Finite Group Databasebeta

← #14811318

Subgroups — #14811318

Order 2816.

884 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078482C212yesmaximal, complemented
2#13077142C212yesmaximal
3#13070149C211yesmaximal, characteristic, complemented
4#13069972C212yesmaximal, complemented
5#13069772C211yesmaximal, characteristic, complemented
6#13068889C212yesmaximal, complemented
7#13068844C212yesmaximal, complemented
8#13068673C212yesmaximal, complemented
9C11×#1792C211yesmaximal, characteristic
10C2×C11×H(5,𝔽2)C2211yescharacteristic
11#10623358C2212yes—
12C2×#67001C2212yes—
13#10623031C2211yescharacteristic, complemented
14C2×C11×#104C2212yes—
15C11×#417C2212yes—
16C2×C11×#100C2211yescharacteristic
17C11×#390C2211yescharacteristic
18#10622846—22no—
19#10622846C2212yes—
20#10622845—22no—
21#10622845C2212yes—
22#10622828—22no—
23#10622828C2212yes—
24C2×#66896—22no—
25C2×#66896C2212yes—
26C2×#66886C2212yescomplemented
27#10622734C2212yescomplemented
28#10622732C2212yescomplemented
29C2×#66872C2212yescomplemented
30#10622548C2211yescharacteristic, complemented
31#10622409—22no—
32#10622404—22no—
33#10622379—22no—
34#10622374—22no—
35#10622192C2212yescomplemented
36#10622168C2211yescharacteristic, complemented
37#10622162C2211yescharacteristic, complemented
38#10622161C2212yescomplemented
39C11×H(5,𝔽2)—24no—
40C11×H(5,𝔽2)—41no—
41C11×H(5,𝔽2)Q814yescomplemented
42C2×C11×#41—22no—
43C2×C11×#41C2312yes—
44C22×D4×C11—22no—
45C22×D4×C11—41no—
46C22×D4×C11C2311yescharacteristic
47C2×C11×M16C2312yes—
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C22⋊C4—41no—
50C2×C42×C11C2311yescharacteristic
51#67001—24no—
52#67001—42no—
53Q8×Dic11—22no—
54D4×Dic11—22no—
55D4×Dic11—42no—
56#66979—22no—
57#66979C2312yes—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—41no—
60C2×C4⋊Dic11C2312yes—
61#66977—41no—
62C2×#4318—22no—
63C2×#4318C2312yes—
64C22×C11⋊C8—22no—
65C22×C11⋊C8C2312yes—
66#66943—22no—
67#66941—22no—
68C11×#104—24no—
69C11×#103—22no—
70C11×#102—22no—
71C11×#100—41no—
72#66899—22no—
73#66899D412yes—
74#66899D412yes—
75#66896—22no—
76#66896—22no—
77#66896—22no—
78#66896—22no—
79#66896—22no—
80#66896D412yes—
81#66896D412yes—
82#66886—42no—
83#66882—22no—
84#66881—22no—
85Dic11⋊C8—22no—
86Dic11⋊C8—22no—
87#66872—22no—
88#66872—22no—
89#25983—111nomaximal, Sylow
90C24×C11—21no—
91C24×C11—41no—
92C11×#41—22no—
93C11×#41—22no—
94C11×#41—28no—
95C11×#41—44no—
96C11×#41C2×Q814yes—
97C11×#41#4114yes—
98C2×Q8×C11C2×D412yes—
99C2×D4×C11—22no—
100C2×D4×C11—28no—
101C2×D4×C11—22no—
102C2×D4×C11—22no—
103C2×D4×C11—21no—
104C2×D4×C11—44no—
105C2×D4×C11—42no—
106C2×D4×C11—44no—
107C2×D4×C11—44no—
108C2×D4×C11C2×D412yes—
109C2×D4×C11C2×Q812yes—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—41no—
114C22×C4×C11C2411yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—42no—
117C2×Dic22—41no—
118C11×M16—22no—
119C11×M16—22no—
120C2×C8×C11—22no—
121C11×C4⋊C4—22no—
122C11×C22⋊C4—82no—
123C42×C11—22no—
124C22⋊Dic11—22no—
125C22⋊Dic11—42no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—42no—
129C4⋊Dic11—41no—
130C4⋊Dic11—82no—
131C4⋊Dic11C2×D412yes—
132C4⋊Dic11C2×D412yes—
133Dic11⋊C4—42no—
134C4×Dic11—22no—
135C4×Dic11—42no—
136#4318—22no—
137#4318—22no—
138#4318—44no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—44no—
143C2×C11⋊C8C2×D412yes—
144C2×C11⋊C8C2×D412yes—
145#3084—112no—
146#2897—112no—
147#2094—111no—
148#2063—112no—
149#2027—111no—
150#1866—112no—
151#1859—112no—
152#1815—112no—
153#1792D1111yescharacteristic
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—44no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—81no—
160C23×C11—81no—
161C23×C11—161no—
162C23×C11—161no—
163C23×C11H(5,𝔽2)11yescharacteristic
164Q8×C11—22no—
165Q8×C11C22⋊Q814yes—
166D4×C11—24no—
167D4×C11—24no—
168D4×C11—24no—
169D4×C11—22no—
170D4×C11—48no—
171D4×C11—42no—
172D4×C11C22⋊Q814yes—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—22no—
177C2×C4×C11—44no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—81no—
182C2×C4×C11C22×D412yes—
183C2×C4×C11C22×Q811yescharacteristic
184C2×C4×C11C2×#4112yes—
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C2×Dic11—22no—
187C2×Dic11—22no—
188C2×Dic11—42no—
189C2×Dic11—82no—
190C2×Dic11—162no—
191Dic22—161no—
192C8×C11—42no—
193C11⋊C8—22no—
194C11⋊C8—22no—
195C11⋊C8—42no—
196C2×H(5,𝔽2)C2×D1111yescharacteristic
197C2×#131—112no—
198#544—111no—
199#520—112no—
200#479—222no—
201#478—222no—
202#476—222no—
203#475—222no—
204C2×#108—112no—
205#428—112no—
206C2×#106—112no—
207#424—112no—
208C2×#104C2×D1112yes—
209#418—112no—
210#418—222no—
211#417—112no—
212#417—222no—
213#417C2×D1112yes—
214#416—112no—
215#416—222no—
216C2×#102—112no—
217C2×#102—222no—
218C2×#100C2×D1111yescharacteristic
219#390C2×D1111yescharacteristic
220#384—111no—
221#343—112no—
222#343—111no—
223#339—112no—
224#336—111no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—24no—
228C22×C11—42no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—82no—
232C22×C11—81no—
233C22×C11—81no—
234C22×C11—161no—
235C22×C11—164no—
236C22×C11#54311yescharacteristic
237C22×C11D4211yescharacteristic
238C22×C11#55111yescharacteristic
239C4×C11—24no—
240C4×C11—42no—
241C4×C11—81no—
242C4×C11C2×C22⋊Q812yes—
243C4×C11#54612yes—
244Dic11—42no—
245Dic11—42no—
246Dic11—82no—
247H(5,𝔽2)—24no—
248H(5,𝔽2)—41no—
249H(5,𝔽2)Dic2214yescomplemented
250C2×#41—22no—
251C2×#41C22×D1112yes—
252C22×D4—22no—
253C22×D4—41no—
254C22×D4C22×D1111yescharacteristic
255#131—224no—
256#131—442no—
257C2×M16—112no—
258C2×M16—222no—
259C2×M16C22×D1112yes—
260C22×C8—112no—
261C22×C8—222no—
262C4⋊Q8—222no—
263#125—222no—
264C22⋊Q8—441no—
265C4×Q8—222no—
266C4×D4—222no—
267C4×D4—442no—
268#117—112no—
269#117—222no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—441no—
273C2×C4⋊C4C22×D1111yescharacteristic
274C2×C22⋊C4—41no—
275C2×C42C22×D1111yescharacteristic
276#108—442no—
277#107—222no—
278#106—222no—
279#106—222no—
280#106—222no—
281C4⋊C8—222no—
282C4⋊C8—222no—
283#104—24no—
284#103—22no—
285#103—112no—
286#103—112no—
287#103—222no—
288#102—22no—
289#102—112no—
290#102—112no—
291#102—222no—
292#102—222no—
293#102—222no—
294#102—222no—
295#102—222no—
296#100—41no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—44no—
300C2×C11—82no—
301C2×C11#243711yescharacteristic
302C2×C11#328811yescharacteristic
303C2×C11#329111yescharacteristic
304C24—21no—
305C24—41no—
306#41—22no—
307#41—22no—
308#41—28no—
309#41—44no—
310#41C2×Dic2214yes—
311#41#434114yes—
312C2×Q8—441no—
313C2×Q8D4×D1112yes—
314C2×D4—22no—
315C2×D4—28no—
316C2×D4—22no—
317C2×D4—22no—
318C2×D4—21no—
319C2×D4—44no—
320C2×D4—42no—
321C2×D4—44no—
322C2×D4—44no—
323C2×D4C2×Dic2212yes—
324C2×D4D4×D1112yes—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—222no—
330C22×C4—442no—
331C22×C4C23×D1111yescharacteristic
332M16—22no—
333M16—22no—
334M16—222no—
335M16—222no—
336M16—444no—
337C2×C8—22no—
338C2×C8—112no—
339C2×C8—112no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—444no—
344C4⋊C4—22no—
345C4⋊C4—112no—
346C4⋊C4—112no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—442no—
350C4⋊C4—441no—
351C4⋊C4—442no—
352C4⋊C4—882no—
353C22⋊C4—82no—
354C22⋊C4—222no—
355C22⋊C4—442no—
356C42—22no—
357C42—222no—
358C42—442no—
359C11#2598311yescharacteristic, complemented, Sylow
360C23—22no—
361C23—22no—
362C23—44no—
363C23—41no—
364C23—41no—
365C23—81no—
366C23—81no—
367C23—161no—
368C23—161no—
369C23#6703711yescharacteristic
370Q8—22no—
371Q8—1761no—
372Q8#6693114yes—
373D4—24no—
374D4—24no—
375D4—24no—
376D4—22no—
377D4—48no—
378D4—42no—
379D4#6693114yes—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—44no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—81no—
389C2×C4—222no—
390C2×C4—222no—
391C2×C4—442no—
392C2×C4—882no—
393C2×C4—1762no—
394C2×C4C22×Dic2211yescharacteristic
395C2×C4C2×D4×D1112yes—
396C2×C4C2×#434112yes—
397C2×C4#6703711yescharacteristic
398C8—42no—
399C8—222no—
400C8—222no—
401C8—442no—
402C22—21no—
403C22—21no—
404C22—24no—
405C22—42no—
406C22—42no—
407C22—42no—
408C22—82no—
409C22—81no—
410C22—81no—
411C22—161no—
412C22—164no—
413C22#1062301411yescharacteristic
414C22#1062311811yescharacteristic
415C22#1062312111yescharacteristic
416C4—24no—
417C4—42no—
418C4—81no—
419C4—442no—
420C4—442no—
421C4—882no—
422C4C2×#6693112yes—
423C4#1062312212yes—
424C2—21no—
425C2—21no—
426C2—44no—
427C2—82no—
428C2#1307228211yescharacteristic
429C2#1308038511yescharacteristic
430C2#1308041111yescharacteristic
subgroupG/H
centerC22#10623121
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1792C2
socleC22×C11D42
prime radicalC2×C11×H(5,𝔽2)C22
hypercenter#1792D11
hypocenterC11#25983
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1792

Complements

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

NH ≅ G/Ntype
1. #13078482C2semidirect
3. #13070149C2semidirect
4. #13069972C2semidirect
5. #13069772C2semidirect
6. #13068889C2semidirect
7. #13068844C2semidirect
8. #13068673C2semidirect
13. #10623031C22semidirect
26. C2×#66886C22semidirect
27. #10622734C22semidirect
28. #10622732C22semidirect
29. C2×#66872C22semidirect
30. #10622548C22semidirect
35. #10622192C22semidirect
36. #10622168C22semidirect
37. #10622162C22semidirect
38. #10622161C22semidirect
41. C11×H(5,𝔽2)Q8semidirect
249. H(5,𝔽2)Dic22semidirect
359. C11#25983semidirect

Maximal subgroups

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

subgroupindex
#130784822
#130771422
#130701492
#130699722
#130697722
#130688892
#130688442
#130686732
C11×#17922
#2598311