Finite Group Databasebeta

← #15834114

Subgroups — #15834114

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123996C211yesmaximal, characteristic
2#13123925C211yesmaximal, characteristic, complemented
3#13113733C211yesmaximal, characteristic, complemented
4#13113727C211yesmaximal, characteristic, complemented
5#13113715C211yesmaximal, characteristic, complemented
6#13113708C211yesmaximal, characteristic, complemented
7#13113708C211yesmaximal, characteristic, complemented
8#13113694C211yesmaximal, characteristic, complemented
9Q16×#1055C211yesmaximal, characteristic, complemented
10SD16×#1055C211yesmaximal, characteristic, complemented
11#13113621C211yesmaximal, characteristic, complemented
12#13113296C211yesmaximal, characteristic
13C2×Q8⋊#1055C211yesmaximal, characteristic, complemented
14#13113120C211yesmaximal, characteristic, complemented
15C13×#3108C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C13×#483C411yescharacteristic
19C13×#480C411yescharacteristic
20C13×#479C411yescharacteristic
21C13×#479C411yescharacteristic
22C13×#464C411yescharacteristic
23C13×#464C411yescharacteristic
24C13×#451C411yescharacteristic
25C13×#448C411yescharacteristic
26C4×C13×Q16C2211yescharacteristic
27C4×C13×Q16C2211yescharacteristic
28C4×C13×SD16C2211yescharacteristic
29C4×C13×SD16C2211yescharacteristic
30C13×#431C2211yescharacteristic
31#11718685—21no—
32#11718685—21no—
33#11718685C2211yescharacteristic
34#11718685C2211yescharacteristic
35#11718685C2211yescharacteristic
36Q8×#1055C2211yescharacteristic
37Q8×#1055C2211yescharacteristic
38Q8×#1055C2211yescharacteristic
39#11718673C2211yescharacteristic
40#11718672—21no—
41D4×#1055—21no—
42D4×#1055C2211yescharacteristic
43#11718661—21no—
44#11718660—21no—
45#11718587—21no—
46#11718587C2211yescharacteristic
47#11718586—21no—
48#11718586C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
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#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Q8×C13C2×C411yescharacteristic
68C2×C13×Q16C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C2×C13×SD16C2×C411yescharacteristic
71C2×C13×SD16C2×C411yescharacteristic
72C13×#126—21no—
73C13×#125C2×C411yescharacteristic
74C13×#124C2×C411yescharacteristic
75C13×#123—21no—
76C13×C22⋊Q8C2×C411yescharacteristic
77C13×#121C2×C411yescharacteristic
78C4×Q8×C13—21no—
79C4×Q8×C13—21no—
80C4×Q8×C13C2×C411yescharacteristic
81C4×Q8×C13C2×C411yescharacteristic
82C4×Q8×C13C2311yescharacteristic
83C4×Q8×C13C2311yescharacteristic
84C4×Q8×C13C2311yescharacteristic
85C4×D4×C13—21no—
86C4×D4×C13C2311yescharacteristic
87C13×#117—21no—
88C2×C13×C4⋊C4—21no—
89C2×C13×C4⋊C4C2×C411yescharacteristic
90C2×C42×C13—21no—
91C2×C42×C13C2311yescharacteristic
92C2×#6099—21no—
93C22×#1055—21no—
94C22×#1055—21no—
95C22×#1055—21no—
96C13×#107C2×C411yescharacteristic
97C13×#107C2×C411yescharacteristic
98C13×#106C2×C411yescharacteristic
99C13×#106C2×C411yescharacteristic
100C13×C4⋊C8C2×C411yescharacteristic
101C13×C4⋊C8C2×C411yescharacteristic
102C13×#103C2×C411yescharacteristic
103C13×#103C2×C411yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#103C2×C411yescharacteristic
108C13×#102C2×C411yescharacteristic
109C13×#102C2×C411yescharacteristic
110C13×C22⋊C8C2×C411yescharacteristic
111C13×C22⋊C8C2×C411yescharacteristic
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055D411yescharacteristic
118C22⋊#1055D411yescharacteristic
119C4⋊#1055—21no—
120C4⋊#1055—21no—
121C4⋊#1055—21no—
122C4⋊#1055—21no—
123C4⋊#1055—21no—
124C4⋊#1055—21no—
125C4⋊#1055—21no—
126C4⋊#1055D411yescharacteristic
127C4⋊#1055D411yescharacteristic
128C4⋊#1055C2311yescharacteristic
129C4⋊#1055C2311yescharacteristic
130C4⋊#1055C2311yescharacteristic
131C4⋊#1055C2311yescharacteristic
132#88043—21no—
133#88043—21no—
134#88043—21no—
135#88043—21no—
136C4×#1055—21no—
137C4×#1055—21no—
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18017—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—22no—
147C2×Q8×C13—41no—
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—41no—
161C13×SD16—22no—
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—81no—
195C2×#1055—24no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—81no—
203C2×#1055—81no—
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#3108D1311yescharacteristic
209#2994—131no—
210#2984—131no—
211#1591—131no—
212#1590—131no—
213#1588—131no—
214#1587—131no—
215#1587—131no—
216#1585—131no—
217C8×Q16—131no—
218C8×SD16—131no—
219#1573—131no—
220#1494—131no—
221C2×Q8⋊C8—131no—
222#1450—131no—
223C23×C13—21no—
224C23×C13C4×D411yescharacteristic
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—42no—
231Q8×C13#13112yes—
232D4×C13—21no—
233D4×C13—21no—
234D4×C13—42no—
235C2×C4×C13—21no—
236C2×C4×C13—22no—
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—42no—
248C2×C4×C13—42no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13C4×D411yescharacteristic
252C2×C4×C13C4×D411yescharacteristic
253C2×C4×C13C4×D411yescharacteristic
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C22×D411yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261#1055—22no—
262#1055—22no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#529C2×D1311yescharacteristic
272C2×C4×Q8C2×D1311yescharacteristic
273#483Dic1311yescharacteristic
274#480Dic1311yescharacteristic
275#479Dic1311yescharacteristic
276#479Dic1311yescharacteristic
277#464Dic1311yescharacteristic
278#464Dic1311yescharacteristic
279#451Dic1311yescharacteristic
280#448Dic1311yescharacteristic
281#446—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8—131no—
289C4×Q16C2×D1311yescharacteristic
290C4×Q16C2×D1311yescharacteristic
291C4×SD16C2×D1311yescharacteristic
292C4×SD16C2×D1311yescharacteristic
293#436—131no—
294#435—261no—
295C8×D4—131no—
296C8×D4—261no—
297#433—261no—
298#432—131no—
299#432—261no—
300#431—131no—
301#431—261no—
302#431C2×D1311yescharacteristic
303#424—261no—
304C2×C4⋊C8—131no—
305C2×C4×C8—131no—
306#335—131no—
307#335—131no—
308#334—131no—
309#334—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322—131no—
319#322—131no—
320C82—131no—
321C82—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—41no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13#44312yes—
328C22×C13C2×C4×D411yescharacteristic
329C4×C13—21no—
330C4×C13—22no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13—41no—
339C4×C13—41no—
340C4×C13C2×#13111yescharacteristic
341C4×C13#56811yescharacteristic
342C4×C13#57711yescharacteristic
343C4×C13#57811yescharacteristic
344C22×Q8C2×Dic1311yescharacteristic
345C2×Q16C2×Dic1311yescharacteristic
346C2×Q16C2×Dic1311yescharacteristic
347C2×SD16C2×Dic1311yescharacteristic
348C2×SD16C2×Dic1311yescharacteristic
349C2×M16—261no—
350C22×C8—261no—
351C22×C8—261no—
352C22×C8—261no—
353#126—21no—
354#125C2×Dic1311yescharacteristic
355#124C2×Dic1311yescharacteristic
356#123—21no—
357C22⋊Q8C2×Dic1311yescharacteristic
358#121C2×Dic1311yescharacteristic
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8C2×Dic1311yescharacteristic
362C4×Q8C2×Dic1311yescharacteristic
363C4×Q8C22×D1311yescharacteristic
364C4×Q8C22×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—21no—
367C4×D4C22×D1311yescharacteristic
368#117—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4C2×Dic1311yescharacteristic
371C2×C42—21no—
372C2×C42C22×D1311yescharacteristic
373#107C2×Dic1311yescharacteristic
374#107C2×Dic1311yescharacteristic
375#106C2×Dic1311yescharacteristic
376#106C2×Dic1311yescharacteristic
377C4⋊C8—131no—
378C4⋊C8—131no—
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⋊C8C2×Dic1311yescharacteristic
391C4⋊C8C2×Dic1311yescharacteristic
392#103C2×Dic1311yescharacteristic
393#103C2×Dic1311yescharacteristic
394#103C2×Dic1311yescharacteristic
395#103C2×Dic1311yescharacteristic
396#103C2×Dic1311yescharacteristic
397#103C2×Dic1311yescharacteristic
398#102C2×Dic1311yescharacteristic
399#102C2×Dic1311yescharacteristic
400C22⋊C8—131no—
401C22⋊C8—131no—
402C22⋊C8—261no—
403C22⋊C8—261no—
404C22⋊C8—261no—
405C22⋊C8C2×Dic1311yescharacteristic
406C22⋊C8C2×Dic1311yescharacteristic
407#97—261no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—22no—
422C2×C13—81no—
423C2×C13#293311yescharacteristic
424C2×C13#294711yescharacteristic
425C2×C13C2×#44311yescharacteristic
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—41no—
429C2×Q8C22×Dic1311yescharacteristic
430C2×Q8C22×Dic1311yescharacteristic
431C2×Q8C22×Dic1311yescharacteristic
432C2×D4—21no—
433C2×D4C22×Dic1311yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4D4×D1311yescharacteristic
438C22×C4#612911yescharacteristic
439C22×C4C22×Dic1311yescharacteristic
440Q16—22no—
441Q16—41no—
442SD16—22no—
443SD16—41no—
444M16—1041no—
445C2×C8—131no—
446C2×C8—131no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—264no—
450C2×C8—261no—
451C2×C8—261no—
452C2×C8—261no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—1041no—
457C2×C8—1041no—
458C2×C8C22×Dic1311yescharacteristic
459C2×C8C22×Dic1311yescharacteristic
460C2×C8C22×Dic1311yescharacteristic
461C2×C8C22×Dic1311yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4C22×Dic1311yescharacteristic
472C4⋊C4C22×Dic1311yescharacteristic
473C4⋊C4C22×Dic1311yescharacteristic
474C4⋊C4C22×Dic1311yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42D4×D1311yescharacteristic
486C42#612911yescharacteristic
487C42C22×Dic1311yescharacteristic
488C42C23×D1311yescharacteristic
489C13#1801711yescharacteristic, complemented, Sylow
490C23—21no—
491C23D4×Dic1311yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8#8820212yes—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—21no—
503C2×C4—22no—
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—42no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4D4×Dic1311yescharacteristic
519C2×C4D4×Dic1311yescharacteristic
520C2×C4D4×Dic1311yescharacteristic
521C2×C4C2×D4×D1311yescharacteristic
522C2×C4C2×#612911yescharacteristic
523C2×C4C23×Dic1311yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—262no—
529C8—262no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—521no—
535C8—521no—
536C8—521no—
537C8—521no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1171885712yes—
544C22C2×D4×Dic1311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—22no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4#1171948311yescharacteristic
557C4#1171948411yescharacteristic
558C4C2×#8820211yescharacteristic
559C4#1171952411yescharacteristic
560C2—22no—
561C2—81no—
562C2#1312356311yescharacteristic
563C2#1312368011yescharacteristic
564C2C2×#1171885711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#3108C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#3108D13
hypocenterC13#18017
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3108

Complements

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

NH ≅ G/Ntype
2. #13123925C2semidirect
3. #13113733C2semidirect
4. #13113727C2semidirect
5. #13113715C2semidirect
6. #13113708C2semidirect
7. #13113708C2semidirect
8. #13113694C2semidirect
9. Q16×#1055C2semidirect
10. SD16×#1055C2semidirect
11. #13113621C2semidirect
13. C2×Q8⋊#1055C2semidirect
14. #13113120C2semidirect
489. C13#18017semidirect

Maximal subgroups

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

subgroupindex
#131239962
#131239252
#131137332
#131137272
#131137152
#131137082
#131136942
Q16×#10552
SD16×#10552
#131136212
#131132962
C2×Q8⋊#10552
#131131202
C13×#31082
#1801713