Finite Group Databasebeta

← #14672940

Subgroups — #14672940

Order 2816.

446 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622801C211yesmaximal, characteristic
2C2×#10622128C211yesmaximal, characteristic, complemented
3C2×#10622202C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C16C211yesmaximal, characteristic
5#13068642C211yesmaximal, characteristic
6#13066708C211yesmaximal, characteristic, complemented
7C2×C11×#358C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C2×#66999—21no—
10C22×C8×D11C2211yescharacteristic
11C22×C11×C16C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×#66899—21no—
14#10622801—22no—
15#10622801—22no—
16C2×#66882C2211yescharacteristic
17C2×#66882C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622600—21no—
20C11×#358—22no—
21#10622202—22no—
22#10622167—21no—
23(C2×D11)⋊C16—22no—
24#10622128—22no—
25C22×Q8×C11—21no—
26C22×C4×D11D411yescharacteristic
27C2×C11×Q16—21no—
28C2×C11×Q16—21no—
29C2×C11×Q16—21no—
30C2×C11×Q16—21no—
31C2×C11×Q16—21no—
32C2×C11×Q16D412yes—
33C22×C8×C11C2311yescharacteristic
34C2×C11×C4⋊C4—21no—
35#66999—24no—
36#66999—42no—
37C2×(C2×D11)⋊C4—41no—
38C2×(C2×D11)⋊C4—41no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×Dic11⋊C4—41no—
42C22×C11⋊C8D411yescharacteristic
43C2×C8×D11—21no—
44C2×C8×D11—21no—
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47C2×C8×D11—21no—
48C2×C8×D11—21no—
49C2×C11×C16—21no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C11×#107—21no—
53C11×#107—21no—
54#66899—24no—
55C11⋊#95—41no—
56#66882—21no—
57#66882—21no—
58#66882—21no—
59#66882D412yes—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16D412yes—
63#13382—111nomaximal, Sylow
64C23×D11D811yescharacteristic
65C2×Q8×C11—22no—
66C2×Q8×C11—41no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C22×Dic11—41no—
75C22×Dic11—41no—
76C22×Dic11D811yescharacteristic
77C2×C4×D11—21no—
78C2×C4×D11—21no—
79C2×C4×D11—21no—
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C11×Q16—22no—
84C11×Q16—22no—
85C11×Q16—41no—
86C11×Q16—41no—
87C2×C8×C11C2×D411yescharacteristic
88C2×C8×C11C2×D411yescharacteristic
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11#4111yescharacteristic
91C2×C8×C11#4111yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C11×C4⋊C4—41no—
94C11×C4⋊C4—41no—
95(C2×D11)⋊C4—44no—
96(C2×D11)⋊C4—82no—
97C4⋊Dic11—22no—
98C4⋊Dic11—41no—
99C4⋊Dic11—41no—
100C4⋊Dic11—41no—
101Dic11⋊C4—44no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C8×D11—41no—
106C8×D11—41no—
107C8×D11—41no—
108C8×D11—41no—
109C11×C16—41no—
110C11⋊C16—22no—
111C2×#467—111no—
112C2×#367—111no—
113C2×#358—111no—
114C2×#358D1111yescharacteristic, complemented
115C2×C22⋊C16—111no—
116#1808—111no—
117#1380—111no—
118C23×C11C2×D811yescharacteristic
119C22×D11—21no—
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11SD3212yes—
126Q8×C11—42no—
127Q8×C11—42no—
128Q8×C11—81no—
129Q8×C11—81no—
130C2×C4×C11—42no—
131C2×C4×C11—81no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×C4×C11—81no—
135C2×C4×C11—81no—
136C2×C4×C11#12011yescharacteristic
137C2×C4×C11#12111yescharacteristic
138C2×C4×C11#12311yescharacteristic
139C2×C4×C11#13511yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—42no—
146C2×Dic11—81no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151C4×D11—41no—
152C4×D11—41no—
153C4×D11—41no—
154C4×D11—41no—
155C8×C11#12111yescharacteristic
156C8×C11#12111yescharacteristic
157C8×C11#12311yescharacteristic
158C8×C11#12411yescharacteristic
159C11⋊C8—41no—
160C22×Q16C2×D1111yescharacteristic
161C23×C8—111no—
162C2×C22⋊Q8—221no—
163C22×C16—111no—
164C22×C16C2×D1111yescharacteristic
165#467—222no—
166#467—222no—
167C2×#107—111no—
168C2×#107—111no—
169C2×#107C2×D1111yescharacteristic
170C2×#103—221no—
171#380—221no—
172#367—222no—
173#358—22no—
174#358—222no—
175C22⋊C16—222no—
176#340—221no—
177C22×C11#44711yescharacteristic
178C22×C11#46611yescharacteristic
179C22×C11#48011yescharacteristic
180C22×C11C2×SD3211yescharacteristic
181C22×C11#50811yescharacteristic
182C22×C11#51011yescharacteristic
183C22×C11#51011yescharacteristic
184C2×D11—22no—
185C2×D11—22no—
186C2×D11—22no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C4×C11—82no—
192C4×C11—161no—
193C4×C11#39411yescharacteristic
194C4×C11#45211yescharacteristic
195C4×C11#46811yescharacteristic
196C4×C11#48211yescharacteristic
197Dic11—41no—
198Dic11—82no—
199Dic11—161no—
200C22×Q8—21no—
201C23×C4—111no—
202C2×Q16—21no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16C22⋊D1112yes—
208C22×C8—111no—
209C22×C8—221no—
210C22×C8—221no—
211C22×C8—221no—
212C22×C8—221no—
213C22×C8—221no—
214C22×C8—221no—
215C22×C8C22×D1111yescharacteristic
216C22⋊Q8—224no—
217C22⋊Q8—442no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4—221no—
221C2×C4⋊C4—441no—
222C2×C22⋊C4—441no—
223C2×C22⋊C4—441no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—112no—
228C2×C16—221no—
229C2×C16—221no—
230#107—21no—
231#107—21no—
232#107—112no—
233#107—221no—
234#107—221no—
235#107—221no—
236#103—224no—
237#95—441no—
238C2×C11#203311yescharacteristic
239C2×C11#218511yescharacteristic
240C2×C11#218911yescharacteristic
241C2×C11#221711yescharacteristic
242C2×C11#221911yescharacteristic
243C2×C11#223511yescharacteristic
244C2×C11#223711yescharacteristic
245D11—42no—
246C24—111no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—111no—
256C22×C4—221no—
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—441no—
263C22×C4—441no—
264C22×C4D4×D1111yescharacteristic
265Q16—22no—
266Q16—22no—
267Q16—41no—
268Q16—41no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8—221no—
272C2×C8—441no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8#433911yescharacteristic
277C2×C8#433911yescharacteristic
278C2×C8D4×D1111yescharacteristic
279C2×C8D4×D1111yescharacteristic
280C2×C8#434111yescharacteristic
281C2×C8C2×C22⋊D1111yescharacteristic
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—222no—
285C4⋊C4—444no—
286C4⋊C4—441no—
287C4⋊C4—441no—
288C4⋊C4—441no—
289C22⋊C4—444no—
290C22⋊C4—882no—
291C16—41no—
292C16—222no—
293C11#1338211yescharacteristic, complemented, Sylow
294C23—112no—
295C23—221no—
296C23—221no—
297C23—221no—
298C23—221no—
299C23—221no—
300C23—221no—
301C23D8×D1111yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—81no—
305Q8—81no—
306C2×C4—42no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4#6693611yescharacteristic
326C2×C4#6693711yescharacteristic
327C2×C4#6696411yescharacteristic
328C2×C4#6696811yescharacteristic
329C2×C4#6696911yescharacteristic
330C2×C4#6699011yescharacteristic
331C8—441no—
332C8#6693711yescharacteristic
333C8#6693811yescharacteristic
334C8#6698211yescharacteristic
335C8#6699211yescharacteristic
336C22—222no—
337C22—222no—
338C22—222no—
339C22—441no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22#1062238711yescharacteristic
344C22#1062238811yescharacteristic
345C22D11×SD3211yescharacteristic
346C22#1062252811yescharacteristic
347C22#1062253111yescharacteristic
348C22#1062253211yescharacteristic
349C22#1062276911yescharacteristic
350C4—82no—
351C4—161no—
352C4—441no—
353C4—882no—
354C4—1761no—
355C4#1062239211yescharacteristic
356C4#1062239311yescharacteristic
357C4#1062257211yescharacteristic
358C4#1062278611yescharacteristic
359C2—442no—
360C2#1306979611yescharacteristic
361C2#1307053111yescharacteristic
362C2#1307055511yescharacteristic
363C2#1307071511yescharacteristic
364C2#1307072311yescharacteristic
365C2#1307081211yescharacteristic
366C2#1307082311yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#358C2
socleC23×C11C2×D8
prime radicalC23×D11D8
hypercenterC2×#358D11
hypocenterC11#13382
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#10622128C2semidirect
3. C2×#10622202C2semidirect
6. #13066708C2semidirect
7. C2×C11×#358C2semidirect
114. C2×#358D11semidirect
293. C11#13382semidirect

Maximal subgroups

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

subgroupindex
C2×#106228012
C2×#106221282
C2×#106222022
C2×(C2×D11)⋊C162
#130686422
#130667082
C2×C11×#3582
#1338211