Finite Group Databasebeta

← #14672931

Subgroups — #14672931

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622496C211yesmaximal, characteristic
2C2×#10622127C211yesmaximal, characteristic, complemented
3C2×#10622147C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
6#13068642C211yesmaximal, characteristic, complemented
7C11×#1380C211yesmaximal, characteristic, complemented
8C22×D88C2211yescharacteristic
9C22×C8×D11C2211yescharacteristic
10C2×#66948—21no—
11C22×C11×C16C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×#66882C2211yescharacteristic
15C22×C11⋊C16C2211yescharacteristic
16#10622600—21no—
17C2×#66873—21no—
18#10622496—22no—
19#10622496—22no—
20#10622167—21no—
21#10622147—22no—
22(C2×D11)⋊C16—22no—
23#10622129—22no—
24#10622127—22no—
25C22×D44—21no—
26C22×D44—41no—
27C22×C4×D11D411yescharacteristic
28C22×C8×C11C2311yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×(C2×D11)⋊C4—41no—
32C2×(C2×D11)⋊C4—41no—
33C2×C4⋊Dic11—21no—
34C22×C11⋊C8D411yescharacteristic
35C2×D88—21no—
36C2×D88—21no—
37C2×D88—21no—
38C2×D88—21no—
39C2×D88—21no—
40C2×D88D412yes—
41C2×C8×D11—21no—
42C2×C8×D11—21no—
43C2×C8×D11—21no—
44C2×C8×D11—21no—
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47#66948—24no—
48#66948—42no—
49C2×C11×C16—21no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C11×#107—21no—
53C11×#107—21no—
54C11×#107—21no—
55C11×#107D412yes—
56C11⋊#95—41no—
57#66882—21no—
58#66882—21no—
59C2×C11⋊C16—21no—
60C2×C11⋊C16—21no—
61C2×C11⋊C16D412yescomplemented
62#66873—24no—
63#13380—111nomaximal, Sylow
64C23×D11—41no—
65C23×D11D811yescharacteristic
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—41no—
70C22×Dic11D811yescharacteristic
71C2×D44—22no—
72C2×D44—44no—
73C2×D44—41no—
74C2×D44—41no—
75C2×D44—41no—
76C2×D44—41no—
77C2×D44—41no—
78C2×D44—82no—
79C2×D44—82no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C8×C11C2×D411yescharacteristic
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11#4111yescharacteristic
90C2×C8×C11#4111yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C11×C4⋊C4—22no—
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95C11×C4⋊C4—41no—
96(C2×D11)⋊C4—44no—
97(C2×D11)⋊C4—82no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103D88—22no—
104D88—22no—
105D88—41no—
106D88—41no—
107C8×D11—41no—
108C8×D11—41no—
109C8×D11—41no—
110C8×D11—41no—
111C11×C16—41no—
112C11⋊C16—22no—
113C2×#466—111no—
114C2×#366—111no—
115C2×#357—111no—
116C2×#357—111no—
117C2×C22⋊C16—111no—
118#1808—111no—
119#1380D1111yescharacteristic, complemented
120C23×C11C2×D811yescharacteristic
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—42no—
128C22×D11—81no—
129C22×D11—81no—
130C22×D11—81no—
131C22×D11—81no—
132C22×D11—81no—
133C22×D11—81no—
134C22×D11D1612yes—
135C2×C4×C11—42no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11#12011yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12311yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153D44—42no—
154D44—42no—
155D44—88no—
156D44—81no—
157D44—81no—
158C4×D11—41no—
159C4×D11—41no—
160C4×D11—41no—
161C4×D11—41no—
162C8×C11#12111yescharacteristic
163C8×C11#12111yescharacteristic
164C8×C11#12311yescharacteristic
165C8×C11#12411yescharacteristic
166C11⋊C8—41no—
167C22×D8—111no—
168C23×C8—111no—
169C2×#121—221no—
170C22×C16—111no—
171C22×C16C2×D1111yescharacteristic
172#466—222no—
173#466—222no—
174C2×#107—111no—
175C2×#107C2×D1111yescharacteristic
176C2×#107C2×D1111yescharacteristic
177C2×#102—221no—
178#380—221no—
179#366—222no—
180#357—222no—
181#357—222no—
182C22⋊C16—222no—
183#340—221no—
184C22×C11#44711yescharacteristic
185C22×C11#46611yescharacteristic
186C22×C11#48011yescharacteristic
187C22×C11C2×D1611yescharacteristic
188C22×C11#50811yescharacteristic
189C22×C11#50911yescharacteristic
190C22×C11#51011yescharacteristic
191C2×D11—22no—
192C2×D11—22no—
193C2×D11—22no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—161no—
202C2×D11—161no—
203C2×D11—161no—
204C2×D11—161no—
205C4×C11—82no—
206C4×C11—161no—
207C4×C11#39411yescharacteristic
208C4×C11#45211yescharacteristic
209C4×C11#46811yescharacteristic
210C4×C11#48211yescharacteristic
211Dic11—41no—
212Dic11—161no—
213C22×D4—221no—
214C22×D4—441no—
215C23×C4—111no—
216C2×D8—112no—
217C2×D8—221no—
218C2×D8—221no—
219C2×D8—221no—
220C2×D8—221no—
221C2×D8—221no—
222C22×C8—111no—
223C22×C8—221no—
224C22×C8—221no—
225C22×C8—221no—
226C22×C8—221no—
227C22×C8—221no—
228C22×C8—221no—
229C22×C8C22×D1111yescharacteristic
230#121—224no—
231#121—442no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—441no—
236C2×C22⋊C4—441no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—112no—
241C2×C16—221no—
242C2×C16—221no—
243#107—21no—
244#107—21no—
245#107—21no—
246#107—221no—
247#107—221no—
248#107D4412yes—
249#102—224no—
250#95—441no—
251C2×C11#203311yescharacteristic
252C2×C11#218411yescharacteristic
253C2×C11#218911yescharacteristic
254C2×C11#221511yescharacteristic
255C2×C11#222011yescharacteristic
256C2×C11#223211yescharacteristic
257C2×C11#223411yescharacteristic
258D11—42no—
259D11—162no—
260C24—111no—
261C24—441no—
262C2×D4—222no—
263C2×D4—444no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—882no—
270C2×D4—882no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—111no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282D8—222no—
283D8—222no—
284D8—441no—
285D8—441no—
286C2×C8—221no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—441no—
290C2×C8—441no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8C2×D4411yescharacteristic
294C2×C8#433911yescharacteristic
295C2×C8#433911yescharacteristic
296C2×C8D4×D1111yescharacteristic
297C2×C8D4×D1111yescharacteristic
298C2×C8#434311yescharacteristic
299C4⋊C4—22no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C22⋊C4—444no—
306C22⋊C4—882no—
307C16—41no—
308C16—222no—
309C11#1338011yescharacteristic, complemented, Sylow
310C23—112no—
311C23—221no—
312C23—221no—
313C23—221no—
314C23—221no—
315C23—221no—
316C23—221no—
317C23—442no—
318C23—881no—
319C23—881no—
320C23—881no—
321C23—881no—
322C23—881no—
323C23—881no—
324C23D8×D1111yescharacteristic
325D4—442no—
326D4—442no—
327D4—888no—
328D4—881no—
329D4—881no—
330C2×C4—42no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4#6693511yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4#6694711yescharacteristic
349C2×C4#6696711yescharacteristic
350C2×C4#6696911yescharacteristic
351C2×C4#6697111yescharacteristic
352C8—441no—
353C8#6692811yescharacteristic
354C8#6693711yescharacteristic
355C8#6694711yescharacteristic
356C8#6694811yescharacteristic
357C22—222no—
358C22—222no—
359C22—222no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22—882no—
365C22—882no—
366C22—882no—
367C22—1761no—
368C22—1761no—
369C22—1761no—
370C22—1761no—
371C22#1062238611yescharacteristic
372C22#1062238811yescharacteristic
373C22#1062249511yescharacteristic
374C22D11×D1611yescharacteristic
375C22#1062252711yescharacteristic
376C22#1062252911yescharacteristic
377C22#1062253111yescharacteristic
378C4—82no—
379C4—161no—
380C4—441no—
381C4—1761no—
382C4#1062228511yescharacteristic
383C4#1062242311yescharacteristic
384C4#1062242511yescharacteristic
385C4#1062247911yescharacteristic
386C2—442no—
387C2—1762no—
388C2#1306980111yescharacteristic
389C2#1307052911yescharacteristic
390C2#1307055911yescharacteristic
391C2#1307070111yescharacteristic
392C2#1307073211yescharacteristic
393C2#1307079811yescharacteristic
394C2#1307080911yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1380C2
socleC23×C11C2×D8
prime radicalC2×#10622496C2
hypercenter#1380D11
hypocenterC11#13380
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
2. C2×#10622127C2semidirect
3. C2×#10622147C2semidirect
4. C2×#10622129C2semidirect
5. C2×(C2×D11)⋊C16C2semidirect
6. #13068642C2semidirect
7. C11×#1380C2semidirect
61. C2×C11⋊C16D4semidirect
119. #1380D11semidirect
309. C11#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#106224962
C2×#106221272
C2×#106221472
C2×#106221292
C2×(C2×D11)⋊C162
#130686422
C11×#13802
#1338011