Finite Group Databasebeta

← #15834784

Subgroups — #15834784

Order 3328.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125443C211yesmaximal, characteristic
2#13123783C211yesmaximal, characteristic, complemented
3#13113738C211yesmaximal, characteristic, complemented
4#13113731C211yesmaximal, characteristic, complemented
5#13113712C211yesmaximal, characteristic, complemented
6#13113707C211yesmaximal, characteristic, complemented
7#13113684C211yesmaximal, characteristic, complemented
8#13113672C211yesmaximal, characteristic, complemented
9#13113653C211yesmaximal, characteristic, complemented
10C8×#6105C211yesmaximal, characteristic, complemented
11#13113589C211yesmaximal, characteristic, complemented
12#13113256C211yesmaximal, characteristic, complemented
13#13113249C211yesmaximal, characteristic
14#13113139C211yesmaximal, characteristic, complemented
15C13×#2969C211yesmaximal, characteristic
16C13×#529C2211yescharacteristic
17#11719175C2211yescharacteristic
18C13×#446C2211yescharacteristic
19C8×Q8×C13C2211yescharacteristic
20C13×#436—21no—
21C13×#436C2211yescharacteristic
22C13×#435—21no—
23C8×D4×C13C2211yescharacteristic
24C13×#433—21no—
25C13×#431C2211yescharacteristic
26C13×#405—21no—
27C4×C13×M16C2211yescharacteristic
28#11718783—21no—
29#11718780—21no—
30#11718730C411yescharacteristic
31#11718726C411yescharacteristic
32#11718721C411yescharacteristic
33#11718716C411yescharacteristic
34#11718713C411yescharacteristic
35#11718713C411yescharacteristic
36#11718703C411yescharacteristic
37#11718703C411yescharacteristic
38C4×#6107C2211yescharacteristic
39C4×#6107C2211yescharacteristic
40C4×#6105C2211yescharacteristic
41C4×#6105C2211yescharacteristic
42C2×C4⋊#1055C2211yescharacteristic
43C4×#6099C2211yescharacteristic
44C4×#6099C2211yescharacteristic
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×M16—21no—
68C2×C13×M16D411yescharacteristic
69C2×C13×M16D411yescharacteristic
70C22×C8×C13—21no—
71C13×#126—21no—
72C13×#125C2×C411yescharacteristic
73C13×#124C2×C411yescharacteristic
74C13×#123—21no—
75C13×C22⋊Q8C2×C411yescharacteristic
76C13×#121C2×C411yescharacteristic
77C4×Q8×C13C2311yescharacteristic
78C4×D4×C13—21no—
79C4×D4×C13C2311yescharacteristic
80C13×#117—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
90C2×#6099—21no—
91C2×#6099C2×C411yescharacteristic
92C2×#6099C2×C411yescharacteristic
93C22×#1055—21no—
94#88124—21no—
95#88123C2×C411yescharacteristic
96#88123C2×C411yescharacteristic
97C4×Dic26—21no—
98C4×Dic26C2311yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8—21no—
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×#97—21no—
108C13×#97D411yescharacteristic
109C13×#97D411yescharacteristic
110C4×C8×C13—21no—
111C4×C8×C13—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88075C2×C411yescharacteristic
115#88075C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117#88072C2×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⋊#1055C2311yescharacteristic
136C4⋊#1055C2311yescharacteristic
137#88043—21no—
138#88043C2×C411yescharacteristic
139#88043C2×C411yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18077—131nomaximal, Sylow
145C2×Q8×C13C22×C411yescharacteristic
146C2×D4×C13—21no—
147C2×D4×C13C22×C411yescharacteristic
148C22×C4×C13—21no—
149C22×C4×C13C22×C411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13#4111yescharacteristic
152C2×Dic26—21no—
153C2×Dic26C22×C411yescharacteristic
154C2×Dic26C22×C411yescharacteristic
155C13×M16—22no—
156C13×M16—41no—
157C13×M16—42no—
158C2×C8×C13—21no—
159C2×C8×C13—21no—
160C2×C8×C13—42no—
161C2×C8×C13C2×D411yescharacteristic
162C2×C8×C13C2×D411yescharacteristic
163C2×C8×C13C2×D411yescharacteristic
164C2×C8×C13C2×D411yescharacteristic
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4C22×C411yescharacteristic
170C13×C4⋊C4C22×C411yescharacteristic
171C13×C22⋊C4—21no—
172C13×C22⋊C4—21no—
173C13×C22⋊C4—21no—
174C13×C22⋊C4—21no—
175C13×C22⋊C4—21no—
176C42×C13—21no—
177C42×C13C22×C411yescharacteristic
178C42×C13C2×D411yescharacteristic
179C42×C13#4111yescharacteristic
180C42×C13C2411yescharacteristic
181C22⋊Dic13—21no—
182C22⋊Dic13—21no—
183#6107—22no—
184#6107—41no—
185#6105—22no—
186#6105—41no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13C22×C411yescharacteristic
191C4⋊Dic13C22×C411yescharacteristic
192#6101—21no—
193#6101—21no—
194#6101—21no—
195#6101—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198#6099—22no—
199#6099—41no—
200#6099—42no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—42no—
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210#3172—131no—
211#2969D1311yescharacteristic
212#2962—131no—
213#1592—131no—
214#1591—131no—
215#1588—131no—
216#1587—131no—
217#1584—131no—
218#1582—131no—
219#1579—131no—
220C8×SD16—131no—
221#1565—131no—
222#1485—131no—
223#1483—131no—
224#1455—131no—
225C23×C13—21no—
226C23×C13C4×D411yescharacteristic
227Q8×C13—21no—
228Q8×C13—21no—
229D4×C13—21no—
230D4×C13—21no—
231D4×C13—81no—
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—41no—
241C2×C4×C13—41no—
242C2×C4×C13C4×D411yescharacteristic
243C2×C4×C13C4×D411yescharacteristic
244C2×C4×C13C4×D411yescharacteristic
245C2×C4×C13C23×C411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C2×#4111yescharacteristic
248C2×Dic13—21no—
249C2×Dic13—21no—
250C2×Dic13—21no—
251C2×Dic13—21no—
252Dic26—21no—
253Dic26—21no—
254Dic26—21no—
255Dic26—21no—
256Dic26—81no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13#13712yes—
263#1055—22no—
264#1055—21no—
265#1055—21no—
266#1055—21no—
267#1055—41no—
268#1055—41no—
269#1055—41no—
270#1055#13112yes—
271#533—131no—
272#529C2×D1311yescharacteristic
273#501—131no—
274#497—131no—
275#491—131no—
276#489—131no—
277#470—131no—
278#470—131no—
279#468—131no—
280#468—131no—
281#446—131no—
282#446—131no—
283#446—261no—
284#446—261no—
285#446C2×D1311yescharacteristic
286C8×Q8—131no—
287C8×Q8—131no—
288C8×Q8C2×D1311yescharacteristic
289C4×Q16—131no—
290C4×Q16—131no—
291C4×SD16—131no—
292C4×SD16—131no—
293#436—21no—
294#436C2×D1311yescharacteristic
295#435—21no—
296C8×D4C2×D1311yescharacteristic
297#433—21no—
298#431C2×D1311yescharacteristic
299#424—261no—
300C2×C4⋊C8—131no—
301#405—21no—
302#405—261no—
303C4×M16—131no—
304C4×M16—131no—
305C4×M16C2×D1311yescharacteristic
306#335—131no—
307#335—131no—
308#334—131no—
309#334—131no—
310Q8⋊C8—131no—
311Q8⋊C8—131no—
312Q8⋊C8—131no—
313Q8⋊C8—131no—
314Q8⋊C8—131no—
315Q8⋊C8—131no—
316D4⋊C8—131no—
317D4⋊C8—131no—
318#322—131no—
319#322—131no—
320#322—131no—
321C82—131no—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13C2×C4×D411yescharacteristic
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—41no—
336C4×C13C2×#13111yescharacteristic
337C4×C13#56811yescharacteristic
338C4×C13C2×#13711yescharacteristic
339C4×C13#57511yescharacteristic
340Dic13—41no—
341Dic13—41no—
342Dic13—41no—
343Dic13—41no—
344C2×Q16—131no—
345C2×Q16—131no—
346C2×SD16—131no—
347C2×SD16—131no—
348C2×M16—21no—
349C2×M16—131no—
350C2×M16—131no—
351C2×M16—261no—
352C2×M16C22⋊D1311yescharacteristic
353C2×M16C22⋊D1311yescharacteristic
354C22×C8—21no—
355C22×C8—261no—
356C4⋊Q8—131no—
357C4⋊Q8—131no—
358#126—21no—
359#125—261no—
360#125C4×D1311yescharacteristic
361#124C4×D1311yescharacteristic
362#123—21no—
363C22⋊Q8—131no—
364C22⋊Q8—131no—
365C22⋊Q8—261no—
366C22⋊Q8C4×D1311yescharacteristic
367#121C4×D1311yescharacteristic
368C4×Q8—131no—
369C4×Q8—131no—
370C4×Q8—261no—
371C4×Q8C22×D1311yescharacteristic
372C4×D4—21no—
373C4×D4C22×D1311yescharacteristic
374#117—21no—
375#117—261no—
376C2×C42C22×D1311yescharacteristic
377#107—131no—
378#107—131no—
379#106—131no—
380#106—131no—
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—131no—
384C4⋊C8—131no—
385C4⋊C8—261no—
386C4⋊C8—261no—
387C4⋊C8—261no—
388C4⋊C8—261no—
389C4⋊C8—261no—
390C4⋊C8C22×D1311yescharacteristic
391C4⋊C8C22×D1311yescharacteristic
392#103—131no—
393#103—131no—
394#103—131no—
395#103—131no—
396#103—131no—
397#103—131no—
398#102—131no—
399#102—131no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403#97—21no—
404#97—131no—
405#97—131no—
406#97—261no—
407#97—261no—
408#97—261no—
409#97C22⋊D1311yescharacteristic
410#97C22⋊D1311yescharacteristic
411C4×C8—21no—
412C4×C8—21no—
413C4×C8—131no—
414C4×C8—131no—
415C4×C8—131no—
416C4×C8—131no—
417C4×C8—261no—
418C4×C8—261no—
419C4×C8C22×D1311yescharacteristic
420C4×C8C22×D1311yescharacteristic
421C2×C13—41no—
422C2×C13—81no—
423C2×C13#293511yescharacteristic
424C2×C13C4×#13711yescharacteristic
425C2×C13#295611yescharacteristic
426C2×Q8—131no—
427C2×Q8—131no—
428C2×Q8—261no—
429C2×Q8C2×C4×D1311yescharacteristic
430C2×D4—21no—
431C2×D4C2×C4×D1311yescharacteristic
432C22×C4—21no—
433C22×C4C2×C4×D1311yescharacteristic
434C22×C4#612711yescharacteristic
435C22×C4C2×C22⋊D1311yescharacteristic
436Q16—262no—
437Q16—521no—
438SD16—262no—
439SD16—521no—
440M16—22no—
441M16—41no—
442M16—42no—
443M16—262no—
444M16—521no—
445M16—522no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—42no—
449C2×C8—131no—
450C2×C8—131no—
451C2×C8—131no—
452C2×C8—131no—
453C2×C8—261no—
454C2×C8—261no—
455C2×C8—261no—
456C2×C8—261no—
457C2×C8—522no—
458C2×C8C2×C22⋊D1311yescharacteristic
459C2×C8C2×C22⋊D1311yescharacteristic
460C2×C8C2×C22⋊D1311yescharacteristic
461C2×C8C2×C22⋊D1311yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
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—21no—
481C22⋊C4—21no—
482C22⋊C4—261no—
483C22⋊C4—261no—
484C42—21no—
485C42—261no—
486C42—261no—
487C42C2×C4×D1311yescharacteristic
488C42#612711yescharacteristic
489C42C2×C22⋊D1311yescharacteristic
490C42C23×D1311yescharacteristic
491C13#1807711yescharacteristic, complemented, Sylow
492C23—21no—
493C23C4×C22⋊D1311yescharacteristic
494Q8—21no—
495Q8—21no—
496Q8—261no—
497Q8—261no—
498Q8—261no—
499Q8—261no—
500Q8—1041no—
501D4—21no—
502D4—21no—
503D4—81no—
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—41no—
513C2×C4—41no—
514C2×C4—261no—
515C2×C4—261no—
516C2×C4—261no—
517C2×C4—261no—
518C2×C4C4×C22⋊D1311yescharacteristic
519C2×C4C4×C22⋊D1311yescharacteristic
520C2×C4C4×C22⋊D1311yescharacteristic
521C2×C4C22×C4×D1311yescharacteristic
522C2×C4C2×#612711yescharacteristic
523C2×C4C22×C22⋊D1311yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—41no—
528C8—41no—
529C8—132no—
530C8—262no—
531C8—261no—
532C8—261no—
533C8—261no—
534C8—521no—
535C8—521no—
536C8—521no—
537C8#8820512yes—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22C2×C4×C22⋊D1311yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—521no—
553C4—521no—
554C4—521no—
555C4—521no—
556C4D13×#13111yescharacteristic
557C4#1171945511yescharacteristic
558C4#1171952711yescharacteristic
559C4C2×#8820511yescharacteristic
560C2—41no—
561C2—81no—
562C2#1312357811yescharacteristic
563C2C4×#8820511yescharacteristic
564C2#1312374311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2969C2
socleC22×C13C2×C4×D4
prime radicalC13×#121C2×C4
cosocleC42×C13C24
hypercenter#2969D13
hypocenterC13#18077
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #13123783C2semidirect
3. #13113738C2semidirect
4. #13113731C2semidirect
5. #13113712C2semidirect
6. #13113707C2semidirect
7. #13113684C2semidirect
8. #13113672C2semidirect
9. #13113653C2semidirect
10. C8×#6105C2semidirect
11. #13113589C2semidirect
12. #13113256C2semidirect
14. #13113139C2semidirect
491. C13#18077semidirect

Maximal subgroups

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

subgroupindex
#131254432
#131237832
#131137382
#131137312
#131137122
#131137072
#131136842
#131136722
#131136532
C8×#61052
#131135892
#131132562
#131132492
#131131392
C13×#29692
#1807713