Finite Group Databasebeta

← #14653947

Subgroups — #14653947

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2C4×C11⋊#95C211yesmaximal, characteristic
3#13066494C214yesmaximal
4C11×#2857C211yesmaximal, characteristic
5C2×C11×C4⋊Q8C411yescharacteristic, complemented
6C2×C11×C22⋊Q8—21no—
7C22×C42×C11C2211yescharacteristic
8C22×C4×Dic11—21no—
9C11×#391—21no—
10C11×#389—21no—
11C11×#389C412yescomplemented
12C11×#384C411yescharacteristic, complemented
13C11×#380—21no—
14C11×#380C2212yes—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18C2×C4⋊(C11⋊C8)—21no—
19#10622162—21no—
20C22×Q8×C11—21no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11—22no—
25C11×C4⋊Q8—42no—
26C11×C22⋊Q8—42no—
27C11×C22⋊Q8—42no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C412yes—
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C22⋊C4—22no—
35C2×C42×C11—42no—
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11D411yescharacteristic
39C2×C42×C11D411yescharacteristic
40C2×C4×Dic11—24no—
41C2×C4×Dic11—42no—
42C2×C4×Dic11—42no—
43C22×C11⋊C8—22no—
44C11×#95—22no—
45C11×#95—22no—
46C11⋊#95—24no—
47C11⋊#95—22no—
48C11⋊#95Q814yescomplemented
49C22⋊(C11⋊C8)—24no—
50C4⋊(C11⋊C8)—42no—
51#9909—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C2×Q8×C11—42no—
54C2×Q8×C11—42no—
55C2×Q8×C11—42no—
56C22×C4×C11—22no—
57C22×C4×C11—22no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—22no—
61C22×C4×C11—22no—
62C22×C4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11—41no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11D812yes—
70C22×C4×C11SD1612yes—
71C22×C4×C11C22×C411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×Q812yes—
74C22×C4×C11#4112yes—
75C22×Dic11—24no—
76C22×Dic11—24no—
77C22×Dic11—24no—
78C22×Dic11—42no—
79C22×Dic11—42no—
80C22×Dic11—42no—
81C22×Dic11—42no—
82C11×C4⋊C4—42no—
83C11×C4⋊C4—42no—
84C11×C4⋊C4—42no—
85C11×C4⋊C4—42no—
86C11×C4⋊C4—44no—
87C11×C4⋊C4—42no—
88C11×C22⋊C4—42no—
89C11×C22⋊C4—42no—
90C42×C11—22no—
91C42×C11—22no—
92C42×C11—41no—
93C42×C11—41no—
94C4×Dic11—48no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98#2857D1111yescharacteristic
99#1797—111no—
100C4×#95—111no—
101#1294—114no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11C2×C22⋊C411yescharacteristic
107C23×C11C22⋊Q812yes—
108C23×C11C2×D811yescharacteristic
109C23×C11C2×SD1611yescharacteristic
110C23×C11#13712yes—
111Q8×C11—84no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—24no—
121C2×C4×C11—24no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—42no—
126C2×C4×C11—42no—
127C2×C4×C11—44no—
128C2×C4×C11—42no—
129C2×C4×C11—42no—
130C2×C4×C11—42no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11#9912yes—
135C2×C4×C11#10212yes—
136C2×C4×C11#10212yes—
137C2×C4×C11#10412yes—
138C2×C4×C11#10412yes—
139C2×C4×C11C4×Q812yes—
140C2×C4×C11#12411yescharacteristic
141C2×C4×C11C4⋊Q811yescharacteristic
142C2×Dic11—28no—
143C2×Dic11—44no—
144C2×Dic11—44no—
145C2×Dic11—44no—
146C2×Dic11—44no—
147C2×Dic11—44no—
148C2×Dic11—44no—
149C11⋊C8—82no—
150C2×C4⋊Q8Dic1111yescharacteristic, complemented
151C2×C22⋊Q8—21no—
152C22×C42—221no—
153C22×C42C2×D1111yescharacteristic
154C2×C4⋊C8—221no—
155C2×C22⋊C8—112no—
156#391—21no—
157#389—21no—
158#389Dic1112yescomplemented
159#384Dic1111yescharacteristic, complemented
160#380—21no—
161#380C2×D1112yes—
162C2×#95—112no—
163C2×#95—221no—
164#336—221no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—21no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11#39111yescharacteristic
174C22×C11C2×#9911yescharacteristic
175C22×C11#41011yescharacteristic
176C22×C11C2×#10211yescharacteristic
177C22×C11#41911yescharacteristic
178C22×C11C2×#10411yescharacteristic
179C22×C11C2×#10411yescharacteristic
180C22×C11#47412yes—
181C22×C11#47512yes—
182C4×C11—22no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—22no—
186C4×C11—22no—
187C4×C11—41no—
188C4×C11—82no—
189C4×C11—82no—
190C4×C11#32714yes—
191Dic11—48no—
192C22×Q8—21no—
193C23×C4—222no—
194C23×C4C22⋊D1111yescharacteristic
195C23×C4C22⋊D1111yescharacteristic
196C23×C4C22×D1111yescharacteristic
197C22×C8—222no—
198C4⋊Q8—42no—
199C22⋊Q8—42no—
200C22⋊Q8—42no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×Dic1112yes—
206C2×C4⋊C4C2×Dic1112yes—
207C2×C22⋊C4—22no—
208C2×C42—42no—
209C2×C42—224no—
210C2×C42—442no—
211C2×C42—442no—
212C2×C42C2×Dic1111yescharacteristic
213C2×C42C2×Dic1111yescharacteristic
214C2×C42C22⋊D1111yescharacteristic
215C2×C42C22⋊D1111yescharacteristic
216C4⋊C8—442no—
217C22⋊C8—224no—
218#95—22no—
219#95—22no—
220#95—114no—
221#95—224no—
222#95—222no—
223C2×C11—22no—
224C2×C11—22no—
225C2×C11C2×#32711yescharacteristic
226C2×C11#150211yescharacteristic
227C2×C11#150611yescharacteristic
228C2×C11#150811yescharacteristic
229C2×C11#198811yescharacteristic
230C2×C11#199411yescharacteristic
231C2×C11#199611yescharacteristic
232C24C2×C22⋊D1111yescharacteristic
233C2×Q8—42no—
234C2×Q8—42no—
235C2×Q8—42no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—224no—
246C22×C4—224no—
247C22×C4—224no—
248C22×C4—442no—
249C22×C4—442no—
250C22×C4—442no—
251C22×C4—442no—
252C22×C4#432312yes—
253C22×C4#432412yes—
254C22×C4C22⋊Dic1111yescharacteristic
255C22×C4C22⋊Dic1111yescharacteristic
256C22×C4C22⋊Dic1111yescharacteristic
257C22×C4C22⋊Dic1111yescharacteristic
258C22×C4Q8×D1112yes—
259C22×C4#434312yes—
260C22×C4C22×Dic1111yescharacteristic
261C22×C4C2×C22⋊D1111yescharacteristic
262C2×C8—442no—
263C2×C8—442no—
264C2×C8—442no—
265C4⋊C4—42no—
266C4⋊C4—42no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—44no—
270C4⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C42—22no—
274C42—22no—
275C42—41no—
276C42—41no—
277C42—448no—
278C11#990911yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23C2×#432311yescharacteristic
284C23C2×#432411yescharacteristic
285C23#6699512yes—
286C23#6699912yes—
287C23C2×C22⋊Dic1111yescharacteristic
288Q8—84no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—24no—
298C2×C4—24no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—44no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—228no—
312C2×C4—444no—
313C2×C4—444no—
314C2×C4—444no—
315C2×C4—444no—
316C2×C4—444no—
317C2×C4—444no—
318C2×C4#6689612yes—
319C2×C4#6689612yes—
320C2×C4#6689812yes—
321C2×C4#6690112yes—
322C2×C4#6690112yes—
323C2×C4#6699711yescharacteristic
324C2×C4Q8×Dic1112yes—
325C2×C4#6700011yescharacteristic
326C8—882no—
327C22—22no—
328C22—22no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22#1062270012yes—
336C22#1062270712yes—
337C22C2×#6689611yescharacteristic
338C22C2×#6689811yescharacteristic
339C22#1062283811yescharacteristic
340C22#1062284311yescharacteristic
341C22C2×#6690111yescharacteristic
342C22C2×#6690111yescharacteristic
343C22#1062285311yescharacteristic
344C4—21no—
345C4—21no—
346C4—22no—
347C4—22no—
348C4—22no—
349C4—41no—
350C4—82no—
351C4—82no—
352C4—448no—
353C4#1062217514yes—
354C2—22no—
355C2—22no—
356C2C2×#1062217511yescharacteristic
357C2#1306711111yescharacteristic
358C2#1306712811yescharacteristic
359C2#1306713611yescharacteristic
360C2#1306956911yescharacteristic
361C2#1306959411yescharacteristic
362C2#1306960211yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2857C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#2857D11
hypocenterC11#9909
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
5. C2×C11×C4⋊Q8C4semidirect
11. C11×#389C4semidirect
12. C11×#384C4semidirect
48. C11⋊#95Q8semidirect
150. C2×C4⋊Q8Dic11semidirect
158. #389Dic11semidirect
159. #384Dic11semidirect
278. C11#9909semidirect

Maximal subgroups

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

subgroupindex
#130685962
C4×C11⋊#952
#130664942
C11×#28572
#990911