Finite Group Databasebeta

← #14908945

Subgroups — #14908945

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#13079268C211yesmaximal, characteristic, complemented
2#13077467C211yesmaximal, characteristic
3#13070824C211yesmaximal, characteristic, complemented
4#13070776C211yesmaximal, characteristic, complemented
5#13070772C211yesmaximal, characteristic, complemented
6#13070660C211yesmaximal, characteristic, complemented
7#13070660C211yesmaximal, characteristic, complemented
8#13070547C211yesmaximal, characteristic
9#13070544C211yesmaximal, characteristic
10#13070483C211yesmaximal, characteristic, complemented
11#13070479C211yesmaximal, characteristic, complemented
12#13070467C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2237C211yesmaximal, characteristic, complemented
16C22×D88C2211yescharacteristic
17#10623156—21no—
18#10623052—21no—
19C11×#467C2211yescharacteristic
20C11×#427C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic, complemented
22#10622794C2211yescharacteristic, complemented
23C2×#66892C2211yescharacteristic
24C2×#66892C2211yescharacteristic
25#10622729C2211yescharacteristic
26#10622714C2211yescharacteristic
27#10622665—21no—
28#10622614—21no—
29C2×#66864C2211yescharacteristic
30C2×#66864C2211yescharacteristic
31#10622491C2211yescharacteristic, complemented
32#10622486C2211yescharacteristic, complemented
33#10622485C2211yescharacteristic
34#10622485C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622485C2211yescharacteristic
37#10622482—21no—
38#10622482—21no—
39#10622410—21no—
40#10622402—21no—
41C11×#367C2211yescharacteristic, complemented
42C11×#366C2211yescharacteristic, complemented
43C11×#358C2211yescharacteristic, complemented
44C11×#358C2211yescharacteristic, complemented
45C11×C22⋊C16C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622147C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622140C2211yescharacteristic, complemented
50Dic11⋊C16C2211yescharacteristic, complemented
51Dic11⋊C16C2211yescharacteristic, complemented
52C16×Dic11C2211yescharacteristic, complemented
53#10622130C2211yescharacteristic, complemented
54#10622130C2211yescharacteristic, complemented
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D44—21no—
60C2×C11×Q16C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×#117—21no—
64Q8×Dic11—21no—
65#66997—21no—
66C2×#4326—21no—
67#66979D411yescharacteristic
68#66977—21no—
69C2×#4318D411yescharacteristic
70C2×Dic44C2311yescharacteristic
71C2×D88—21no—
72C2×D88—22no—
73C2×D88—22no—
74C2×D88C2311yescharacteristic
75C2×D88C2311yescharacteristic
76#66946—21no—
77#66946—21no—
78#66946—21no—
79#66946—21no—
80#66943—21no—
81#66943—41no—
82#66942—41no—
83#66940—21no—
84C22⋊C4×D11—41no—
85C22⋊C4×D11—41no—
86#66932—41no—
87#66932—41no—
88C4×D44—41no—
89C4×D44—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#103—21no—
97#66899—21no—
98#66892—22no—
99#66892—22no—
100#66882C2311yescharacteristic
101#66880—21no—
102#66879D411yescharacteristic
103#66879D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66873—21no—
110#66873—21no—
111#66873—21no—
112#66873—21no—
113#66872—21no—
114#66864—22no—
115#66864—22no—
116#33683—111nomaximal, Sylow
117C23×D11—41no—
118C2×Q8×C11—21no—
119C22×C4×C11C2×D411yescharacteristic
120C2×D44—24no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—42no—
124C2×D44—41no—
125C2×C4×D11—41no—
126C2×C4×D11—41no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×Dic22—21no—
130C11×Q16—21no—
131C11×Q16—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2411yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142C42×C11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11D811yescharacteristic
145C22⋊Dic11D811yescharacteristic
146#4326—42no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151C4⋊Dic11—21no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154C4⋊Dic11D811yescharacteristic
155C4⋊Dic11D811yescharacteristic
156Dic11⋊C4—41no—
157Dic11⋊C4—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11—41no—
163C4×Dic11C2×D411yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165#4318—41no—
166C2×C11⋊C8C2×D411yescharacteristic
167C2×C11⋊C8C2×D411yescharacteristic
168Dic44—21no—
169Dic44—21no—
170D88—24no—
171D88—21no—
172D88—21no—
173D88#4112yes—
174D88#4112yes—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3177—111no—
180#2948—111no—
181#2237—111no—
182#2237D1111yescharacteristic, complemented
183#2228—111no—
184#2228—111no—
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×C11C2×D811yescharacteristic
195C22×D11—41no—
196C22×D11—41no—
197C22×D11—44no—
198C22×D11—161no—
199C22×D11—161no—
200Q8×C11—41no—
201Q8×C11—41no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216D44—22no—
217D44—22no—
218D44—44no—
219D44—41no—
220D44—41no—
221C4×D11—161no—
222C4×D11—161no—
223C4×D11—161no—
224C4×D11—161no—
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#499—111no—
240#494—111no—
241#491—221no—
242#470—221no—
243#467—111no—
244#467C2×D1111yescharacteristic
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×D8—111no—
254#427C2×D1111yescharacteristic
255#418—221no—
256#405—111no—
257#367—111no—
258#367C2×D1111yescharacteristic, complemented
259#366—111no—
260#366C2×D1111yescharacteristic, complemented
261C4⋊C16—111no—
262C4⋊C16—111no—
263#358—111no—
264#358—111no—
265#358C2×D1111yescharacteristic, complemented
266#358C2×D1111yescharacteristic, complemented
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271C22⋊C16—111no—
272C22⋊C16C2×D1111yescharacteristic
273#346—111no—
274C4×C16—111no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11C22×D811yescharacteristic
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—164no—
286C4×C11—21no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11—81no—
291C4×C11#52511yescharacteristic
292C4×C11#57511yescharacteristic
293Dic11—21no—
294Dic11—21no—
295Dic11—21no—
296Dic11—21no—
297Dic11—81no—
298Dic11—81no—
299C22×D4—221no—
300C2×Q16—111no—
301C2×Q16—221no—
302C2×Q16C22×D1111yescharacteristic
303C2×D8—111no—
304C2×D8—111no—
305C2×D8—222no—
306C2×D8—222no—
307C2×D8—221no—
308C2×M16—111no—
309C22×C8C22×D1111yescharacteristic
310C4⋊Q8—221no—
311#126—441no—
312#126—441no—
313#125—221no—
314#125—441no—
315#125—441no—
316C22⋊Q8—21no—
317C22⋊Q8—221no—
318C4×Q8—221no—
319C4×Q8—221no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4—221no—
323C4×D4—221no—
324C4×D4—441no—
325C4×D4—441no—
326#117—21no—
327#117—111no—
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—21no—
345#103—221no—
346#103—221no—
347#103—221no—
348#102—221no—
349#102—221no—
350#102—221no—
351#102—221no—
352#97—111no—
353#97—111no—
354C4×C8—111no—
355C4×C8—111no—
356C2×C11—41no—
357C2×C11#310011yescharacteristic
358C2×C11#341611yescharacteristic
359C2×C11#341611yescharacteristic
360D11—82no—
361D11—82no—
362C24—441no—
363C2×Q8—21no—
364C2×Q8—221no—
365C2×D4—224no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—442no—
369C2×D4—441no—
370C22×C4—441no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4D4×D1111yescharacteristic
375Q16—21no—
376Q16—21no—
377Q16—221no—
378Q16—221no—
379Q16—442no—
380D8—112no—
381D8—112no—
382D8—224no—
383D8—221no—
384D8—221no—
385M16—441no—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—111no—
389C2×C8—111no—
390C2×C8D4×D1111yescharacteristic
391C2×C8C23×D1111yescharacteristic
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—111no—
397C4⋊C4—111no—
398C4⋊C4—221no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C4⋊C4—441no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—111no—
409C22⋊C4—111no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C42—41no—
416C42—111no—
417C42—111no—
418C42—441no—
419C42—441no—
420C16—21no—
421C16—21no—
422C16—221no—
423C16—221no—
424C11#3368311yescharacteristic, complemented, Sylow
425C23—444no—
426C23—441no—
427C23—441no—
428C23—1761no—
429C23—1761no—
430C23D8×D1111yescharacteristic
431Q8—41no—
432Q8—41no—
433Q8—441no—
434Q8—441no—
435D4—222no—
436D4—222no—
437D4—444no—
438D4—441no—
439D4—441no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—111no—
447C2×C4—111no—
448C2×C4—111no—
449C2×C4—111no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—1761no—
453C2×C4—1761no—
454C2×C4—1761no—
455C2×C4—1761no—
456C2×C4D8×D1111yescharacteristic
457C2×C4C2×D4×D1111yescharacteristic
458C8—21no—
459C8—221no—
460C8—221no—
461C8#41×D1111yescharacteristic
462C8#41×D1111yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—442no—
467C22—442no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—1764no—
473C22C2×D8×D1111yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—221no—
480C4—221no—
481C4—221no—
482C4—221no—
483C4—881no—
484C4—881no—
485C4#1062318711yescharacteristic
486C4#1062330811yescharacteristic
487C2—41no—
488C2—882no—
489C2—882no—
490C2#1307861311yescharacteristic
491C2#1308175911yescharacteristic
492C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2237C2
socleC22×C11C22×D8
prime radicalC22×D88C22
hypercenter#2237D11
hypocenterC11#33683
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2237

Complements

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

NH ≅ G/Ntype
1. #13079268C2semidirect
3. #13070824C2semidirect
4. #13070776C2semidirect
5. #13070772C2semidirect
6. #13070660C2semidirect
7. #13070660C2semidirect
10. #13070483C2semidirect
11. #13070479C2semidirect
12. #13070467C2semidirect
13. #13070465C2semidirect
14. #13070420C2semidirect
15. C11×#2237C2semidirect
21. Q16×Dic11C22semidirect
22. #10622794C22semidirect
31. #10622491C22semidirect
32. #10622486C22semidirect
41. C11×#367C22semidirect
42. C11×#366C22semidirect
43. C11×#358C22semidirect
44. C11×#358C22semidirect
49. #10622140C22semidirect
50. Dic11⋊C16C22semidirect
51. Dic11⋊C16C22semidirect
52. C16×Dic11C22semidirect
53. #10622130C22semidirect
54. #10622130C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
182. #2237D11semidirect
258. #367C2×D11semidirect
260. #366C2×D11semidirect
265. #358C2×D11semidirect
266. #358C2×D11semidirect
424. C11#33683semidirect

Maximal subgroups

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

subgroupindex
#130792682
#130774672
#130708242
#130707762
#130707722
#130706602
#130705472
#130705442
#130704832
#130704792
#130704672
#130704652
#130704202
C11×#22372
#3368311