Finite Group Databasebeta

← #14908947

Subgroups — #14908947

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#13079272C211yesmaximal, characteristic, complemented
2#13077463C211yesmaximal, characteristic
3#13070823C211yesmaximal, characteristic, complemented
4#13070822C211yesmaximal, characteristic, complemented
5#13070774C211yesmaximal, characteristic, complemented
6#13070773C211yesmaximal, characteristic, complemented
7#13070658C211yesmaximal, characteristic, complemented
8#13070543C211yesmaximal, characteristic
9#13070543C211yesmaximal, characteristic
10#13070483C211yesmaximal, characteristic, complemented
11#13070481C211yesmaximal, characteristic, complemented
12SD32×Dic11C211yesmaximal, characteristic, complemented
13#13070465C211yesmaximal, characteristic, complemented
14#13070422C211yesmaximal, characteristic, complemented
15C11×#2208C211yesmaximal, characteristic, complemented
16C2×D8×D11C2211yescharacteristic
17#10623262—21no—
18#10623076—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C11×#494C2211yescharacteristic, complemented
22C4×C11×D8C2211yescharacteristic
23#10622802—21no—
24#10622801C2211yescharacteristic
25#10622801C2211yescharacteristic
26#10622797—21no—
27Q16×Dic11C2211yescharacteristic, complemented
28Q16×Dic11C2211yescharacteristic, complemented
29C2×#66892C2211yescharacteristic
30C2×#66892C2211yescharacteristic
31D8×Dic11C2211yescharacteristic
32#10622695—21no—
33#10622627—21no—
34#10622493C2211yescharacteristic
35#10622485C2211yescharacteristic
36#10622398—21no—
37#10622383—21no—
38C4×D88C2211yescharacteristic
39#10622302C2211yescharacteristic
40#10622296C2211yescharacteristic, complemented
41C11×C4⋊C16C2211yescharacteristic, complemented
42C11×#358C2211yescharacteristic, complemented
43C11×#358C2211yescharacteristic, complemented
44#10622202C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622147C2211yescharacteristic
50(C2×D11)⋊C16C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622143C2211yescharacteristic, complemented
53#10622142C2211yescharacteristic, complemented
54#10622140C2211yescharacteristic, complemented
55C16×Dic11C2211yescharacteristic, complemented
56#10622128C2211yescharacteristic, complemented
57#10622127C2211yescharacteristic, complemented
58C4⋊(C11⋊C16)C2211yescharacteristic, complemented
59C2×D4×D11—21no—
60C2×C11×Q16—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×Q16C2311yescharacteristic
63C2×C11×D8C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C4×D4×C11—21no—
66#66999—21no—
67#66999—21no—
68Q8×Dic11—21no—
69Q8×Dic11—21no—
70D4×Dic11—21no—
71C2×#4323—21no—
72C4×C22⋊D11—41no—
73C2×(C2×D11)⋊C4—41no—
74D8×D11—22no—
75D8×D11—22no—
76C2×D88C2311yescharacteristic
77C2×#4313D411yescharacteristic
78C2×C8×D11C2311yescharacteristic
79#66951—41no—
80#66951—41no—
81#66946—21no—
82#66945—21no—
83#66942—41no—
84#66942—41no—
85(C22⋊D11)⋊C4—41no—
86C22⋊C4×D11—41no—
87C4×D44—21no—
88#66925D411yescharacteristic
89#66923—21no—
90C11×SD32—22no—
91C11×SD32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96C4×C8×C11C2311yescharacteristic
97#66899—21no—
98#66899—21no—
99#66899—21no—
100#66899—21no—
101#66896—21no—
102#66892—22no—
103#66892—22no—
104#66885—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66882C2311yescharacteristic
108#66881—21no—
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66872—21no—
115#66867D411yescharacteristic
116#33683—111nomaximal, Sylow
117C23×D11—41no—
118C2×Q8×C11—21no—
119C2×Q8×C11—21no—
120C2×D4×C11—21no—
121C22×C4×C11—41no—
122C2×C22⋊D11—41no—
123C22×Dic11—41no—
124D4×D11—24no—
125D4×D11—42no—
126C2×D44—21no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11C2×D411yescharacteristic
130C11×Q16—21no—
131C11×Q16—21no—
132C11×Q16—21no—
133C11×Q16—21no—
134C11×Q16—42no—
135C11×D8—21no—
136C11×D8#4112yes—
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2411yescharacteristic
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C22⋊C4—41no—
143C42×C11C2×D411yescharacteristic
144C22⋊Dic11—41no—
145#4323—24no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4D811yescharacteristic
152(C2×D11)⋊C4D811yescharacteristic
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4D811yescharacteristic
163Dic11⋊C4D811yescharacteristic
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169C2×C11⋊C8C2×D411yescharacteristic
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#2228—111no—
185#2208—111no—
186#2208D1111yescharacteristic, complemented
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
200Q8×C11—41no—
201Q8×C11—41no—
202Q8×C11—41no—
203Q8×C11—41no—
204D4×C11—22no—
205D4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—161no—
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C22⋊D11—44no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—161no—
218C2×Dic11C2×D811yescharacteristic
219C2×Dic11C2×D811yescharacteristic
220C2×Dic11C2×D811yescharacteristic
221D44—22no—
222D44—41no—
223C4×D11—21no—
224C4×D11—21no—
225C4×D11—161no—
226C4×D11—161no—
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×SD32C2×D1111yescharacteristic
238C2×SD32C2×D1111yescharacteristic
239#499—111no—
240#494C2×D1111yescharacteristic, complemented
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#367—111no—
259#366—111no—
260#366—111no—
261C4⋊C16—111no—
262C4⋊C16C2×D1111yescharacteristic, complemented
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⋊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—21no—
301C2×Q16C22×D1111yescharacteristic
302C2×Q16C22×D1111yescharacteristic
303C2×D8—111no—
304C2×D8—221no—
305C2×D8—222no—
306C2×D8—222no—
307C2×D8C22×D1111yescharacteristic
308C2×M16—111no—
309C22×C8—111no—
310C4⋊Q8—21no—
311#126—441no—
312#126—441no—
313#125—221no—
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—22no—
331SD32—22no—
332SD32—222no—
333SD32—222no—
334C2×C16—111no—
335C2×C16—111no—
336C2×C16C22×D1111yescharacteristic
337C2×C16C22×D1111yescharacteristic
338#107—111no—
339#107—111no—
340#107—111no—
341#107C22×D1111yescharacteristic
342#106—221no—
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—21no—
364C2×Q8—21no—
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—21no—
376Q16—21no—
377Q16—21no—
378Q16—21no—
379Q16—42no—
380D8—21no—
381D8—112no—
382D8—224no—
383D8—221no—
384D8#434112yes—
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—41no—
394C4⋊C4—41no—
395C4⋊C4—111no—
396C4⋊C4—111no—
397C4⋊C4—221no—
398C4⋊C4—221no—
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—41no—
432Q8—41no—
433Q8—41no—
434Q8—41no—
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×#434111yescharacteristic
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#1062313711yescharacteristic
486C4#1062330411yescharacteristic
487C2—82no—
488C2—441no—
489C2—882no—
490C2#1307861511yescharacteristic
491C2#1308175811yescharacteristic
492C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2208C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2208D11
hypocenterC11#33683
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2208

Complements

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

NH ≅ G/Ntype
1. #13079272C2semidirect
3. #13070823C2semidirect
4. #13070822C2semidirect
5. #13070774C2semidirect
6. #13070773C2semidirect
7. #13070658C2semidirect
10. #13070483C2semidirect
11. #13070481C2semidirect
12. SD32×Dic11C2semidirect
13. #13070465C2semidirect
14. #13070422C2semidirect
15. C11×#2208C2semidirect
21. C11×#494C22semidirect
27. Q16×Dic11C22semidirect
28. Q16×Dic11C22semidirect
40. #10622296C22semidirect
41. C11×C4⋊C16C22semidirect
42. C11×#358C22semidirect
43. C11×#358C22semidirect
44. #10622202C22semidirect
45. #10622202C22semidirect
52. #10622143C22semidirect
53. #10622142C22semidirect
54. #10622140C22semidirect
55. C16×Dic11C22semidirect
56. #10622128C22semidirect
57. #10622127C22semidirect
58. C4⋊(C11⋊C16)C22semidirect
186. #2208D11semidirect
240. #494C2×D11semidirect
262. C4⋊C16C2×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
#130792722
#130774632
#130708232
#130708222
#130707742
#130707732
#130706582
#130705432
#130704832
#130704812
SD32×Dic112
#130704652
#130704222
C11×#22082
#3368311