Finite Group Databasebeta

← #14720156

Subgroups — #14720156

Order 2816.

1290 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67042C211yesmaximal, characteristic
2#13077727C211yesmaximal, characteristic, complemented
3#13067008C213yesmaximal, complemented
4#13067004C213yesmaximal, complemented
5#13066999C213yesmaximal, complemented
6C2×#10622097C213yesmaximal, complemented
7C8×C11×#41C211yesmaximal, characteristic, complemented
8C2×#67042C411yescharacteristic
9C4×C11×#41C2211yescharacteristic
10#10623358C411yescharacteristic
11#10623105—21no—
12C4×#4343—21no—
13#10623076—23no—
14C4×D4×D11—23no—
15#10623054C413yes—
16#10623052C413yes—
17C4×#4339C2213yes—
18C2×C4×D44C2213yes—
19C8×Q8×C11—21no—
20C8×D4×C11—23no—
21C11×#431C2213yescomplemented
22C2×C4×C8×C11C2213yescomplemented
23Q8×C11⋊C8—21no—
24D4×C11⋊C8—23no—
25#10622538C2213yescomplemented
26C2×C4⋊(C11⋊C8)C2213yescomplemented
27#10622097C2213yescomplemented
28#10622097C2216yescomplemented
29#10622097C2213yescomplemented
30#10622094C2211yescharacteristic, complemented
31#10622094C2213yescomplemented
32C2×C11×#41C2×C411yescharacteristic
33#67042—24no—
34#67042C818yescomplemented
35C2×#4343—21no—
36C2×D4×D11—23no—
37C2×#4339C2×C413yes—
38C22×D44C2×C413yes—
39C22×C4×D11—23no—
40C22×C8×C11—23no—
41C4×Q8×C11D411yescharacteristic
42C4×Q8×C11D411yescharacteristic
43C4×D4×C11D413yes—
44C4×D4×C11D413yes—
45C11×#117C2×C413yes—
46C2×C42×C11C2313yes—
47Q8×Dic11—21no—
48D4×Dic11—23no—
49C4×C22⋊D11—23no—
50C4×C22⋊D11—23no—
51C2×(C2×D11)⋊C4—23no—
52#66979C2×C413yes—
53C2×C4⋊Dic11C2×C413yes—
54C22×C11⋊C8—23no—
55#66946—23no—
56#66946—23no—
57#66945—23no—
58C4⋊C4×D11—23no—
59(C22⋊D11)⋊C4—26no—
60C22⋊C4×D11—26no—
61C4×D44—23no—
62C4×D44—23no—
63C4×D44C2×C416yes—
64C4×D44C2×C413yes—
65C4×D44C2313yes—
66#66925—23no—
67C42×D11—23no—
68C4×Dic22C2×C413yes—
69C4×Dic22C2311yescharacteristic
70C11×C4⋊C8—23no—
71C11×C22⋊C8—23no—
72C4×C8×C11—23no—
73C4×C8×C11C2311yescharacteristic
74C4×C8×C11C2313yes—
75C22⋊(C11⋊C8)—23no—
76C4⋊(C11⋊C8)—23no—
77C4⋊(C11⋊C8)C2313yes—
78C4⋊(C11⋊C8)C2311yescharacteristic
79C4×C11⋊C8—23no—
80#17438—111nomaximal, Sylow
81C23×D11—23no—
82C11×#41C2×C814yes—
83C11×#41M1614yes—
84C2×Q8×C11C22⋊C411yescharacteristic
85C2×D4×C11C22⋊C413yes—
86C22×C4×C11C22×C413yes—
87C22×C4×C11C2×D413yes—
88C22×C4×C11C2×D413yes—
89C2×C22⋊D11—23no—
90C22×Dic11—23no—
91#4343—28no—
92D4×D11—224no—
93#4339—26no—
94#4339C2×C8112yescomplemented
95C2×D44—23no—
96C2×D44—26no—
97C2×D44C2×C8112yescomplemented
98C2×D44C22×C413yes—
99C2×C4×D11—23no—
100C2×C4×D11—23no—
101C2×C4×D11—26no—
102C2×C4×D11—23no—
103C2×C4×D11—83no—
104C2×C4×D11—83no—
105C2×Dic22C22×C411yescharacteristic
106C2×C8×C11—21no—
107C2×C8×C11—23no—
108C2×C8×C11—46no—
109C11×C4⋊C4C22⋊C413yes—
110C11×C4⋊C4C22⋊C413yes—
111C11×C22⋊C4C22⋊C416yes—
112C42×C11C22×C413yes—
113C42×C11C2×D413yes—
114C42×C11C2×D413yes—
115C42×C11C2411yescharacteristic
116C22⋊Dic11—23no—
117(C2×D11)⋊C4—23no—
118(C2×D11)⋊C4—26no—
119(C2×D11)⋊C4—23no—
120C4⋊Dic11—23no—
121C4⋊Dic11C22×C413yes—
122C4⋊Dic11C22×C411yescharacteristic
123Dic11⋊C4—23no—
124Dic11⋊C4—21no—
125C4×Dic11—23no—
126C4×Dic11—23no—
127C4×Dic11—21no—
128C2×C11⋊C8—21no—
129C2×C11⋊C8—23no—
130C2×C11⋊C8—83no—
131C4×H(5,𝔽2)—111no—
132#2988—111no—
133C8×#41D1111yescharacteristic, complemented
134#1478—113no—
135#1477—113no—
136#1476—113no—
137C2×D4⋊C8—113no—
138C23×C11C2×C22⋊C413yes—
139C22×D11—23no—
140C22×D11—212no—
141C22×D11—83no—
142C22×D11—83no—
143Q8×C11C22⋊C814yes—
144D4×C11C22⋊C8112yes—
145C2×C4×C11—23no—
146C2×C4×C11—23no—
147C2×C4×C11—43no—
148C2×C4×C11C2×C22⋊C413yes—
149C2×C4×C11C2×C22⋊C413yes—
150C2×C4×C11C2×C22⋊C413yes—
151C2×C4×C11C22×C816yes—
152C2×C4×C11C2×M1616yes—
153C2×C4×C11C23×C411yescharacteristic
154C2×C4×C11C22×D411yescharacteristic
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—212no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—23no—
160C2×Dic11—83no—
161D44—23no—
162D44—212no—
163D44C22×C816yes—
164C4×D11—212no—
165C4×D11—43no—
166C4×D11—43no—
167C4×D11—83no—
168C4×D11—86no—
169Dic22—21no—
170Dic22C22×C812yes—
171C8×C11—22no—
172C8×C11—43no—
173C11⋊C8—43no—
174C11⋊C8—41no—
175C2×H(5,𝔽2)—111no—
176#520—111no—
177#520—113no—
178#520—221no—
179#518—113no—
180#518—223no—
181C4×#41—113no—
182C4×#41—221no—
183C4×#41C2×D1111yescharacteristic
184C2×C4×D4—113no—
185C2×C4×D4—223no—
186C8×Q8—21no—
187C8×Q8—221no—
188C8×D4—23no—
189C8×D4—223no—
190#431—113no—
191#431C2×D1113yescomplemented
192C2×C4⋊C8—113no—
193C2×C4×C8C2×D1113yescomplemented
194Q8⋊C8—111no—
195Q8⋊C8—113no—
196D4⋊C8—113no—
197D4⋊C8—116no—
198D4⋊C8—113no—
199C22×C11—23no—
200C22×C11—23no—
201C22×C11C2×C22⋊C816yes—
202C22×C11C22×C22⋊C411yescharacteristic
203C2×D11—26no—
204C2×D11—43no—
205C2×D11—43no—
206C2×D11—812no—
207C4×C11—23no—
208C4×C11—21no—
209C4×C11—23no—
210C4×C11C2×C22⋊C816yes—
211C4×C11C23×C811yescharacteristic
212C4×C11C22×M1611yescharacteristic
213C4×C11#57611yescharacteristic
214C4×C11#57711yescharacteristic
215Dic11—22no—
216Dic11—43no—
217Dic11—41no—
218H(5,𝔽2)—118no—
219H(5,𝔽2)—224no—
220C2×#41—113no—
221C2×#41—221no—
222C2×#41C4×D1111yescharacteristic
223C22×D4—113no—
224C22×D4—223no—
225C23×C4—223no—
226C22×C8—23no—
227C22×C8—223no—
228C4×Q8—113no—
229C4×Q8—111no—
230C4×Q8—221no—
231C4×Q8D4411yescharacteristic
232C4×Q8C22⋊D1111yescharacteristic
233C4×D4—116no—
234C4×D4—113no—
235C4×D4—113no—
236C4×D4—223no—
237C4×D4—223no—
238C4×D4—223no—
239C4×D4—223no—
240C4×D4—223no—
241C4×D4—226no—
242C4×D4—223no—
243C4×D4—223no—
244C4×D4D4413yes—
245C4×D4C22⋊D1113yes—
246#117—113no—
247#117—223no—
248#117—223no—
249#117C4×D1113yes—
250C2×C4⋊C4—113no—
251C2×C4⋊C4—223no—
252C2×C22⋊C4—223no—
253C2×C22⋊C4—226no—
254C2×C42—223no—
255C2×C42C22×D1113yes—
256C4⋊C8—23no—
257C4⋊C8—113no—
258C4⋊C8—111no—
259C4⋊C8—223no—
260C22⋊C8—23no—
261C22⋊C8—223no—
262C4×C8—23no—
263C4×C8—223no—
264C4×C8C22×D1111yescharacteristic
265C4×C8C22×D1113yes—
266C2×C11—26no—
267C2×C11C22×C22⋊C811yescharacteristic
268C2×C11#289711yescharacteristic
269C2×C11#290111yescharacteristic
270D11—46no—
271C24—223no—
272#41—1112no—
273#41—228no—
274#41—226no—
275#41C8×D1114yes—
276#41#431314yes—
277C2×Q8—111no—
278C2×Q8(C2×D11)⋊C411yescharacteristic
279C2×D4—1112no—
280C2×D4—113no—
281C2×D4—223no—
282C2×D4—2224no—
283C2×D4—226no—
284C2×D4—223no—
285C2×D4(C2×D11)⋊C413yes—
286C22×C4—223no—
287C22×C4—223no—
288C22×C4—223no—
289C22×C4—223no—
290C22×C4—226no—
291C22×C4—883no—
292C22×C4—883no—
293C22×C4C2×C4×D1113yes—
294C22×C4C2×D4413yes—
295C22×C4C2×C22⋊D1113yes—
296C2×C8—21no—
297C2×C8—23no—
298C2×C8—46no—
299C2×C8—221no—
300C2×C8—223no—
301C2×C8—883no—
302C4⋊C4—113no—
303C4⋊C4—111no—
304C4⋊C4—223no—
305C4⋊C4—223no—
306C4⋊C4—221no—
307C4⋊C4(C2×D11)⋊C413yes—
308C4⋊C4(C2×D11)⋊C413yes—
309C22⋊C4—223no—
310C22⋊C4—223no—
311C22⋊C4—226no—
312C22⋊C4—223no—
313C22⋊C4(C2×D11)⋊C416yes—
314C42—223no—
315C42—223no—
316C42—221no—
317C42C2×C4×D1113yes—
318C42C2×D4413yes—
319C42C2×C22⋊D1113yes—
320C42C23×D1111yescharacteristic
321C11#1743811yescharacteristic, complemented, Sylow
322C23—223no—
323C23—2212no—
324C23—883no—
325C23—883no—
326C23C2×(C2×D11)⋊C413yes—
327Q8—112no—
328Q8—221no—
329Q8(C2×D11)⋊C814yes—
330D4—116no—
331D4—2212no—
332D4—2212no—
333D4—223no—
334D4(C2×D11)⋊C8112yes—
335C2×C4—23no—
336C2×C4—23no—
337C2×C4—43no—
338C2×C4—221no—
339C2×C4—2212no—
340C2×C4—221no—
341C2×C4—223no—
342C2×C4—443no—
343C2×C4—443no—
344C2×C4—886no—
345C2×C4—883no—
346C2×C4—883no—
347C2×C4C2×C8×D1116yes—
348C2×C4C2×#431316yes—
349C2×C4C2×(C2×D11)⋊C413yes—
350C2×C4C2×(C2×D11)⋊C413yes—
351C2×C4C2×(C2×D11)⋊C413yes—
352C2×C4C22×C4×D1111yescharacteristic
353C2×C4C22×D4411yescharacteristic
354C2×C4C22×C22⋊D1111yescharacteristic
355C8—22no—
356C8—43no—
357C8—441no—
358C8—443no—
359C22—23no—
360C22—23no—
361C22—226no—
362C22—443no—
363C22—443no—
364C22—8812no—
365C22C2×(C2×D11)⋊C816yes—
366C22C22×(C2×D11)⋊C411yescharacteristic
367C4—23no—
368C4—21no—
369C4—23no—
370C4—222no—
371C4—443no—
372C4—441no—
373C4C2×(C2×D11)⋊C816yes—
374C4C22×C8×D1111yescharacteristic
375C4C22×#431311yescharacteristic
376C4#1062328211yescharacteristic
377C4#1062328311yescharacteristic
378C2—26no—
379C2—446no—
380C2C22×(C2×D11)⋊C811yescharacteristic
381C2#1307714311yescharacteristic
382C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC8×C11×#41C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#67042C4
cosocleC42×C11C24
hypercenterC8×#41D11
hypocenterC11#17438
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
2. #13077727C2semidirect
3. #13067008C2semidirect
4. #13067004C2semidirect
5. #13066999C2semidirect
6. C2×#10622097C2semidirect
7. C8×C11×#41C2semidirect
21. C11×#431C22semidirect
22. C2×C4×C8×C11C22semidirect
25. #10622538C22semidirect
26. C2×C4⋊(C11⋊C8)C22semidirect
27. #10622097C22semidirect
28. #10622097C22semidirect
29. #10622097C22semidirect
30. #10622094C22semidirect
31. #10622094C22semidirect
34. #67042C8semidirect
94. #4339C2×C8semidirect
97. C2×D44C2×C8semidirect
133. C8×#41D11semidirect
191. #431C2×D11semidirect
193. C2×C4×C8C2×D11semidirect
321. C11#17438semidirect

Maximal subgroups

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

subgroupindex
C4×#670422
#130777272
#130670082
#130670042
#130669992
C2×#106220972
C8×C11×#412
#1743811