Finite Group Databasebeta

← #14673121

Subgroups — #14673121

Order 2816.

482 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622804C211yesmaximal, characteristic
2C2×#10622202C211yesmaximal, characteristic, complemented
3C2×#10622147C211yesmaximal, characteristic
4C2×#10622129C211yesmaximal, characteristic
5#13069350C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C2×C11×#358C211yesmaximal, characteristic, complemented
8C22×C11×Q16C2211yescharacteristic
9C2×#67000—21no—
10C22×#4325—21no—
11C22×D88C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14#10622804—22no—
15#10622804—22no—
16C2×#66882C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622598—21no—
20C11×#358—22no—
21#10622202—22no—
22#10622167—21no—
23#10622147—22no—
24#10622129—22no—
25C22×Q8×C11—21no—
26C22×D44—21no—
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#67000—24no—
36#67000—42no—
37C2×#4325—24no—
38C2×#4325—42no—
39C2×#4325—42no—
40C2×(C2×D11)⋊C4—41no—
41C2×(C2×D11)⋊C4—41no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—41no—
44C2×C4×Dic11D411yescharacteristic
45C22×C11⋊C8D411yescharacteristic
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88D412yes—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C11×#107—21no—
56C11×#107D412yes—
57C11⋊#95—41no—
58#66882—21no—
59#66882—21no—
60C8×Dic11—21no—
61C8×Dic11—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65#13408—111nomaximal, Sylow
66C23×D11—41no—
67C2×Q8×C11—22no—
68C2×Q8×C11—41no—
69C2×Q8×C11—41no—
70C2×Q8×C11—41no—
71C2×Q8×C11—41no—
72C2×Q8×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C22×Dic11—41no—
77C22×Dic11D811yescharacteristic
78C22×Dic11D811yescharacteristic
79C2×D44—22no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C11×Q16—22no—
86C11×Q16—22no—
87C11×Q16—41no—
88C11×Q16—41no—
89C2×C8×C11C2×D411yescharacteristic
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11#4111yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97#4325—48no—
98(C2×D11)⋊C4—44no—
99(C2×D11)⋊C4—44no—
100C4⋊Dic11—41no—
101C4⋊Dic11—41no—
102C4⋊Dic11—82no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8SD1612yes—
108D88—22no—
109D88—22no—
110D88—41no—
111D88—41no—
112C11×C16—41no—
113C11⋊C16—41no—
114C2×#495—111no—
115C2×#358—111no—
116C2×#358D1111yescharacteristic, complemented
117C2×#357—111no—
118C2×#357—111no—
119#1942—111no—
120#1374—111no—
121C23×C11C2×D811yescharacteristic
122C22×D11—42no—
123C22×D11—81no—
124C22×D11—81no—
125C22×D11—81no—
126C22×D11—81no—
127C22×D11—81no—
128C22×D11—81no—
129Q8×C11—42no—
130Q8×C11—42no—
131Q8×C11—81no—
132Q8×C11—81no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11—81no—
136C2×C4×C11—81no—
137C2×C4×C11—81no—
138C2×C4×C11—81no—
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12411yescharacteristic
142C2×C4×C11C2×SD1611yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×Dic11—21no—
146C2×Dic11—21no—
147C2×Dic11—21no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154D44—42no—
155D44—42no—
156D44—81no—
157D44—81no—
158C8×C11#12111yescharacteristic
159C8×C11#12111yescharacteristic
160C8×C11#12311yescharacteristic
161C8×C11#12311yescharacteristic
162C11⋊C8—22no—
163C22×Q16C2×D1111yescharacteristic
164C22×SD16—221no—
165C22×D8—111no—
166C2×#124—221no—
167C22×C16—111no—
168C22×C16C2×D1111yescharacteristic
169#495—222no—
170#495—222no—
171C2×#107—111no—
172C2×#107C2×D1111yescharacteristic
173C2×C4×C8—111no—
174#389—221no—
175#358—22no—
176#358—222no—
177#357—222no—
178#357—222no—
179#340—221no—
180C22×C11#44711yescharacteristic
181C22×C11#45911yescharacteristic
182C22×C11#48611yescharacteristic
183C22×C11#50811yescharacteristic
184C22×C11#50811yescharacteristic
185C22×C11#50911yescharacteristic
186C22×C11#51011yescharacteristic
187C2×D11—82no—
188C2×D11—82no—
189C2×D11—82no—
190C2×D11—161no—
191C2×D11—161no—
192C2×D11—161no—
193C2×D11—161no—
194C4×C11—82no—
195C4×C11—82no—
196C4×C11#39411yescharacteristic
197C4×C11#45011yescharacteristic
198C4×C11#46011yescharacteristic
199C4×C11#49011yescharacteristic
200Dic11—41no—
201Dic11—41no—
202Dic11—161no—
203C22×Q8—21no—
204C22×D4—221no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16D4412yes—
211C2×SD16—224no—
212C2×SD16—442no—
213C2×SD16—442no—
214C2×D8—112no—
215C2×D8—221no—
216C2×D8—221no—
217C2×D8—221no—
218C2×D8—221no—
219C2×D8—221no—
220C22×C8—111no—
221C22×C8C22×D1111yescharacteristic
222#124—224no—
223#124—442no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—221no—
226C2×C4⋊C4—441no—
227C2×C22⋊C4—441no—
228C2×C22⋊C4—441no—
229C2×C42—111no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—221no—
234C2×C16—221no—
235C2×C16—221no—
236#107—21no—
237#107—221no—
238#107—221no—
239#107C22⋊D1112yes—
240C4×C8—221no—
241C4×C8—221no—
242#95—441no—
243C2×C11#204111yescharacteristic
244C2×C11#218611yescharacteristic
245C2×C11#218911yescharacteristic
246C2×C11#221011yescharacteristic
247C2×C11#221111yescharacteristic
248C2×C11#224211yescharacteristic
249C2×C11#224311yescharacteristic
250D11—162no—
251C24—441no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8—41no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—41no—
258C2×D4—222no—
259C2×D4—441no—
260C2×D4—441no—
261C2×D4—441no—
262C2×D4—441no—
263C2×D4—441no—
264C22×C4—41no—
265C22×C4—41no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—441no—
269C22×C4D4×D1111yescharacteristic
270Q16—22no—
271Q16—22no—
272Q16—41no—
273Q16—41no—
274SD16—448no—
275D8—222no—
276D8—222no—
277D8—441no—
278D8—441no—
279C2×C8—112no—
280C2×C8—221no—
281C2×C8—221no—
282C2×C8C2×D4411yescharacteristic
283C2×C8#433911yescharacteristic
284C2×C8D4×D1111yescharacteristic
285C2×C8#434111yescharacteristic
286C2×C8#434111yescharacteristic
287C2×C8C2×C22⋊D1111yescharacteristic
288C4⋊C4—22no—
289C4⋊C4—41no—
290C4⋊C4—441no—
291C4⋊C4—441no—
292C4⋊C4—882no—
293C22⋊C4—444no—
294C22⋊C4—444no—
295C42—221no—
296C42—221no—
297C16—41no—
298C16—441no—
299C11#1340811yescharacteristic, complemented, Sylow
300C23—442no—
301C23—881no—
302C23—881no—
303C23—881no—
304C23—881no—
305C23—881no—
306C23—881no—
307C23D8×D1111yescharacteristic
308Q8—42no—
309Q8—42no—
310Q8—81no—
311Q8—81no—
312D4—442no—
313D4—442no—
314D4—881no—
315D4—881no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—221no—
327C2×C4—221no—
328C2×C4—881no—
329C2×C4—881no—
330C2×C4—881no—
331C2×C4#6693511yescharacteristic
332C2×C4#6693811yescharacteristic
333C2×C4#6696411yescharacteristic
334C2×C4SD16×D1111yescharacteristic
335C2×C4#6696711yescharacteristic
336C2×C4#6699211yescharacteristic
337C8—222no—
338C8#6693611yescharacteristic
339C8#6693911yescharacteristic
340C8#6698311yescharacteristic
341C8#6699111yescharacteristic
342C22—882no—
343C22—882no—
344C22—882no—
345C22—1761no—
346C22—1761no—
347C22—1761no—
348C22—1761no—
349C22#1062237311yescharacteristic
350C22#1062238611yescharacteristic
351C22#1062252711yescharacteristic
352C22#1062252911yescharacteristic
353C22#1062253111yescharacteristic
354C22#1062253211yescharacteristic
355C22#1062276311yescharacteristic
356C4—82no—
357C4—82no—
358C4—441no—
359C4—441no—
360C4—1761no—
361C4#1062237711yescharacteristic
362C4#1062238911yescharacteristic
363C4#1062257411yescharacteristic
364C4#1062277611yescharacteristic
365C2—1762no—
366C2#1306984911yescharacteristic
367C2#1307054211yescharacteristic
368C2#1307055911yescharacteristic
369C2#1307067311yescharacteristic
370C2#1307068011yescharacteristic
371C2#1307084911yescharacteristic
372C2#1307085411yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#358C2
socleC23×C11C2×D8
prime radicalC22×D88C22
hypercenterC2×#358D11
hypocenterC11#13408
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×#10622202C2semidirect
5. #13069350C2semidirect
6. #13066693C2semidirect
7. C2×C11×#358C2semidirect
116. C2×#358D11semidirect
299. C11#13408semidirect

Maximal subgroups

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

subgroupindex
C2×#106228042
C2×#106222022
C2×#106221472
C2×#106221292
#130693502
#130666932
C2×C11×#3582
#1340811