Finite Group Databasebeta

← #15834319

Subgroups — #15834319

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#13124871C211yesmaximal, characteristic
2#13123938C211yesmaximal, characteristic
3#13123926C211yesmaximal, characteristic
4#13113742C211yesmaximal, characteristic, complemented
5#13113730C211yesmaximal, characteristic, complemented
6#13113710C211yesmaximal, characteristic, complemented
7#13113704C211yesmaximal, characteristic, complemented
8#13113689C211yesmaximal, characteristic, complemented
9#13113683C211yesmaximal, characteristic, complemented
10#13113652C211yesmaximal, characteristic, complemented
11#13113640C211yesmaximal, characteristic, complemented
12#13113617C211yesmaximal, characteristic
13#13113232C211yesmaximal, characteristic
14#13113136C211yesmaximal, characteristic
15C13×#1497C211yesmaximal, characteristic
16C13×#533C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718752C411yescharacteristic
21#11718752C411yescharacteristic
22#11718751C411yescharacteristic
23#11718751C411yescharacteristic
24#11718711C411yescharacteristic
25#11718711C411yescharacteristic
26#11718705C411yescharacteristic
27#11718705C411yescharacteristic
28C4×#6107C2211yescharacteristic
29C4×#6107C2211yescharacteristic
30C4×#6107C2211yescharacteristic
31C4×#6107C2211yescharacteristic
32#11718685—21no—
33#11718685C2211yescharacteristic
34#11718685C2211yescharacteristic
35Q8×#1055—21no—
36Q8×#1055C2211yescharacteristic
37Q8×#1055C2211yescharacteristic
38#11718661—21no—
39#11718661—21no—
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718492C2211yescharacteristic
44#11718492C2211yescharacteristic
45#11718491C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718380—21no—
48#11718379—21no—
49#11718362—21no—
50#11718362—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×Q8⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718048C2211yescharacteristic
60#11718048C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C13×C4⋊Q8C2×C411yescharacteristic
69C13×C4⋊Q8C2×C411yescharacteristic
70C13×#125—21no—
71C13×C22⋊Q8—21no—
72C13×C22⋊Q8C2×C411yescharacteristic
73C13×C22⋊Q8C2×C411yescharacteristic
74C4×Q8×C13—21no—
75C4×Q8×C13C2311yescharacteristic
76C4×Q8×C13C2311yescharacteristic
77C13×#117—21no—
78C2×C42×C13C2311yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6107C2×C411yescharacteristic
81C2×#6107C2×C411yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×#6101—21no—
85C2×C4×Dic13—21no—
86C4×Dic26—21no—
87C4×Dic26—21no—
88C4×Dic26C2×C411yescharacteristic
89C4×Dic26C2×C411yescharacteristic
90C4×Dic26C2311yescharacteristic
91C4×Dic26C2311yescharacteristic
92C13×C4⋊C8—21no—
93C13×C4⋊C8C2311yescharacteristic
94C13×C4⋊C8C2311yescharacteristic
95C13×C22⋊C8—21no—
96C13×C22⋊C8—21no—
97C13×#97—21no—
98C4×C8×C13C2311yescharacteristic
99C4×C8×C13C2311yescharacteristic
100#88075C2×C411yescharacteristic
101#88075C2×C411yescharacteristic
102#88075C2×C411yescharacteristic
103#88075C2×C411yescharacteristic
104C22⋊#1055—21no—
105C22⋊#1055C2×C411yescharacteristic
106C22⋊#1055C2×C411yescharacteristic
107C22⋊#1055D411yescharacteristic
108C22⋊#1055D411yescharacteristic
109#88055—21no—
110#88055—21no—
111#88054—21no—
112#88054—21no—
113#88054—21no—
114#88054—21no—
115C8×Dic13—21no—
116C8×Dic13—21no—
117#88050C2×C411yescharacteristic
118#88050C2×C411yescharacteristic
119#88050C2×C411yescharacteristic
120#88050C2×C411yescharacteristic
121#88047C2×C411yescharacteristic
122#88047C2×C411yescharacteristic
123#88047C2×C411yescharacteristic
124#88047C2×C411yescharacteristic
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055C2×C411yescharacteristic
130C4⋊#1055C2×C411yescharacteristic
131C4⋊#1055D411yescharacteristic
132C4⋊#1055D411yescharacteristic
133C4⋊#1055C2311yescharacteristic
134C4⋊#1055C2311yescharacteristic
135#88043—21no—
136#88043—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18032—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148C22×C4×C13C22×C411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13#4111yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C2×Dic26—22no—
154C2×Dic26—21no—
155C2×Dic26—41no—
156C2×Dic26C22×C411yescharacteristic
157C2×Dic26C22×C411yescharacteristic
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13C22×C411yescharacteristic
176C42×C13C2×D411yescharacteristic
177C42×C13#4111yescharacteristic
178C42×C13C2411yescharacteristic
179#6107—22no—
180#6107—22no—
181#6107—41no—
182#6107—41no—
183C4⋊Dic13—21no—
184C4⋊Dic13C22×C411yescharacteristic
185C4⋊Dic13C22×C411yescharacteristic
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055C22×C411yescharacteristic
197C2×#1055C22×C411yescharacteristic
198C2×#1055C22×C411yescharacteristic
199C2×#1055C22×C411yescharacteristic
200C2×#1055C2×D411yescharacteristic
201C2×#1055C2×D411yescharacteristic
202C2×#1055C2×D411yescharacteristic
203C2×#1055C2×D411yescharacteristic
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#1497D1311yescharacteristic
217#1479—131no—
218#1454—131no—
219C23×C13C4×D411yescharacteristic
220Q8×C13—21no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—42no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—41no—
234C2×C4×C13C4×D411yescharacteristic
235C2×C4×C13C4×D411yescharacteristic
236C2×C4×C13C4×D411yescharacteristic
237C2×C4×C13C23×C411yescharacteristic
238C2×C4×C13C22×D411yescharacteristic
239C2×C4×C13C2×#4111yescharacteristic
240C2×Dic13—21no—
241C2×Dic13—21no—
242C2×Dic13—21no—
243C2×Dic13—21no—
244C2×Dic13—42no—
245C2×Dic13—42no—
246Dic26—21no—
247Dic26—21no—
248Dic26—21no—
249Dic26—42no—
250Dic26#13112yes—
251C8×C13—41no—
252C8×C13—41no—
253C8×C13—41no—
254C8×C13—41no—
255#1055—21no—
256#1055—21no—
257#1055—21no—
258#1055—21no—
259#1055—21no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—41no—
264#1055—41no—
265#533C2×D1311yescharacteristic
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—261no—
294#432C2×D1311yescharacteristic
295#431—131no—
296#431—131no—
297#431—131no—
298#431—261no—
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⋊C8C2×D1311yescharacteristic
309Q8⋊C8C2×D1311yescharacteristic
310Q8⋊C8C2×D1311yescharacteristic
311Q8⋊C8C2×D1311yescharacteristic
312#322—131no—
313#322—131no—
314#322—131no—
315C82—131no—
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×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13C2×#13111yescharacteristic
329C4×C13#56811yescharacteristic
330C4×C13#57811yescharacteristic
331C4×C13#57811yescharacteristic
332Dic13—22no—
333Dic13—41no—
334Dic13—41no—
335Dic13—41no—
336C22×Q8—131no—
337C2×Q16—131no—
338C2×Q16—131no—
339C2×Q16—131no—
340C2×Q16—131no—
341C4⋊Q8C4×D1311yescharacteristic
342C4⋊Q8C4×D1311yescharacteristic
343#125—21no—
344C22⋊Q8—21no—
345C22⋊Q8C4×D1311yescharacteristic
346C22⋊Q8C4×D1311yescharacteristic
347C4×Q8—21no—
348C4×Q8—131no—
349C4×Q8—131no—
350C4×Q8—131no—
351C4×Q8—131no—
352C4×Q8—261no—
353C4×Q8—261no—
354C4×Q8C22×D1311yescharacteristic
355C4×Q8C22×D1311yescharacteristic
356#117—21no—
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—131no—
371C4⋊C8—131no—
372C4⋊C8—261no—
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#103—131no—
389#103—131no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—131no—
393C22⋊C8—131no—
394C22⋊C8—131no—
395C22⋊C8—131no—
396C22⋊C8—261no—
397#97—21no—
398#97—261no—
399#97—261no—
400#97—261no—
401#97—261no—
402C4×C8—131no—
403C4×C8—131no—
404C4×C8—131no—
405C4×C8—131no—
406C4×C8—261no—
407C4×C8—261no—
408C4×C8—261no—
409C4×C8—261no—
410C4×C8—261no—
411C4×C8C22×D1311yescharacteristic
412C4×C8C22×D1311yescharacteristic
413C2×C13—41no—
414C2×C13#293311yescharacteristic
415C2×C13#295011yescharacteristic
416C2×C13#295511yescharacteristic
417C2×Q8—21no—
418C2×Q8—131no—
419C2×Q8—131no—
420C2×Q8—262no—
421C2×Q8—261no—
422C2×Q8—521no—
423C2×Q8C2×C4×D1311yescharacteristic
424C2×Q8C2×C4×D1311yescharacteristic
425C22×C4—261no—
426C22×C4—261no—
427C22×C4C2×C4×D1311yescharacteristic
428C22×C4D4×D1311yescharacteristic
429C22×C4#612911yescharacteristic
430Q16—262no—
431Q16—262no—
432Q16—521no—
433Q16—521no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—131no—
439C2×C8—131no—
440C2×C8—131no—
441C2×C8—131no—
442C2×C8—131no—
443C2×C8—131no—
444C2×C8—131no—
445C2×C8—131no—
446C2×C8—261no—
447C2×C8—261no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—131no—
456C4⋊C4—131no—
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—21no—
465C22⋊C4—21no—
466C42—21no—
467C42—21no—
468C42—261no—
469C42—261no—
470C42—261no—
471C42—261no—
472C42C2×C4×D1311yescharacteristic
473C42D4×D1311yescharacteristic
474C42#612911yescharacteristic
475C42C23×D1311yescharacteristic
476C13#1803211yescharacteristic, complemented, Sylow
477C23#8813511yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—42no—
483Q8—132no—
484Q8—261no—
485Q8—261no—
486Q8—261no—
487Q8—522no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—261no—
498C2×C4—261no—
499C2×C4—261no—
500C2×C4—261no—
501C2×C4—522no—
502C2×C4—522no—
503C2×C4#8813511yescharacteristic
504C2×C4#8813511yescharacteristic
505C2×C4#8813511yescharacteristic
506C2×C4C22×C4×D1311yescharacteristic
507C2×C4C2×D4×D1311yescharacteristic
508C2×C4C2×#612911yescharacteristic
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—261no—
514C8—261no—
515C8—261no—
516C8—261no—
517C8—261no—
518C8—261no—
519C8—261no—
520C8—261no—
521C8—521no—
522C8—521no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22C2×#8813511yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—262no—
536C4—521no—
537C4—521no—
538C4—521no—
539C4D13×#13111yescharacteristic
540C4#1171945511yescharacteristic
541C4#1171948411yescharacteristic
542C4#1171948411yescharacteristic
543C2—41no—
544C2#1312356611yescharacteristic
545C2#1312370011yescharacteristic
546C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1497C2
socleC22×C13C2×C4×D4
prime radicalC23×C13C4×D4
cosocleC42×C13C24
hypercenter#1497D13
hypocenterC13#18032
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1497

Complements

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

NH ≅ G/Ntype
4. #13113742C2semidirect
5. #13113730C2semidirect
6. #13113710C2semidirect
7. #13113704C2semidirect
8. #13113689C2semidirect
9. #13113683C2semidirect
10. #13113652C2semidirect
11. #13113640C2semidirect
476. C13#18032semidirect

Maximal subgroups

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

subgroupindex
#131248712
#131239382
#131239262
#131137422
#131137302
#131137102
#131137042
#131136892
#131136832
#131136522
#131136402
#131136172
#131132322
#131131362
C13×#14972
#1803213