⋊Q8—261no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—131no—
360C4×Q8—131no—
361C4×Q8—261no—
362C4×Q8—261no—
363C4×Q8—261no—
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366#117—261no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—261no—
369C2×C42—131no—
370C2×C42—261no—
371#107—131no—
372#107—131no—
373#107—131no—
374#107C4×D1311yescharacteristic
375C4⋊C8—21no—
376C4⋊C8—21no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—261no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103C4×D1311yescharacteristic
398#103C4×D1311yescharacteristic
399C22⋊C8—131no—
400C22⋊C8—131no—
401#97—21no—
402#97—21no—
403#97—131no—
404#97—131no—
405#97—261no—
406#97—261no—
407C4×C8—131no—
408C4×C8—131no—
409C4×C8—131no—
410C4×C8—261no—
411C4×C8—261no—
412C4×C8—261no—
413C4×C8—261no—
414C4×C8—261no—
415C4×C8C22×D1311yescharacteristic
416C4×C8C22×D1311yescharacteristic
417C4×C8C22×D1311yescharacteristic
418C2×C13#293311yescharacteristic
419C2×C13C2×C4×Q1611yescharacteristic
420C2×C13#295611yescharacteristic
421D13—22no—
422C2×Q8—131no—
423C2×Q8—131no—
424C2×Q8—261no—
425C2×Q8—261no—
426C2×Q8—262no—
427C2×Q8—521no—
428C2×Q8C2×C4×D1311yescharacteristic
429C2×Q8C2×C4×D1311yescharacteristic
430C22×C4—131no—
431C22×C4—131no—
432C22×C4—131no—
433C22×C4—261no—
434C22×C4—261no—
435Q16—41no—
436Q16—262no—
437Q16—262no—
438Q16—521no—
439M16—134no—
440M16—262no—
441M16—522no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—261no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—522no—
453C2×C8—522no—
454C2×C8C2×C4×D1311yescharacteristic
455C2×C8C2×C4×D1311yescharacteristic
456C2×C8D4×D1311yescharacteristic
457C2×C8D4×D1311yescharacteristic
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—131no—
461C4⋊C4—131no—
462C4⋊C4—261no—
463C4⋊C4—261no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4C2×C4×D1311yescharacteristic
473C4⋊C4C2×C4×D1311yescharacteristic
474C22⋊C4—261no—
475C22⋊C4—261no—
476C42—21no—
477C42—21no—
478C42—131no—
479C42—131no—
480C42—131no—
481C42—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42C23×D1311yescharacteristic
486C13#1799811yescharacteristic, complemented, Sylow
487C23—131no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—132no—
493Q8—261no—
494Q8—261no—
495Q8—261no—
496Q8—522no—
497Q8—1041no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—131no—
503C2×C4—132no—
504C2×C4—132no—
505C2×C4—131no—
506C2×C4—131no—
507C2×C4—261no—
508C2×C4—261no—
509C2×C4—261no—
510C2×C4—261no—
511C2×C4—261no—
512C2×C4—261no—
513C2×C4—521no—
514C2×C4—522no—
515C2×C4—1041no—
516C2×C4C22×C4×D1311yescharacteristic
517C2×C4C2×D4×D1311yescharacteristic
518C2×C4#41×D1311yescharacteristic
519C8—22no—
520C8—21no—
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—132no—
526C8—261no—
527C8—261no—
528C8—261no—
529C8—521no—
530C8—521no—
531C8—521no—
532C8Q16×D1312yes—
533C22—132no—
534C22—261no—
535C22—261no—
536C22C4×D4×D1311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—132no—
543C4—261no—
544C4—261no—
545C4—262no—
546C4—521no—
547C4—521no—
548C4—521no—
549C4#1171945011yescharacteristic
550C4D13×#13111yescharacteristic
551C4C2×Q16×D1311yescharacteristic
552C4D13×#13511yescharacteristic
553C2—262no—
554C2#1312356511yescharacteristic
555C2C4×Q16×D1311yescharacteristic
556C2#1312374111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1591C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1591D13
hypocenterC13#17998
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1591

Complements

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

NH ≅ G/Ntype
4. #13113730C2semidirect
5. #13113687C2semidirect
6. #13113685C2semidirect
7. #13113684C2semidirect
8. #13113684C2semidirect
9. C8×Dic52C2semidirect
10. #13113640C2semidirect
15. C13×#1591C2semidirect
206. #6094Q16semidirect
213. #1591D13semidirect
486. C13#17998semidirect

Maximal subgroups

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

subgroupindex
#131248732
#131237882
#131237842
#131137302
#131136872
#131136852
#131136842
C8×Dic522
#131136402
#131136092
#131132892
D13×Q8⋊C82
C8×#60942
C13×#15912
#1799813