Finite Group Databasebeta

← #14652907

Subgroups — #14652907

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076968C211yesmaximal, characteristic
2C2×#10622105C214yesmaximal
3#13066843C211yesmaximal, characteristic
4C11×#1797C211yesmaximal, characteristic
5C22×C42×C11C2211yescharacteristic
6C2×#66977C2212yes—
7C2×#66922C411yescharacteristic, complemented
8C2×C11×C4⋊C8—21no—
9C2×C11×C22⋊C8C2212yes—
10#10622825—21no—
11#10622825—21no—
12C2×C11⋊#95—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2212yes—
15#10622548C411yescharacteristic, complemented
16#10622542C412yescomplemented
17#10622541—21no—
18#10622541—21no—
19C11×#336—21no—
20#10622105—28no—
21C23×C4×C11D411yescharacteristic
22C23×C4×C11D411yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C23×Dic11—22no—
25C22×Dic22C2×C412yes—
26C22×C8×C11—22no—
27C2×C42×C11—42no—
28C2×C42×C11C2×C411yescharacteristic
29C2×C42×C11C2×C411yescharacteristic
30C2×C42×C11D411yescharacteristic
31C2×C42×C11D411yescharacteristic
32C2×C22⋊Dic11—22no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C412yes—
38#66977—24no—
39#66977—24no—
40C2×Dic11⋊C4—22no—
41#66922—42no—
42C11×C4⋊C8—42no—
43C11×C22⋊C8—24no—
44C11⋊#95—22no—
45C11⋊#95—22no—
46C11⋊#95—22no—
47C11⋊#95—42no—
48C11⋊#95—42no—
49C11⋊#95D414yes—
50#9714—111nomaximal, Sylow
51C24×C11C2×D411yescharacteristic
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—41no—
55C22×C4×C11—41no—
56C22×C4×C11—41no—
57C22×C4×C11—41no—
58C22×C4×C11—41no—
59C22×C4×C11C22⋊C411yescharacteristic
60C22×C4×C11C22⋊C411yescharacteristic
61C22×C4×C11C22⋊C411yescharacteristic
62C22×C4×C11C22⋊C411yescharacteristic
63C22×C4×C11SD1612yes—
64C22×C4×C11Q1612yes—
65C22×C4×C11C22×C411yescharacteristic
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D412yes—
68C22×C4×C11#4112yes—
69C22×Dic11—22no—
70C22×Dic11—22no—
71C22×Dic11—24no—
72C22×Dic11—42no—
73C22×Dic11—42no—
74C22×Dic11—42no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C22×Dic11—42no—
78C2×Dic22—24no—
79C2×Dic22—42no—
80C2×Dic22—42no—
81C2×C8×C11—42no—
82C2×C8×C11—42no—
83C2×C8×C11—42no—
84C42×C11—22no—
85C42×C11—22no—
86C42×C11—41no—
87C42×C11—41no—
88C22⋊Dic11—44no—
89C4⋊Dic11—24no—
90C4⋊Dic11—42no—
91C4⋊Dic11—42no—
92C4⋊Dic11—42no—
93C4⋊Dic11—42no—
94Dic11⋊C4—42no—
95Dic11⋊C4—42no—
96#2857—111no—
97#1797D1111yescharacteristic
98C2×#328—114no—
99#1434—111no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—21no—
104C23×C11C2×C22⋊C411yescharacteristic
105C23×C11#12112yes—
106C23×C11C2×SD1611yescharacteristic
107C23×C11C2×Q1611yescharacteristic
108C23×C11#13712yes—
109C2×C4×C11—21no—
110C2×C4×C11—21no—
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—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11—44no—
127C2×C4×C11#9912yes—
128C2×C4×C11#10312yes—
129C2×C4×C11#10312yes—
130C2×C4×C11C4×D412yes—
131C2×C4×C11#12411yescharacteristic
132C2×C4×C11#12711yescharacteristic
133C2×Dic11—44no—
134C2×Dic11—44no—
135C2×Dic11—42no—
136C2×Dic11—42no—
137C2×Dic11—42no—
138C2×Dic11—42no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11—44no—
142C2×Dic11—82no—
143C2×Dic11—82no—
144C2×Dic11—82no—
145C2×Dic11—82no—
146Dic22—84no—
147C8×C11—82no—
148C2×C4⋊Q8—111no—
149C2×C22⋊Q8—112no—
150C22×C42C2×D1111yescharacteristic
151C2×C4⋊C8—21no—
152C2×C22⋊C8C2×D1112yes—
153#391—112no—
154#389—221no—
155#389—221no—
156#384—111no—
157#380—221no—
158#380—221no—
159C2×#95—112no—
160C2×#95—221no—
161C2×#95—221no—
162#336—21no—
163#328—228no—
164C22×C11—22no—
165C22×C11—22no—
166C22×C11—22no—
167C22×C11—22no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11#39011yescharacteristic
173C22×C11C2×#9911yescharacteristic
174C22×C11#41011yescharacteristic
175C22×C11C2×#10311yescharacteristic
176C22×C11#41911yescharacteristic
177C22×C11#42111yescharacteristic
178C22×C11#42111yescharacteristic
179C22×C11#46112yes—
180C22×C11#46212yes—
181C4×C11—22no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—22no—
187C4×C11—41no—
188Dic11—84no—
189Dic11—82no—
190Dic11—82no—
191C22×Q8—112no—
192C23×C4—222no—
193C23×C4D4411yescharacteristic
194C23×C4D4411yescharacteristic
195C23×C4C22×D1111yescharacteristic
196C22×C8—22no—
197C4⋊Q8—442no—
198C22⋊Q8—224no—
199C22⋊Q8—224no—
200C2×C4⋊C4—112no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4—221no—
203C2×C4⋊C4—221no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—222no—
206C2×C22⋊C4—222no—
207C2×C42—42no—
208C2×C42C4×D1111yescharacteristic
209C2×C42C4×D1111yescharacteristic
210C2×C42C22⋊D1111yescharacteristic
211C2×C42C22⋊D1111yescharacteristic
212C4⋊C8—42no—
213C22⋊C8—24no—
214#95—114no—
215#95—222no—
216#95—222no—
217#95—222no—
218#95—442no—
219#95—442no—
220C2×C11—22no—
221C2×C11—22no—
222C2×C11#151111yescharacteristic
223C2×C11#151511yescharacteristic
224C2×C11#151811yescharacteristic
225C2×C11#152011yescharacteristic
226C2×C11#196311yescharacteristic
227C2×C11#196411yescharacteristic
228C2×C11#198111yescharacteristic
229C24C2×D4411yescharacteristic
230C2×Q8—224no—
231C2×Q8—442no—
232C2×Q8—442no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—224no—
241C22×C4—222no—
242C22×C4—222no—
243C22×C4—442no—
244C22×C4—442no—
245C22×C4—442no—
246C22×C4—442no—
247C22×C4—442no—
248C22×C4—442no—
249C22×C4#431412yes—
250C22×C4Dic4412yes—
251C22×C4(C2×D11)⋊C411yescharacteristic
252C22×C4(C2×D11)⋊C411yescharacteristic
253C22×C4(C2×D11)⋊C411yescharacteristic
254C22×C4(C2×D11)⋊C411yescharacteristic
255C22×C4C2×C4×D1111yescharacteristic
256C22×C4D4×D1112yes—
257C22×C4#434312yes—
258C22×C4C2×C22⋊D1111yescharacteristic
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C4⋊C4—224no—
263C4⋊C4—442no—
264C4⋊C4—442no—
265C4⋊C4—442no—
266C4⋊C4—442no—
267C4⋊C4—442no—
268C4⋊C4—442no—
269C22⋊C4—444no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C11#971411yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23#6694812yes—
280C23C2×#431411yescharacteristic
281C23C2×Dic4411yescharacteristic
282C23#6696212yes—
283C23C2×(C2×D11)⋊C411yescharacteristic
284Q8—884no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
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—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—444no—
304C2×C4—444no—
305C2×C4—442no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—442no—
310C2×C4—442no—
311C2×C4—444no—
312C2×C4—882no—
313C2×C4—882no—
314C2×C4—882no—
315C2×C4—882no—
316C2×C4#6687012yes—
317C2×C4#6688012yes—
318C2×C4#6688012yes—
319C2×C4#6694612yes—
320C2×C4#6699311yescharacteristic
321C2×C4#6700011yescharacteristic
322C8—82no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22#1062245412yes—
332C22#1062246212yes—
333C22C2×#6687011yescharacteristic
334C22#1062260111yescharacteristic
335C22#1062261911yescharacteristic
336C22C2×#6688011yescharacteristic
337C22#1062273311yescharacteristic
338C22#1062275211yescharacteristic
339C22#1062275211yescharacteristic
340C4—21no—
341C4—22no—
342C4—21no—
343C4—22no—
344C4—22no—
345C4—22no—
346C4—41no—
347C4—884no—
348C4—882no—
349C4—882no—
350C2—22no—
351C2—22no—
352C2#1306715011yescharacteristic
353C2#1306716811yescharacteristic
354C2#1306718111yescharacteristic
355C2#1306718911yescharacteristic
356C2#1306944711yescharacteristic
357C2#1306945111yescharacteristic
358C2#1306953811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#9714
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
7. C2×#66922C4semidirect
15. #10622548C4semidirect
16. #10622542C4semidirect
274. C11#9714semidirect

Maximal subgroups

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

subgroupindex
#130769682
C2×#106221052
#130668432
C11×#17972
#971411