Finite Group Databasebeta

← #14738839

Subgroups — #14738839

Order 2816.

584 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#13079983C211yesmaximal, characteristic
2#13079643C211yesmaximal, characteristic
3#13077620C211yesmaximal, characteristic
4#13068131C211yesmaximal, characteristic, complemented
5#13068126C211yesmaximal, characteristic, complemented
6#13068119C211yesmaximal, characteristic, complemented
7#13068112C211yesmaximal, characteristic, complemented
8#13068007C211yesmaximal, characteristic, complemented
9#13068002C211yesmaximal, characteristic, complemented
10#13067995C211yesmaximal, characteristic, complemented
11#13067988C211yesmaximal, characteristic, complemented
12#13067383C211yesmaximal, characteristic, complemented
13#13067326C211yesmaximal, characteristic, complemented
14#13067288C211yesmaximal, characteristic, complemented
15C11×#3165C211yesmaximal, characteristic, complemented
16C11×#533C2211yescharacteristic
17C2×C11×C4⋊Q8C2211yescharacteristic
18#10623010C2211yescharacteristic
19C11×#501—21no—
20C11×#501—21no—
21C11×#500C2211yescharacteristic
22C11×#500C2211yescharacteristic
23C11×#498C2211yescharacteristic
24C11×#498C2211yescharacteristic
25C11×#428—21no—
26C11×#428—21no—
27C4×C11×M16C2211yescharacteristic
28#10622841—21no—
29#10622840—21no—
30#10622741—21no—
31#10622740—21no—
32#10622704C2211yescharacteristic
33#10622703C2211yescharacteristic
34#10622703C2211yescharacteristic
35#10622703C2211yescharacteristic
36#10622699—21no—
37#10622697C2211yescharacteristic
38#10622696C2211yescharacteristic
39#10622696C2211yescharacteristic
40#10622696C2211yescharacteristic
41#10622695—21no—
42#10622665—21no—
43#10622662—21no—
44#10622641—21no—
45#10622635—21no—
46#10622539C2211yescharacteristic
47#10622538C2211yescharacteristic
48#10622537C2211yescharacteristic
49#10622322—21no—
50#10622321—21no—
51#10622301C2211yescharacteristic
52C8×D44C2211yescharacteristic
53#10622292C2211yescharacteristic
54C8×Dic22C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622185C2211yescharacteristic
60#10622185C2211yescharacteristic
61#10622184C2211yescharacteristic
62#10622184C2211yescharacteristic
63#10622096C2211yescharacteristic
64#10622096C2211yescharacteristic
65#10622095C2211yescharacteristic
66#10622095C2211yescharacteristic
67C22×Q8×C11—21no—
68C2×C11×M16D411yescharacteristic
69C2×C11×M16D411yescharacteristic
70C11×C4⋊Q8—21no—
71C11×C4⋊Q8—21no—
72C11×C4⋊Q8—21no—
73C11×C4⋊Q8C2311yescharacteristic
74C11×C4⋊Q8C2311yescharacteristic
75C11×C4⋊Q8C2311yescharacteristic
76C11×C4⋊Q8C2311yescharacteristic
77C11×#125—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—21no—
80C4×Q8×C11—21no—
81C4×Q8×C11—21no—
82C11×#117—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×#4326—21no—
87C2×#4326—21no—
88C2×#4326—21no—
89C2×#4325—21no—
90C2×#4325—21no—
91C2×#4325—21no—
92#66983D411yescharacteristic
93#66982—21no—
94C4×C22⋊D11—21no—
95#66977D411yescharacteristic
96C2×#4318—21no—
97C2×#4313—21no—
98C2×C8×D11—21no—
99#66929—21no—
100#66928D411yescharacteristic
101C4×D44C2311yescharacteristic
102#66925—21no—
103#66923D411yescharacteristic
104C4×Dic22C2311yescharacteristic
105C11×#107—21no—
106C11×#107—21no—
107C11×#107—21no—
108C11×#107—21no—
109C11×#106—21no—
110C11×#106—21no—
111C11×#106—21no—
112C11×#106—21no—
113C11×#97D411yescharacteristic
114C11×#97D411yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66899—21no—
118#66899—21no—
119#66899—21no—
120#66899—21no—
121#66899—21no—
122#66899—21no—
123C22⋊(C11⋊C8)—21no—
124C22⋊(C11⋊C8)—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127#66879—21no—
128Dic11⋊C8—21no—
129Dic11⋊C8—21no—
130C8×Dic11—21no—
131#66874—21no—
132#66873—21no—
133#66872—21no—
134#66871—21no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2311yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142#66867—21no—
143C4×C11⋊C8—21no—
144#19378—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—41no—
150C2×Q8×C11—81no—
151C2×Q8×C11—81no—
152C22×C4×C11—41no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C2×C22⋊D11—21no—
157C2×D44C2×D411yescharacteristic
158C2×C4×D11—21no—
159C2×Dic22C2×D411yescharacteristic
160C11×M16—22no—
161C11×M16—22no—
162C2×C8×C11C2×D411yescharacteristic
163C2×C8×C11C2×D411yescharacteristic
164C2×C8×C11C2×D411yescharacteristic
165C2×C8×C11C2×D411yescharacteristic
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—41no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177C11×C4⋊C4—41no—
178C11×C22⋊C4—41no—
179C42×C11—41no—
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11#4111yescharacteristic
183C42×C11C2411yescharacteristic
184C22⋊Dic11—21no—
185#4326—81no—
186#4326—81no—
187#4326—81no—
188#4325—81no—
189#4325—81no—
190#4325—81no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—21no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195C4⋊Dic11C2×D411yescharacteristic
196C4⋊Dic11C2×D411yescharacteristic
197Dic11⋊C4—21no—
198Dic11⋊C4—21no—
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201C4×Dic11—21no—
202#4318—81no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209#4313—42no—
210C8×D11—42no—
211#3252—111no—
212#3218—111no—
213#3165D1111yescharacteristic, complemented
214#2969—111no—
215#1694—111no—
216#1693—111no—
217#1692—111no—
218#1691—111no—
219#1674—111no—
220#1673—111no—
221#1672—111no—
222#1671—111no—
223#1569—111no—
224#1554—111no—
225#1546—111no—
226C23×C11#12111yescharacteristic
227C22×D11—21no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—41no—
231Q8×C11—41no—
232Q8×C11—41no—
233Q8×C11—41no—
234Q8×C11—81no—
235Q8×C11—82no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—82no—
246C2×C4×C11#12111yescharacteristic
247C2×C4×C11#12111yescharacteristic
248C2×C4×C11#12111yescharacteristic
249C2×C4×C11C22×D411yescharacteristic
250C2×C4×C11C22×D411yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C22⋊D11—81no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256D44—21no—
257D44—21no—
258C4×D11—41no—
259C4×D11—41no—
260Dic22—21no—
261Dic22—21no—
262C8×C11—21no—
263C8×C11—21no—
264C8×C11#13712yes—
265C8×C11#13712yes—
266C11⋊C8—41no—
267C11⋊C8—41no—
268C11⋊C8—41no—
269C11⋊C8—41no—
270C11⋊C8—41no—
271C11⋊C8—41no—
272#533C2×D1111yescharacteristic
273C2×C4⋊Q8C2×D1111yescharacteristic
274#529—111no—
275#501—21no—
276#501—21no—
277#500C2×D1111yescharacteristic
278#500C2×D1111yescharacteristic
279#498C2×D1111yescharacteristic
280#498C2×D1111yescharacteristic
281#497—221no—
282#491—221no—
283#479—221no—
284#477—111no—
285#476—111no—
286#470—221no—
287#468—221no—
288#464—221no—
289#462—111no—
290#462—111no—
291#462—111no—
292#461—111no—
293#461—111no—
294#461—111no—
295#451—221no—
296#448—221no—
297#446—111no—
298C8×Q8—111no—
299#436—111no—
300#436—221no—
301#435—221no—
302C8×D4—111no—
303#433—221no—
304#432—111no—
305#431—111no—
306#428—21no—
307#428—21no—
308#423—111no—
309#405—221no—
310C4×M16C2×D1111yescharacteristic
311#335—111no—
312#335—111no—
313#334—111no—
314#334—111no—
315#333—111no—
316#333—111no—
317#332—111no—
318#332—111no—
319#332—111no—
320#332—111no—
321#332—111no—
322#332—111no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11C2×#12111yescharacteristic
327C2×D11—41no—
328C2×D11—41no—
329C2×D11—41no—
330C4×C11—21no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11C2×#13711yescharacteristic
339C4×C11C2×#13711yescharacteristic
340C4×C11#57611yescharacteristic
341C4×C11#57711yescharacteristic
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345C22×Q8—21no—
346C2×Q16—221no—
347C2×Q16—221no—
348C2×Q16—221no—
349C2×SD16—221no—
350C2×SD16—221no—
351C2×SD16—221no—
352C2×M16—221no—
353C2×M16—221no—
354C2×M16C22⋊D1111yescharacteristic
355C2×M16C22⋊D1111yescharacteristic
356C22×C8—221no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8C22×D1111yescharacteristic
361C4⋊Q8C22×D1111yescharacteristic
362C4⋊Q8C22×D1111yescharacteristic
363C4⋊Q8C22×D1111yescharacteristic
364#126—221no—
365#125—21no—
366#125—111no—
367#124—111no—
368#123—221no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—111no—
372#121—111no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—111no—
376C4×D4—111no—
377C4×D4—221no—
378#117—21no—
379#117—221no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C42C22×D1111yescharacteristic
383#107—21no—
384#107—21no—
385#107—21no—
386#107—21no—
387#107—221no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
392#106—221no—
393C4⋊C8—111no—
394C4⋊C8—111no—
395C4⋊C8—111no—
396C4⋊C8—111no—
397C4⋊C8—111no—
398C4⋊C8—111no—
399C4⋊C8—221no—
400C4⋊C8—221no—
401C4⋊C8—221no—
402#103—221no—
403#103—221no—
404#103—221no—
405#103—221no—
406#103—221no—
407#103—221no—
408#103—221no—
409#102—221no—
410C22⋊C8—221no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414#97—221no—
415#97—221no—
416#97C22⋊D1111yescharacteristic
417#97C22⋊D1111yescharacteristic
418C4×C8—221no—
419C4×C8—221no—
420C4×C8C22×D1111yescharacteristic
421C4×C8C22×D1111yescharacteristic
422C2×C11—41no—
423C2×C11#303911yescharacteristic
424C2×C11#306211yescharacteristic
425C2×C11#306911yescharacteristic
426D11—81no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—81no—
433C2×Q8—81no—
434C2×Q8—111no—
435C2×D4—111no—
436C2×D4—221no—
437C22×C4—41no—
438C22×C4—221no—
439C22×C4D4×D1111yescharacteristic
440C22×C4#434111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442Q16—881no—
443Q16—881no—
444Q16—881no—
445SD16—881no—
446SD16—881no—
447SD16—881no—
448M16—22no—
449M16—22no—
450M16—442no—
451M16—881no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—442no—
459C2×C8C2×C22⋊D1111yescharacteristic
460C2×C8C2×C22⋊D1111yescharacteristic
461C2×C8C2×C22⋊D1111yescharacteristic
462C2×C8C2×C22⋊D1111yescharacteristic
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—111no—
476C4⋊C4—111no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C22⋊C4—41no—
482C22⋊C4—221no—
483C22⋊C4—221no—
484C22⋊C4—221no—
485C22⋊C4—221no—
486C22⋊C4—221no—
487C42—41no—
488C42—221no—
489C42D4×D1111yescharacteristic
490C42#434111yescharacteristic
491C42C2×C22⋊D1111yescharacteristic
492C42C23×D1111yescharacteristic
493C11#1937811yescharacteristic, complemented, Sylow
494C23—221no—
495C23#6699111yescharacteristic
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503Q8—82no—
504Q8—221no—
505Q8—221no—
506D4—221no—
507D4—221no—
508D4—881no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—82no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4#6699111yescharacteristic
525C2×C4#6699111yescharacteristic
526C2×C4#6699111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—21no—
531C8—21no—
532C8—441no—
533C8—441no—
534C8—441no—
535C8—441no—
536C8—441no—
537C8—441no—
538C8#6699512yes—
539C8#6699512yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—441no—
544C22—441no—
545C22—441no—
546C22C2×#6699111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—81no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—441no—
556C4—441no—
557C4—441no—
558C4#1062330511yescharacteristic
559C4#1062330611yescharacteristic
560C4C2×#6699511yescharacteristic
561C4C2×#6699511yescharacteristic
562C2—41no—
563C2—881no—
564C2#1307809911yescharacteristic
565C2#1307829011yescharacteristic
566C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3165C2
socleC22×C11C2×#121
prime radical#66983D4
hypercenter#3165D11
hypocenterC11#19378
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
4. #13068131C2semidirect
5. #13068126C2semidirect
6. #13068119C2semidirect
7. #13068112C2semidirect
8. #13068007C2semidirect
9. #13068002C2semidirect
10. #13067995C2semidirect
11. #13067988C2semidirect
12. #13067383C2semidirect
13. #13067326C2semidirect
14. #13067288C2semidirect
15. C11×#3165C2semidirect
213. #3165D11semidirect
493. C11#19378semidirect

Maximal subgroups

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

subgroupindex
#130799832
#130796432
#130776202
#130681312
#130681262
#130681192
#130681122
#130680072
#130680022
#130679952
#130679882
#130673832
#130673262
#130672882
C11×#31652
#1937811