Finite Group Databasebeta

← #14738804

Subgroups — #14738804

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079826C211yesmaximal, characteristic
2#13079357C211yesmaximal, characteristic
3#13077565C211yesmaximal, characteristic
4#13068196C211yesmaximal, characteristic, complemented
5#13068172C211yesmaximal, characteristic, complemented
6#13068120C211yesmaximal, characteristic, complemented
7#13068108C211yesmaximal, characteristic, complemented
8#13068072C211yesmaximal, characteristic, complemented
9#13068048C211yesmaximal, characteristic, complemented
10#13067996C211yesmaximal, characteristic, complemented
11#13067984C211yesmaximal, characteristic, complemented
12#13067381C211yesmaximal, characteristic
13#13067316C211yesmaximal, characteristic
14#13067307C211yesmaximal, characteristic
15C11×#3255C211yesmaximal, characteristic
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18#10623001C2211yescharacteristic
19C11×#475—21no—
20C11×#475C2211yescharacteristic
21C11×#475C2211yescharacteristic
22C11×#470—21no—
23C11×#470—21no—
24C11×#462—21no—
25C11×#462C2211yescharacteristic
26C11×#462C2211yescharacteristic
27C11×#423C2211yescharacteristic
28#10622706C2211yescharacteristic
29#10622705C2211yescharacteristic
30#10622695—21no—
31#10622694C2211yescharacteristic
32#10622693—21no—
33#10622692C2211yescharacteristic
34#10622665—21no—
35#10622665—21no—
36#10622658—21no—
37#10622658—21no—
38#10622643—21no—
39#10622643—21no—
40#10622637—21no—
41#10622637—21no—
42#10622637C2211yescharacteristic
43#10622637C2211yescharacteristic
44Q8×C11⋊C8C2211yescharacteristic
45Q8×C11⋊C8C2211yescharacteristic
46#10622634C2211yescharacteristic
47#10622634C2211yescharacteristic
48#10622633C2211yescharacteristic
49#10622633C2211yescharacteristic
50#10622612—21no—
51#10622610—21no—
52#10622539C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C4×#4318C2211yescharacteristic
55#10622185C2211yescharacteristic
56#10622185C2211yescharacteristic
57#10622185C2211yescharacteristic
58#10622185C2211yescharacteristic
59#10622124C2211yescharacteristic
60#10622124C2211yescharacteristic
61#10622119C2211yescharacteristic
62#10622119C2211yescharacteristic
63#10622118C2211yescharacteristic
64#10622118C2211yescharacteristic
65#10622117C2211yescharacteristic
66#10622117C2211yescharacteristic
67C2×C11×Q16—21no—
68C2×C11×Q16—21no—
69C2×C11×M16—21no—
70C11×C4⋊Q8D411yescharacteristic
71C11×C4⋊Q8D411yescharacteristic
72C11×C4⋊Q8C2311yescharacteristic
73C11×C4⋊Q8C2311yescharacteristic
74C11×#125—21no—
75C11×#125—21no—
76C11×C22⋊Q8—21no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8D411yescharacteristic
80C11×C22⋊Q8D411yescharacteristic
81C4×Q8×C11—21no—
82C4×Q8×C11—21no—
83C4×Q8×C11—21no—
84C4×Q8×C11C2311yescharacteristic
85C4×Q8×C11C2311yescharacteristic
86C11×#117—21no—
87C11×#117—21no—
88C2×C42×C11C2311yescharacteristic
89C2×#4326—21no—
90C2×#4326—21no—
91#66979—21no—
92#66977—21no—
93#66977—21no—
94C2×#4318D411yescharacteristic
95C2×#4318D411yescharacteristic
96C22×C11⋊C8—21no—
97#66923—21no—
98#66922C2311yescharacteristic
99#66922C2311yescharacteristic
100C4×Dic22—21no—
101C4×Dic22—21no—
102C11×#106—21no—
103C11×#106—21no—
104C11×C4⋊C8—21no—
105C11×C4⋊C8C2311yescharacteristic
106C11×C4⋊C8C2311yescharacteristic
107C11×#103—21no—
108C11×#103—21no—
109C11×#103—21no—
110C11×#103—21no—
111#66899—21no—
112#66899—21no—
113#66899—21no—
114#66899—21no—
115#66899—21no—
116#66899—21no—
117C22⋊(C11⋊C8)—21no—
118#66874—21no—
119#66874—21no—
120#66872—21no—
121#66872—21no—
122#66872—21no—
123#66872—21no—
124#66871—21no—
125#66871—21no—
126C4⋊(C11⋊C8)—21no—
127C4⋊(C11⋊C8)—21no—
128C4⋊(C11⋊C8)—21no—
129C4⋊(C11⋊C8)—21no—
130C4⋊(C11⋊C8)—21no—
131C4⋊(C11⋊C8)C2311yescharacteristic
132C4⋊(C11⋊C8)C2311yescharacteristic
133C4⋊(C11⋊C8)C2311yescharacteristic
134C4⋊(C11⋊C8)C2311yescharacteristic
135#66867—21no—
136#66867—21no—
137#66867—21no—
138#66867D411yescharacteristic
139#66867D411yescharacteristic
140C4×C11⋊C8—21no—
141C4×C11⋊C8—21no—
142C4×C11⋊C8C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144#19375—111nomaximal, Sylow
145C2×Q8×C11—21no—
146C2×Q8×C11—21no—
147C2×Q8×C11—21no—
148C2×Q8×C11C2×D411yescharacteristic
149C2×Q8×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C2×Dic22—21no—
154C2×Dic22—21no—
155C11×Q16—81no—
156C11×Q16—81no—
157C11×M16—81no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—41no—
172C11×C4⋊C4—41no—
173C11×C4⋊C4C2×D411yescharacteristic
174C11×C4⋊C4C2×D411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—41no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—41no—
181C42×C11C2×D411yescharacteristic
182C42×C11C2×D411yescharacteristic
183C42×C11#4111yescharacteristic
184C42×C11C2411yescharacteristic
185C22⋊Dic11—41no—
186#4326—42no—
187#4326—42no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192Dic11⋊C4—41no—
193Dic11⋊C4—41no—
194C4×Dic11—41no—
195#4318—22no—
196#4318—41no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—42no—
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205C2×C11⋊C8C2×D411yescharacteristic
206#3255D1111yescharacteristic
207#3237—111no—
208#3185—111no—
209#2962—111no—
210#1704—111no—
211#1700—111no—
212#1692—111no—
213#1690—111no—
214#1684—111no—
215#1680—111no—
216#1672—111no—
217#1670—111no—
218#1569—111no—
219#1552—111no—
220#1550—111no—
221C23×C11#12111yescharacteristic
222Q8×C11—21no—
223Q8×C11—21no—
224Q8×C11—21no—
225Q8×C11—21no—
226Q8×C11—41no—
227Q8×C11—41no—
228Q8×C11—41no—
229Q8×C11—41no—
230Q8×C11—81no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11#12111yescharacteristic
243C2×C4×C11#12111yescharacteristic
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×Dic11—41no—
249C2×Dic11—41no—
250Dic22—41no—
251Dic22—41no—
252Dic22—81no—
253C8×C11—41no—
254C8×C11—41no—
255C11⋊C8—21no—
256C11⋊C8—21no—
257C11⋊C8—21no—
258C11⋊C8—41no—
259C11⋊C8—41no—
260C11⋊C8—41no—
261C11⋊C8—41no—
262C11⋊C8#13712yes—
263#533—111no—
264#533C2×D1111yescharacteristic
265#533C2×D1111yescharacteristic
266#501—221no—
267#498—111no—
268#494—111no—
269#491—221no—
270#487—111no—
271#487—111no—
272#485—221no—
273#485—221no—
274#477—111no—
275#477—111no—
276#475—21no—
277#475—111no—
278#475—111no—
279#475C2×D1111yescharacteristic
280#475C2×D1111yescharacteristic
281#470—21no—
282#470—21no—
283#470—221no—
284#470—221no—
285#462—21no—
286#462C2×D1111yescharacteristic
287#462C2×D1111yescharacteristic
288#446—111no—
289#446—111no—
290#446—221no—
291#446—221no—
292C8×Q8—111no—
293C8×Q8—111no—
294#441—221no—
295#441—221no—
296#432—111no—
297#424—221no—
298#423C2×D1111yescharacteristic
299C2×C4⋊C8—111no—
300#405—221no—
301C4×M16—111no—
302#335—111no—
303#335—111no—
304#334—111no—
305#334—111no—
306#333—111no—
307#333—111no—
308#332—111no—
309#332—111no—
310#332—111no—
311#332—111no—
312#332—111no—
313#332—111no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11C2×#12111yescharacteristic
318C4×C11—21no—
319C4×C11—21no—
320C4×C11—21no—
321C4×C11—21no—
322C4×C11—41no—
323C4×C11—41no—
324C4×C11—41no—
325C4×C11—41no—
326C4×C11—81no—
327C4×C11—81no—
328C4×C11C2×#13711yescharacteristic
329C4×C11#57511yescharacteristic
330C4×C11#57711yescharacteristic
331C4×C11#57811yescharacteristic
332Dic11—81no—
333Dic11—81no—
334C2×Q16—21no—
335C2×Q16—21no—
336C2×Q16—221no—
337C2×Q16—221no—
338C2×M16—21no—
339C2×M16—111no—
340C2×M16—111no—
341C22×C8—221no—
342C4⋊Q8—111no—
343C4⋊Q8—111no—
344C4⋊Q8C22⋊D1111yescharacteristic
345C4⋊Q8C22⋊D1111yescharacteristic
346C4⋊Q8C22×D1111yescharacteristic
347C4⋊Q8C22×D1111yescharacteristic
348#125—21no—
349#125—21no—
350#125—221no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—221no—
355C22⋊Q8—221no—
356C22⋊Q8C22⋊D1111yescharacteristic
357C22⋊Q8C22⋊D1111yescharacteristic
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—221no—
362C4×Q8—221no—
363C4×Q8C22×D1111yescharacteristic
364C4×Q8C22×D1111yescharacteristic
365#117—21no—
366#117—21no—
367#117—221no—
368C2×C42C22×D1111yescharacteristic
369#107—221no—
370#107—221no—
371#106—21no—
372#106—21no—
373#106—221no—
374#106—221no—
375#106—221no—
376#106—221no—
377C4⋊C8—21no—
378C4⋊C8—111no—
379C4⋊C8—111no—
380C4⋊C8—111no—
381C4⋊C8—111no—
382C4⋊C8—221no—
383C4⋊C8—221no—
384C4⋊C8—221no—
385C4⋊C8—221no—
386C4⋊C8—221no—
387C4⋊C8C22×D1111yescharacteristic
388C4⋊C8C22×D1111yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—221no—
394#103—221no—
395#103—221no—
396#103—221no—
397#103—221no—
398#103—221no—
399#103—221no—
400#103—221no—
401C22⋊C8—221no—
402#97—111no—
403#97—111no—
404#97—221no—
405#97—221no—
406#97—221no—
407C4×C8—111no—
408C4×C8—111no—
409C4×C8—221no—
410C4×C8—221no—
411C2×C11—41no—
412C2×C11#303711yescharacteristic
413C2×C11#306311yescharacteristic
414C2×C11#306911yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8C2×C22⋊D1111yescharacteristic
421C2×Q8C2×C22⋊D1111yescharacteristic
422C22×C4D4×D1111yescharacteristic
423C22×C4#434111yescharacteristic
424C22×C4C2×C22⋊D1111yescharacteristic
425Q16—81no—
426Q16—81no—
427Q16—442no—
428Q16—442no—
429M16—81no—
430M16—222no—
431M16—441no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—111no—
435C2×C8—111no—
436C2×C8—111no—
437C2×C8—111no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—442no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—441no—
461C4⋊C4—441no—
462C4⋊C4C2×C22⋊D1111yescharacteristic
463C4⋊C4C2×C22⋊D1111yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—41no—
467C22⋊C4—441no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—441no—
472C42D4×D1111yescharacteristic
473C42#434111yescharacteristic
474C42C2×C22⋊D1111yescharacteristic
475C42C23×D1111yescharacteristic
476C11#1937511yescharacteristic, complemented, Sylow
477C23#6699211yescharacteristic
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—441no—
488Q8—441no—
489Q8—881no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—441no—
502C2×C4—441no—
503C2×C4#6699211yescharacteristic
504C2×C4#6699211yescharacteristic
505C2×C4#6699211yescharacteristic
506C2×C4C2×D4×D1111yescharacteristic
507C2×C4C2×#434111yescharacteristic
508C2×C4C22×C22⋊D1111yescharacteristic
509C8—41no—
510C8—41no—
511C8—112no—
512C8—221no—
513C8—221no—
514C8—221no—
515C8—441no—
516C8—441no—
517C8—441no—
518C8—441no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22C2×#6699211yescharacteristic
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—81no—
532C4—81no—
533C4—881no—
534C4—881no—
535C4D11×#13711yescharacteristic
536C4#1062330811yescharacteristic
537C4#1062336711yescharacteristic
538C4#1062336911yescharacteristic
539C2—41no—
540C2#1307808511yescharacteristic
541C2#1307830911yescharacteristic
542C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3255C2
socleC22×C11C2×#121
prime radicalC23×C11#121
hypercenter#3255D11
hypocenterC11#19375
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
4. #13068196C2semidirect
5. #13068172C2semidirect
6. #13068120C2semidirect
7. #13068108C2semidirect
8. #13068072C2semidirect
9. #13068048C2semidirect
10. #13067996C2semidirect
11. #13067984C2semidirect
476. C11#19375semidirect

Maximal subgroups

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

subgroupindex
#130798262
#130793572
#130775652
#130681962
#130681722
#130681202
#130681082
#130680722
#130680482
#130679962
#130679842
#130673812
#130673162
#130673072
C11×#32552
#1937511