Finite Group Databasebeta

← #14653946

Subgroups — #14653946

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#13076968C211yesmaximal, characteristic
2#13068596C211yesmaximal, characteristic
3#13066495C214yesmaximal
4C4×C11×#95C211yesmaximal, characteristic
5C22×C42×C11—21no—
6C22×C42×C11C2211yescharacteristic
7C2×#66977—21no—
8C2×#66922C411yescharacteristic, complemented
9C2×C11×#95—21no—
10C2×C11×#95C2212yes—
11#10622825—21no—
12#10622825C2212yes—
13C2×C22⋊(C11⋊C8)C2212yes—
14#10622548C411yescharacteristic, complemented
15#10622542—21no—
16#10622541—21no—
17#10622541C412yescomplemented
18C2×C4⋊(C11⋊C8)—21no—
19#10622162—21no—
20C23×C4×C11—22no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C22×Dic22—21no—
25C2×C42×C11—24no—
26C2×C42×C11—42no—
27C2×C42×C11—42no—
28C2×C42×C11—42no—
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11C2×C411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C42×C11D411yescharacteristic
33C2×C22⋊Dic11—22no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38C2×C4⋊Dic11C2×C412yes—
39#66977—42no—
40#66977—42no—
41C2×Dic11⋊C4—22no—
42C22×C11⋊C8—22no—
43#66922—42no—
44C11×#95—24no—
45C11×#95—22no—
46C11×#95Q814yescomplemented
47C11⋊#95—22no—
48C11⋊#95—22no—
49C22⋊(C11⋊C8)—24no—
50C4⋊(C11⋊C8)—42no—
51#9909—111nomaximal, Sylow
52C24×C11C2×D411yescharacteristic
53C22×C4×C11—22no—
54C22×C4×C11—22no—
55C22×C4×C11—24no—
56C22×C4×C11—24no—
57C22×C4×C11—24no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—41no—
61C22×C4×C11—41no—
62C22×C4×C11—41no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11—42no—
66C22×C4×C11—42no—
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11D812yes—
72C22×C4×C11SD1612yes—
73C22×C4×C11C22×C411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×C4×C11C2×Q812yes—
76C22×C4×C11#4112yes—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×Dic22—42no—
82C42×C11—22no—
83C42×C11—22no—
84C42×C11—41no—
85C42×C11—41no—
86C42×C11—48no—
87C22⋊Dic11—42no—
88C22⋊Dic11—42no—
89C4⋊Dic11—42no—
90C4⋊Dic11—42no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—42no—
94Dic11⋊C4—44no—
95C2×C11⋊C8—42no—
96C2×C11⋊C8—42no—
97C2×C11⋊C8—42no—
98#2857—111no—
99#1797—111no—
100C4×#95D1111yescharacteristic
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—
111C2×C4×C11—21no—
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—24no—
120C2×C4×C11—24no—
121C2×C4×C11—28no—
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—44no—
129C2×C4×C11—44no—
130C2×C4×C11—44no—
131C2×C4×C11—44no—
132C2×C4×C11—44no—
133C2×C4×C11—44no—
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—42no—
143C2×Dic11—42no—
144C2×Dic11—42no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148Dic22—84no—
149C11⋊C8—82no—
150C2×C4⋊Q8—111no—
151C2×C22⋊Q8—221no—
152C22×C42—21no—
153C22×C42C2×D1111yescharacteristic
154C2×C4⋊C8—221no—
155C2×C22⋊C8—112no—
156#391—221no—
157#389—112no—
158#389—221no—
159#384—111no—
160#380—112no—
161#380—221no—
162C2×#95—21no—
163C2×#95C2×D1112yes—
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—48no—
188C4×C11—41no—
189C4×C11#32714yes—
190Dic11—82no—
191Dic11—82no—
192C22×Q8—221no—
193C23×C4—22no—
194C23×C4C22⋊D1111yescharacteristic
195C23×C4C22⋊D1111yescharacteristic
196C23×C4C22×D1111yescharacteristic
197C22×C8—222no—
198C4⋊Q8—442no—
199C22⋊Q8—442no—
200C22⋊Q8—442no—
201C2×C4⋊C4—112no—
202C2×C4⋊C4—112no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—222no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C22⋊C4—222no—
208C2×C42—24no—
209C2×C42—42no—
210C2×C42—42no—
211C2×C42—42no—
212C2×C42C4×D1111yescharacteristic
213C2×C42C4×D1111yescharacteristic
214C2×C42D4411yescharacteristic
215C2×C42D4411yescharacteristic
216C4⋊C8—442no—
217C22⋊C8—224no—
218#95—24no—
219#95—22no—
220#95—222no—
221#95—222no—
222#95Dic2214yescomplemented
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—442no—
234C2×Q8—442no—
235C2×Q8—442no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4(C2×D11)⋊C411yescharacteristic
256C22×C4#432312yes—
257C22×C4#432512yes—
258C22×C4C2×Dic2212yes—
259C22×C4C2×C4×D1111yescharacteristic
260C22×C4C2×D4411yescharacteristic
261C22×C4#433912yes—
262C2×C8—442no—
263C2×C8—442no—
264C2×C8—442no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C4⋊C4—444no—
270C4⋊C4—442no—
271C22⋊C4—442no—
272C22⋊C4—442no—
273C42—22no—
274C42—22no—
275C42—41no—
276C42—41no—
277C42—48no—
278C11#990911yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23#6697712yes—
284C23C2×(C2×D11)⋊C411yescharacteristic
285C23C2×#432311yescharacteristic
286C23C2×#432511yescharacteristic
287C23#6700412yes—
288Q8—884no—
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—28no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—44no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—44no—
312C2×C4—442no—
313C2×C4—442no—
314C2×C4—442no—
315C2×C4—442no—
316C2×C4—442no—
317C2×C4—442no—
318C2×C4#6686912yes—
319C2×C4#6686912yes—
320C2×C4#6687012yes—
321C2×C4#6687312yes—
322C2×C4#6687312yes—
323C2×C4C4×Dic2212yes—
324C2×C4#6692211yescharacteristic
325C2×C4#6692811yescharacteristic
326C8—882no—
327C22—22no—
328C22—22no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—22no—
334C22—22no—
335C22C2×#6686911yescharacteristic
336C22C2×#6686911yescharacteristic
337C22#1062254211yescharacteristic
338C22C2×#6687011yescharacteristic
339C22C2×#6687311yescharacteristic
340C22#1062261711yescharacteristic
341C22#1062261911yescharacteristic
342C22#1062262012yes—
343C22#1062263312yes—
344C4—21no—
345C4—22no—
346C4—21no—
347C4—22no—
348C4—22no—
349C4—48no—
350C4—41no—
351C4—882no—
352C4—882no—
353C4#1062208914yes—
354C2—22no—
355C2—22no—
356C2C2×#1062208911yescharacteristic
357C2#1306711011yescharacteristic
358C2#1306712711yescharacteristic
359C2#1306713511yescharacteristic
360C2#1306956811yescharacteristic
361C2#1306959311yescharacteristic
362C2#1306960111yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC4×C11×#95C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4×#95D11
hypocenterC11#9909
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
8. C2×#66922C4semidirect
14. #10622548C4semidirect
17. #10622541C4semidirect
46. C11×#95Q8semidirect
222. #95Dic22semidirect
278. C11#9909semidirect

Maximal subgroups

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

subgroupindex
#130769682
#130685962
#130664952
C4×C11×#952
#990911