Finite Group Databasebeta

← #15833843

Subgroups — #15833843

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124865C211yesmaximal, characteristic
2Q8×#6094C211yesmaximal, characteristic, complemented
3#13123581C211yesmaximal, characteristic
4#13113725C211yesmaximal, characteristic, complemented
5#13113724C211yesmaximal, characteristic, complemented
6#13113676C211yesmaximal, characteristic, complemented
7#13113674C211yesmaximal, characteristic, complemented
8#13113669C211yesmaximal, characteristic, complemented
9SD16×#1055C211yesmaximal, characteristic, complemented
10C8×#6106C211yesmaximal, characteristic, complemented
11#13113605C211yesmaximal, characteristic, complemented
12#13113285C211yesmaximal, characteristic
13D13×Q8⋊C8C211yesmaximal, characteristic, complemented
14#13113115C211yesmaximal, characteristic, complemented
15C13×#1583C211yesmaximal, characteristic, complemented
16C2×#88161—21no—
17C4×Q8×D13C2211yescharacteristic
18#11719253C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C4×C13×SD16C2211yescharacteristic
21C13×#436C2211yescharacteristic
22#11718831C411yescharacteristic
23#11718824C411yescharacteristic
24#11718788—21no—
25C4×#6106C2211yescharacteristic
26Q8×#1055C2211yescharacteristic
27C4×#6105C2211yescharacteristic
28D4×#1055C2211yescharacteristic
29#11718524C411yescharacteristic
30#11718515C411yescharacteristic
31#11718499C2211yescharacteristic
32#11718498—21no—
33#11718498C2211yescharacteristic
34D13×C4⋊C8C2211yescharacteristic
35#11718492—21no—
36#11718492C2211yescharacteristic
37#11718467C411yescharacteristic
38#11718452C411yescharacteristic
39#11718438C411yescharacteristic
40#11718423C411yescharacteristic
41#11718391—21no—
42#11718388—21no—
43C4×#6095C2211yescharacteristic
44C4×#6094—21no—
45C4×#6094C2211yescharacteristic
46C8×D52C2211yescharacteristic
47#11718346C2211yescharacteristic
48C4×C8×D13C2211yescharacteristic
49#11718340—21no—
50#11718340C2211yescharacteristic
51C13×#334C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×#322C2211yescharacteristic
55Q8⋊#1055C2211yescharacteristic
56D4⋊#1055C2211yescharacteristic
57#11718076C2211yescharacteristic
58#11718075C2211yescharacteristic
59#11718072C2211yescharacteristic
60#11718072C2211yescharacteristic
61#11718051C2211yescharacteristic
62#11718049C2211yescharacteristic
63#11718048C2211yescharacteristic
64#11718046C2211yescharacteristic
65C8×#1055C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×Q8×D13C2×C411yescharacteristic
68C2×#6127—21no—
69C2×C13×SD16C2×C411yescharacteristic
70C2×C13×M16—21no—
71C4×Q8×C13C2311yescharacteristic
72C4×D4×C13C2311yescharacteristic
73Q8×Dic13C2×C411yescharacteristic
74C2×#6106C2×C411yescharacteristic
75#88194C2×C411yescharacteristic
76#88192C2×C411yescharacteristic
77C2×#6105C2×C411yescharacteristic
78C4×C22⋊D13—21no—
79C22×#1055—21no—
80#88161—44no—
81C2×#6095C2×C411yescharacteristic
82C2×#6094—21no—
83C2×#6094—21no—
84C2×#6094D411yescharacteristic
85C2×#6094D411yescharacteristic
86C2×C8×D13—21no—
87C2×C8×D13—21no—
88C2×C8×D13—21no—
89#88149C2×C411yescharacteristic
90C4⋊C4×D13—21no—
91C4⋊C4×D13C2×C411yescharacteristic
92#88142C2×C411yescharacteristic
93#88141—21no—
94#88141C2×C411yescharacteristic
95#88139—21no—
96#88138—21no—
97C4×D52C2311yescharacteristic
98C42×D13—21no—
99C42×D13C2311yescharacteristic
100C4×Dic26—21no—
101C4×Dic26C2311yescharacteristic
102C13×#106C2×C411yescharacteristic
103C13×C4⋊C8—21no—
104C13×C4⋊C8C2311yescharacteristic
105C13×C4⋊C8C2311yescharacteristic
106C13×#103C2×C411yescharacteristic
107C13×#102C2×C411yescharacteristic
108C13×C22⋊C8—21no—
109C4×C8×C13—21no—
110C4×C8×C13C2311yescharacteristic
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88075C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115C22⋊#1055—21no—
116#88061C2×C411yescharacteristic
117#88060—21no—
118#88060—21no—
119#88060C2×C411yescharacteristic
120#88060C2×C411yescharacteristic
121#88057C2×C411yescharacteristic
122#88056C2×C411yescharacteristic
123#88055—21no—
124#88055—21no—
125#88055D411yescharacteristic
126#88055D411yescharacteristic
127#88054—21no—
128#88054—21no—
129#88054—21no—
130#88054—21no—
131#88054C2×C411yescharacteristic
132#88054C2×C411yescharacteristic
133C8×Dic13—21no—
134#88050C2×C411yescharacteristic
135#88049C2×C411yescharacteristic
136#88048C2×C411yescharacteristic
137#88048C2×C411yescharacteristic
138C4⋊#1055—21no—
139C4⋊#1055C2311yescharacteristic
140C4⋊#1055C2311yescharacteristic
141C4×#1055—21no—
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144C4×#1055C2311yescharacteristic
145#17997—131nomaximal, Sylow
146C2×Q8×C13C22×C411yescharacteristic
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C2×C22⋊D13—21no—
150C2×C22⋊D13—21no—
151C2×C22⋊D13—21no—
152Q8×D13—22no—
153Q8×D13—41no—
154#6127—42no—
155#6127—42no—
156C2×D52—21no—
157C2×D52C22×C411yescharacteristic
158C2×C4×D13—21no—
159C2×C4×D13—21no—
160C2×C4×D13—21no—
161C2×C4×D13C22×C411yescharacteristic
162C2×C4×D13C2×D411yescharacteristic
163C2×C4×D13#4111yescharacteristic
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26C22×C411yescharacteristic
167C13×SD16—22no—
168C13×M16—42no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13C22×C411yescharacteristic
173C2×C8×C13C22×C411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C13×C4⋊C4—21no—
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C22⋊C4—21no—
180C42×C13—21no—
181C42×C13C2411yescharacteristic
182C22⋊Dic13—21no—
183#6106—22no—
184#6105—41no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13C22×C411yescharacteristic
189C4⋊Dic13C22×C411yescharacteristic
190#6101—21no—
191#6101—21no—
192#6101—21no—
193#6101—21no—
194C4×Dic13—21no—
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13C22×C411yescharacteristic
198C4×Dic13C2×D411yescharacteristic
199C4×Dic13#4111yescharacteristic
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—42no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C2×D411yescharacteristic
207C2×#1055C2×D411yescharacteristic
208#6095—41no—
209#6094—22no—
210#6094—42no—
211#6094—42no—
212#6094SD1614yescomplemented
213C8×D13—42no—
214C8×D13—42no—
215C8×D13—42no—
216#3103—131no—
217Q8×M16—131no—
218#2935—131no—
219#1590—131no—
220#1590—131no—
221#1583—131no—
222#1583D1311yescharacteristic, complemented
223#1582—131no—
224#1582—131no—
225C8×SD16—131no—
226C8×SD16—131no—
227#1570—131no—
228#1492—131no—
229C2×Q8⋊C8—131no—
230C8×M16—131no—
231C23×C13—21no—
232C22×D13—21no—
233C22×D13C4×D411yescharacteristic
234Q8×C13—21no—
235Q8×C13#13112yescomplemented
236D4×C13—21no—
237D4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13C23×C411yescharacteristic
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C22⋊D13—42no—
247C22⋊D13—42no—
248C22⋊D13—81no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13C4×D411yescharacteristic
253C2×Dic13C4×D411yescharacteristic
254C2×Dic13C4×D411yescharacteristic
255D52—21no—
256D52—21no—
257D52—42no—
258C4×D13—21no—
259C4×D13—21no—
260C4×D13—41no—
261C4×D13—42no—
262C4×D13—41no—
263C4×D13—41no—
264C4×D13—81no—
265C4×D13C2×SD1612yes—
266C4×D13#13512yes—
267Dic26—21no—
268Dic26—21no—
269Dic26—42no—
270Dic26—42no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—41no—
275C8×C13—41no—
276C8×C13—41no—
277C8×C13C2×SD1612yes—
278#1055—22no—
279#1055—21no—
280#1055—21no—
281#1055—21no—
282#1055—41no—
283#1055—41no—
284#1055C2×SD1612yes—
285C2×#131—261no—
286#532—131no—
287C2×C4×Q8—131no—
288#481—131no—
289#481—131no—
290#475—131no—
291#475—131no—
292#460—131no—
293#460—131no—
294#448—131no—
295#448—131no—
296#446—131no—
297#446—131no—
298#446—261no—
299#446—261no—
300C8×Q8—131no—
301C8×Q8C2×D1311yescharacteristic
302C4×SD16—131no—
303C4×SD16—131no—
304C4×SD16—131no—
305C4×SD16C2×D1311yescharacteristic
306#436—131no—
307#436C2×D1311yescharacteristic
308#435—261no—
309#435—261no—
310C8×D4—131no—
311C8×D4—131no—
312#431—131no—
313#423—131no—
314#423—261no—
315C2×C4⋊C8—131no—
316#408—261no—
317C4×M16—131no—
318C4×M16—261no—
319C2×C4×C8—131no—
320#334—131no—
321#334—131no—
322#334—131no—
323#334C2×D1311yescharacteristic
324Q8⋊C8—131no—
325Q8⋊C8—131no—
326Q8⋊C8—131no—
327Q8⋊C8C2×D1311yescharacteristic
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8C2×D1311yescharacteristic
332#322—131no—
333#322C2×D1311yescharacteristic
334C82—131no—
335C82—131no—
336C22×C13—41no—
337C22×C13—41no—
338C22×C13—41no—
339C22×C13C2×C4×D411yescharacteristic
340C2×D13—21no—
341C2×D13—21no—
342C2×D13—41no—
343C2×D13—41no—
344C2×D13—41no—
345C2×D13C4×SD1612yes—
346C4×C13—22no—
347C4×C13—21no—
348C4×C13—41no—
349C4×C13—41no—
350C4×C13C2×#13111yescharacteristic
351C4×C13#56811yescharacteristic
352C4×C13C22×SD1611yescharacteristic
353C4×C13C2×#13511yescharacteristic
354Dic13—21no—
355Dic13—21no—
356Dic13—41no—
357Dic13—41no—
358Dic13—41no—
359Dic13C4×SD1612yes—
360C2×#41—261no—
361C22×Q8—131no—
362C2×SD16—131no—
363C2×SD16—131no—
364C2×SD16—131no—
365C2×SD16C4×D1311yescharacteristic
366#131—524no—
367C2×M16—21no—
368C2×M16—131no—
369C2×M16—131no—
370C2×M16—261no—
371C2×M16—261no—
372C22×C8—261no—
373C22×C8—261no—
374C22×C8—261no—
375C22×C8—261no—
376C4⋊Q8—131no—
377#127—131no—
378#124—261no—
379#121—131no—
380#121—131no—
381#121—261no—
382C4×Q8—131no—
383C4×Q8—131no—
384C4×Q8—131no—
385C4×Q8—261no—
386C4×Q8—261no—
387C4×Q8C22×D1311yescharacteristic
388C4×D4—131no—
389C4×D4—261no—
390C4×D4C22×D1311yescharacteristic
391C2×C4⋊C4—131no—
392C2×C4⋊C4—261no—
393C2×C42—131no—
394C2×C42—261no—
395#106—131no—
396#106—131no—
397#106—131no—
398#106C4×D1311yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8—261no—
408C4⋊C8—261no—
409C4⋊C8C22×D1311yescharacteristic
410C4⋊C8C22×D1311yescharacteristic
411#103—131no—
412#103—131no—
413#103—131no—
414#103C4×D1311yescharacteristic
415#102—131no—
416#102—131no—
417#102—131no—
418#102C4×D1311yescharacteristic
419C22⋊C8—21no—
420C22⋊C8—131no—
421C22⋊C8—131no—
422C22⋊C8—261no—
423C22⋊C8—261no—
424C22⋊C8—261no—
425#97—131no—
426#97—131no—
427#97—261no—
428#97—261no—
429C4×C8—21no—
430C4×C8—131no—
431C4×C8—131no—
432C4×C8—131no—
433C4×C8—261no—
434C4×C8—261no—
435C4×C8C22×D1311yescharacteristic
436C4×C8C22×D1311yescharacteristic
437C4×C8C22×D1311yescharacteristic
438C2×C13—81no—
439C2×C13#293311yescharacteristic
440C2×C13C2×C4×SD1611yescharacteristic
441C2×C13#295611yescharacteristic
442D13—22no—
443D13—81no—
444#41—522no—
445#41—522no—
446C2×Q8—131no—
447C2×Q8—261no—
448C2×Q8—261no—
449C2×Q8—262no—
450C2×Q8—521no—
451C2×Q8C2×C4×D1311yescharacteristic
452C2×D4—131no—
453C2×D4—261no—
454C2×D4—261no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4C2×C4×D1311yescharacteristic
458C22×C4—21no—
459C22×C4—131no—
460C22×C4—131no—
461C22×C4—131no—
462C22×C4—261no—
463C22×C4—261no—
464C22×C4—261no—
465SD16—22no—
466SD16—262no—
467SD16—521no—
468SD16—521no—
469M16—42no—
470M16—134no—
471M16—262no—
472M16—522no—
473M16—522no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—131no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—522no—
485C2×C8—522no—
486C2×C8—522no—
487C2×C8—522no—
488C2×C8C2×C4×D1311yescharacteristic
489C2×C8C2×C4×D1311yescharacteristic
490C2×C8D4×D1311yescharacteristic
491C2×C8D4×D1311yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—131no—
494C4⋊C4—131no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4C2×C4×D1311yescharacteristic
501C4⋊C4C2×C4×D1311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—261no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C42—21no—
507C42—131no—
508C42—131no—
509C42—131no—
510C42—261no—
511C42—261no—
512C42—261no—
513C42C23×D1311yescharacteristic
514C13#1799711yescharacteristic, complemented, Sylow
515C23—21no—
516C23—131no—
517C23—261no—
518Q8—21no—
519Q8—261no—
520Q8—261no—
521Q8—522no—
522Q8—522no—
523Q8#8816112yescomplemented
524D4—21no—
525D4—21no—
526D4—261no—
527D4—261no—
528D4—522no—
529D4—522no—
530D4—522no—
531D4—1041no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—131no—
538C2×C4—132no—
539C2×C4—132no—
540C2×C4—131no—
541C2×C4—131no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—521no—
548C2×C4—522no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4—1041no—
552C2×C4C22×C4×D1311yescharacteristic
553C2×C4C2×D4×D1311yescharacteristic
554C2×C4#41×D1311yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—132no—
562C8—262no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—521no—
567C8—521no—
568C8SD16×D1312yes—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—132no—
573C22—261no—
574C22—261no—
575C22—521no—
576C22—521no—
577C22—521no—
578C22C4×D4×D1311yescharacteristic
579C4—21no—
580C4—22no—
581C4—41no—
582C4—41no—
583C4—132no—
584C4—261no—
585C4—261no—
586C4—521no—
587C4—521no—
588C4—521no—
589C4C2×#8816111yescharacteristic
590C4#1171945511yescharacteristic
591C4C2×SD16×D1311yescharacteristic
592C4D13×#13511yescharacteristic
593C2—81no—
594C2—262no—
595C2—1041no—
596C2#1312356211yescharacteristic
597C2C4×SD16×D1311yescharacteristic
598C2#1312374411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1583C2
socleC22×C13C2×C4×D4
prime radical#11719253C22
cosocleC42×C13C24
hypercenter#1583D13
hypocenterC13#17997
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1583

Complements

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

NH ≅ G/Ntype
2. Q8×#6094C2semidirect
4. #13113725C2semidirect
5. #13113724C2semidirect
6. #13113676C2semidirect
7. #13113674C2semidirect
8. #13113669C2semidirect
9. SD16×#1055C2semidirect
10. C8×#6106C2semidirect
11. #13113605C2semidirect
13. D13×Q8⋊C8C2semidirect
14. #13113115C2semidirect
15. C13×#1583C2semidirect
212. #6094SD16semidirect
222. #1583D13semidirect
235. Q8×C13#131semidirect
514. C13#17997semidirect
523. Q8#88161semidirect

Maximal subgroups

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

subgroupindex
#131248652
Q8×#60942
#131235812
#131137252
#131137242
#131136762
#131136742
#131136692
SD16×#10552
C8×#61062
#131136052
#131132852
D13×Q8⋊C82
#131131152
C13×#15832
#1799713