Finite Group Databasebeta

← #15834060

Subgroups — #15834060

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#13124907C211yesmaximal, characteristic
2#13123783C211yesmaximal, characteristic, complemented
3#13113738C211yesmaximal, characteristic, complemented
4#13113724C211yesmaximal, characteristic, complemented
5#13113712C211yesmaximal, characteristic, complemented
6#13113707C211yesmaximal, characteristic, complemented
7#13113686C211yesmaximal, characteristic, complemented
8#13113677C211yesmaximal, characteristic, complemented
9#13113653C211yesmaximal, characteristic, complemented
10C8×#6107C211yesmaximal, characteristic, complemented
11#13113622C211yesmaximal, characteristic, complemented
12#13113308C211yesmaximal, characteristic, complemented
13#13113223C211yesmaximal, characteristic
14#13113133C211yesmaximal, characteristic, complemented
15C13×#2971C211yesmaximal, characteristic
16C4×C13×#41C2211yescharacteristic
17#11719175C2211yescharacteristic
18C8×Q8×C13C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436—21no—
21C13×#436—21no—
22C13×#436C2211yescharacteristic
23C13×#436C2211yescharacteristic
24C13×#432—21no—
25C13×#432C2211yescharacteristic
26C4×C13×M16—21no—
27C4×C13×M16C2211yescharacteristic
28#11718900C411yescharacteristic
29#11718900C411yescharacteristic
30#11718783—21no—
31#11718780—21no—
32#11718692C411yescharacteristic
33C4×#6107C2211yescharacteristic
34C4×#6107C2211yescharacteristic
35#11718681C411yescharacteristic
36#11718680C411yescharacteristic
37C4×#6105C2211yescharacteristic
38C4×#6105C2211yescharacteristic
39#11718668C411yescharacteristic
40#11718657C411yescharacteristic
41#11718657C411yescharacteristic
42#11718586C2211yescharacteristic
43#11718586C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718362—21no—
46#11718362—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#11718047C2211yescharacteristic
64#11718046C2211yescharacteristic
65#11718046C2211yescharacteristic
66C8×#1055C2211yescharacteristic
67C2×C13×#41C2×C411yescharacteristic
68C2×C13×M16—21no—
69C2×C13×M16—21no—
70C2×C13×M16D411yescharacteristic
71C2×C13×M16D411yescharacteristic
72C4×Q8×C13C2×C411yescharacteristic
73C4×Q8×C13C2311yescharacteristic
74C4×D4×C13—21no—
75C4×D4×C13—21no—
76C4×D4×C13C2×C411yescharacteristic
77C4×D4×C13C2311yescharacteristic
78C13×#117—21no—
79C13×#117C2×C411yescharacteristic
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6107C2×C411yescharacteristic
83C2×#6107C2×C411yescharacteristic
84C2×#6105C2×C411yescharacteristic
85C2×#6105C2×C411yescharacteristic
86#88180—21no—
87#88178—21no—
88#88178C2×C411yescharacteristic
89#88178C2×C411yescharacteristic
90C22×#1055—21no—
91#88124—21no—
92#88123C2×C411yescharacteristic
93#88123C2×C411yescharacteristic
94C4×Dic26—21no—
95C4×Dic26C2311yescharacteristic
96C4×Dic26C2311yescharacteristic
97C13×C4⋊C8—21no—
98C13×C4⋊C8—21no—
99C13×C4⋊C8C2311yescharacteristic
100C13×C4⋊C8C2311yescharacteristic
101C13×C22⋊C8—21no—
102C13×C22⋊C8—21no—
103C13×C22⋊C8—21no—
104C13×#97—21no—
105C13×#97D411yescharacteristic
106C13×#97D411yescharacteristic
107C4×C8×C13—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⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18013—131nomaximal, Sylow
145C13×#41—22no—
146C13×#41—41no—
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
159C13×M16—22no—
160C13×M16—41no—
161C13×M16—42no—
162C13×M16—42no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13C2×D411yescharacteristic
166C2×C8×C13C2×D411yescharacteristic
167C2×C8×C13C2×D411yescharacteristic
168C2×C8×C13C2×D411yescharacteristic
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4C22×C411yescharacteristic
172C13×C4⋊C4C22×C411yescharacteristic
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13C22×C411yescharacteristic
180C42×C13C2×D411yescharacteristic
181C42×C13#4111yescharacteristic
182C42×C13C2411yescharacteristic
183C22⋊Dic13—21no—
184C22⋊Dic13—21no—
185#6107—22no—
186#6107—22no—
187#6105—41no—
188#6105—41no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13C22×C411yescharacteristic
193C4⋊Dic13C22×C411yescharacteristic
194#6101—21no—
195#6101—21no—
196#6101—21no—
197#6101—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—42no—
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209#3107—131no—
210#2971D1311yescharacteristic
211#2962—131no—
212#1592—131no—
213#1590—131no—
214#1588—131no—
215#1587—131no—
216#1584—131no—
217#1583—131no—
218#1579—131no—
219C8×Q16—131no—
220#1573—131no—
221#1497—131no—
222#1477—131no—
223#1453—131no—
224C23×C13—21no—
225C23×C13C4×D411yescharacteristic
226Q8×C13—21no—
227Q8×C13#13112yes—
228D4×C13—21no—
229D4×C13—21no—
230D4×C13—42no—
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—42no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—81no—
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C4×D411yescharacteristic
246C2×C4×C13C23×C411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×C4×C13C2×#4111yescharacteristic
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252C2×Dic13—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—21no—
257Dic26—81no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13#13712yes—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—21no—
268#1055—41no—
269#1055—41no—
270#1055—41no—
271#1055—41no—
272#533—131no—
273C4×#41C2×D1311yescharacteristic
274#485—131no—
275#485—131no—
276#475—131no—
277#474—131no—
278#462—131no—
279#461—131no—
280#452—131no—
281#452—131no—
282#446—131no—
283#446—131no—
284#446—261no—
285#446—261no—
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C8×Q8C2×D1311yescharacteristic
290C4×Q16—131no—
291C4×Q16—131no—
292C4×SD16—131no—
293C4×SD16—131no—
294#436—21no—
295#436—21no—
296#436C2×D1311yescharacteristic
297#436C2×D1311yescharacteristic
298#432—21no—
299#432C2×D1311yescharacteristic
300#431—131no—
301#431—131no—
302#424—261no—
303C2×C4⋊C8—131no—
304#405—261no—
305C4×M16—21no—
306C4×M16C2×D1311yescharacteristic
307#335—131no—
308#335—131no—
309#334—131no—
310#334—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316Q8⋊C8—131no—
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×C13—41no—
327C22×C13—41no—
328C22×C13—41no—
329C22×C13C2×C4×D411yescharacteristic
330C4×C13—21no—
331C4×C13—22no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—41no—
336C4×C13—41no—
337C4×C13C2×#13111yescharacteristic
338C4×C13#56811yescharacteristic
339C4×C13C2×#13711yescharacteristic
340C4×C13#57511yescharacteristic
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344Dic13—41no—
345C2×#41C4×D1311yescharacteristic
346C2×Q16—131no—
347C2×Q16—131no—
348C2×SD16—131no—
349C2×SD16—131no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16C22⋊D1311yescharacteristic
353C2×M16C22⋊D1311yescharacteristic
354C22×C8—261no—
355C4⋊Q8—131no—
356C4⋊Q8—131no—
357#125—261no—
358C22⋊Q8—131no—
359C22⋊Q8—131no—
360C22⋊Q8—261no—
361C4×Q8—131no—
362C4×Q8—131no—
363C4×Q8—261no—
364C4×Q8C4×D1311yescharacteristic
365C4×Q8C22×D1311yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C4×D1311yescharacteristic
369C4×D4C22×D1311yescharacteristic
370#117—21no—
371#117—261no—
372#117C4×D1311yescharacteristic
373C2×C42—21no—
374C2×C42C22×D1311yescharacteristic
375#107—131no—
376#107—131no—
377#106—131no—
378#106—131no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—131no—
382C4⋊C8—131no—
383C4⋊C8—131no—
384C4⋊C8—131no—
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—21no—
404C22⋊C8—131no—
405C22⋊C8—131no—
406C22⋊C8—261no—
407#97—21no—
408#97—261no—
409#97—261no—
410#97C22⋊D1311yescharacteristic
411#97C22⋊D1311yescharacteristic
412C4×C8—21no—
413C4×C8—21no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—131no—
418C4×C8—261no—
419C4×C8—261no—
420C4×C8C22×D1311yescharacteristic
421C4×C8C22×D1311yescharacteristic
422C2×C13—41no—
423C2×C13—81no—
424C2×C13#293311yescharacteristic
425C2×C13C4×#13711yescharacteristic
426C2×C13#295711yescharacteristic
427#41—22no—
428#41—41no—
429C2×Q8—131no—
430C2×Q8—131no—
431C2×Q8—261no—
432C2×Q8C2×C4×D1311yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D1311yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4C2×C4×D1311yescharacteristic
439C22×C4#612711yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441Q16—262no—
442Q16—262no—
443SD16—521no—
444SD16—521no—
445M16—22no—
446M16—41no—
447M16—42no—
448M16—42no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—131no—
454C2×C8—131no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—261no—
458C2×C8—261no—
459C2×C8—522no—
460C2×C8C2×C22⋊D1311yescharacteristic
461C2×C8C2×C22⋊D1311yescharacteristic
462C2×C8C2×C22⋊D1311yescharacteristic
463C2×C8C2×C22⋊D1311yescharacteristic
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⋊C4—261no—
474C4⋊C4—261no—
475C4⋊C4C2×C4×D1311yescharacteristic
476C4⋊C4C2×C4×D1311yescharacteristic
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—261no—
481C22⋊C4—261no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42#612711yescharacteristic
489C42C2×C22⋊D1311yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1801311yescharacteristic, complemented, Sylow
492C23—21no—
493C23C4×C22⋊D1311yescharacteristic
494Q8—21no—
495Q8—261no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—1041no—
500Q8#8816112yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4—261no—
519C2×C4—261no—
520C2×C4C4×C22⋊D1311yescharacteristic
521C2×C4C4×C22⋊D1311yescharacteristic
522C2×C4C4×C22⋊D1311yescharacteristic
523C2×C4C22×C4×D1311yescharacteristic
524C2×C4C2×#612711yescharacteristic
525C2×C4C22×C22⋊D1311yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—261no—
535C8—521no—
536C8—521no—
537C8—521no—
538C8—521no—
539C8#8820512yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C4×C22⋊D1311yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—22no—
552C4—41no—
553C4—41no—
554C4—521no—
555C4—521no—
556C4—521no—
557C4—521no—
558C4C2×#8816111yescharacteristic
559C4#1171945011yescharacteristic
560C4#1171952711yescharacteristic
561C4C2×#8820511yescharacteristic
562C2—41no—
563C2—81no—
564C2#1312356111yescharacteristic
565C2C4×#8820511yescharacteristic
566C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2971C2
socleC22×C13C2×C4×D4
prime radicalC2×C13×#41C2×C4
cosocleC42×C13C24
hypercenter#2971D13
hypocenterC13#18013
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2971

Complements

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

NH ≅ G/Ntype
2. #13123783C2semidirect
3. #13113738C2semidirect
4. #13113724C2semidirect
5. #13113712C2semidirect
6. #13113707C2semidirect
7. #13113686C2semidirect
8. #13113677C2semidirect
9. #13113653C2semidirect
10. C8×#6107C2semidirect
11. #13113622C2semidirect
12. #13113308C2semidirect
14. #13113133C2semidirect
491. C13#18013semidirect

Maximal subgroups

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

subgroupindex
#131249072
#131237832
#131137382
#131137242
#131137122
#131137072
#131136862
#131136772
#131136532
C8×#61072
#131136222
#131133082
#131132232
#131131332
C13×#29712
#1801313