Finite Group Databasebeta

← #14910674

Subgroups — #14910674

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#13080987C211yesmaximal, characteristic, complemented
2#13080357C211yesmaximal, characteristic
3#13070849C211yesmaximal, characteristic, complemented
4#13070823C211yesmaximal, characteristic, complemented
5#13070797C211yesmaximal, characteristic, complemented
6#13070782C211yesmaximal, characteristic, complemented
7#13070714C211yesmaximal, characteristic, complemented
8#13070704C211yesmaximal, characteristic, complemented
9#13070680C211yesmaximal, characteristic, complemented
10#13070555C211yesmaximal, characteristic, complemented
11Q32×Dic11C211yesmaximal, characteristic, complemented
12(C22⋊D11)⋊C16C211yesmaximal, characteristic, complemented
13#13070322C211yesmaximal, characteristic, complemented
14C2×#10622202C211yesmaximal, characteristic, complemented
15C11×#2188C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17#10623348—21no—
18C2×#66972C2211yescharacteristic
19#10623173—21no—
20C2×C11×Q32C2211yescharacteristic
21C2×C11×Q32C2211yescharacteristic
22C11×#467C2211yescharacteristic
23#10622840—21no—
24#10622804C2211yescharacteristic
25#10622801C2211yescharacteristic
26#10622801C2211yescharacteristic
27#10622800—21no—
28#10622798—21no—
29Q16×Dic11C2211yescharacteristic
30Q16×Dic11C2211yescharacteristic
31C2×#66892C2211yescharacteristic
32#10622728C2211yescharacteristic
33C8×C22⋊D11C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C22×C11⋊C16C2211yescharacteristic
36#10622656—21no—
37C2×C16×D11C2211yescharacteristic
38#10622493C2211yescharacteristic
39#10622491C2211yescharacteristic
40#10622427—21no—
41#10622409—21no—
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×C22⋊C16C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48#10622202C2211yescharacteristic
49#10622202C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622147C2211yescharacteristic
52(C2×D11)⋊C16C2211yescharacteristic
53#10622142C2211yescharacteristic
54#10622142C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56C16×Dic11C2211yescharacteristic
57#10622129C2211yescharacteristic
58#10622128C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×#4343—21no—
61C2×C11×Q16—22no—
62C2×C11×Q16—21no—
63C2×C11×Q16—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C2×C11×Q16C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×C22⋊Q8—21no—
69#67000—21no—
70#67000—41no—
71#66999—21no—
72#66999—21no—
73#66999—41no—
74Q8×Dic11—21no—
75Q8×Dic11—21no—
76C2×#4325—21no—
77C2×#4325—21no—
78#66983—21no—
79#66983—41no—
80C4×C22⋊D11—41no—
81C4×C22⋊D11D411yescharacteristic
82C2×C4⋊Dic11—21no—
83#66972—22no—
84#66972—41no—
85C2×D88C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66951—41no—
88#66945—21no—
89#66943—21no—
90#66943—41no—
91#66939—41no—
92#66930—41no—
93C11×Q32—22no—
94C11×Q32—41no—
95C2×C11×C16C2311yescharacteristic
96C2×C11×C16C2311yescharacteristic
97C11×#107C2311yescharacteristic
98C11×#103—21no—
99#66899—21no—
100#66899—21no—
101#66899—21no—
102#66899—21no—
103C22⋊(C11⋊C8)D411yescharacteristic
104#66892—41no—
105#66885—21no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882—21no—
108#66882C2311yescharacteristic
109#66882C2311yescharacteristic
110#66882C2311yescharacteristic
111Dic11⋊C8D411yescharacteristic
112C8×Dic11C2311yescharacteristic
113C2×C11⋊C16—41no—
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#66872—21no—
117#66872—21no—
118C16×D11—41no—
119#33867—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—42no—
124C2×Q8×C11—41no—
125C2×Q8×C11—81no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11D811yescharacteristic
130C22×Dic11—41no—
131#4343—42no—
132#4343—81no—
133C2×D44—21no—
134C2×D44—41no—
135C2×C4×D11—41no—
136C2×C4×D11C2×D411yescharacteristic
137C11×Q16—21no—
138C11×Q16—21no—
139C11×Q16—21no—
140C11×Q16—21no—
141C11×Q16—21no—
142C11×Q16—42no—
143C11×Q16#4112yes—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11C2×D411yescharacteristic
147C2×C8×C11C2411yescharacteristic
148C11×C4⋊C4—21no—
149C11×C4⋊C4—41no—
150C11×C22⋊C4—41no—
151C22⋊Dic11D811yescharacteristic
152#4325—42no—
153#4325—81no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4D811yescharacteristic
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11—41no—
165C4⋊Dic11—41no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171Dic11⋊C4D811yescharacteristic
172C4×Dic11—41no—
173C4×Dic11—41no—
174C4×Dic11—41no—
175C4×Dic11C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178D88—21no—
179D88—21no—
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#2232—111no—
191#2229—111no—
192#2217—111no—
193#2216—111no—
194#2211—111no—
195#2189—111no—
196#2188D1111yescharacteristic, complemented
197C4×Q32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#358—111no—
201C23×C11C2×D811yescharacteristic
202C22×D11—41no—
203C22×D11C2×D811yescharacteristic
204Q8×C11—22no—
205Q8×C11—41no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—41no—
210Q8×C11—82no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—82no—
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—22no—
221C22⋊D11—82no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—82no—
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228C2×Dic11C2×D811yescharacteristic
229D44—41no—
230D44—41no—
231D44—82no—
232C4×D11—21no—
233C4×D11—21no—
234C4×D11—82no—
235C8×C11—21no—
236C8×C11C2×#4111yescharacteristic
237C8×C11H(5,𝔽2)11yescharacteristic
238C11⋊C8—21no—
239C11⋊C8—21no—
240C2×#135—111no—
241C22×Q16C2×D1111yescharacteristic
242#552—221no—
243#548—221no—
244C2×Q32C2×D1111yescharacteristic
245C2×Q32C2×D1111yescharacteristic
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#467C2×D1111yescharacteristic
257#466—111no—
258#464—221no—
259#452—221no—
260#448—221no—
261C4×Q16—111no—
262C4×Q16—111no—
263C8×D4—111no—
264#427—111no—
265C2×#107—111no—
266#367—111no—
267#366—111no—
268#366—111no—
269C4⋊C16—111no—
270#358—111no—
271#358—111no—
272#358—111no—
273#358—111no—
274#358—111no—
275#358C2×D1111yescharacteristic
276#358C2×D1111yescharacteristic
277#357—111no—
278#357—111no—
279#357—111no—
280C22⋊C16—111no—
281C22⋊C16C2×D1111yescharacteristic
282C4×C16—111no—
283C22×C11—21no—
284C22×C11—21no—
285C22×C11#50812yes—
286C22×C11C22×D811yescharacteristic
287C2×D11—21no—
288C2×D11—21no—
289C2×D11—21no—
290C2×D11—81no—
291C2×D11—81no—
292C2×D11—81no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11—81no—
298C4×C11#54611yescharacteristic
299C4×C11#57711yescharacteristic
300Dic11—21no—
301Dic11—21no—
302Dic11—21no—
303Dic11—81no—
304Dic11—81no—
305Dic11—81no—
306C2×#41—221no—
307C22×Q8—21no—
308#135—222no—
309#135—441no—
310C2×Q16—22no—
311C2×Q16—21no—
312C2×Q16—41no—
313C2×Q16C22×D1111yescharacteristic
314C2×Q16C22×D1111yescharacteristic
315C2×Q16C22×D1111yescharacteristic
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8—111no—
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—21no—
328C22⋊Q8—221no—
329C22⋊Q8—221no—
330C22⋊Q8—441no—
331#121—221no—
332#121—441no—
333C4×Q8—221no—
334C4×Q8—221no—
335C4×D4—111no—
336C4×D4—441no—
337#117—221no—
338#117—441no—
339C2×C4⋊C4—221no—
340Q32—22no—
341Q32—41no—
342SD32—441no—
343C2×C16—111no—
344C2×C16—111no—
345C2×C16—441no—
346C2×C16—441no—
347C2×C16C22×D1111yescharacteristic
348C2×C16C22×D1111yescharacteristic
349#107—111no—
350#107—111no—
351#107—111no—
352#107—221no—
353#107C22×D1111yescharacteristic
354#106—221no—
355#106—221no—
356C4⋊C8—111no—
357#103—21no—
358#103—221no—
359#103—221no—
360#103—221no—
361#103—221no—
362#102—221no—
363C22⋊C8—111no—
364C22⋊C8—111no—
365C4×C8—111no—
366C2×C11—22no—
367C2×C11#329411yescharacteristic
368C2×C11C2×#50811yescharacteristic
369C2×C11#341711yescharacteristic
370D11—41no—
371D11—161no—
372#41—442no—
373#41—881no—
374C2×Q8—21no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—42no—
378C2×Q8—41no—
379C2×Q8—81no—
380C2×D4—111no—
381C2×D4—221no—
382C2×D4—441no—
383C2×D4—441no—
384C22×C4—41no—
385C22×C4—111no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4D4×D1111yescharacteristic
389Q16—21no—
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—21no—
394Q16—42no—
395Q16#434112yes—
396SD16—442no—
397SD16—881no—
398D8—221no—
399D8—221no—
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—41no—
410C4⋊C4—111no—
411C4⋊C4—221no—
412C4⋊C4—221no—
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—111no—
440C23—441no—
441C23D8×D1111yescharacteristic
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448Q8—82no—
449D4—222no—
450D4—441no—
451D4—441no—
452D4—882no—
453D4—882no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—111no—
462C2×C4—111no—
463C2×C4—111no—
464C2×C4—221no—
465C2×C4—221no—
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—
476C8C2×#434111yescharacteristic
477C8#6703711yescharacteristic
478C22—21no—
479C22—21no—
480C22—221no—
481C22—221no—
482C22—221no—
483C22—881no—
484C22—881no—
485C22—881no—
486C22#1062253212yes—
487C22C2×D8×D1111yescharacteristic
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—221no—
494C4—221no—
495C4—221no—
496C4—881no—
497C4—881no—
498C4—881no—
499C4#1062312211yescharacteristic
500C4#1062330611yescharacteristic
501C2—22no—
502C2—441no—
503C2—1761no—
504C2#1308042211yescharacteristic
505C2C2×#1062253211yescharacteristic
506C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2188C2
socleC22×C11C22×D8
prime radical#13080357C2
hypercenter#2188D11
hypocenterC11#33867
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
1. #13080987C2semidirect
3. #13070849C2semidirect
4. #13070823C2semidirect
5. #13070797C2semidirect
6. #13070782C2semidirect
7. #13070714C2semidirect
8. #13070704C2semidirect
9. #13070680C2semidirect
10. #13070555C2semidirect
11. Q32×Dic11C2semidirect
12. (C22⋊D11)⋊C16C2semidirect
13. #13070322C2semidirect
14. C2×#10622202C2semidirect
15. C11×#2188C2semidirect
196. #2188D11semidirect
438. C11#33867semidirect

Maximal subgroups

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

subgroupindex
#130809872
#130803572
#130708492
#130708232
#130707972
#130707822
#130707142
#130707042
#130706802
#130705552
Q32×Dic112
(C22⋊D11)⋊C162
#130703222
C2×#106222022
C11×#21882
#3386711