Finite Group Databasebeta

← #15834320

Subgroups — #15834320

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124873C211yesmaximal, characteristic
2#13123934C211yesmaximal, characteristic
3#13123922C211yesmaximal, characteristic
4#13113730C211yesmaximal, characteristic, complemented
5#13113708C211yesmaximal, characteristic, complemented
6#13113706C211yesmaximal, characteristic, complemented
7#13113684C211yesmaximal, characteristic, complemented
8#13113684C211yesmaximal, characteristic, complemented
9#13113656C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113613C211yesmaximal, characteristic
12#13113307C211yesmaximal, characteristic
13#13113229C211yesmaximal, characteristic
14#13113137C211yesmaximal, characteristic
15C13×#1593C211yesmaximal, 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#11718501—21no—
30#11718496C2211yescharacteristic
31#11718494—21no—
32#11718494C2211yescharacteristic
33#11718492C2211yescharacteristic
34#11718491—21no—
35#11718491C2211yescharacteristic
36#11718489—21no—
37#11718470C411yescharacteristic
38#11718469C411yescharacteristic
39#11718455C411yescharacteristic
40#11718454C411yescharacteristic
41#11718370—21no—
42#11718366—21no—
43#11718362—21no—
44#11718362—21no—
45C4×Dic52C2211yescharacteristic
46#11718346C2211yescharacteristic
47#11718346C2211yescharacteristic
48#11718346C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718049C2211yescharacteristic
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
77#88151C2×C411yescharacteristic
78#88150—21no—
79C4⋊C4×D13—21no—
80C4⋊C4×D13C2×C411yescharacteristic
81#88143—21no—
82#88142C2×C411yescharacteristic
83#88141—21no—
84#88141C2×C411yescharacteristic
85#88126—21no—
86C42×D13—21no—
87C42×D13C2311yescharacteristic
88C4×Dic26—21no—
89C4×Dic26—21no—
90C4×Dic26C2311yescharacteristic
91C4×Dic26C2311yescharacteristic
92C13×#107C2×C411yescharacteristic
93C13×C4⋊C8—21no—
94C13×C4⋊C8—21no—
95C13×C4⋊C8C2311yescharacteristic
96C13×C4⋊C8C2311yescharacteristic
97C13×#103C2×C411yescharacteristic
98C13×#103C2×C411yescharacteristic
99C13×#97—21no—
100C13×#97—21no—
101C4×C8×C13C2311yescharacteristic
102C4×C8×C13C2311yescharacteristic
103C4×C8×C13C2311yescharacteristic
104#88075C2×C411yescharacteristic
105#88075C2×C411yescharacteristic
106#88060—21no—
107#88060—21no—
108#88060—21no—
109#88060C2×C411yescharacteristic
110#88060C2×C411yescharacteristic
111#88060D411yescharacteristic
112#88060D411yescharacteristic
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88055—21no—
117#88055—21no—
118#88054—21no—
119#88054—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054C2×C411yescharacteristic
124#88054C2×C411yescharacteristic
125#88054D411yescharacteristic
126#88054D411yescharacteristic
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#18032—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#3104—131no—
205#2986—131no—
206#2984—131no—
207#1593D1311yescharacteristic, complemented
208#1591—131no—
209#1587—131no—
210#1587—131no—
211#1584—131no—
212#1584—131no—
213#1579—131no—
214C8×Q16—131no—
215#1572—131no—
216#1497—131no—
217#1479—131no—
218#1454—131no—
219C22×D13C4×D411yescharacteristic
220Q8×C13—21no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13C23×C411yescharacteristic
229C2×C4×C13C22×D411yescharacteristic
230C2×C4×C13C2×#4111yescharacteristic
231C2×Dic13—21no—
232C2×Dic13—21no—
233C2×Dic13—21no—
234C2×Dic13—21no—
235C2×Dic13C4×D411yescharacteristic
236C2×Dic13C4×D411yescharacteristic
237C2×Dic13C4×D411yescharacteristic
238C4×D13—21no—
239C4×D13—21no—
240C4×D13—21no—
241C4×D13—21no—
242C4×D13—41no—
243C4×D13—42no—
244C4×D13—42no—
245Dic26—21no—
246Dic26—21no—
247Dic26—21no—
248Dic26—42no—
249Dic26—42no—
250Dic26#13112yes—
251C8×C13—21no—
252C8×C13—21no—
253C8×C13—21no—
254C8×C13—21no—
255C8×C13—41no—
256C8×C13—41no—
257C8×C13—41no—
258#1055—21no—
259#1055—21no—
260#1055—21no—
261#1055—21no—
262#1055—41no—
263#1055—41no—
264#1055—41no—
265#533—131no—
266C2×C4×Q8—131no—
267#484—131no—
268#484—131no—
269#477—131no—
270#477—131no—
271#462—131no—
272#462—131no—
273#451—131no—
274#451—131no—
275#446—131no—
276#446—131no—
277#446—261no—
278#446—261no—
279#446—261no—
280#446C2×D1311yescharacteristic
281#446C2×D1311yescharacteristic
282C8×Q8—131no—
283C8×Q8—131no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—261no—
287C4×Q16—131no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×Q16C2×D1311yescharacteristic
291#433—261no—
292#433—261no—
293#432—131no—
294#432—261no—
295#431—131no—
296#431—131no—
297#431—131no—
298#431—131no—
299#431—261no—
300#335—131no—
301#335—131no—
302#334—131no—
303#334C2×D1311yescharacteristic
304Q8⋊C8—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8C2×D1311yescharacteristic
311Q8⋊C8C2×D1311yescharacteristic
312#322—131no—
313#322—131no—
314#322C2×D1311yescharacteristic
315C82—131no—
316C22×C13C2×C4×D411yescharacteristic
317C2×D13—21no—
318C2×D13—21no—
319C2×D13—21no—
320C4×C13—21no—
321C4×C13—41no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13C2×#13111yescharacteristic
326C4×C13#56811yescharacteristic
327C4×C13#57811yescharacteristic
328C4×C13#57811yescharacteristic
329Dic13—22no—
330Dic13—21no—
331Dic13—21no—
332Dic13—21no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336C22×Q8—131no—
337C2×Q16—131no—
338C2×Q16—131no—
339C2×Q16—131no—
340C2×Q16C4×D1311yescharacteristic
341C4⋊Q8—131no—
342C4⋊Q8—131no—
343#125—261no—
344C22⋊Q8—131no—
345C22⋊Q8—131no—
346C22⋊Q8—261no—
347C4×Q8—131no—
348C4×Q8—131no—
349C4×Q8—131no—
350C4×Q8—131no—
351C4×Q8—261no—
352C4×Q8—261no—
353C4×Q8—261no—
354C4×Q8C22×D1311yescharacteristic
355C4×Q8C22×D1311yescharacteristic
356#117—261no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—261no—
359C2×C42—131no—
360C2×C42—261no—
361#107—131no—
362#107—131no—
363#107—131no—
364#107C4×D1311yescharacteristic
365C4⋊C8—21no—
366C4⋊C8—21no—
367C4⋊C8—131no—
368C4⋊C8—131no—
369C4⋊C8—131no—
370C4⋊C8—131no—
371C4⋊C8—131no—
372C4⋊C8—131no—
373C4⋊C8—261no—
374C4⋊C8—261no—
375C4⋊C8—261no—
376C4⋊C8—261no—
377C4⋊C8—261no—
378C4⋊C8—261no—
379C4⋊C8—261no—
380C4⋊C8C22×D1311yescharacteristic
381C4⋊C8C22×D1311yescharacteristic
382#103—131no—
383#103—131no—
384#103—131no—
385#103—131no—
386#103—131no—
387#103—131no—
388#103C4×D1311yescharacteristic
389#103C4×D1311yescharacteristic
390C22⋊C8—131no—
391C22⋊C8—131no—
392C22⋊C8—131no—
393C22⋊C8—131no—
394C22⋊C8—261no—
395C22⋊C8—261no—
396C22⋊C8—261no—
397#97—21no—
398#97—21no—
399#97—261no—
400#97—261no—
401#97—261no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—261no—
406C4×C8—261no—
407C4×C8—261no—
408C4×C8—261no—
409C4×C8—261no—
410C4×C8C22×D1311yescharacteristic
411C4×C8C22×D1311yescharacteristic
412C4×C8C22×D1311yescharacteristic
413C2×C13#293311yescharacteristic
414C2×C13#295011yescharacteristic
415C2×C13#295511yescharacteristic
416D13—41no—
417C2×Q8—131no—
418C2×Q8—131no—
419C2×Q8—261no—
420C2×Q8—261no—
421C2×Q8—262no—
422C2×Q8—521no—
423C2×Q8C2×C4×D1311yescharacteristic
424C2×Q8C2×C4×D1311yescharacteristic
425C22×C4—131no—
426C22×C4—131no—
427C22×C4—131no—
428C22×C4—261no—
429C22×C4—261no—
430Q16—41no—
431Q16—262no—
432Q16—262no—
433Q16—521no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—131no—
438C2×C8—131no—
439C2×C8—131no—
440C2×C8—131no—
441C2×C8—261no—
442C2×C8—261no—
443C2×C8—261no—
444C2×C8C2×C4×D1311yescharacteristic
445C2×C8C2×C4×D1311yescharacteristic
446C2×C8D4×D1311yescharacteristic
447C2×C8D4×D1311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—131no—
451C4⋊C4—131no—
452C4⋊C4—261no—
453C4⋊C4—261no—
454C4⋊C4—261no—
455C4⋊C4—261no—
456C4⋊C4—261no—
457C4⋊C4—261no—
458C4⋊C4—261no—
459C4⋊C4—261no—
460C4⋊C4—261no—
461C4⋊C4—261no—
462C4⋊C4C2×C4×D1311yescharacteristic
463C4⋊C4C2×C4×D1311yescharacteristic
464C22⋊C4—261no—
465C22⋊C4—261no—
466C42—21no—
467C42—21no—
468C42—131no—
469C42—131no—
470C42—131no—
471C42—261no—
472C42—261no—
473C42—261no—
474C42—261no—
475C42C23×D1311yescharacteristic
476C13#1803211yescharacteristic, complemented, Sylow
477C23—131no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—132no—
483Q8—261no—
484Q8—261no—
485Q8—261no—
486Q8—522no—
487Q8—522no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—131no—
493C2×C4—131no—
494C2×C4—131no—
495C2×C4—261no—
496C2×C4—261no—
497C2×C4—261no—
498C2×C4—261no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—261no—
502C2×C4—261no—
503C2×C4—521no—
504C2×C4—522no—
505C2×C4—522no—
506C2×C4C22×C4×D1311yescharacteristic
507C2×C4C2×D4×D1311yescharacteristic
508C2×C4#41×D1311yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—261no—
517C8—261no—
518C8—261no—
519C8—261no—
520C8—521no—
521C8—521no—
522C8—521no—
523C22—261no—
524C22—261no—
525C22—261no—
526C22C4×D4×D1311yescharacteristic
527C4—21no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—261no—
533C4—261no—
534C4—261no—
535C4—262no—
536C4—521no—
537C4—521no—
538C4—521no—
539C4#1171945011yescharacteristic
540C4D13×#13111yescharacteristic
541C4#1171948411yescharacteristic
542C4#1171948411yescharacteristic
543C2—521no—
544C2#1312356511yescharacteristic
545C2#1312370111yescharacteristic
546C2#1312373611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1593C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1593D13
hypocenterC13#18032
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1593

Complements

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

NH ≅ G/Ntype
4. #13113730C2semidirect
5. #13113708C2semidirect
6. #13113706C2semidirect
7. #13113684C2semidirect
8. #13113684C2semidirect
9. #13113656C2semidirect
10. #13113640C2semidirect
15. C13×#1593C2semidirect
207. #1593D13semidirect
476. C13#18032semidirect

Maximal subgroups

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

subgroupindex
#131248732
#131239342
#131239222
#131137302
#131137082
#131137062
#131136842
#131136562
#131136402
#131136132
#131133072
#131132292
#131131372
C13×#15932
#1803213