Finite Group Databasebeta

← #14910668

Subgroups — #14910668

Order 2816.

546 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080980C211yesmaximal, characteristic, complemented
2#13080354C211yesmaximal, characteristic
3#13070846C211yesmaximal, characteristic, complemented
4#13070826C211yesmaximal, characteristic, complemented
5#13070779C211yesmaximal, characteristic, complemented
6#13070710C211yesmaximal, characteristic, complemented
7#13070708C211yesmaximal, characteristic, complemented
8#13070677C211yesmaximal, characteristic, complemented
9#13070557C211yesmaximal, characteristic, complemented
10#13070552C211yesmaximal, characteristic, complemented
11#13070474C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
13#13070320C211yesmaximal, characteristic, complemented
14C2×#10622130C211yesmaximal, characteristic, complemented
15C11×#2232C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic
17C22×Dic44C2211yescharacteristic
18#10623129—21no—
19#10623044—21no—
20C11×#466C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622768C2211yescharacteristic
23C2×#66891C2211yescharacteristic
24#10622729C2211yescharacteristic
25C8×C22⋊D11C2211yescharacteristic
26C22×C11⋊C16C2211yescharacteristic
27#10622653—21no—
28#10622584—21no—
29C2×Dic88C2211yescharacteristic
30C2×Dic88C2211yescharacteristic
31C2×C16×D11C2211yescharacteristic
32#10622501—21no—
33#10622500C2211yescharacteristic
34#10622500C2211yescharacteristic
35#10622493C2211yescharacteristic
36#10622491C2211yescharacteristic
37#10622490—21no—
38#10622486C2211yescharacteristic
39#10622486C2211yescharacteristic
40#10622396—21no—
41#10622380—21no—
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C11×C22⋊C16C2211yescharacteristic
47#10622200C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52C16×Dic11C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622130C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×#4341—21no—
60C22×Dic22—21no—
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C11×#121—21no—
64C2×C11×C4⋊C4—21no—
65#66992—41no—
66#66989—21no—
67D4×Dic11—41no—
68C2×#4324—21no—
69C2×#4324—21no—
70#66982—41no—
71C4×C22⋊D11D411yescharacteristic
72#66979—41no—
73#66977—21no—
74#66965—22no—
75#66965—41no—
76C2×Dic44—22no—
77C2×Dic44—21no—
78C2×Dic44—41no—
79C2×Dic44C2311yescharacteristic
80C2×Dic44C2311yescharacteristic
81C2×Dic44C2311yescharacteristic
82C2×C8×D11C2311yescharacteristic
83#66951—41no—
84#66950—21no—
85#66950—21no—
86#66945—21no—
87#66943—21no—
88#66942—41no—
89#66940—21no—
90#66940—21no—
91#66938—41no—
92#66931—41no—
93C2×C11×C16C2311yescharacteristic
94C2×C11×C16C2311yescharacteristic
95C11×#107—21no—
96C11×#107C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99C11×#102—21no—
100C22⋊(C11⋊C8)D411yescharacteristic
101#66891—41no—
102(C2×D11)⋊C8D411yescharacteristic
103#66882C2311yescharacteristic
104#66880—21no—
105Dic11⋊C8D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C2×C11⋊C16—41no—
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66874—21no—
111#66874—21no—
112#66874—21no—
113#66874—21no—
114#66872—21no—
115#66872—21no—
116Dic88—22no—
117Dic88—41no—
118C16×D11—41no—
119#33867—111nomaximal, Sylow
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×C22⋊D11D811yescharacteristic
126C22×Dic11—41no—
127C22×Dic11—41no—
128#4341—42no—
129#4341—81no—
130C2×C4×D11C2×D411yescharacteristic
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—21no—
134C2×Dic22—42no—
135C2×Dic22—41no—
136C2×Dic22—81no—
137C11×D8—21no—
138C11×D8—21no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2411yescharacteristic
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C22⋊C4—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11—41no—
151C22⋊Dic11D811yescharacteristic
152#4324—42no—
153#4324—81no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4D811yescharacteristic
158C4⋊Dic11—21no—
159C4⋊Dic11—41no—
160C4⋊Dic11—41no—
161C4⋊Dic11—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4D811yescharacteristic
167C4×Dic11—41no—
168C4×Dic11—41no—
169C4×Dic11—41no—
170C4×Dic11C2×D411yescharacteristic
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173Dic44—21no—
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44—21no—
178Dic44—42no—
179Dic44#4112yes—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3336—111no—
187#3285—111no—
188#2242—111no—
189#2237—111no—
190#2232D1111yescharacteristic, complemented
191#2229—111no—
192#2217—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2188—111no—
197C4×Q32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#358—111no—
201C23×C11—41no—
202C23×C11C2×D811yescharacteristic
203C22×D11C2×D811yescharacteristic
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—82no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—82no—
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C22×D411yescharacteristic
215C22⋊D11—22no—
216C22⋊D11—82no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—82no—
222C2×Dic11—82no—
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225C2×Dic11C2×D811yescharacteristic
226C4×D11—21no—
227C4×D11—21no—
228Dic22—22no—
229Dic22—41no—
230Dic22—41no—
231Dic22—41no—
232Dic22—41no—
233Dic22—41no—
234Dic22—82no—
235C8×C11—21no—
236C8×C11C2×#4111yescharacteristic
237C8×C11H(5,𝔽2)11yescharacteristic
238C11⋊C8—21no—
239C11⋊C8—21no—
240C2×#135—111no—
241C22×Q16—111no—
242#552—221no—
243#548—221no—
244C2×Q32—111no—
245C2×Q32—111no—
246C2×SD32—111no—
247C22×C16—111no—
248C22×C16—111no—
249#499—111no—
250#495—111no—
251#485—221no—
252#483—221no—
253#479—221no—
254#467—111no—
255#467—111no—
256#467—111no—
257#466C2×D1111yescharacteristic
258#464—221no—
259#452—221no—
260#448—221no—
261C4×Q16—111no—
262C4×Q16—111no—
263C8×D4—111no—
264#427—111no—
265C2×#107C2×D1111yescharacteristic
266#367—111no—
267#366C2×D1111yescharacteristic
268#366C2×D1111yescharacteristic
269C4⋊C16—111no—
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358—111no—
276#358—111no—
277#357—111no—
278#357C2×D1111yescharacteristic
279#357C2×D1111yescharacteristic
280C22⋊C16—111no—
281C22⋊C16C2×D1111yescharacteristic
282C4×C16—111no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11#50812yes—
289C22×C11C22×D811yescharacteristic
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C4×C11—21no—
294C4×C11—81no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11#54611yescharacteristic
298C4×C11#57711yescharacteristic
299Dic11—21no—
300Dic11—21no—
301Dic11—21no—
302Dic11—42no—
303Dic11—81no—
304Dic11—81no—
305Dic11—81no—
306C2×#41—221no—
307C22×Q8—221no—
308#135—222no—
309#135—441no—
310C2×Q16—111no—
311C2×Q16—111no—
312C2×Q16—111no—
313C2×Q16—222no—
314C2×Q16—221no—
315C2×Q16—441no—
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8C22×D1111yescharacteristic
319C22×C8—111no—
320C22×C8C22×D1111yescharacteristic
321#126—441no—
322#125—221no—
323#125—441no—
324#124—221no—
325#124—441no—
326#123—441no—
327C22⋊Q8—221no—
328C22⋊Q8—221no—
329C22⋊Q8—221no—
330C22⋊Q8—441no—
331#121—21no—
332#121—441no—
333C4×Q8—221no—
334C4×Q8—221no—
335C4×D4—111no—
336C4×D4—441no—
337#117—221no—
338#117—441no—
339C2×C4⋊C4—21no—
340Q32—222no—
341Q32—441no—
342SD32—441no—
343C2×C16—111no—
344C2×C16—111no—
345C2×C16—441no—
346C2×C16—441no—
347C2×C16C22×D1111yescharacteristic
348C2×C16C22×D1111yescharacteristic
349#107—21no—
350#107—111no—
351#107C22×D1111yescharacteristic
352#107C22×D1111yescharacteristic
353#107C22×D1111yescharacteristic
354#106—221no—
355#106—221no—
356C4⋊C8—111no—
357#103—221no—
358#103—221no—
359#103—221no—
360#103—221no—
361#103—221no—
362#102—21no—
363C22⋊C8—111no—
364C22⋊C8—111no—
365C4×C8—111no—
366C2×C11—22no—
367C2×C11—161no—
368C2×C11#329411yescharacteristic
369C2×C11C2×#50811yescharacteristic
370C2×C11#341711yescharacteristic
371D11—41no—
372#41—442no—
373#41—881no—
374C2×Q8—221no—
375C2×Q8—221no—
376C2×Q8—221no—
377C2×Q8—442no—
378C2×Q8—441no—
379C2×Q8—881no—
380C2×D4—21no—
381C2×D4—41no—
382C2×D4—111no—
383C2×D4—441no—
384C22×C4—41no—
385C22×C4—111no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4D4×D1111yescharacteristic
389Q16—112no—
390Q16—221no—
391Q16—221no—
392Q16—221no—
393Q16—221no—
394Q16—221no—
395Q16—442no—
396SD16—442no—
397SD16—881no—
398D8—21no—
399D8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—111no—
403C2×C8—111no—
404C2×C8—221no—
405C2×C8—221no—
406C2×C8D4×D1111yescharacteristic
407C2×C8C23×D1111yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—41no—
412C4⋊C4—111no—
413C4⋊C4—221no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4—441no—
421C22⋊C4—41no—
422C22⋊C4—111no—
423C22⋊C4—111no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C22⋊C4—441no—
427C22⋊C4—441no—
428C22⋊C4—441no—
429C22⋊C4—441no—
430C42—111no—
431C42—441no—
432C42—441no—
433C42—441no—
434C16—21no—
435C16—21no—
436C16—221no—
437C16—221no—
438C11#3386711yescharacteristic, complemented, Sylow
439C23—41no—
440C23—111no—
441C23D8×D1111yescharacteristic
442Q8—222no—
443Q8—441no—
444Q8—441no—
445Q8—441no—
446Q8—441no—
447Q8—441no—
448Q8—882no—
449D4—41no—
450D4—41no—
451D4—82no—
452D4—222no—
453D4—882no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—82no—
460C2×C4—111no—
461C2×C4—111no—
462C2×C4—111no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—882no—
470C2×C4—882no—
471C2×C4D8×D1111yescharacteristic
472C2×C4C2×D4×D1111yescharacteristic
473C8—21no—
474C8—221no—
475C8—221no—
476C8#41×D1111yescharacteristic
477C8#6704211yescharacteristic
478C22—21no—
479C22—21no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—221no—
484C22—221no—
485C22—221no—
486C22#1062252512yes—
487C22C2×D8×D1111yescharacteristic
488C4—21no—
489C4—81no—
490C4—81no—
491C4—81no—
492C4—221no—
493C4—221no—
494C4—221no—
495C4—442no—
496C4—881no—
497C4—881no—
498C4—881no—
499C4#1062318511yescharacteristic
500C4#1062330911yescharacteristic
501C2—22no—
502C2—161no—
503C2—441no—
504C2#1308042711yescharacteristic
505C2C2×#1062252511yescharacteristic
506C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2232C2
socleC22×C11C22×D8
prime radical#13080354C2
hypercenter#2232D11
hypocenterC11#33867
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2232

Complements

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

NH ≅ G/Ntype
1. #13080980C2semidirect
3. #13070846C2semidirect
4. #13070826C2semidirect
5. #13070779C2semidirect
6. #13070710C2semidirect
7. #13070708C2semidirect
8. #13070677C2semidirect
9. #13070557C2semidirect
10. #13070552C2semidirect
11. #13070474C2semidirect
12. (C22⋊D11)⋊C16C2semidirect
13. #13070320C2semidirect
14. C2×#10622130C2semidirect
15. C11×#2232C2semidirect
190. #2232D11semidirect
438. C11#33867semidirect

Maximal subgroups

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

subgroupindex
#130809802
#130803542
#130708462
#130708262
#130707792
#130707102
#130707082
#130706772
#130705572
#130705522
#130704742
(C22⋊D11)⋊C162
#130703202
C2×#106221302
C11×#22322
#3386711