Finite Group Databasebeta

← #15834039

Subgroups — #15834039

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124916C211yesmaximal, characteristic
2#13123834C211yesmaximal, characteristic
3Q8×#6099C211yesmaximal, characteristic, complemented
4#13113742C211yesmaximal, characteristic, complemented
5#13113723C211yesmaximal, characteristic, complemented
6#13113704C211yesmaximal, characteristic, complemented
7#13113696C211yesmaximal, characteristic, complemented
8#13113689C211yesmaximal, characteristic, complemented
9#13113676C211yesmaximal, characteristic, complemented
10#13113651C211yesmaximal, characteristic, complemented
11#13113640C211yesmaximal, characteristic, complemented
12#13113624C211yesmaximal, characteristic, complemented
13#13113302C211yesmaximal, characteristic
14#13113131C211yesmaximal, characteristic, complemented
15C13×#1479C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C13C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718889C411yescharacteristic
21#11718888C411yescharacteristic
22C4×#6107C2211yescharacteristic
23C4×#6107C2211yescharacteristic
24#11718689C411yescharacteristic
25#11718689C411yescharacteristic
26C4×#6106C2211yescharacteristic
27C4×#6106C2211yescharacteristic
28#11718685—21no—
29#11718685—21no—
30#11718685C2211yescharacteristic
31#11718685C2211yescharacteristic
32Q8×#1055C2211yescharacteristic
33Q8×#1055C2211yescharacteristic
34#11718683C411yescharacteristic
35#11718683C411yescharacteristic
36#11718632C411yescharacteristic
37#11718628C411yescharacteristic
38#11718586C2211yescharacteristic
39#11718585—21no—
40#11718585C2211yescharacteristic
41C4×#6099—21no—
42C4×#6099C2211yescharacteristic
43#11718499C2211yescharacteristic
44#11718495C2211yescharacteristic
45#11718492C2211yescharacteristic
46#11718491C2211yescharacteristic
47#11718390—21no—
48#11718389—21no—
49#11718351—21no—
50#11718350—21no—
51C13×Q8⋊C8C2211yescharacteristic
52C13×Q8⋊C8C2211yescharacteristic
53C13×Q8⋊C8C2211yescharacteristic
54C13×Q8⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic
56#11718072C2211yescharacteristic
57#11718071C2211yescharacteristic
58#11718071C2211yescharacteristic
59#11718051C2211yescharacteristic
60#11718051C2211yescharacteristic
61#11718048C2211yescharacteristic
62#11718048C2211yescharacteristic
63#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C22×Q8×C13C2×C411yescharacteristic
68C4×Q8×C13—21no—
69C4×Q8×C13—21no—
70C4×Q8×C13C2×C411yescharacteristic
71C4×Q8×C13C2×C411yescharacteristic
72C4×Q8×C13C2311yescharacteristic
73C4×Q8×C13C2311yescharacteristic
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4C2×C411yescharacteristic
76C2×C42×C13—21no—
77C2×C42×C13C2311yescharacteristic
78C2×#6107C2×C411yescharacteristic
79C2×#6107C2×C411yescharacteristic
80C2×#6106C2×C411yescharacteristic
81C2×#6106C2×C411yescharacteristic
82#88184C2×C411yescharacteristic
83#88183—21no—
84C4×C22⋊D13—21no—
85#88178C2×C411yescharacteristic
86C2×#6099—21no—
87C2×#6099D411yescharacteristic
88C2×#6099D411yescharacteristic
89C2×#6094—21no—
90C2×C8×D13—21no—
91#88130—21no—
92#88129C2×C411yescharacteristic
93C4×D52C2311yescharacteristic
94#88126—21no—
95#88124C2×C411yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8C2311yescharacteristic
99C13×C4⋊C8C2311yescharacteristic
100C13×C22⋊C8—21no—
101C13×C22⋊C8—21no—
102C4×C8×C13—21no—
103C4×C8×C13C2311yescharacteristic
104C4×C8×C13C2311yescharacteristic
105#88075C2×C411yescharacteristic
106#88075C2×C411yescharacteristic
107#88075C2×C411yescharacteristic
108#88075C2×C411yescharacteristic
109C22⋊#1055C2×C411yescharacteristic
110C22⋊#1055C2×C411yescharacteristic
111#88060—21no—
112#88060—21no—
113#88055—21no—
114#88054—21no—
115#88054—21no—
116C8×Dic13—21no—
117#88050C2×C411yescharacteristic
118#88050C2×C411yescharacteristic
119#88049C2×C411yescharacteristic
120#88049C2×C411yescharacteristic
121#88048C2×C411yescharacteristic
122#88048C2×C411yescharacteristic
123#88047C2×C411yescharacteristic
124#88047C2×C411yescharacteristic
125C4⋊#1055—21no—
126C4⋊#1055—21no—
127C4⋊#1055—21no—
128C4⋊#1055—21no—
129C4⋊#1055—21no—
130C4⋊#1055C2×C411yescharacteristic
131C4⋊#1055C2×C411yescharacteristic
132C4⋊#1055C2311yescharacteristic
133C4⋊#1055C2311yescharacteristic
134#88043—21no—
135#88043—21no—
136#88043D411yescharacteristic
137#88043D411yescharacteristic
138C4×#1055—21no—
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18012—131nomaximal, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—22no—
147C2×Q8×C13—41no—
148C2×Q8×C13C22×C411yescharacteristic
149C2×Q8×C13C22×C411yescharacteristic
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13C22×C411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13#4111yescharacteristic
155C2×C22⋊D13—21no—
156C2×D52C22×C411yescharacteristic
157C2×C4×D13—21no—
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⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4C22×C411yescharacteristic
169C13×C4⋊C4C22×C411yescharacteristic
170C42×C13—21no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13C22×C411yescharacteristic
175C42×C13C2×D411yescharacteristic
176C42×C13#4111yescharacteristic
177C42×C13C2411yescharacteristic
178C22⋊Dic13—21no—
179#6107—22no—
180#6107—41no—
181#6106—22no—
182#6106—41no—
183#6103—21no—
184#6103—21no—
185#6103—21no—
186#6103—21no—
187C4⋊Dic13C22×C411yescharacteristic
188C4⋊Dic13C22×C411yescharacteristic
189#6101—21no—
190#6101—21no—
191#6101—21no—
192#6101—21no—
193C4×Dic13—21no—
194#6099—22no—
195#6099—41no—
196#6099—42no—
197C2×#1055—21no—
198C2×#1055—21no—
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#6094—42no—
208C8×D13—42no—
209#3108—131no—
210#2969—131no—
211Q8×M16—131no—
212#1593—131no—
213#1590—131no—
214#1587—131no—
215#1585—131no—
216#1584—131no—
217#1583—131no—
218SD16⋊C8—131no—
219C8×Q16—131no—
220#1574—131no—
221#1495—131no—
222#1479D1311yescharacteristic, complemented
223#1453—131no—
224C23×C13C4×D411yescharacteristic
225C22×D13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—42no—
230Q8×C13#13112yes—
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—21no—
239C2×C4×C13—41no—
240C2×C4×C13—42no—
241C2×C4×C13—81no—
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C23×C411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C22⋊D13—81no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252D52—21no—
253D52—21no—
254C4×D13—41no—
255C4×D13—41no—
256Dic26—21no—
257Dic26—21no—
258C8×C13—41no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13—41no—
262#1055—21no—
263#1055—21no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—21no—
269#1055—41no—
270#1055—41no—
271#1055#13712yes—
272#529—131no—
273C2×C4×Q8C2×D1311yescharacteristic
274#483—131no—
275#480—131no—
276#479—131no—
277#479—131no—
278#464—131no—
279#464—131no—
280#451—131no—
281#448—131no—
282#446—131no—
283#446—131no—
284#446—131no—
285#446—261no—
286#446—261no—
287C8×Q8—131no—
288C8×Q8—131no—
289C8×Q8—131no—
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294#436—131no—
295#436—261no—
296#435—261no—
297C8×D4—131no—
298#433—261no—
299#431—131no—
300#431C2×D1311yescharacteristic
301#431C2×D1311yescharacteristic
302#423—131no—
303#423—261no—
304#405—261no—
305C4×M16—131no—
306C4×M16—261no—
307#335—131no—
308#335—131no—
309#334—131no—
310#334—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8C2×D1311yescharacteristic
314Q8⋊C8C2×D1311yescharacteristic
315Q8⋊C8C2×D1311yescharacteristic
316Q8⋊C8C2×D1311yescharacteristic
317D4⋊C8—131no—
318D4⋊C8—131no—
319#322—131no—
320#322—131no—
321#322—131no—
322C82—131no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—21no—
326C22×C13C2×C4×D411yescharacteristic
327C2×D13—41no—
328C2×D13—41no—
329C2×D13—41no—
330C4×C13—21no—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13—41no—
338C4×C13C2×#13111yescharacteristic
339C4×C13#56811yescharacteristic
340C4×C13C2×#13711yescharacteristic
341C4×C13#57511yescharacteristic
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C22×Q8C4×D1311yescharacteristic
346C2×Q16—131no—
347C2×Q16—131no—
348C2×SD16—131no—
349C2×SD16—131no—
350C2×M16—131no—
351C2×M16—131no—
352C2×M16—261no—
353C2×M16—261no—
354C22×C8—261no—
355#126—261no—
356#125—131no—
357#124—131no—
358#123—261no—
359C22⋊Q8—131no—
360#121—131no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—131no—
364C4×Q8C4×D1311yescharacteristic
365C4×Q8C4×D1311yescharacteristic
366C4×Q8C22×D1311yescharacteristic
367C4×Q8C22×D1311yescharacteristic
368C4×D4—131no—
369C4×D4—261no—
370#117—261no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C4×D1311yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1311yescharacteristic
375#107—131no—
376#107—131no—
377#106—131no—
378#106—131no—
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⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8—261no—
391C4⋊C8C22×D1311yescharacteristic
392C4⋊C8C22×D1311yescharacteristic
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#103—131no—
399#102—131no—
400#102—131no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8—131no—
404C22⋊C8—131no—
405C22⋊C8—261no—
406C22⋊C8—261no—
407#97—131no—
408#97—131no—
409#97—261no—
410#97—261no—
411#97—261no—
412C4×C8—21no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—41no—
423C2×C13#293311yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295711yescharacteristic
426D13—81no—
427C2×Q8—21no—
428C2×Q8—22no—
429C2×Q8—41no—
430C2×Q8—131no—
431C2×Q8C2×C4×D1311yescharacteristic
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—131no—
434C2×D4—261no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—261no—
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4D4×D1311yescharacteristic
440C22×C4#612911yescharacteristic
441Q16—262no—
442Q16—521no—
443SD16—262no—
444SD16—521no—
445M16—262no—
446M16—522no—
447M16—521no—
448M16—522no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—131no—
456C2×C8—131no—
457C2×C8—131no—
458C2×C8—131no—
459C2×C8—131no—
460C2×C8—131no—
461C2×C8—261no—
462C2×C8—261no—
463C2×C8—522no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—131no—
470C4⋊C4—131no—
471C4⋊C4—261no—
472C4⋊C4—261no—
473C4⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4C2×C4×D1311yescharacteristic
476C4⋊C4C2×C4×D1311yescharacteristic
477C22⋊C4—261no—
478C22⋊C4—261no—
479C22⋊C4—261no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42D4×D1311yescharacteristic
489C42#612911yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1801211yescharacteristic, complemented, Sylow
492C23—261no—
493C23#8813511yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—42no—
498Q8—261no—
499Q8—261no—
500Q8#8815512yes—
501D4—261no—
502D4—261no—
503D4—1041no—
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—41no—
513C2×C4—42no—
514C2×C4—81no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—521no—
519C2×C4—521no—
520C2×C4#8813511yescharacteristic
521C2×C4#8813511yescharacteristic
522C2×C4#8813511yescharacteristic
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C2×D4×D1311yescharacteristic
525C2×C4C2×#612911yescharacteristic
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—132no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—261no—
536C8—261no—
537C8—261no—
538C8—521no—
539C8—521no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—521no—
544C22—521no—
545C22—521no—
546C22C2×#8813511yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4C2×#8815511yescharacteristic
559C4#1171945011yescharacteristic
560C4D13×#13711yescharacteristic
561C4#1171948211yescharacteristic
562C2—41no—
563C2—1041no—
564C2#1312355711yescharacteristic
565C2#1312365111yescharacteristic
566C2#1312374911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1479C2
socleC22×C13C2×C4×D4
prime radical#88184C2×C4
cosocleC42×C13C24
hypercenter#1479D13
hypocenterC13#18012
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
3. Q8×#6099C2semidirect
4. #13113742C2semidirect
5. #13113723C2semidirect
6. #13113704C2semidirect
7. #13113696C2semidirect
8. #13113689C2semidirect
9. #13113676C2semidirect
10. #13113651C2semidirect
11. #13113640C2semidirect
12. #13113624C2semidirect
14. #13113131C2semidirect
15. C13×#1479C2semidirect
222. #1479D13semidirect
491. C13#18012semidirect

Maximal subgroups

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

subgroupindex
#131249162
#131238342
Q8×#60992
#131137422
#131137232
#131137042
#131136962
#131136892
#131136762
#131136512
#131136402
#131136242
#131133022
#131131312
C13×#14792
#1801213