Finite Group Databasebeta

← #14760706

Subgroups — #14760706

Order 2816.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078332C211yesmaximal, characteristic
2#13077517C212yesmaximal, complemented
3C4×#66954C211yesmaximal, characteristic, complemented
4#13069515C211yesmaximal, characteristic, complemented
5#13069404C211yesmaximal, characteristic, complemented
6#13069282C212yesmaximal, complemented
7#13069120C212yesmaximal, complemented
8#13068671C211yesmaximal, characteristic, complemented
9#13068495C211yesmaximal, characteristic, complemented
10#13068416C212yesmaximal, complemented
11C2×C11×#443C211yesmaximal, characteristic, complemented
12C2×C11×#135C2211yescharacteristic
13C2×C11×#131C2212yes—
14#10623353C2212yes—
15C2×#66954C2211yescharacteristic
16C2×#66954C2211yescharacteristic
17C4×#4339C2211yescharacteristic
18C11×#443—21no—
19C11×#443—21no—
20C11×#443—21no—
21C11×#443—21no—
22C2×C11×#108C2211yescharacteristic
23C2×C11×#104C2212yes—
24C2×C4×C8×C11C2211yescharacteristic
25#10622853C2212yes—
26#10622850C2212yes—
27#10622849C2212yes—
28#10622805C412yescomplemented
29#10622790C414yescomplemented
30#10622773C412yescomplemented
31#10622758—24no—
32#10622757—24no—
33#10622752C2212yes—
34#10622737C2212yes—
35C2×#66883C2211yescharacteristic
36#10622719C2211yescharacteristic
37#10622714C2212yes—
38#10622714C2211yescharacteristic
39#10622714C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622302—21no—
42#10622302—21no—
43C4×#4313—21no—
44C4×C8×D11—21no—
45#10622194C2212yes—
46#10622194C2212yes—
47#10622161C2212yes—
48C2×C11×#41C2312yes—
49C2×#4339C2311yescharacteristic
50C11×#135—21no—
51C11×#135—21no—
52C11×#135—21no—
53C11×#135—21no—
54C2×C11×Q16C2×C411yescharacteristic, complemented
55C2×C11×SD16C2×C412yescomplemented
56C2×C11×D8C2×C411yescharacteristic, complemented
57C11×#131—22no—
58C11×#131—22no—
59C11×#131—22no—
60C11×#131—22no—
61C2×C11×M16—22no—
62C2×C11×M16C2312yes—
63C22×C8×C11—22no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67#67004—22no—
68#67003—24no—
69#67002—22no—
70#66995C2×C414yes—
71#66985C2×C414yes—
72C4×C22⋊D11—22no—
73#66979C2312yes—
74#66979C2311yescharacteristic
75C2×#4318C2312yes—
76C2×#4318C2311yescharacteristic
77C2×#4318C2311yescharacteristic
78#66954—21no—
79#66954—21no—
80#66954—21no—
81#66954—21no—
82#66954C2×C412yes—
83#66954C2×C412yes—
84#66954D412yes—
85#66954D412yes—
86C2×#4313—21no—
87C2×#4313—21no—
88C2×C8×D11—21no—
89C2×C8×D11—21no—
90C4×D44—21no—
91#66925—21no—
92C42×D11—21no—
93C4×Dic22—21no—
94C11×#108—21no—
95C11×#108—21no—
96C11×#104—22no—
97C11×#104—22no—
98C4×C8×C11D411yescharacteristic
99C4×C8×C11D411yescharacteristic
100C4×C8×C11D411yescharacteristic
101C4×C8×C11D411yescharacteristic
102#66901—24no—
103#66900C2×C414yescomplemented
104#66898—24no—
105#66897C2×C414yescomplemented
106#66889—24no—
107#66886—24no—
108#66883C2×C412yescomplemented
109#66883C2×C412yescomplemented
110#66882—21no—
111#66881—21no—
112#66879—22no—
113#66879—21no—
114#66879—21no—
115C8×Dic11—22no—
116C8×Dic11—21no—
117C8×Dic11—21no—
118#66867—21no—
119C4×C11⋊C8—21no—
120#21558—111nomaximal, Sylow
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—22no—
124C11×#41—22no—
125C2×Q8×C11C22×C412yes—
126C2×D4×C11—22no—
127C2×D4×C11C22×C412yes—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11C2411yescharacteristic
131C2×C22⋊D11—21no—
132#4339—21no—
133#4339—21no—
134#4339C22×C412yes—
135#4339C2×D412yes—
136C2×D44#4111yescharacteristic
137C2×C4×D11—22no—
138C2×C4×D11—21no—
139C2×Dic22#4111yescharacteristic
140C11×Q16—21no—
141C11×Q16—21no—
142C11×SD16—22no—
143C11×SD16—22no—
144C11×D8—21no—
145C11×D8—21no—
146C11×M16—22no—
147C11×M16—22no—
148C11×M16—42no—
149C11×M16—42no—
150C2×C8×C11—22no—
151C2×C8×C11—42no—
152C2×C8×C11—42no—
153C2×C8×C11C22×C411yescharacteristic
154C2×C8×C11C22×C411yescharacteristic
155C2×C8×C11C2×D411yescharacteristic
156C2×C8×C11C2×D411yescharacteristic
157C2×C8×C11C2×D411yescharacteristic
158C2×C8×C11C2×D411yescharacteristic
159C2×C8×C11C2×D411yescharacteristic
160C2×C8×C11C2×D411yescharacteristic
161C2×C8×C11#4111yescharacteristic
162C2×C8×C11#4111yescharacteristic
163C2×C8×C11#4111yescharacteristic
164C2×C8×C11#4111yescharacteristic
165C42×C11—21no—
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C22⋊Dic11—22no—
169C22⋊Dic11#4112yes—
170#4326—24no—
171#4325—24no—
172#4324—24no—
173#4323—24no—
174(C2×D11)⋊C4—22no—
175C4⋊Dic11—21no—
176C4⋊Dic11—22no—
177Dic11⋊C4—22no—
178C4×Dic11—22no—
179C4×Dic11—21no—
180C4×Dic11—22no—
181#4318—21no—
182#4318—21no—
183#4318—22no—
184#4318C22×C414yes—
185#4318C22×C412yes—
186#4318C2×D412yes—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—22no—
190#4313—22no—
191#4313—22no—
192#4313—22no—
193#4313—22no—
194C8×D11—22no—
195C8×D11—22no—
196C8×D11—22no—
197C8×D11—22no—
198#3067—111no—
199#2955—112no—
200C2×#443D1111yescharacteristic, complemented
201C4×#131—111no—
202#1976—111no—
203#1953—111no—
204#1932—112no—
205#1906—112no—
206#1814—111no—
207#1772—111no—
208#1757—112no—
209C23×C11—22no—
210C23×C11C2×#4111yescharacteristic
211C22×D11—21no—
212Q8×C11—22no—
213Q8×C11—22no—
214D4×C11—22no—
215D4×C11—22no—
216D4×C11—42no—
217D4×C11—42no—
218C2×C4×C11—21no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C2×C4×C11C2×#4111yescharacteristic
230C22⋊D11—22no—
231C22⋊D11—22no—
232C2×Dic11—21no—
233C2×Dic11—22no—
234C2×Dic11—42no—
235D44—21no—
236D44C4×D412yes—
237C4×D11—22no—
238C4×D11—22no—
239C4×D11—44no—
240Dic22—21no—
241Dic22C4×D412yes—
242C8×C11—42no—
243C8×C11C4×D411yescharacteristic
244C8×C11C4×D411yescharacteristic
245C8×C11C4×D411yescharacteristic
246C8×C11C4×D411yescharacteristic
247C8×C11#12111yescharacteristic
248C8×C11#12111yescharacteristic
249C8×C11#12111yescharacteristic
250C8×C11#12111yescharacteristic
251C11⋊C8—22no—
252C11⋊C8—24no—
253C11⋊C8—22no—
254#575—112no—
255C2×#135C2×D1111yescharacteristic
256C2×#131—111no—
257C2×#131—111no—
258C2×#131C2×D1112yes—
259C4×#41—111no—
260#473—112no—
261#472—112no—
262#471—114no—
263#444—224no—
264#443—21no—
265#443—21no—
266#443—21no—
267#443—21no—
268#443—224no—
269#430—112no—
270C2×#108—111no—
271C2×#108C2×D1111yescharacteristic
272#427—111no—
273#421—112no—
274#421—112no—
275C2×#104C2×D1112yes—
276#413—112no—
277#410—112no—
278#405—111no—
279#405—111no—
280#405—112no—
281#405—221no—
282#405—221no—
283C4×M16—111no—
284C4×M16—221no—
285C2×C4×C8—221no—
286C2×C4×C8C2×D1111yescharacteristic
287#344—112no—
288#344—112no—
289#339—112no—
290C22×C11—41no—
291C22×C11—42no—
292C22×C11—82no—
293C22×C11C4×#4111yescharacteristic
294C22×C11#52511yescharacteristic
295C22×C11#53211yescharacteristic
296C2×D11—22no—
297C2×D11—42no—
298C4×C11—22no—
299C4×C11—41no—
300C4×C11—42no—
301C4×C11C2×C4×D411yescharacteristic
302C4×C11C2×C4×D411yescharacteristic
303C4×C11C2×#12111yescharacteristic
304C4×C11#52911yescharacteristic
305Dic11—22no—
306Dic11—42no—
307Dic11—82no—
308C2×#41—111no—
309C2×#41C22×D1112yes—
310#137—114no—
311#137—222no—
312AGL(1,ℤ/8)—114no—
313AGL(1,ℤ/8)—222no—
314#135—21no—
315#135—21no—
316#135—21no—
317#135—21no—
318#135—224no—
319C2×Q16C4×D1111yescharacteristic, complemented
320C2×SD16C4×D1112yescomplemented
321C2×D8C4×D1111yescharacteristic, complemented
322#131—22no—
323#131—22no—
324#131—22no—
325#131—22no—
326#131—112no—
327#131—112no—
328#131—112no—
329#131—112no—
330#131—221no—
331#131—221no—
332#131—221no—
333#131—221no—
334C2×M16—22no—
335C2×M16—111no—
336C2×M16—111no—
337C2×M16—112no—
338C2×M16—221no—
339C2×M16—221no—
340C2×M16C22×D1112yes—
341C22×C8—22no—
342C22×C8—221no—
343C22×C8—221no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346C4×Q8—221no—
347C4×D4—221no—
348C4×D4—222no—
349#117—111no—
350#117—112no—
351#117—221no—
352C2×C42—221no—
353C2×C42C22×D1111yescharacteristic
354#108—21no—
355#108—21no—
356#108—112no—
357#108—112no—
358#108—224no—
359#107—221no—
360#106—221no—
361#104—22no—
362#104—22no—
363#104—224no—
364#104—224no—
365#101—114no—
366#100—114no—
367#99—224no—
368#97—222no—
369#97—221no—
370#97—221no—
371#97—221no—
372C4×C8—222no—
373C4×C8—221no—
374C4×C8—221no—
375C4×C8—221no—
376C4×C8C22⋊D1111yescharacteristic
377C4×C8C22⋊D1111yescharacteristic
378C4×C8C22⋊D1111yescharacteristic
379C4×C8C22⋊D1111yescharacteristic
380C2×C11—21no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—82no—
384C2×C11C4×#12111yescharacteristic
385D11—42no—
386#41—22no—
387#41—22no—
388#41—22no—
389#41—22no—
390#41—112no—
391#41—112no—
392#41—221no—
393#41—221no—
394C2×Q8—111no—
395C2×Q8C2×C4×D1112yes—
396C2×D4—22no—
397C2×D4—111no—
398C2×D4—221no—
399C2×D4C2×C4×D1112yes—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—222no—
403C22×C4—221no—
404C22×C4C23×D1111yescharacteristic
405Q16—21no—
406Q16—21no—
407Q16—224no—
408SD16—22no—
409SD16—22no—
410SD16—224no—
411SD16—224no—
412D8—21no—
413D8—21no—
414D8—224no—
415M16—22no—
416M16—22no—
417M16—42no—
418M16—42no—
419M16—112no—
420M16—114no—
421M16—112no—
422M16—221no—
423M16—221no—
424M16—222no—
425M16—222no—
426M16—222no—
427M16—222no—
428M16—222no—
429C2×C8—22no—
430C2×C8—42no—
431C2×C8—42no—
432C2×C8—222no—
433C2×C8—221no—
434C2×C8—221no—
435C2×C8—222no—
436C2×C8—222no—
437C2×C8—222no—
438C2×C8—222no—
439C2×C8C2×C4×D1111yescharacteristic
440C2×C8C2×C4×D1111yescharacteristic
441C2×C8#433911yescharacteristic
442C2×C8#433911yescharacteristic
443C2×C8D4×D1111yescharacteristic
444C2×C8D4×D1111yescharacteristic
445C2×C8#434111yescharacteristic
446C2×C8#434111yescharacteristic
447C2×C8C2×C22⋊D1111yescharacteristic
448C2×C8C2×C22⋊D1111yescharacteristic
449C2×C8C2×C22⋊D1111yescharacteristic
450C2×C8C2×C22⋊D1111yescharacteristic
451C4⋊C4—222no—
452C4⋊C4—221no—
453C4⋊C4—222no—
454C22⋊C4—112no—
455C22⋊C4—222no—
456C22⋊C4—222no—
457C42—21no—
458C42—222no—
459C42—221no—
460C42—222no—
461C42C2×C22⋊D1111yescharacteristic
462C42C2×C22⋊D1111yescharacteristic
463C11#2155811yescharacteristic, complemented, Sylow
464C23—22no—
465C23—221no—
466C23#41×D1111yescharacteristic
467Q8—22no—
468Q8—22no—
469Q8—112no—
470Q8—221no—
471D4—22no—
472D4—22no—
473D4—42no—
474D4—42no—
475D4—112no—
476D4—222no—
477D4—222no—
478D4—221no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—221no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—444no—
490C2×C4—442no—
491C2×C4C22×C4×D1111yescharacteristic
492C2×C4C2×#433911yescharacteristic
493C2×C4C2×D4×D1111yescharacteristic
494C2×C4C2×#434111yescharacteristic
495C2×C4#41×D1111yescharacteristic
496C2×C4C22×C22⋊D1111yescharacteristic
497C8—42no—
498C8—222no—
499C8—224no—
500C8—222no—
501C8C4×C22⋊D1111yescharacteristic
502C8C4×C22⋊D1111yescharacteristic
503C8C4×C22⋊D1111yescharacteristic
504C8C4×C22⋊D1111yescharacteristic
505C8#6699111yescharacteristic
506C8#6699111yescharacteristic
507C8#6699111yescharacteristic
508C8#6699111yescharacteristic
509C22—41no—
510C22—42no—
511C22—82no—
512C22—222no—
513C22—442no—
514C22C4×#434111yescharacteristic
515C22#1062307911yescharacteristic
516C22#1062335911yescharacteristic
517C4—22no—
518C4—41no—
519C4—42no—
520C4—222no—
521C4—442no—
522C4—882no—
523C4C4×D4×D1111yescharacteristic
524C4#1062308811yescharacteristic
525C4C2×C4×C22⋊D1111yescharacteristic
526C4C2×#6699111yescharacteristic
527C2—21no—
528C2—21no—
529C2—21no—
530C2—82no—
531C2—442no—
532C2C4×#6699111yescharacteristic
subgroupG/H
centerC8#66991
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#443C2
socleC2×C11C4×#121
prime radical#13078332C2
cosocleC22×C4×C11C24
hypercenterC2×#443D11
hypocenterC11#21558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. #13077517C2semidirect
3. C4×#66954C2semidirect
4. #13069515C2semidirect
5. #13069404C2semidirect
6. #13069282C2semidirect
7. #13069120C2semidirect
8. #13068671C2semidirect
9. #13068495C2semidirect
10. #13068416C2semidirect
11. C2×C11×#443C2semidirect
28. #10622805C4semidirect
29. #10622790C4semidirect
30. #10622773C4semidirect
54. C2×C11×Q16C2×C4semidirect
55. C2×C11×SD16C2×C4semidirect
56. C2×C11×D8C2×C4semidirect
103. #66900C2×C4semidirect
105. #66897C2×C4semidirect
108. #66883C2×C4semidirect
109. #66883C2×C4semidirect
200. C2×#443D11semidirect
319. C2×Q16C4×D11semidirect
320. C2×SD16C4×D11semidirect
321. C2×D8C4×D11semidirect
463. C11#21558semidirect

Maximal subgroups

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

subgroupindex
#130783322
#130775172
C4×#669542
#130695152
#130694042
#130692822
#130691202
#130686712
#130684952
#130684162
C2×C11×#4432
#2155811