Finite Group Databasebeta

← #15834317

Subgroups — #15834317

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#13124876C211yesmaximal, characteristic
2#13123937C211yesmaximal, characteristic
3#13123923C211yesmaximal, characteristic
4#13113746C211yesmaximal, characteristic, complemented
5#13113734C211yesmaximal, characteristic, complemented
6#13113709C211yesmaximal, characteristic, complemented
7#13113709C211yesmaximal, characteristic, complemented
8#13113688C211yesmaximal, characteristic, complemented
9#13113688C211yesmaximal, characteristic, complemented
10#13113656C211yesmaximal, characteristic, complemented
11C8×Dic52C211yesmaximal, characteristic, complemented
12#13113616C211yesmaximal, characteristic
13#13113310C211yesmaximal, characteristic
14#13113232C211yesmaximal, characteristic
15C13×#1454C211yesmaximal, characteristic
16#11719175C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20C13×#431C2211yescharacteristic
21#11718587C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718511C411yescharacteristic
24#11718511C411yescharacteristic
25#11718510C411yescharacteristic
26#11718510C411yescharacteristic
27#11718492—21no—
28#11718491—21no—
29#11718489—21no—
30#11718489—21no—
31#11718400C411yescharacteristic
32#11718400C411yescharacteristic
33#11718383C411yescharacteristic
34#11718383C411yescharacteristic
35#11718381—21no—
36#11718381—21no—
37#11718380—21no—
38#11718379—21no—
39C4×Dic52C2211yescharacteristic
40C4×Dic52C2211yescharacteristic
41C4×Dic52C2211yescharacteristic
42C4×Dic52C2211yescharacteristic
43#11718340C2211yescharacteristic
44#11718340C2211yescharacteristic
45#11718340C2211yescharacteristic
46#11718340C2211yescharacteristic
47C8×Dic26C2211yescharacteristic
48C8×Dic26C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#322C2211yescharacteristic
52C13×#322C2211yescharacteristic
53C13×#322C2211yescharacteristic
54C82×C13C2211yescharacteristic
55#11718050C2211yescharacteristic
56#11718050C2211yescharacteristic
57#11718049C2211yescharacteristic
58#11718049C2211yescharacteristic
59#11718048C2211yescharacteristic
60#11718048C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718048C2211yescharacteristic
65#11718048C2211yescharacteristic
66#11718048C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C2×C42×C13C2311yescharacteristic
69#88180—21no—
70C2×C4⋊Dic13C2×C411yescharacteristic
71#88178—21no—
72#88178C2×C411yescharacteristic
73#88178C2×C411yescharacteristic
74C2×#6101—21no—
75C2×C4×Dic13—21no—
76C2×Dic52C2×C411yescharacteristic
77C2×Dic52C2×C411yescharacteristic
78C2×Dic52C2×C411yescharacteristic
79C2×Dic52C2×C411yescharacteristic
80#88124—21no—
81#88123C2×C411yescharacteristic
82#88123C2×C411yescharacteristic
83C4×Dic26—21no—
84C4×Dic26—21no—
85C4×Dic26—21no—
86C4×Dic26C2×C411yescharacteristic
87C4×Dic26C2×C411yescharacteristic
88C4×Dic26C2311yescharacteristic
89C4×Dic26C2311yescharacteristic
90C4×Dic26C2311yescharacteristic
91C4×Dic26C2311yescharacteristic
92C13×C4⋊C8—21no—
93C13×C4⋊C8C2×C411yescharacteristic
94C13×C4⋊C8C2×C411yescharacteristic
95C13×C4⋊C8D411yescharacteristic
96C13×C4⋊C8D411yescharacteristic
97C13×C22⋊C8—21no—
98C13×C22⋊C8C2×C411yescharacteristic
99C13×C22⋊C8C2×C411yescharacteristic
100C13×C22⋊C8D411yescharacteristic
101C13×C22⋊C8D411yescharacteristic
102C4×C8×C13C2311yescharacteristic
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105C4×C8×C13C2311yescharacteristic
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108C22⋊#1055—21no—
109C22⋊#1055—21no—
110#88058C2×C411yescharacteristic
111#88058C2×C411yescharacteristic
112#88058C2×C411yescharacteristic
113#88058C2×C411yescharacteristic
114#88056C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88056C2×C411yescharacteristic
118#88056C2×C411yescharacteristic
119#88056C2×C411yescharacteristic
120#88056C2×C411yescharacteristic
121#88056C2×C411yescharacteristic
122#88055—21no—
123#88055—21no—
124#88055—21no—
125#88055—21no—
126#88054—21no—
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054—21no—
132#88054—21no—
133#88054—21no—
134C8×Dic13—21no—
135C8×Dic13—21no—
136C8×Dic13—21no—
137C8×Dic13—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4⋊#1055C2311yescharacteristic
142#88043—21no—
143C4×#1055—21no—
144#18032—131nomaximal, Sylow
145C22×C4×C13C22×C411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13#4111yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C2×Dic26—22no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—41no—
154C2×Dic26C22×C411yescharacteristic
155C2×Dic26C22×C411yescharacteristic
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13C22×C411yescharacteristic
161C2×C8×C13C22×C411yescharacteristic
162C2×C8×C13C22×C411yescharacteristic
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C42×C13C22×C411yescharacteristic
169C42×C13C2×D411yescharacteristic
170C42×C13#4111yescharacteristic
171C42×C13C2411yescharacteristic
172C22⋊Dic13—21no—
173C22⋊Dic13—21no—
174C4⋊Dic13—21no—
175C4⋊Dic13—21no—
176C4⋊Dic13—21no—
177C4⋊Dic13—21no—
178C4⋊Dic13C22×C411yescharacteristic
179C4⋊Dic13C22×C411yescharacteristic
180C4⋊Dic13C22×C411yescharacteristic
181C4⋊Dic13C22×C411yescharacteristic
182#6101—21no—
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×Dic13—21no—
195C4×Dic13—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200Dic52—22no—
201Dic52—22no—
202Dic52—41no—
203Dic52—41no—
204#3104—131no—
205#2986—131no—
206#2984—131no—
207#1593—131no—
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#1454D1311yescharacteristic
219C23×C13C4×D411yescharacteristic
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—41no—
225C2×C4×C13C4×D411yescharacteristic
226C2×C4×C13C4×D411yescharacteristic
227C2×C4×C13C4×D411yescharacteristic
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×Dic13—21no—
236C2×Dic13—21no—
237C2×Dic13—21no—
238C2×Dic13—21no—
239C2×Dic13—42no—
240C2×Dic13—42no—
241Dic26—21no—
242Dic26—21no—
243Dic26—21no—
244Dic26—21no—
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—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—41no—
260C8×C13—41no—
261#1055—41no—
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—131no—
278#446—131no—
279#446—261no—
280#446—261no—
281#446—261no—
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×Q16—131no—
291#433—261no—
292#433—261no—
293#432—131no—
294#432—261no—
295#431—131no—
296#431—261no—
297#431C2×D1311yescharacteristic
298#431C2×D1311yescharacteristic
299#431C2×D1311yescharacteristic
300#335—131no—
301#335—131no—
302#334—131no—
303#334—131no—
304Q8⋊C8—131no—
305Q8⋊C8—131no—
306Q8⋊C8—131no—
307Q8⋊C8—131no—
308Q8⋊C8—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312#322C2×D1311yescharacteristic
313#322C2×D1311yescharacteristic
314#322C2×D1311yescharacteristic
315C82C2×D1311yescharacteristic
316C22×C13—21no—
317C22×C13—21no—
318C22×C13—21no—
319C22×C13C2×C4×D411yescharacteristic
320C4×C13—21no—
321C4×C13—21no—
322C4×C13—21no—
323C4×C13—21no—
324C4×C13C2×#13111yescharacteristic
325C4×C13#56811yescharacteristic
326C4×C13#57811yescharacteristic
327C4×C13#57811yescharacteristic
328Dic13—22no—
329Dic13—41no—
330Dic13—41no—
331Dic13—41no—
332Dic13—41no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336C22×Q8—131no—
337C2×Q16—131no—
338C2×Q16—131no—
339C2×Q16—131no—
340C2×Q16—131no—
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—131no—
352C4×Q8—131no—
353C4×Q8—261no—
354C4×Q8—261no—
355C4×Q8—261no—
356#117—261no—
357C2×C4⋊C4—131no—
358C2×C4⋊C4—261no—
359C2×C42—261no—
360C2×C42C22×D1311yescharacteristic
361#107—131no—
362#107—131no—
363#107—131no—
364#107—131no—
365C4⋊C8—21no—
366C4⋊C8—131no—
367C4⋊C8—131no—
368C4⋊C8—131no—
369C4⋊C8—131no—
370C4⋊C8—261no—
371C4⋊C8—261no—
372C4⋊C8—261no—
373C4⋊C8—261no—
374C4⋊C8—261no—
375C4⋊C8—261no—
376C4⋊C8—261no—
377C4⋊C8—261no—
378C4⋊C8C4×D1311yescharacteristic
379C4⋊C8C4×D1311yescharacteristic
380C4⋊C8D5211yescharacteristic
381C4⋊C8D5211yescharacteristic
382#103—131no—
383#103—131no—
384#103—131no—
385#103—131no—
386#103—131no—
387#103—131no—
388#103—131no—
389#103—131no—
390C22⋊C8—21no—
391C22⋊C8—261no—
392C22⋊C8—261no—
393C22⋊C8C4×D1311yescharacteristic
394C22⋊C8C4×D1311yescharacteristic
395C22⋊C8D5211yescharacteristic
396C22⋊C8D5211yescharacteristic
397#97—261no—
398#97—261no—
399#97—261no—
400#97—261no—
401#97—261no—
402C4×C8—261no—
403C4×C8—261no—
404C4×C8—261no—
405C4×C8—261no—
406C4×C8—261no—
407C4×C8C22×D1311yescharacteristic
408C4×C8C22×D1311yescharacteristic
409C4×C8C22×D1311yescharacteristic
410C4×C8C22×D1311yescharacteristic
411C4×C8C22×D1311yescharacteristic
412C4×C8C22×D1311yescharacteristic
413C2×C13—41no—
414C2×C13#293311yescharacteristic
415C2×C13#295011yescharacteristic
416C2×C13#295511yescharacteristic
417C2×Q8—131no—
418C2×Q8—131no—
419C2×Q8—131no—
420C2×Q8—131no—
421C2×Q8—262no—
422C2×Q8—261no—
423C2×Q8—261no—
424C2×Q8—521no—
425C22×C4—261no—
426C22×C4—261no—
427C22×C4C2×C4×D1311yescharacteristic
428C22×C4C2×D5211yescharacteristic
429C22×C4#612711yescharacteristic
430Q16—262no—
431Q16—262no—
432Q16—521no—
433Q16—521no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—261no—
437C2×C8—261no—
438C2×C8—261no—
439C2×C8—261no—
440C2×C8C2×C4×D1311yescharacteristic
441C2×C8C2×C4×D1311yescharacteristic
442C2×C8C2×C4×D1311yescharacteristic
443C2×C8C2×C4×D1311yescharacteristic
444C2×C8C2×D5211yescharacteristic
445C2×C8C2×D5211yescharacteristic
446C2×C8C2×D5211yescharacteristic
447C2×C8C2×D5211yescharacteristic
448C4⋊C4—131no—
449C4⋊C4—131no—
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⋊C4—261no—
463C4⋊C4—261no—
464C22⋊C4—261no—
465C22⋊C4—261no—
466C42—261no—
467C42—261no—
468C42—261no—
469C42—261no—
470C42—261no—
471C42—261no—
472C42C2×C4×D1311yescharacteristic
473C42C2×D5211yescharacteristic
474C42#612711yescharacteristic
475C42C23×D1311yescharacteristic
476C13#1803211yescharacteristic, complemented, Sylow
477C23C4×D5211yescharacteristic
478Q8—132no—
479Q8—261no—
480Q8—261no—
481Q8—261no—
482Q8—261no—
483Q8—261no—
484Q8—261no—
485Q8—261no—
486Q8—522no—
487Q8—522no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—261no—
494C2×C4—261no—
495C2×C4—261no—
496C2×C4—261no—
497C2×C4—261no—
498C2×C4—261no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4C4×D5211yescharacteristic
504C2×C4C4×D5211yescharacteristic
505C2×C4C4×D5211yescharacteristic
506C2×C4C22×C4×D1311yescharacteristic
507C2×C4C22×D5211yescharacteristic
508C2×C4C2×#612711yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—21no—
517C8—41no—
518C8—41no—
519C8—521no—
520C8—521no—
521C8—521no—
522C8—521no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×C4×D5211yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—262no—
532C4—521no—
533C4—521no—
534C4—521no—
535C4—521no—
536C4—521no—
537C4—521no—
538C4—521no—
539C4D13×#13111yescharacteristic
540C4#1171945511yescharacteristic
541C4#1171945811yescharacteristic
542C4#1171945811yescharacteristic
543C2—41no—
544C2#1312356411yescharacteristic
545C2#1312370511yescharacteristic
546C2#1312374011yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1454C2
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC42×C13C24
hypercenter#1454D13
hypocenterC13#18032
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
4. #13113746C2semidirect
5. #13113734C2semidirect
6. #13113709C2semidirect
7. #13113709C2semidirect
8. #13113688C2semidirect
9. #13113688C2semidirect
10. #13113656C2semidirect
11. C8×Dic52C2semidirect
476. C13#18032semidirect

Maximal subgroups

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

subgroupindex
#131248762
#131239372
#131239232
#131137462
#131137342
#131137092
#131136882
#131136562
C8×Dic522
#131136162
#131133102
#131132322
C13×#14542
#1803213