Finite Group Databasebeta

← #14908943

Subgroups — #14908943

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#13077468C211yesmaximal, characteristic
3#13070825C211yesmaximal, characteristic, complemented
4#13070821C211yesmaximal, characteristic, complemented
5#13070775C211yesmaximal, characteristic, complemented
6#13070771C211yesmaximal, characteristic, complemented
7#13070659C211yesmaximal, characteristic, complemented
8#13070659C211yesmaximal, characteristic, complemented
9#13070545C211yesmaximal, characteristic
10#13070481C211yesmaximal, characteristic, complemented
11#13070477C211yesmaximal, characteristic, complemented
12#13070471C211yesmaximal, characteristic, complemented
13SD32×Dic11C211yesmaximal, characteristic, complemented
14#13070420C211yesmaximal, characteristic, complemented
15C11×#2187C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17#10623329—21no—
18#10623156—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×SD32C2211yescharacteristic
21C11×#467C2211yescharacteristic
22#10622828—21no—
23Q16×Dic11C2211yescharacteristic, complemented
24#10622794C2211yescharacteristic, complemented
25#10622765—21no—
26#10622765—21no—
27D8×Dic11C2211yescharacteristic
28D8×Dic11C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31C2×#66891C2211yescharacteristic
32C2×#66891C2211yescharacteristic
33#10622729C2211yescharacteristic
34#10622719C2211yescharacteristic
35#10622714C2211yescharacteristic
36#10622665—21no—
37#10622491C2211yescharacteristic, complemented
38#10622486C2211yescharacteristic, complemented
39#10622410—21no—
40#10622402—21no—
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic, complemented
45#10622202C2211yescharacteristic, complemented
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622143C2211yescharacteristic, complemented
50#10622142C2211yescharacteristic, complemented
51#10622141C2211yescharacteristic, complemented
52#10622141C2211yescharacteristic, complemented
53#10622140C2211yescharacteristic, complemented
54Dic11⋊C16C2211yescharacteristic, complemented
55Dic11⋊C16C2211yescharacteristic, complemented
56C16×Dic11C2211yescharacteristic, complemented
57#10622128C2211yescharacteristic, complemented
58#10622127C2211yescharacteristic, complemented
59C22×D4×C11—21no—
60C2×C11×Q16C2311yescharacteristic
61C2×C11×D8—22no—
62C2×C11×D8—22no—
63C2×C11×D8—21no—
64C2×C11×D8C2311yescharacteristic
65C2×C11×D8C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—21no—
68C2×C22⋊Dic11—41no—
69C2×C22⋊Dic11—41no—
70Q8×Dic11—21no—
71#66997—21no—
72C2×#4326—21no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75D4×Dic11—21no—
76D4×Dic11—21no—
77D4×Dic11—41no—
78D4×Dic11—41no—
79#66979—21no—
80#66979D411yescharacteristic
81#66977—21no—
82C2×#4318D411yescharacteristic
83C2×Dic44C2311yescharacteristic
84#66943—21no—
85#66943—41no—
86#66942—41no—
87#66940—21no—
88#66932—41no—
89#66932—41no—
90C11×SD32—22no—
91C11×SD32—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#103—21no—
96#66899—21no—
97#66896—21no—
98#66896—21no—
99#66896—21no—
100#66896—21no—
101#66891—22no—
102#66891—22no—
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66881—21no—
107#66880—21no—
108#66879D411yescharacteristic
109#66879D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66874—21no—
115#66872—21no—
116#33683—111nomaximal, Sylow
117C24×C11—41no—
118C2×Q8×C11—21no—
119C2×D4×C11—24no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—42no—
123C2×D4×C11—41no—
124C22×C4×C11C2×D411yescharacteristic
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C2×Dic22—21no—
130C11×Q16—21no—
131C11×Q16—21no—
132C11×D8—24no—
133C11×D8—21no—
134C11×D8—21no—
135C11×D8#4112yes—
136C11×D8#4112yes—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—41no—
143C11×C22⋊C4—41no—
144C22⋊Dic11—41no—
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149C22⋊Dic11—41no—
150C22⋊Dic11D811yescharacteristic
151C22⋊Dic11D811yescharacteristic
152#4326—42no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158C4⋊Dic11D811yescharacteristic
159C4⋊Dic11D811yescharacteristic
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11—41no—
168C4×Dic11C2×D411yescharacteristic
169C4×Dic11C2×D411yescharacteristic
170#4318—41no—
171C2×C11⋊C8C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173Dic44—21no—
174Dic44—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#2208—111no—
187#2187—111no—
188#2187D1111yescharacteristic
189#2175—111no—
190#2175—111no—
191C4×SD32—111no—
192C4×SD32—111no—
193#2164—111no—
194C23×C11—44no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—161no—
198C23×C11—161no—
199C23×C11C2×D811yescharacteristic
200Q8×C11—41no—
201Q8×C11—41no—
202D4×C11—22no—
203D4×C11—22no—
204D4×C11—44no—
205D4×C11—41no—
206D4×C11—41no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C22×D411yescharacteristic
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—161no—
218C2×Dic11—161no—
219C2×Dic11—161no—
220C2×Dic11—161no—
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223C2×Dic11C2×D811yescharacteristic
224C2×Dic11C2×D811yescharacteristic
225Dic22—41no—
226Dic22—41no—
227C8×C11—21no—
228C8×C11C2×#4111yescharacteristic
229C8×C11C2×#4111yescharacteristic
230C11⋊C8—21no—
231C11⋊C8—21no—
232C22×D8C2×D1111yescharacteristic
233#541—221no—
234#518—221no—
235C2×SD32—111no—
236C2×SD32—111no—
237C2×SD32C2×D1111yescharacteristic
238C2×SD32C2×D1111yescharacteristic
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#427—111no—
255#418—221no—
256#405—111no—
257#367—111no—
258#367—111no—
259#366—111no—
260#366—111no—
261C4⋊C16—111no—
262C4⋊C16—111no—
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⋊C16C2×D1111yescharacteristic
273#346—111no—
274C4×C16—111no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—42no—
279C22×C11—42no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11—164no—
285C22×C11C22×D811yescharacteristic
286C4×C11—21no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11#52511yescharacteristic
290C4×C11#57511yescharacteristic
291Dic11—21no—
292Dic11—21no—
293Dic11—21no—
294Dic11—21no—
295Dic11—81no—
296Dic11—81no—
297Dic11—81no—
298Dic11—81no—
299C22×D4—21no—
300C2×Q16—111no—
301C2×Q16—221no—
302C2×Q16C22×D1111yescharacteristic
303C2×D8—22no—
304C2×D8—22no—
305C2×D8—21no—
306C2×D8C22×D1111yescharacteristic
307C2×D8C22×D1111yescharacteristic
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—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—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—82no—
358C2×C11—82no—
359C2×C11#310011yescharacteristic
360C2×C11#341611yescharacteristic
361C2×C11#341611yescharacteristic
362C24—41no—
363C2×Q8—21no—
364C2×Q8—221no—
365C2×D4—24no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—42no—
369C2×D4—41no—
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—24no—
381D8—21no—
382D8—21no—
383D8#434112yes—
384D8#434112yes—
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—41no—
394C4⋊C4—111no—
395C4⋊C4—111no—
396C4⋊C4—221no—
397C4⋊C4—221no—
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—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—111no—
417C42—441no—
418C42—441no—
419C42—441no—
420C16—21no—
421C16—21no—
422C16—221no—
423C16—221no—
424C11#3368311yescharacteristic, complemented, Sylow
425C23—44no—
426C23—41no—
427C23—41no—
428C23—161no—
429C23—161no—
430C23D8×D1111yescharacteristic
431Q8—41no—
432Q8—41no—
433Q8—441no—
434Q8—441no—
435D4—22no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—41no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—111no—
445C2×C4—111no—
446C2×C4—111no—
447C2×C4—111no—
448C2×C4—441no—
449C2×C4—441no—
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—
461C8C2×#434111yescharacteristic
462C8C2×#434111yescharacteristic
463C22—21no—
464C22—21no—
465C22—21no—
466C22—42no—
467C22—42no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—81no—
472C22—164no—
473C22C2×D8×D1111yescharacteristic
474C4—21no—
475C4—81no—
476C4—81no—
477C4—221no—
478C4—221no—
479C4—221no—
480C4—221no—
481C4—881no—
482C4—881no—
483C4—881no—
484C4—881no—
485C4#1062311711yescharacteristic
486C4#1062330411yescharacteristic
487C2—41no—
488C2—82no—
489C2—82no—
490C2#1307861111yescharacteristic
491C2#1308175811yescharacteristic
492C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2187C2
socleC22×C11C22×D8
prime radicalC22×C11×D8C22
hypercenter#2187D11
hypocenterC11#33683
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2187

Complements

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

NH ≅ G/Ntype
1. #13079268C2semidirect
3. #13070825C2semidirect
4. #13070821C2semidirect
5. #13070775C2semidirect
6. #13070771C2semidirect
7. #13070659C2semidirect
8. #13070659C2semidirect
10. #13070481C2semidirect
11. #13070477C2semidirect
12. #13070471C2semidirect
13. SD32×Dic11C2semidirect
14. #13070420C2semidirect
23. Q16×Dic11C22semidirect
24. #10622794C22semidirect
37. #10622491C22semidirect
38. #10622486C22semidirect
44. #10622202C22semidirect
45. #10622202C22semidirect
49. #10622143C22semidirect
50. #10622142C22semidirect
51. #10622141C22semidirect
52. #10622141C22semidirect
53. #10622140C22semidirect
54. Dic11⋊C16C22semidirect
55. Dic11⋊C16C22semidirect
56. C16×Dic11C22semidirect
57. #10622128C22semidirect
58. #10622127C22semidirect
424. C11#33683semidirect

Maximal subgroups

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

subgroupindex
#130792682
#130774682
#130708252
#130708212
#130707752
#130707712
#130706592
#130705452
#130704812
#130704772
#130704712
SD32×Dic112
#130704202
C11×#21872
#3368311