Finite Group Databasebeta

← #14908951

Subgroups — #14908951

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079276C211yesmaximal, characteristic, complemented
2#13077463C211yesmaximal, characteristic
3#13070827C211yesmaximal, characteristic, complemented
4#13070826C211yesmaximal, characteristic, complemented
5#13070770C211yesmaximal, characteristic, complemented
6#13070662C211yesmaximal, characteristic, complemented
7#13070661C211yesmaximal, characteristic, complemented
8#13070546C211yesmaximal, characteristic
9#13070546C211yesmaximal, characteristic
10#13070479C211yesmaximal, characteristic, complemented
11#13070477C211yesmaximal, characteristic, complemented
12#13070471C211yesmaximal, characteristic, complemented
13#13070467C211yesmaximal, characteristic, complemented
14#13070422C211yesmaximal, characteristic, complemented
15C11×#2228C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623228—21no—
18#10623076—21no—
19C11×#499C2211yescharacteristic, complemented
20C4×C11×D8C2211yescharacteristic
21D8×Dic11C2211yescharacteristic
22C2×#66891C2211yescharacteristic
23C2×#66891C2211yescharacteristic
24#10622682—21no—
25#10622627—21no—
26C2×#66864C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622500C2211yescharacteristic
30#10622493C2211yescharacteristic
31#10622486C2211yescharacteristic, complemented
32#10622486C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic
34#10622481—21no—
35#10622466—21no—
36#10622398—21no—
37#10622383—21no—
38#10622312C2211yescharacteristic, complemented
39C4×D88C2211yescharacteristic
40#10622302C2211yescharacteristic
41C11×#367C2211yescharacteristic, complemented
42C11×#366C2211yescharacteristic, complemented
43C11×C4⋊C16C2211yescharacteristic, complemented
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46(C2×D11)⋊C16C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622141C2211yescharacteristic, complemented
49#10622141C2211yescharacteristic, complemented
50#10622140C2211yescharacteristic, complemented
51C16×Dic11C2211yescharacteristic, complemented
52#10622130C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622129C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×C11×D8C2311yescharacteristic
61C11×#125—21no—
62C4×D4×C11—21no—
63D4×Dic11—21no—
64C2×#4323—21no—
65C4×C22⋊D11—41no—
66C2×(C2×D11)⋊C4—41no—
67D8×D11—22no—
68D8×D11—22no—
69C2×Dic44—21no—
70C2×Dic44C2311yescharacteristic
71C2×Dic44C2311yescharacteristic
72C2×D88C2311yescharacteristic
73C2×#4313D411yescharacteristic
74C2×C8×D11C2311yescharacteristic
75#66951—41no—
76#66951—41no—
77#66950—21no—
78#66950—21no—
79#66946—21no—
80#66945—21no—
81#66943—41no—
82#66943—41no—
83#66940—21no—
84#66940—21no—
85(C22⋊D11)⋊C4—41no—
86C22⋊C4×D11—41no—
87C4×D44—21no—
88#66925D411yescharacteristic
89#66922—21no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#102—21no—
97C4×C8×C11C2311yescharacteristic
98#66896—21no—
99#66891—22no—
100#66891—22no—
101#66885—21no—
102#66882C2311yescharacteristic
103#66879D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66874—21no—
108#66874—21no—
109#66874—21no—
110#66874—21no—
111#66873—21no—
112#66872—21no—
113#66867D411yescharacteristic
114#66864—22no—
115#66864—22no—
116#33683—111nomaximal, Sylow
117C23×D11—41no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—41no—
122D4×D11—24no—
123D4×D11—42no—
124C2×D44—21no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11C2×D411yescharacteristic
128C2×Dic22—21no—
129C2×Dic22—21no—
130C11×D8—21no—
131C11×D8#4112yes—
132C2×C8×C11C2×D411yescharacteristic
133C2×C8×C11C2411yescharacteristic
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C42×C11C2×D411yescharacteristic
141C22⋊Dic11—41no—
142#4323—24no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4D811yescharacteristic
149(C2×D11)⋊C4D811yescharacteristic
150C4⋊Dic11—21no—
151C4⋊Dic11—41no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154C4⋊Dic11—41no—
155Dic11⋊C4—41no—
156Dic11⋊C4—41no—
157Dic11⋊C4D811yescharacteristic
158Dic11⋊C4D811yescharacteristic
159C4×Dic11—41no—
160C4×Dic11—41no—
161C4×Dic11—41no—
162C4×Dic11C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165Dic44—21no—
166Dic44—21no—
167Dic44—21no—
168Dic44—21no—
169Dic44—42no—
170D88—21no—
171D88#4112yes—
172#4313—41no—
173C8×D11—21no—
174C8×D11—21no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3177—111no—
180#2948—111no—
181#2237—111no—
182#2237—111no—
183#2228—111no—
184#2228D1111yescharacteristic, complemented
185#2208—111no—
186#2208—111no—
187#2187—111no—
188#2187—111no—
189#2175—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11—41no—
195C22×D11—44no—
196C22×D11—41no—
197C22×D11—161no—
198C22×D11—161no—
199C22×D11C2×D811yescharacteristic
200D4×C11—22no—
201D4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—161no—
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C2×D811yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C22⋊D11—44no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—161no—
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217D44—22no—
218D44—41no—
219C4×D11—21no—
220C4×D11—21no—
221C4×D11—161no—
222C4×D11—161no—
223Dic22—41no—
224Dic22—41no—
225Dic22—41no—
226Dic22—41no—
227C8×C11—21no—
228C8×C11C2×#4111yescharacteristic
229C8×C11C2×#4111yescharacteristic
230C11⋊C8—21no—
231C11⋊C8—21no—
232C22×D8—111no—
233#541—221no—
234#518—221no—
235C2×SD32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×SD32—111no—
239#499C2×D1111yescharacteristic, complemented
240#494—111no—
241#491—221no—
242#470—221no—
243#467—111no—
244#467—111no—
245#442—221no—
246#442—221no—
247#441—221no—
248C4×Q16—111no—
249C4×Q16—111no—
250C4×D8—111no—
251C4×D8—111no—
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254#427—111no—
255#418—221no—
256#405—111no—
257#367—111no—
258#367C2×D1111yescharacteristic, complemented
259#366—111no—
260#366C2×D1111yescharacteristic, complemented
261C4⋊C16—111no—
262C4⋊C16C2×D1111yescharacteristic, complemented
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357C2×D1111yescharacteristic
270#357C2×D1111yescharacteristic
271C22⋊C16—111no—
272C22⋊C16—111no—
273#346—111no—
274C4×C16—111no—
275C22×C11—42no—
276C22×C11—81no—
277C22×C11—81no—
278C22×C11C22×D811yescharacteristic
279C2×D11—21no—
280C2×D11—21no—
281C2×D11—21no—
282C2×D11—42no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—164no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11—81no—
291C4×C11#52511yescharacteristic
292C4×C11#57511yescharacteristic
293Dic11—21no—
294Dic11—21no—
295Dic11—21no—
296Dic11—81no—
297Dic11—81no—
298Dic11—81no—
299C22×D4—221no—
300C2×Q16—111no—
301C2×Q16—111no—
302C2×Q16—221no—
303C2×D8—111no—
304C2×D8—221no—
305C2×D8—222no—
306C2×D8—222no—
307C2×D8C22×D1111yescharacteristic
308C2×M16—111no—
309C22×C8—111no—
310C4⋊Q8—221no—
311#126—441no—
312#126—441no—
313#125—21no—
314#125—441no—
315#125—441no—
316C22⋊Q8—221no—
317C22⋊Q8—221no—
318C4×Q8—221no—
319C4×Q8—221no—
320C4×D4—21no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4—221no—
324C4×D4—441no—
325C4×D4—441no—
326#117—111no—
327#117—221no—
328C2×C22⋊C4—441no—
329C2×C22⋊C4—441no—
330SD32—222no—
331SD32—222no—
332SD32—222no—
333SD32—222no—
334C2×C16—111no—
335C2×C16—111no—
336C2×C16C22×D1111yescharacteristic
337C2×C16C22×D1111yescharacteristic
338#107—111no—
339#107C22×D1111yescharacteristic
340#107C22×D1111yescharacteristic
341#107C22×D1111yescharacteristic
342#106—21no—
343#106—221no—
344#103—221no—
345#103—221no—
346#103—221no—
347#103—221no—
348#102—21no—
349#102—221no—
350#102—221no—
351#102—221no—
352#97—111no—
353#97—111no—
354C4×C8—111no—
355C4×C8C22×D1111yescharacteristic
356C2×C11—82no—
357C2×C11#310011yescharacteristic
358C2×C11#341611yescharacteristic
359C2×C11#341611yescharacteristic
360D11—41no—
361D11—82no—
362C24—441no—
363C2×Q8—221no—
364C2×Q8—221no—
365C2×D4—21no—
366C2×D4—224no—
367C2×D4—221no—
368C2×D4—441no—
369C2×D4—442no—
370C22×C4—41no—
371C22×C4—111no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375Q16—221no—
376Q16—221no—
377Q16—221no—
378Q16—221no—
379Q16—442no—
380D8—21no—
381D8—112no—
382D8—224no—
383D8—221no—
384D8#434312yes—
385M16—441no—
386C2×C8—111no—
387C2×C8—111no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8D4×D1111yescharacteristic
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—111no—
398C4⋊C4—111no—
399C4⋊C4—221no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C22⋊C4—41no—
407C22⋊C4—111no—
408C22⋊C4—111no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42—111no—
416C42—441no—
417C42—441no—
418C42—441no—
419C42D4×D1111yescharacteristic
420C16—21no—
421C16—21no—
422C16—221no—
423C16—221no—
424C11#3368311yescharacteristic, complemented, Sylow
425C23—41no—
426C23—111no—
427C23—444no—
428C23—441no—
429C23—1761no—
430C23—1761no—
431Q8—441no—
432Q8—441no—
433Q8—441no—
434Q8—441no—
435D4—22no—
436D4—41no—
437D4—222no—
438D4—444no—
439D4—441no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—111no—
444C2×C4—111no—
445C2×C4—111no—
446C2×C4—161no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—1761no—
453C2×C4—1761no—
454C2×C4—1761no—
455C2×C4D8×D1111yescharacteristic
456C2×C4D8×D1111yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C8—21no—
459C8—221no—
460C8—221no—
461C8C2×#434311yescharacteristic
462C8#41×D1111yescharacteristic
463C22—42no—
464C22—81no—
465C22—81no—
466C22—221no—
467C22—221no—
468C22—221no—
469C22—442no—
470C22—881no—
471C22—881no—
472C22—1764no—
473C22C2×D8×D1111yescharacteristic
474C4—21no—
475C4—21no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—221no—
480C4—221no—
481C4—221no—
482C4—881no—
483C4—881no—
484C4—881no—
485C4#1062315811yescharacteristic
486C4#1062330811yescharacteristic
487C2—82no—
488C2—441no—
489C2—882no—
490C2#1307861811yescharacteristic
491C2#1308175911yescharacteristic
492C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2228C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2228D11
hypocenterC11#33683
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2228

Complements

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

NH ≅ G/Ntype
1. #13079276C2semidirect
3. #13070827C2semidirect
4. #13070826C2semidirect
5. #13070770C2semidirect
6. #13070662C2semidirect
7. #13070661C2semidirect
10. #13070479C2semidirect
11. #13070477C2semidirect
12. #13070471C2semidirect
13. #13070467C2semidirect
14. #13070422C2semidirect
15. C11×#2228C2semidirect
19. C11×#499C22semidirect
31. #10622486C22semidirect
32. #10622486C22semidirect
38. #10622312C22semidirect
41. C11×#367C22semidirect
42. C11×#366C22semidirect
43. C11×C4⋊C16C22semidirect
48. #10622141C22semidirect
49. #10622141C22semidirect
50. #10622140C22semidirect
51. C16×Dic11C22semidirect
52. #10622130C22semidirect
53. #10622130C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
184. #2228D11semidirect
239. #499C2×D11semidirect
258. #367C2×D11semidirect
260. #366C2×D11semidirect
262. C4⋊C16C2×D11semidirect
424. C11#33683semidirect

Maximal subgroups

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

subgroupindex
#130792762
#130774632
#130708272
#130708262
#130707702
#130706622
#130706612
#130705462
#130704792
#130704772
#130704712
#130704672
#130704222
C11×#22282
#3368311