Finite Group Databasebeta

← #15834376

Subgroups — #15834376

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123788C211yesmaximal, characteristic
2Q8×#6094C211yesmaximal, characteristic
3C4×Q16×D13C211yesmaximal, characteristic
4#13113731C211yesmaximal, characteristic, complemented
5#13113730C211yesmaximal, characteristic, complemented
6#13113688C211yesmaximal, characteristic, complemented
7#13113687C211yesmaximal, characteristic, complemented
8#13113685C211yesmaximal, characteristic, complemented
9C8×#6107C211yesmaximal, characteristic, complemented
10#13113640C211yesmaximal, characteristic, complemented
11#13113593C211yesmaximal, characteristic
12#13113263C211yesmaximal, characteristic
13#13113263C211yesmaximal, characteristic
14#13113115C211yesmaximal, characteristic
15C13×#1584C211yesmaximal, characteristic, complemented
16C2×Q16×D13C411yescharacteristic
17C4×Q8×D13C2211yescharacteristic
18C4×Q8×D13C2211yescharacteristic
19C13×#446C2211yescharacteristic
20C8×Q8×C13C2211yescharacteristic
21C4×C13×Q16C2211yescharacteristic
22Q16×Dic13C411yescharacteristic
23C4×#6107C2211yescharacteristic
24C4×#6107C2211yescharacteristic
25#11718685C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27D13×#107C411yescharacteristic
28#11718534C411yescharacteristic
29#11718498—21no—
30#11718498—21no—
31#11718498C2211yescharacteristic
32#11718498C2211yescharacteristic
33#11718492—21no—
34#11718492C2211yescharacteristic
35#11718491C2211yescharacteristic
36#11718489—21no—
37D13×#103C411yescharacteristic
38D13×#103C411yescharacteristic
39#11718451C411yescharacteristic
40#11718451C411yescharacteristic
41#11718368—21no—
42#11718362—21no—
43C4×Dic52C2211yescharacteristic
44C4×#6094—21no—
45C4×#6094C2211yescharacteristic
46#11718346C2211yescharacteristic
47C4×C8×D13C2211yescharacteristic
48#11718340—21no—
49#11718340C2211yescharacteristic
50C8×Dic26C2211yescharacteristic
51C13×#335C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56Q8⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718076C2211yescharacteristic
59#11718071C2211yescharacteristic
60#11718071C2211yescharacteristic
61#11718050C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×Q8×D13C2×C411yescharacteristic
69C2×C13×Q16C2×C411yescharacteristic
70C4×Q8×C13C2311yescharacteristic
71C4×Q8×C13C2311yescharacteristic
72Q8×Dic13C2×C411yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6107C2×C411yescharacteristic
75C2×#6107C2×C411yescharacteristic
76Q16×D13—24no—
77C2×Dic52C2×C411yescharacteristic
78C2×#6094—21no—
79C2×#6094—21no—
80C2×#6094D411yescharacteristic
81C2×#6094D411yescharacteristic
82C2×C8×D13C2×C411yescharacteristic
83C2×C8×D13C2×C411yescharacteristic
84C4⋊C4×D13—21no—
85C4⋊C4×D13—21no—
86C4⋊C4×D13C2×C411yescharacteristic
87C4⋊C4×D13C2×C411yescharacteristic
88#88141—21no—
89#88141—21no—
90#88141C2×C411yescharacteristic
91#88141C2×C411yescharacteristic
92C42×D13—21no—
93C42×D13—21no—
94C42×D13C2311yescharacteristic
95C4×Dic26—21no—
96C4×Dic26—21no—
97C4×Dic26C2311yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×#107C2×C411yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×#103C2×C411yescharacteristic
105C13×#103C2×C411yescharacteristic
106C13×#97—21no—
107C4×C8×C13—21no—
108C4×C8×C13C2311yescharacteristic
109C4×C8×C13C2311yescharacteristic
110C4×C8×C13C2311yescharacteristic
111#88075C2×C411yescharacteristic
112#88075C2×C411yescharacteristic
113#88060—21no—
114#88058C2×C411yescharacteristic
115#88056C2×C411yescharacteristic
116#88056C2×C411yescharacteristic
117#88055—21no—
118#88055—21no—
119#88055D411yescharacteristic
120#88055D411yescharacteristic
121#88054—21no—
122#88054—21no—
123#88054—21no—
124#88054—21no—
125#88054—21no—
126#88054—21no—
127#88054—21no—
128C8×Dic13—21no—
129C8×Dic13—21no—
130C8×Dic13C2×C411yescharacteristic
131C8×Dic13C2×C411yescharacteristic
132#88050C2×C411yescharacteristic
133#88050C2×C411yescharacteristic
134#88047C2×C411yescharacteristic
135#88047C2×C411yescharacteristic
136C4⋊#1055—21no—
137C4⋊#1055—21no—
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140#88043—21no—
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145M16×Q16—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×Q8×C13C22×C411yescharacteristic
148Q8×D13—22no—
149Q8×D13—22no—
150Q8×D13—41no—
151Q8×D13—41no—
152C2×C4×D13—21no—
153C2×C4×D13—21no—
154C2×C4×D13—21no—
155C2×C4×D13—21no—
156C2×C4×D13C22×C411yescharacteristic
157C2×C4×D13C2×D411yescharacteristic
158C2×C4×D13#4111yescharacteristic
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26C22×C411yescharacteristic
162C2×Dic26C22×C411yescharacteristic
163C13×Q16—22no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13C22×C411yescharacteristic
168C2×C8×C13C22×C411yescharacteristic
169C2×C8×C13C2×D411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C411yescharacteristic
174C13×C4⋊C4C22×C411yescharacteristic
175C42×C13—21no—
176C42×C13—21no—
177C42×C13C2411yescharacteristic
178#6107—22no—
179#6107M1614yescomplemented
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13C22×C411yescharacteristic
183C4⋊Dic13C22×C411yescharacteristic
184#6101—21no—
185#6101—21no—
186#6101—21no—
187#6101—21no—
188#6101—21no—
189#6101—21no—
190C4×Dic13—21no—
191C4×Dic13—21no—
192C4×Dic13—21no—
193C4×Dic13—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13C22×C411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13#4111yescharacteristic
199C2×#1055—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055C22×C411yescharacteristic
203C2×#1055C22×C411yescharacteristic
204C2×#1055C2×D411yescharacteristic
205C2×#1055C2×D411yescharacteristic
206Dic52—22no—
207#6094—22no—
208#6094—42no—
209#6094—42no—
210#6094Q1614yescomplemented
211C8×D13—22no—
212C8×D13—41no—
213Q8×M16—131no—
214Q8×M16—131no—
215C2×C4×Q16—131no—
216#1591—131no—
217#1591—131no—
218#1584—131no—
219#1584—131no—
220#1584—131no—
221#1584D1311yescharacteristic, complemented
222C8×Q16—131no—
223C8×Q16—131no—
224#1567—131no—
225#1487—131no—
226#1487—131no—
227C8×M16—131no—
228C22×D13C4×D411yescharacteristic
229Q8×C13—21no—
230Q8×C13—21no—
231Q8×C13—21no—
232Q8×C13C2×M1612yes—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
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×Dic13C4×D411yescharacteristic
245C2×Dic13C4×D411yescharacteristic
246C2×Dic13C4×D411yescharacteristic
247C4×D13—21no—
248C4×D13—21no—
249C4×D13—41no—
250C4×D13—42no—
251C4×D13—42no—
252C4×D13—81no—
253C4×D13—81no—
254C4×D13C2×Q1612yes—
255C4×D13#13512yes—
256Dic26—21no—
257Dic26—21no—
258Dic26—21no—
259Dic26—42no—
260Dic26—42no—
261Dic26C2×M1612yes—
262C8×C13—21no—
263C8×C13—21no—
264C8×C13—21no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13C2×Q1612yescomplemented
269#1055—21no—
270#1055—21no—
271#1055—41no—
272#1055—41no—
273#1055—41no—
274#1055C2×M1612yes—
275#1055C2×Q1612yescomplemented
276C22×Q16—131no—
277C2×C4×Q8—131no—
278C2×C4×Q8—131no—
279#446—131no—
280#446—131no—
281#446—131no—
282#446—261no—
283#446—261no—
284#446—261no—
285#446—261no—
286#446C2×D1311yescharacteristic
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C8×Q8C2×D1311yescharacteristic
291C4×Q16—131no—
292C4×Q16—131no—
293C4×Q16—131no—
294C4×Q16—131no—
295C4×Q16—131no—
296C4×Q16—131no—
297C4×Q16—131no—
298C4×Q16C2×D1311yescharacteristic
299#431—131no—
300C2×#107—131no—
301#423—131no—
302#423—131no—
303#423—261no—
304#423—261no—
305C2×#103—131no—
306C2×#103—131no—
307C4×M16—131no—
308C4×M16—261no—
309C4×M16—261no—
310C2×C4×C8—131no—
311#335—131no—
312#335—131no—
313#335—131no—
314#335C2×D1311yescharacteristic
315Q8⋊C8—131no—
316Q8⋊C8—131no—
317Q8⋊C8—131no—
318Q8⋊C8—131no—
319Q8⋊C8—131no—
320Q8⋊C8—131no—
321Q8⋊C8C2×D1311yescharacteristic
322Q8⋊C8C2×D1311yescharacteristic
323#322—131no—
324#322C2×D1311yescharacteristic
325C82—131no—
326C82—131no—
327C22×C13C2×C4×D411yescharacteristic
328C2×D13—21no—
329C2×D13—21no—
330C2×D13C4×Q1612yes—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13C22×M1611yescharacteristic
337C4×C13#56811yescharacteristic
338C4×C13C22×Q1611yescharacteristic
339C4×C13C2×#13511yescharacteristic
340Dic13—22no—
341Dic13—21no—
342Dic13—21no—
343Dic13—41no—
344Dic13—41no—
345Dic13—41no—
346Dic13C4×Q1612yes—
347C22×Q8—131no—
348C22×Q8—131no—
349C2×Q16—131no—
350C2×Q16—131no—
351C2×Q16—131no—
352C2×Q16—264no—
353C2×Q16C4×D1311yescharacteristic
354C2×M16—131no—
355C2×M16—131no—
356C2×M16—261no—
357C2×M16—261no—
358C22×C8—131no—
359C22×C8—131no—
360C4×Q8—131no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—131no—
364C4×Q8—131no—
365C4×Q8—131no—
366C4×Q8—261no—
367C4×Q8—261no—
368C4×Q8—261no—
369C4×Q8—261no—
370C4×Q8C22×D1311yescharacteristic
371C4×Q8C22×D1311yescharacteristic
372C2×C4⋊C4—131no—
373C2×C4⋊C4—131no—
374C2×C4⋊C4—261no—
375C2×C4⋊C4—261no—
376C2×C42—131no—
377C2×C42—261no—
378C2×C42—261no—
379#107—131no—
380#107—131no—
381#107—131no—
382#107C4×D1311yescharacteristic
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—131no—
386C4⋊C8—131no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8—261no—
392C4⋊C8—261no—
393C4⋊C8—261no—
394C4⋊C8—261no—
395C4⋊C8—261no—
396C4⋊C8C22×D1311yescharacteristic
397C4⋊C8C22×D1311yescharacteristic
398#103—131no—
399#103—131no—
400#103—131no—
401#103—131no—
402#103—131no—
403#103—131no—
404#103C4×D1311yescharacteristic
405#103C4×D1311yescharacteristic
406C22⋊C8—261no—
407#97—21no—
408#97—131no—
409#97—131no—
410#97—261no—
411#97—261no—
412#97—261no—
413C4×C8—21no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—131no—
419C4×C8—261no—
420C4×C8—261no—
421C4×C8—261no—
422C4×C8C22×D1311yescharacteristic
423C4×C8C22×D1311yescharacteristic
424C4×C8C22×D1311yescharacteristic
425C2×C13D4×M1611yescharacteristic
426C2×C13C2×C4×Q1611yescharacteristic
427C2×C13#295711yescharacteristic
428D13—22no—
429C2×Q8—131no—
430C2×Q8—131no—
431C2×Q8—261no—
432C2×Q8—261no—
433C2×Q8—262no—
434C2×Q8—262no—
435C2×Q8—521no—
436C2×Q8—521no—
437C2×Q8C2×C4×D1311yescharacteristic
438C2×Q8C2×C4×D1311yescharacteristic
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—261no—
443C22×C4—261no—
444C22×C4—261no—
445C22×C4—261no—
446Q16—22no—
447Q16—134no—
448Q16—262no—
449Q16—262no—
450M16—134no—
451M16—262no—
452M16—522no—
453M16—522no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—262no—
462C2×C8—261no—
463C2×C8—261no—
464C2×C8—261no—
465C2×C8—521no—
466C2×C8C2×C4×D1311yescharacteristic
467C2×C8C2×C4×D1311yescharacteristic
468C2×C8D4×D1311yescharacteristic
469C2×C8D4×D1311yescharacteristic
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—131no—
473C4⋊C4—131no—
474C4⋊C4—261no—
475C4⋊C4—261no—
476C4⋊C4—261no—
477C4⋊C4—261no—
478C4⋊C4—261no—
479C4⋊C4—261no—
480C4⋊C4—261no—
481C4⋊C4—261no—
482C4⋊C4C2×C4×D1311yescharacteristic
483C4⋊C4C2×C4×D1311yescharacteristic
484C42—21no—
485C42—21no—
486C42—131no—
487C42—131no—
488C42—131no—
489C42—261no—
490C42—261no—
491C42—261no—
492C42—261no—
493C42—261no—
494C42—261no—
495C42C23×D1311yescharacteristic
496C13M16×Q1611yescharacteristic, complemented, Sylow
497C23—131no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—132no—
502Q8—261no—
503Q8—261no—
504Q8—261no—
505Q8—522no—
506Q8—522no—
507Q8M16×D1312yes—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—131no—
513C2×C4—132no—
514C2×C4—132no—
515C2×C4—131no—
516C2×C4—131no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4—261no—
521C2×C4—261no—
522C2×C4—261no—
523C2×C4—521no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—1041no—
527C2×C4—1041no—
528C2×C4C22×C4×D1311yescharacteristic
529C2×C4C2×D4×D1311yescharacteristic
530C2×C4#41×D1311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—132no—
538C8—132no—
539C8—261no—
540C8—261no—
541C8—521no—
542C8—521no—
543C8—521no—
544C8Q16×D1312yescomplemented
545C22—132no—
546C22—261no—
547C22—261no—
548C22C4×D4×D1311yescharacteristic
549C4—21no—
550C4—22no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—132no—
555C4—261no—
556C4—261no—
557C4—262no—
558C4—521no—
559C4—521no—
560C4—521no—
561C4C2×M16×D1311yescharacteristic
562C4#1171945511yescharacteristic
563C4C2×Q16×D1311yescharacteristic
564C4D13×#13511yescharacteristic
565C2—262no—
566C2#1312356911yescharacteristic
567C2C4×Q16×D1311yescharacteristic
568C2#1312375011yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1584C2
socleC22×C13C2×C4×D4
prime radicalC22×D13C4×D4
cosocleC42×C13C24
hypercenter#1584D13
hypocenterC13M16×Q16
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #13113731C2semidirect
5. #13113730C2semidirect
6. #13113688C2semidirect
7. #13113687C2semidirect
8. #13113685C2semidirect
9. C8×#6107C2semidirect
10. #13113640C2semidirect
15. C13×#1584C2semidirect
179. #6107M16semidirect
210. #6094Q16semidirect
221. #1584D13semidirect
268. C8×C13C2×Q16semidirect
275. #1055C2×Q16semidirect
496. C13M16×Q16semidirect
544. C8Q16×D13semidirect

Maximal subgroups

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

subgroupindex
#131237882
Q8×#60942
C4×Q16×D132
#131137312
#131137302
#131136882
#131136872
#131136852
C8×#61072
#131136402
#131135932
#131132632
#131131152
C13×#15842
M16×Q1613