Finite Group Databasebeta

← #15833018

Subgroups — #15833018

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124907C211yesmaximal, characteristic
2#13123947C211yesmaximal, characteristic
3#13123933C211yesmaximal, characteristic, complemented
4#13113704C211yesmaximal, characteristic, complemented
5#13113690C211yesmaximal, characteristic, complemented
6#13113683C211yesmaximal, characteristic, complemented
7#13113669C211yesmaximal, characteristic, complemented
8#13113652C211yesmaximal, characteristic, complemented
9#13113645C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113639C211yesmaximal, characteristic, complemented
12#13113622C211yesmaximal, characteristic, complemented
13#13113240C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1488C211yesmaximal, characteristic
16C4×C13×#41C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#432C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718900C411yescharacteristic
21#11718900C411yescharacteristic
22#11718692C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25Q8×#1055C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27#11718681C411yescharacteristic
28#11718680C411yescharacteristic
29C4×#6105C2211yescharacteristic
30C4×#6105C2211yescharacteristic
31D4×#1055—21no—
32D4×#1055—21no—
33D4×#1055C2211yescharacteristic
34D4×#1055C2211yescharacteristic
35#11718668C411yescharacteristic
36#11718657C411yescharacteristic
37#11718657C411yescharacteristic
38#11718586—21no—
39#11718586C2211yescharacteristic
40#11718586C2211yescharacteristic
41C2×C4⋊#1055—21no—
42C2×C4⋊#1055C2211yescharacteristic
43#11718492C2211yescharacteristic
44#11718492C2211yescharacteristic
45#11718491C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718381—21no—
48#11718381—21no—
49#11718362—21no—
50#11718362—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊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
67C2×C13×#41C2×C411yescharacteristic
68C4×Q8×C13C2×C411yescharacteristic
69C4×Q8×C13C2311yescharacteristic
70C4×D4×C13—21no—
71C4×D4×C13—21no—
72C4×D4×C13C2×C411yescharacteristic
73C4×D4×C13C2311yescharacteristic
74C13×#117—21no—
75C13×#117C2×C411yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6105C2×C411yescharacteristic
81C2×#6105C2×C411yescharacteristic
82#88180—21no—
83#88178—21no—
84#88178C2×C411yescharacteristic
85#88178C2×C411yescharacteristic
86C22×#1055—21no—
87C22×#1055—21no—
88C22×#1055—21no—
89#88124—21no—
90#88123C2×C411yescharacteristic
91#88123C2×C411yescharacteristic
92C4×Dic26—21no—
93C4×Dic26C2311yescharacteristic
94C4×Dic26C2311yescharacteristic
95C13×C4⋊C8—21no—
96C13×C4⋊C8C2311yescharacteristic
97C13×C4⋊C8C2311yescharacteristic
98C13×C22⋊C8—21no—
99C13×C22⋊C8—21no—
100C13×#97—21no—
101C4×C8×C13C2311yescharacteristic
102C4×C8×C13C2311yescharacteristic
103#88075C2×C411yescharacteristic
104#88075C2×C411yescharacteristic
105#88072C2×C411yescharacteristic
106#88072C2×C411yescharacteristic
107C22⋊#1055—21no—
108C22⋊#1055—21no—
109C22⋊#1055C2×C411yescharacteristic
110C22⋊#1055C2×C411yescharacteristic
111C22⋊#1055D411yescharacteristic
112C22⋊#1055D411yescharacteristic
113#88055—21no—
114#88055—21no—
115#88054—21no—
116#88054—21no—
117#88054—21no—
118#88054—21no—
119C8×Dic13—21no—
120C8×Dic13—21no—
121#88050C2×C411yescharacteristic
122#88050C2×C411yescharacteristic
123#88050C2×C411yescharacteristic
124#88050C2×C411yescharacteristic
125#88048C2×C411yescharacteristic
126#88048C2×C411yescharacteristic
127#88047C2×C411yescharacteristic
128#88047C2×C411yescharacteristic
129C4⋊#1055—21no—
130C4⋊#1055—21no—
131C4⋊#1055—21no—
132C4⋊#1055C2×C411yescharacteristic
133C4⋊#1055C2×C411yescharacteristic
134C4⋊#1055D411yescharacteristic
135C4⋊#1055D411yescharacteristic
136C4⋊#1055C2311yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17921—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—22no—
147C2×Q8×C13C22×C411yescharacteristic
148C2×D4×C13—21no—
149C2×D4×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C22×C411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4111yescharacteristic
156C2×Dic26—21no—
157C2×Dic26C22×C411yescharacteristic
158C2×Dic26C22×C411yescharacteristic
159C2×C8×C13—21no—
160C2×C8×C13—21no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4C22×C411yescharacteristic
166C13×C4⋊C4C22×C411yescharacteristic
167C13×C22⋊C4—21no—
168C13×C22⋊C4—21no—
169C13×C22⋊C4—21no—
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13C22×C411yescharacteristic
174C42×C13C2×D411yescharacteristic
175C42×C13#4111yescharacteristic
176C42×C13C2411yescharacteristic
177C22⋊Dic13—21no—
178C22⋊Dic13—21no—
179#6107—22no—
180#6107—22no—
181#6105—22no—
182#6105—22no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13C22×C411yescharacteristic
187C4⋊Dic13C22×C411yescharacteristic
188#6101—21no—
189#6101—21no—
190#6101—21no—
191#6101—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C2×#1055—21no—
195C2×#1055—21no—
196C2×#1055—81no—
197C2×#1055—81no—
198C2×#1055—81no—
199C2×#1055C22×C411yescharacteristic
200C2×#1055C22×C411yescharacteristic
201C2×#1055C22×C411yescharacteristic
202C2×#1055C22×C411yescharacteristic
203C2×#1055C2×D411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207#3107—131no—
208#2988—131no—
209#2985—131no—
210#1587—131no—
211#1585—131no—
212#1584—131no—
213#1582—131no—
214#1579—131no—
215SD16⋊C8—131no—
216C8×Q16—131no—
217C8×SD16—131no—
218#1573—131no—
219#1488D1311yescharacteristic
220#1481—131no—
221#1454—131no—
222C23×C13—21no—
223C23×C13C4×D411yescharacteristic
224Q8×C13—21no—
225Q8×C13#13112yes—
226D4×C13—24no—
227D4×C13—21no—
228D4×C13#13112yes—
229C2×C4×C13—24no—
230C2×C4×C13—21no—
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—41no—
238C2×C4×C13—41no—
239C2×C4×C13—41no—
240C2×C4×C13—81no—
241C2×C4×C13C4×D411yescharacteristic
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C23×C411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×Dic13—21no—
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251Dic26—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—81no—
256C8×C13—41no—
257C8×C13—41no—
258C8×C13—41no—
259C8×C13—41no—
260#1055—21no—
261#1055—21no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#1055—41no—
270#533—131no—
271C4×#41C2×D1311yescharacteristic
272#485—131no—
273#485—131no—
274#475—131no—
275#474—131no—
276#462—131no—
277#461—131no—
278#452—131no—
279#452—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284C8×Q8—131no—
285C8×Q8—131no—
286C8×Q8—131no—
287C8×Q8—131no—
288C4×Q16—131no—
289C4×Q16—131no—
290C4×SD16—131no—
291C4×SD16—131no—
292C8×D4—131no—
293C8×D4—131no—
294C8×D4—261no—
295C8×D4—261no—
296#433—261no—
297#433—261no—
298#432C2×D1311yescharacteristic
299#431—131no—
300#431—131no—
301#431—261no—
302#431C2×D1311yescharacteristic
303C2×C4⋊C8—131no—
304C2×C4⋊C8—261no—
305#335—131no—
306#335—131no—
307#334—131no—
308#334—131no—
309Q8⋊C8—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8C2×D1311yescharacteristic
314Q8⋊C8C2×D1311yescharacteristic
315D4⋊C8C2×D1311yescharacteristic
316D4⋊C8C2×D1311yescharacteristic
317#322—131no—
318#322—131no—
319#322—131no—
320C82—131no—
321C22×C13—21no—
322C22×C13—22no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13C2×C4×D411yescharacteristic
328C4×C13—21no—
329C4×C13—22no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13C2×#13111yescharacteristic
336C4×C13C2×#13111yescharacteristic
337C4×C13#57711yescharacteristic
338C4×C13#57811yescharacteristic
339Dic13—41no—
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343C2×#41C4×D1311yescharacteristic
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C22×C8—261no—
349C22×C8—261no—
350C22×C8—261no—
351C4⋊Q8—131no—
352C4⋊Q8—131no—
353#125—261no—
354C22⋊Q8—131no—
355C22⋊Q8—131no—
356C22⋊Q8—261no—
357C4×Q8—131no—
358C4×Q8—131no—
359C4×Q8—261no—
360C4×Q8C4×D1311yescharacteristic
361C4×Q8C22×D1311yescharacteristic
362C4×D4—21no—
363C4×D4—21no—
364C4×D4C4×D1311yescharacteristic
365C4×D4C22×D1311yescharacteristic
366#117—21no—
367#117—261no—
368#117C4×D1311yescharacteristic
369C2×C42—21no—
370C2×C42C22×D1311yescharacteristic
371#107—131no—
372#107—131no—
373#106—131no—
374#106—131no—
375C4⋊C8—21no—
376C4⋊C8—131no—
377C4⋊C8—131no—
378C4⋊C8—131no—
379C4⋊C8—131no—
380C4⋊C8—131no—
381C4⋊C8—131no—
382C4⋊C8—261no—
383C4⋊C8—261no—
384C4⋊C8—261no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8C22×D1311yescharacteristic
390C4⋊C8C22×D1311yescharacteristic
391#103—131no—
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#102—131no—
398#102—131no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—131no—
402C22⋊C8—131no—
403C22⋊C8—131no—
404C22⋊C8—131no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—21no—
408#97—261no—
409#97—261no—
410C4×C8—131no—
411C4×C8—131no—
412C4×C8—131no—
413C4×C8—131no—
414C4×C8—261no—
415C4×C8—261no—
416C4×C8—261no—
417C4×C8—261no—
418C4×C8C22×D1311yescharacteristic
419C4×C8C22×D1311yescharacteristic
420C2×C13—41no—
421C2×C13—42no—
422C2×C13#292911yescharacteristic
423C2×C13#294711yescharacteristic
424C2×C13#295711yescharacteristic
425#41—22no—
426#41—22no—
427C2×Q8—131no—
428C2×Q8—131no—
429C2×Q8—261no—
430C2×Q8C2×C4×D1311yescharacteristic
431C2×D4—21no—
432C2×D4C2×C4×D1311yescharacteristic
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4C2×C4×D1311yescharacteristic
437C22×C4D4×D1311yescharacteristic
438C22×C4#612911yescharacteristic
439Q16—262no—
440Q16—262no—
441SD16—262no—
442SD16—262no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—131no—
448C2×C8—131no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—1041no—
458C2×C8—1041no—
459C2×C8—1041no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—131no—
463C4⋊C4—131no—
464C4⋊C4—261no—
465C4⋊C4—261no—
466C4⋊C4—261no—
467C4⋊C4—261no—
468C4⋊C4—261no—
469C4⋊C4—261no—
470C4⋊C4—261no—
471C4⋊C4C2×C4×D1311yescharacteristic
472C4⋊C4C2×C4×D1311yescharacteristic
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—261no—
477C22⋊C4—261no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—261no—
482C42—261no—
483C42C2×C4×D1311yescharacteristic
484C42D4×D1311yescharacteristic
485C42#612911yescharacteristic
486C42C23×D1311yescharacteristic
487C13#1792111yescharacteristic, complemented, Sylow
488C23—21no—
489C23#8813511yescharacteristic
490Q8—21no—
491Q8—261no—
492Q8—261no—
493Q8—261no—
494Q8—261no—
495Q8—1041no—
496Q8#8816112yes—
497D4—24no—
498D4—21no—
499D4#8816112yes—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—81no—
512C2×C4—261no—
513C2×C4—261no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4#8813511yescharacteristic
517C2×C4#8813511yescharacteristic
518C2×C4#8813511yescharacteristic
519C2×C4C22×C4×D1311yescharacteristic
520C2×C4C2×D4×D1311yescharacteristic
521C2×C4C2×#612911yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—261no—
527C8—261no—
528C8—261no—
529C8—261no—
530C8—261no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—521no—
535C8—521no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—41no—
541C22—41no—
542C22C2×#8813511yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—22no—
548C4—41no—
549C4—41no—
550C4—521no—
551C4—521no—
552C4—521no—
553C4—521no—
554C4C2×#8816111yescharacteristic
555C4C2×#8816111yescharacteristic
556C4#1171947511yescharacteristic
557C4#1171947611yescharacteristic
558C2—41no—
559C2—42no—
560C2#1312352611yescharacteristic
561C2#1312368211yescharacteristic
562C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1488C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C2×C4
cosocleC42×C13C24
hypercenter#1488D13
hypocenterC13#17921
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
3. #13123933C2semidirect
4. #13113704C2semidirect
5. #13113690C2semidirect
6. #13113683C2semidirect
7. #13113669C2semidirect
8. #13113652C2semidirect
9. #13113645C2semidirect
10. #13113640C2semidirect
11. #13113639C2semidirect
12. #13113622C2semidirect
13. #13113240C2semidirect
14. #13113136C2semidirect
487. C13#17921semidirect

Maximal subgroups

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

subgroupindex
#131249072
#131239472
#131239332
#131137042
#131136902
#131136832
#131136692
#131136522
#131136452
#131136402
#131136392
#131136222
#131132402
#131131362
C13×#14882
#1792113