Finite Group Databasebeta

← #15834108

Subgroups — #15834108

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#13124912C211yesmaximal, characteristic
2#13123923C211yesmaximal, characteristic, complemented
3#13113731C211yesmaximal, characteristic, complemented
4#13113724C211yesmaximal, characteristic, complemented
5#13113712C211yesmaximal, characteristic, complemented
6#13113707C211yesmaximal, characteristic, complemented
7#13113705C211yesmaximal, characteristic, complemented
8#13113693C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10C8×#6105C211yesmaximal, characteristic, complemented
11#13113619C211yesmaximal, characteristic, complemented
12#13113296C211yesmaximal, characteristic
13C2×#11718076C211yesmaximal, characteristic, complemented
14#13113120C211yesmaximal, characteristic, complemented
15C13×#2994C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17C2×C4×Dic26C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436C2211yescharacteristic
21C13×#435—21no—
22C8×D4×C13—21no—
23C8×D4×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#431C2211yescharacteristic
26C13×#424—21no—
27C2×C13×C4⋊C8C2211yescharacteristic
28#11718724C411yescharacteristic
29#11718724C411yescharacteristic
30#11718715C411yescharacteristic
31#11718715C411yescharacteristic
32#11718711C411yescharacteristic
33#11718704C411yescharacteristic
34#11718701C411yescharacteristic
35#11718694C411yescharacteristic
36C4×#6107C2211yescharacteristic
37C4×#6107C2211yescharacteristic
38C4×#6105C2211yescharacteristic
39C4×#6105C2211yescharacteristic
40#11718587C2211yescharacteristic
41#11718586C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718489—21no—
44#11718489—21no—
45#11718380—21no—
46#11718379—21no—
47#11718340C2211yescharacteristic
48#11718340C2211yescharacteristic
49C8×Dic26C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51Q8⋊#1055C2211yescharacteristic
52Q8⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic
56#11718076C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718071C2211yescharacteristic
62#11718071C2211yescharacteristic
63#11718046C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Dic26C2×C411yescharacteristic
68C2×C13×M16—21no—
69C22×C8×C13—21no—
70C22×C8×C13—21no—
71C13×#126—21no—
72C13×#125C2×C411yescharacteristic
73C13×#124C2×C411yescharacteristic
74C13×#123—21no—
75C13×C22⋊Q8C2×C411yescharacteristic
76C13×#121C2×C411yescharacteristic
77C4×Q8×C13C2311yescharacteristic
78C4×D4×C13—21no—
79C4×D4×C13C2311yescharacteristic
80C13×#117—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6107C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85C2×#6105C2×C411yescharacteristic
86C2×C4⋊Dic13C2×C411yescharacteristic
87C2×#6101—21no—
88C2×C4×Dic13—21no—
89C22×#1055—21no—
90C4×Dic26—21no—
91C4×Dic26—21no—
92C4×Dic26C2×C411yescharacteristic
93C4×Dic26C2×C411yescharacteristic
94C4×Dic26C2311yescharacteristic
95C4×Dic26C2311yescharacteristic
96C13×C4⋊C8—21no—
97C13×C4⋊C8—21no—
98C13×C4⋊C8—21no—
99C13×C4⋊C8D411yescharacteristic
100C13×C4⋊C8D411yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C13×C22⋊C8D411yescharacteristic
106C13×C22⋊C8D411yescharacteristic
107C13×#97—21no—
108C4×C8×C13—21no—
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88072C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116C22⋊#1055C2×C411yescharacteristic
117C22⋊#1055C2×C411yescharacteristic
118#88055—21no—
119#88055—21no—
120#88054—21no—
121#88054—21no—
122#88054—21no—
123#88054—21no—
124C8×Dic13—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88050C2×C411yescharacteristic
129#88050C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055C2×C411yescharacteristic
135C4⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138#88043—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18017—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C22×Dic13—21no—
153C22×Dic13—21no—
154C2×Dic26—22no—
155C2×Dic26—21no—
156C2×Dic26—41no—
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C13×M16—81no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—81no—
163C2×C8×C13—81no—
164C2×C8×C13C2×D411yescharacteristic
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C13×C22⋊C4—21no—
177C13×C22⋊C4—21no—
178C13×C22⋊C4—21no—
179C42×C13—21no—
180C42×C13C22×C411yescharacteristic
181C42×C13C2×D411yescharacteristic
182C42×C13#4111yescharacteristic
183C42×C13C2411yescharacteristic
184#6107—22no—
185#6107—41no—
186#6105—22no—
187#6105—41no—
188C4⋊Dic13—21no—
189C4⋊Dic13C22×C411yescharacteristic
190C4⋊Dic13C22×C411yescharacteristic
191#6101—21no—
192#6101—21no—
193#6101—21no—
194#6101—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C2×#1055—24no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208#3108—131no—
209#2994D1311yescharacteristic
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—
227D4×C13—21no—
228D4×C13—21no—
229D4×C13—42no—
230C2×C4×C13—22no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13C4×D411yescharacteristic
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×Dic13—21no—
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—42no—
256Dic26#13112yes—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263#1055—22no—
264#1055—22no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#529C2×D1311yescharacteristic
272C2×C4×Q8—131no—
273#483—131no—
274#480—131no—
275#479—131no—
276#479—131no—
277#464—131no—
278#464—131no—
279#451—131no—
280#448—131no—
281#446—131no—
282#446—131no—
283#446—261no—
284#446—261no—
285#446C2×D1311yescharacteristic
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293#436C2×D1311yescharacteristic
294#435—21no—
295C8×D4—21no—
296C8×D4C2×D1311yescharacteristic
297#433—21no—
298#432—131no—
299#432—261no—
300#431—131no—
301#431—261no—
302#431C2×D1311yescharacteristic
303#424—21no—
304C2×C4⋊C8C2×D1311yescharacteristic
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—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13C2×#13111yescharacteristic
337C4×C13#56811yescharacteristic
338C4×C13#57711yescharacteristic
339C4×C13#57811yescharacteristic
340Dic13—22no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C22×Q8—131no—
345C2×Q16—131no—
346C2×Q16—131no—
347C2×SD16—131no—
348C2×SD16—131no—
349C2×M16—21no—
350C22×C8—21no—
351C22×C8—21no—
352C22×C8—261no—
353#126—21no—
354#125C4×D1311yescharacteristic
355#124C4×D1311yescharacteristic
356#123—21no—
357C22⋊Q8C4×D1311yescharacteristic
358#121C4×D1311yescharacteristic
359C4×Q8—131no—
360C4×Q8—131no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—261no—
364C4×Q8—261no—
365C4×Q8C22×D1311yescharacteristic
366C4×D4—21no—
367C4×D4C22×D1311yescharacteristic
368#117—21no—
369C2×C4⋊C4—131no—
370C2×C4⋊C4—261no—
371C2×C42—261no—
372C2×C42C22×D1311yescharacteristic
373#107—131no—
374#107—131no—
375#106—131no—
376#106—131no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8C22⋊D1311yescharacteristic
389C4⋊C8C22⋊D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—261no—
405C22⋊C8C22⋊D1311yescharacteristic
406C22⋊C8C22⋊D1311yescharacteristic
407#97—21no—
408#97—261no—
409#97—261no—
410#97—261no—
411C4×C8—21no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
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—131no—
427C2×Q8—131no—
428C2×Q8—262no—
429C2×Q8—261no—
430C2×Q8—521no—
431C2×Q8C2×C4×D1311yescharacteristic
432C2×D4—21no—
433C2×D4C2×C4×D1311yescharacteristic
434C22×C4—21no—
435C22×C4—261no—
436C22×C4—261no—
437C22×C4C2×C4×D1311yescharacteristic
438C22×C4#612711yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440Q16—262no—
441Q16—521no—
442SD16—262no—
443SD16—521no—
444M16—81no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—81no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—264no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8C2×C22⋊D1311yescharacteristic
459C2×C8C2×C22⋊D1311yescharacteristic
460C2×C8C2×C22⋊D1311yescharacteristic
461C2×C8C2×C22⋊D1311yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—131no—
467C4⋊C4—131no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4C2×C4×D1311yescharacteristic
474C4⋊C4C2×C4×D1311yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C42—21no—
481C42—261no—
482C42—261no—
483C42—261no—
484C42—261no—
485C42C2×C4×D1311yescharacteristic
486C42#612711yescharacteristic
487C42C2×C22⋊D1311yescharacteristic
488C42C23×D1311yescharacteristic
489C13#1801711yescharacteristic, complemented, Sylow
490C23—21no—
491C23C4×C22⋊D1311yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—132no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—522no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—522no—
517C2×C4—522no—
518C2×C4C4×C22⋊D1311yescharacteristic
519C2×C4C4×C22⋊D1311yescharacteristic
520C2×C4C4×C22⋊D1311yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×#612711yescharacteristic
523C2×C4C22×C22⋊D1311yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—262no—
531C8—262no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—521no—
537C8—521no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1171880512yes—
544C22C2×C4×C22⋊D1311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—262no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4D13×#13111yescharacteristic
557C4#1171945511yescharacteristic
558C4#1171954111yescharacteristic
559C4#1171954311yescharacteristic
560C2—22no—
561C2—81no—
562C2#1312355811yescharacteristic
563C2#1312367511yescharacteristic
564C2C2×#1171880511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2994C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#2994D13
hypocenterC13#18017
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #13123923C2semidirect
3. #13113731C2semidirect
4. #13113724C2semidirect
5. #13113712C2semidirect
6. #13113707C2semidirect
7. #13113705C2semidirect
8. #13113693C2semidirect
9. C8×#6107C2semidirect
10. C8×#6105C2semidirect
11. #13113619C2semidirect
13. C2×#11718076C2semidirect
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
#131249122
#131239232
#131137312
#131137242
#131137122
#131137072
#131137052
#131136932
C8×#61072
C8×#61052
#131136192
#131132962
C2×#117180762
#131131202
C13×#29942
#1801713