Finite Group Databasebeta

← #14649534

Subgroups — #14649534

Order 2816.

630 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622549C211yesmaximal, characteristic
2#13068684C211yesmaximal, characteristic
3C2×#10622176C212yesmaximal
4#13066494C212yesmaximal
5C11×#2855C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C22×C42×C11C2211yescharacteristic
8C22×C4⋊Dic11—21no—
9C11×#391C412yescomplemented
10C11×#389C412yescomplemented
11C11×#387—22no—
12C11×#385—21no—
13C11×#381—21no—
14C11×#380C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18#10622549—24no—
19#10622176—24no—
20#10622162—22no—
21C22×Q8×C11C2×C411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C23×Dic11—22no—
26C11×C22⋊Q8—22no—
27C11×C22⋊Q8—22no—
28C2×C11×C4⋊C4—22no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C412yes—
32C2×C11×C22⋊C4—21no—
33C2×C11×C22⋊C4—21no—
34C2×C42×C11—22no—
35C2×C42×C11—22no—
36C2×C42×C11C2×C412yes—
37C2×C42×C11D412yes—
38C2×C4⋊Dic11—24no—
39C2×C4⋊Dic11—42no—
40C2×C4⋊Dic11—42no—
41C22×C11⋊C8—22no—
42C11×#95—22no—
43C11×#95—22no—
44C11×#95—22no—
45C11×#95—21no—
46C11⋊#95—24no—
47C11⋊#95—22no—
48C11⋊#95D414yes—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)—22no—
51#9152—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—22no—
54C2×Q8×C11—42no—
55C22×C4×C11—21no—
56C22×C4×C11—21no—
57C22×C4×C11—21no—
58C22×C4×C11—21no—
59C22×C4×C11—21no—
60C22×C4×C11—21no—
61C22×C4×C11—22no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11C22⋊C412yes—
67C22×C4×C11C22⋊C412yes—
68C22×C4×C11SD1612yes—
69C22×C4×C11Q1612yes—
70C22×C4×C11C22×C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D412yes—
73C22×C4×C11#4112yes—
74C22×Dic11—24no—
75C22×Dic11—44no—
76C22×Dic11—44no—
77C22×Dic11—42no—
78C22×Dic11—42no—
79C11×C4⋊C4—22no—
80C11×C4⋊C4—44no—
81C11×C4⋊C4—42no—
82C11×C4⋊C4—42no—
83C11×C22⋊C4—41no—
84C11×C22⋊C4—41no—
85C11×C22⋊C4—41no—
86C11×C22⋊C4—41no—
87C42×C11—24no—
88C42×C11—24no—
89C4⋊Dic11—48no—
90C2×C11⋊C8—44no—
91C2×C11⋊C8—42no—
92#2855D1111yescharacteristic
93C2×#382—111no—
94#1817—111no—
95C2×#328—112no—
96#1294—112no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11C2×C22⋊C411yescharacteristic
100C23×C11#12011yescharacteristic
101C23×C11#12311yescharacteristic
102C23×C11C2×SD1611yescharacteristic
103C23×C11C2×Q1611yescharacteristic
104C23×C11AGL(1,ℤ/8)11yescharacteristic
105C23×C11#13711yescharacteristic
106Q8×C11—82no—
107C2×C4×C11—22no—
108C2×C4×C11—22no—
109C2×C4×C11—22no—
110C2×C4×C11—22no—
111C2×C4×C11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—22no—
114C2×C4×C11—22no—
115C2×C4×C11—22no—
116C2×C4×C11—22no—
117C2×C4×C11—22no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—42no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—42no—
128C2×C4×C11—42no—
129C2×C4×C11#10314yes—
130C2×C4×C11C4×D412yes—
131C2×C4×C11#12112yes—
132C2×Dic11—44no—
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11—84no—
136C2×Dic11—84no—
137C11⋊C8—82no—
138C2×C22⋊Q8C2×D1111yescharacteristic
139C22×C4⋊C4—221no—
140C22×C42C2×D1111yescharacteristic
141C2×C22⋊C8—112no—
142#391Dic1112yescomplemented
143#389Dic1112yescomplemented
144#387—22no—
145#385—21no—
146#382—224no—
147#381—21no—
148#380C2×D1111yescharacteristic
149C2×#95—112no—
150C2×#95—221no—
151#336—222no—
152#328—224no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—22no—
160C22×C11—22no—
161C22×C11#38611yescharacteristic
162C22×C11#41012yes—
163C22×C11C2×#10311yescharacteristic
164C22×C11#41711yescharacteristic
165C22×C11#42112yes—
166C22×C11#45011yescharacteristic
167C22×C11#45111yescharacteristic
168C22×C11#48311yescharacteristic
169C22×C11#48411yescharacteristic
170C4×C11—24no—
171C4×C11—22no—
172C4×C11—22no—
173C4×C11—42no—
174C4×C11—81no—
175C4×C11—81no—
176C4×C11—82no—
177Dic11—84no—
178C22×Q8C2×Dic1111yescharacteristic
179C23×C4—222no—
180C23×C4C22⋊D1111yescharacteristic
181C23×C4C22⋊D1111yescharacteristic
182C23×C4C22×D1111yescharacteristic
183C22×C8—222no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—224no—
189C2×C4⋊C4—442no—
190C2×C4⋊C4—442no—
191C2×C4⋊C4C2×Dic1111yescharacteristic
192C2×C4⋊C4C2×Dic1112yes—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—21no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42C2×Dic1112yes—
198C2×C42C22⋊D1112yes—
199C22⋊C8—222no—
200C22⋊C8—222no—
201#95—22no—
202#95—22no—
203#95—22no—
204#95—21no—
205#95—114no—
206#95—224no—
207#95—222no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—21no—
211C2×C11—21no—
212C2×C11#151212yes—
213C2×C11#151812yes—
214C2×C11#187211yescharacteristic
215C2×C11#189711yescharacteristic
216C2×C11#189911yescharacteristic
217C24C2×C22⋊D1111yescharacteristic
218C2×Q8—22no—
219C2×Q8—42no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—224no—
232C22×C4—444no—
233C22×C4—444no—
234C22×C4—442no—
235C22×C4—442no—
236C22×C4#432512yes—
237C22×C4#432612yes—
238C22×C4C22⋊Dic1112yes—
239C22×C4C22⋊Dic1112yes—
240C22×C4D4×D1112yes—
241C22×C4#434112yes—
242C22×C4C22×Dic1111yescharacteristic
243C22×C4C2×C22⋊D1111yescharacteristic
244C2×C8—444no—
245C2×C8—442no—
246C4⋊C4—22no—
247C4⋊C4—42no—
248C4⋊C4—44no—
249C4⋊C4—42no—
250C4⋊C4—448no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C42—24no—
256C42—24no—
257C11#915211yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23#6698811yescharacteristic
261C23#6699011yescharacteristic
262C23C2×#432511yescharacteristic
263C23C2×#432611yescharacteristic
264C23#6700211yescharacteristic
265C23#6700411yescharacteristic
266C23C2×C22⋊Dic1111yescharacteristic
267Q8—82no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—444no—
291C2×C4—444no—
292C2×C4—444no—
293C2×C4—884no—
294C2×C4—884no—
295C2×C4#6689914yes—
296C2×C4D4×Dic1112yes—
297C2×C4#6699212yes—
298C8—882no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22#1062265611yescharacteristic
308C22#1062265711yescharacteristic
309C22#1062265911yescharacteristic
310C22#1062266311yescharacteristic
311C22#1062283311yescharacteristic
312C22C2×#6689911yescharacteristic
313C22#1062284511yescharacteristic
314C22#1062284912yes—
315C22#1062285312yes—
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—81no—
321C4—81no—
322C4—82no—
323C4—884no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2#1306715412yes—
329C2#1306718012yes—
330C2#1306892411yescharacteristic
331C2#1306906511yescharacteristic
332C2#1306907511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2855C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2855D11
hypocenterC11#9152
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
9. C11×#391C4semidirect
10. C11×#389C4semidirect
142. #391Dic11semidirect
143. #389Dic11semidirect
257. C11#9152semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
#130686842
C2×#106221762
#130664942
C11×#28552
#915211