Finite Group Databasebeta

← #15834062

Subgroups — #15834062

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123856C211yesmaximal, characteristic
2#13123785C211yesmaximal, characteristic, complemented
3#13113739C211yesmaximal, characteristic, complemented
4#13113727C211yesmaximal, characteristic, complemented
5#13113715C211yesmaximal, characteristic, complemented
6#13113708C211yesmaximal, characteristic, complemented
7#13113687C211yesmaximal, characteristic, complemented
8#13113680C211yesmaximal, characteristic, complemented
9#13113655C211yesmaximal, characteristic, complemented
10Q16×#1055C211yesmaximal, characteristic, complemented
11#13113621C211yesmaximal, characteristic, complemented
12#13113309C211yesmaximal, characteristic, complemented
13#13113223C211yesmaximal, characteristic
14#13113131C211yesmaximal, characteristic, complemented
15C13×#3107C211yesmaximal, characteristic
16C13×#533C2211yescharacteristic
17C4×C13×#41C2211yescharacteristic
18C13×#485C411yescharacteristic
19C13×#485C411yescharacteristic
20C13×#475C411yescharacteristic
21C13×#474C411yescharacteristic
22C13×#462C411yescharacteristic
23C13×#461C411yescharacteristic
24C13×#452C411yescharacteristic
25C13×#452C411yescharacteristic
26C4×C13×Q16C2211yescharacteristic
27C4×C13×Q16C2211yescharacteristic
28C4×C13×SD16C2211yescharacteristic
29C4×C13×SD16C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718685—21no—
32#11718685—21no—
33#11718685C2211yescharacteristic
34#11718685C2211yescharacteristic
35Q8×#1055C2211yescharacteristic
36Q8×#1055C2211yescharacteristic
37Q8×#1055C2211yescharacteristic
38Q8×#1055C2211yescharacteristic
39#11718673—21no—
40#11718673—21no—
41#11718673C2211yescharacteristic
42#11718673C2211yescharacteristic
43#11718660—21no—
44#11718658—21no—
45#11718587—21no—
46#11718587C2211yescharacteristic
47#11718586C2211yescharacteristic
48C2×C4⋊#1055C2211yescharacteristic
49C4×#6099—21no—
50C4×#6099C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53Q8⋊#1055C2211yescharacteristic
54Q8⋊#1055C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57D4⋊#1055C2211yescharacteristic
58D4⋊#1055C2211yescharacteristic
59#11718050C2211yescharacteristic
60#11718050C2211yescharacteristic
61#11718049C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×SD16C2×C411yescharacteristic
72C13×C4⋊Q8C2×C411yescharacteristic
73C13×C4⋊Q8C2×C411yescharacteristic
74C13×#125—21no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8C2×C411yescharacteristic
77C13×C22⋊Q8C2×C411yescharacteristic
78C4×Q8×C13—21no—
79C4×Q8×C13C2×C411yescharacteristic
80C4×Q8×C13C2311yescharacteristic
81C4×Q8×C13C2311yescharacteristic
82C4×Q8×C13C2311yescharacteristic
83C4×D4×C13—21no—
84C4×D4×C13—21no—
85C4×D4×C13C2×C411yescharacteristic
86C4×D4×C13C2311yescharacteristic
87C13×#117—21no—
88C13×#117—21no—
89C13×#117C2×C411yescharacteristic
90C2×C42×C13—21no—
91C2×C42×C13C2311yescharacteristic
92C2×#6099—21no—
93C2×#6099—21no—
94C2×#6099D411yescharacteristic
95C2×#6099D411yescharacteristic
96C22×#1055—21no—
97C13×#107C2×C411yescharacteristic
98C13×#107C2×C411yescharacteristic
99C13×#106C2×C411yescharacteristic
100C13×#106C2×C411yescharacteristic
101C13×C4⋊C8C2×C411yescharacteristic
102C13×C4⋊C8C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#103C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×#102C2×C411yescharacteristic
111C13×C22⋊C8C2×C411yescharacteristic
112C13×C22⋊C8C2×C411yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C4×C8×C13C2311yescharacteristic
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055—21no—
118C22⋊#1055—21no—
119C4⋊#1055—21no—
120C4⋊#1055—21no—
121C4⋊#1055—21no—
122C4⋊#1055—21no—
123C4⋊#1055—21no—
124C4⋊#1055—21no—
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055C2311yescharacteristic
128C4⋊#1055C2311yescharacteristic
129C4⋊#1055C2311yescharacteristic
130C4⋊#1055C2311yescharacteristic
131#88043—21no—
132#88043—21no—
133#88043—21no—
134#88043D411yescharacteristic
135#88043D411yescharacteristic
136C4×#1055—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18013—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—41no—
147C2×Q8×C13—21no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×Q8×C13C22×C411yescharacteristic
150C2×Q8×C13C22×C411yescharacteristic
151C2×D4×C13—21no—
152C2×D4×C13C22×C411yescharacteristic
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13C22×C411yescharacteristic
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13#4111yescharacteristic
159C13×Q16—22no—
160C13×Q16—22no—
161C13×SD16—41no—
162C13×SD16—41no—
163C2×C8×C13C22×C411yescharacteristic
164C2×C8×C13C22×C411yescharacteristic
165C2×C8×C13C22×C411yescharacteristic
166C2×C8×C13C22×C411yescharacteristic
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C4⋊C4C22×C411yescharacteristic
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C13×C22⋊C4—21no—
184C13×C22⋊C4—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13C22×C411yescharacteristic
191C42×C13C2×D411yescharacteristic
192C42×C13#4111yescharacteristic
193C42×C13C2411yescharacteristic
194#6099—22no—
195#6099—41no—
196#6099—42no—
197#6099—42no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—42no—
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209#3107D1311yescharacteristic
210#2971—131no—
211#2962—131no—
212#1592—131no—
213#1590—131no—
214#1588—131no—
215#1587—131no—
216#1584—131no—
217#1583—131no—
218#1579—131no—
219C8×Q16—131no—
220#1573—131no—
221#1497—131no—
222#1477—131no—
223#1453—131no—
224C23×C13—21no—
225C23×C13C4×D411yescharacteristic
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231Q8×C13—81no—
232Q8×C13#13112yes—
233D4×C13—21no—
234D4×C13—21no—
235D4×C13—42no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—41no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—81no—
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C4×D411yescharacteristic
255C2×C4×C13C23×C411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—41no—
266#1055—41no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#1055#13712yes—
272#533C2×D1311yescharacteristic
273C4×#41C2×D1311yescharacteristic
274#485Dic1311yescharacteristic
275#485Dic1311yescharacteristic
276#475Dic1311yescharacteristic
277#474Dic1311yescharacteristic
278#462Dic1311yescharacteristic
279#461Dic1311yescharacteristic
280#452Dic1311yescharacteristic
281#452Dic1311yescharacteristic
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C4×Q16C2×D1311yescharacteristic
291C4×Q16C2×D1311yescharacteristic
292C4×SD16C2×D1311yescharacteristic
293C4×SD16C2×D1311yescharacteristic
294#436—131no—
295#436—131no—
296#436—261no—
297#436—261no—
298#432—131no—
299#432—261no—
300#431—131no—
301#431C2×D1311yescharacteristic
302#424—261no—
303C2×C4⋊C8—131no—
304#405—261no—
305C4×M16—131no—
306C4×M16—261no—
307#335—131no—
308#335—131no—
309#334—131no—
310#334—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317D4⋊C8—131no—
318D4⋊C8—131no—
319#322—131no—
320#322—131no—
321#322—131no—
322C82—131no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13C2×C4×D411yescharacteristic
330C4×C13—21no—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13—41no—
341C4×C13C2×#13111yescharacteristic
342C4×C13#56811yescharacteristic
343C4×C13C2×#13711yescharacteristic
344C4×C13#57511yescharacteristic
345C2×#41C2×Dic1311yescharacteristic
346C2×Q16C2×Dic1311yescharacteristic
347C2×Q16C2×Dic1311yescharacteristic
348C2×SD16C2×Dic1311yescharacteristic
349C2×SD16C2×Dic1311yescharacteristic
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—261no—
353C2×M16—261no—
354C22×C8—261no—
355C4⋊Q8C2×Dic1311yescharacteristic
356C4⋊Q8C2×Dic1311yescharacteristic
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8C2×Dic1311yescharacteristic
360C22⋊Q8C2×Dic1311yescharacteristic
361C4×Q8—21no—
362C4×Q8C2×Dic1311yescharacteristic
363C4×Q8C22×D1311yescharacteristic
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C2×Dic1311yescharacteristic
369C4×D4C22×D1311yescharacteristic
370#117—21no—
371#117—21no—
372#117C2×Dic1311yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1311yescharacteristic
375#107C2×Dic1311yescharacteristic
376#107C2×Dic1311yescharacteristic
377#106C2×Dic1311yescharacteristic
378#106C2×Dic1311yescharacteristic
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8C2×Dic1311yescharacteristic
392C4⋊C8C2×Dic1311yescharacteristic
393#103C2×Dic1311yescharacteristic
394#103C2×Dic1311yescharacteristic
395#103C2×Dic1311yescharacteristic
396#103C2×Dic1311yescharacteristic
397#103C2×Dic1311yescharacteristic
398#103C2×Dic1311yescharacteristic
399#102C2×Dic1311yescharacteristic
400#102C2×Dic1311yescharacteristic
401C22⋊C8—261no—
402C22⋊C8—261no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C2×Dic1311yescharacteristic
406C22⋊C8C2×Dic1311yescharacteristic
407#97—131no—
408#97—131no—
409#97—261no—
410#97—261no—
411#97—261no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—41no—
423C2×C13—81no—
424C2×C13#293311yescharacteristic
425C2×C13C4×#13711yescharacteristic
426C2×C13#295711yescharacteristic
427#41—22no—
428#41—41no—
429C2×Q8—21no—
430C2×Q8C22×Dic1311yescharacteristic
431C2×Q8C22×Dic1311yescharacteristic
432C2×Q8C22×Dic1311yescharacteristic
433C2×D4—21no—
434C2×D4C22×Dic1311yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4D4×D1311yescharacteristic
439C22×C4#612911yescharacteristic
440C22×C4C22×Dic1311yescharacteristic
441Q16—22no—
442Q16—22no—
443SD16—41no—
444SD16—41no—
445M16—262no—
446M16—522no—
447M16—521no—
448M16—522no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—522no—
460C2×C8C22×Dic1311yescharacteristic
461C2×C8C22×Dic1311yescharacteristic
462C2×C8C22×Dic1311yescharacteristic
463C2×C8C22×Dic1311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4C22×Dic1311yescharacteristic
474C4⋊C4C22×Dic1311yescharacteristic
475C4⋊C4C22×Dic1311yescharacteristic
476C4⋊C4C22×Dic1311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42D4×D1311yescharacteristic
488C42#612911yescharacteristic
489C42C22×Dic1311yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1801311yescharacteristic, complemented, Sylow
492C23—21no—
493C23D4×Dic1311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—81no—
500Q8#8820212yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—81no—
520C2×C4D4×Dic1311yescharacteristic
521C2×C4D4×Dic1311yescharacteristic
522C2×C4D4×Dic1311yescharacteristic
523C2×C4C2×D4×D1311yescharacteristic
524C2×C4C2×#612911yescharacteristic
525C2×C4C23×Dic1311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—132no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—521no—
535C8—521no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8—521no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×D4×Dic1311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4D13×#13711yescharacteristic
559C4#1171948211yescharacteristic
560C4C2×#8820211yescharacteristic
561C4#1171952411yescharacteristic
562C2—41no—
563C2—81no—
564C2#1312356311yescharacteristic
565C2#137×Dic1311yescharacteristic
566C2#1312375311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#3107C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C2×C4
cosocleC42×C13C24
hypercenter#3107D13
hypocenterC13#18013
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
2. #13123785C2semidirect
3. #13113739C2semidirect
4. #13113727C2semidirect
5. #13113715C2semidirect
6. #13113708C2semidirect
7. #13113687C2semidirect
8. #13113680C2semidirect
9. #13113655C2semidirect
10. Q16×#1055C2semidirect
11. #13113621C2semidirect
12. #13113309C2semidirect
14. #13113131C2semidirect
491. C13#18013semidirect

Maximal subgroups

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

subgroupindex
#131238562
#131237852
#131137392
#131137272
#131137152
#131137082
#131136872
#131136802
#131136552
Q16×#10552
#131136212
#131133092
#131132232
#131131312
C13×#31072
#1801313