Finite Group Databasebeta

← #14720650

Subgroups — #14720650

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×C11⋊C8C211yesmaximal, characteristic
2#13077184C211yesmaximal, characteristic
3#13067071C213yesmaximal, complemented
4#13067045C213yesmaximal, complemented
5#13067019C213yesmaximal, complemented
6C2×Q8⋊(C11⋊C8)C213yesmaximal, complemented
7Q8×C11×#41C211yesmaximal, characteristic
8Q82×C11C411yescharacteristic
9C11×#557—21no—
10C11×#557C411yescharacteristic
11C11×#554—23no—
12C11×#554C413yes—
13D4×Q8×C11C413yes—
14C11×#533—23no—
15C11×#533C2213yes—
16C4×C11×#41—21no—
17C4×C11×#41C2211yescharacteristic
18C2×C4×Q8×C11C2213yes—
19C2×#67001—21no—
20Q8×C11⋊C8—21no—
21D4×C11⋊C8—23no—
22#10622612—23no—
23#10622538C2213yes—
24#10622537C2213yes—
25C2×C4⋊(C11⋊C8)C2213yes—
26C2×C4×C11⋊C8C2213yes—
27Q8⋊(C11⋊C8)C2213yes—
28Q8⋊(C11⋊C8)C2216yes—
29Q8⋊(C11⋊C8)C2213yes—
30Q8⋊(C11⋊C8)C2213yes—
31Q8⋊(C11⋊C8)C2211yescharacteristic
32C2×C11×#41D411yescharacteristic
33C22×Q8×C11C2×C413yes—
34C11×C4⋊Q8—23no—
35C11×C4⋊Q8—23no—
36C11×C4⋊Q8C2×C413yes—
37C11×C4⋊Q8C2×C413yes—
38C11×#125—23no—
39C11×#125—23no—
40C11×#125—23no—
41C11×C22⋊Q8—23no—
42C11×C22⋊Q8—26no—
43C11×C22⋊Q8—26no—
44C11×C22⋊Q8C2×C416yes—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—23no—
48C4×Q8×C11—23no—
49C4×Q8×C11—23no—
50C4×Q8×C11C2×C413yes—
51C4×Q8×C11C2×C413yes—
52C4×Q8×C11C2×C411yescharacteristic
53C4×Q8×C11D411yescharacteristic
54C4×Q8×C11C2311yescharacteristic
55C4×Q8×C11C2313yes—
56C4×D4×C11—23no—
57C4×D4×C11—23no—
58C4×D4×C11C2×C413yes—
59C4×D4×C11D413yes—
60C11×#117—23no—
61C11×#117D413yes—
62C2×C11×C4⋊C4—23no—
63C2×C11×C4⋊C4C2×C413yes—
64C2×C42×C11—23no—
65C2×C42×C11C2313yes—
66#67001—44no—
67C2×#4318—23no—
68C22×C11⋊C8—23no—
69C22×C11⋊C8—23no—
70C22⋊(C11⋊C8)—23no—
71C4⋊(C11⋊C8)—23no—
72C4⋊(C11⋊C8)—23no—
73C4⋊(C11⋊C8)—23no—
74C4⋊(C11⋊C8)C2311yescharacteristic
75C4⋊(C11⋊C8)C2313yes—
76C4×C11⋊C8—23no—
77C4×C11⋊C8C2311yescharacteristic
78C4×C11⋊C8C2313yes—
79#17509—111nomaximal, Sylow
80C11×#41SD1614yes—
81C11×#41Q1614yes—
82C2×Q8×C11—23no—
83C2×Q8×C11—23no—
84C2×Q8×C11—26no—
85C2×Q8×C11—43no—
86C2×Q8×C11C22⋊C411yescharacteristic
87C2×Q8×C11C22×C413yes—
88C2×Q8×C11C22×C411yescharacteristic
89C2×D4×C11C22⋊C413yes—
90C22×C4×C11—23no—
91C22×C4×C11—23no—
92C22×C4×C11C22×C413yes—
93C22×C4×C11C2×D413yes—
94C22×C4×C11C2×D413yes—
95C11×C4⋊C4—23no—
96C11×C4⋊C4—23no—
97C11×C4⋊C4—23no—
98C11×C4⋊C4—23no—
99C11×C4⋊C4—23no—
100C11×C4⋊C4—23no—
101C11×C4⋊C4—26no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—23no—
104C11×C4⋊C4C22⋊C413yes—
105C11×C4⋊C4C22⋊C413yes—
106C11×C4⋊C4C22×C411yescharacteristic
107C11×C4⋊C4C22×C413yes—
108C11×C22⋊C4—26no—
109C11×C22⋊C4C22⋊C416yes—
110C42×C11—23no—
111C42×C11—23no—
112C42×C11—21no—
113C42×C11—23no—
114C42×C11C22×C413yes—
115C42×C11C2×D413yes—
116C42×C11C2×D413yes—
117C42×C11C2411yescharacteristic
118#4318—46no—
119C2×C11⋊C8—21no—
120C2×C11⋊C8—23no—
121C2×C11⋊C8—21no—
122C2×C11⋊C8—23no—
123C2×C11⋊C8—46no—
124C2×C11⋊C8—46no—
125Q8×#41D1111yescharacteristic
126C8×#41—111no—
127#2906—111no—
128#1493—113no—
129#1487—113no—
130#1481—113no—
131C2×Q8⋊C8—113no—
132C23×C11C2×C22⋊C413yes—
133Q8×C11—21no—
134Q8×C11—23no—
135Q8×C11—23no—
136Q8×C11—46no—
137Q8×C11—83no—
138Q8×C11#10314yes—
139Q8×C11#13112yescomplemented
140D4×C11#103112yes—
141C2×C4×C11—21no—
142C2×C4×C11—23no—
143C2×C4×C11—23no—
144C2×C4×C11—21no—
145C2×C4×C11—23no—
146C2×C4×C11—23no—
147C2×C4×C11—43no—
148C2×C4×C11—46no—
149C2×C4×C11—83no—
150C2×C4×C11C2×C22⋊C413yes—
151C2×C4×C11C2×C22⋊C413yes—
152C2×C4×C11C2×C22⋊C413yes—
153C2×C4×C11C2×SD1616yes—
154C2×C4×C11C2×Q1616yes—
155C2×C4×C11C23×C411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×C4×C11C22×D411yescharacteristic
158C11⋊C8—22no—
159C11⋊C8—43no—
160C11⋊C8—41no—
161C11⋊C8—43no—
162C2×#131—221no—
163Q82Dic1111yescharacteristic
164#557—21no—
165#557Dic1111yescharacteristic
166#554—23no—
167#554Dic1113yes—
168D4×Q8Dic1113yes—
169#533—23no—
170#533C2×D1113yes—
171C4×#41—21no—
172C4×#41C2×D1111yescharacteristic
173C2×C4×Q8C2×D1113yes—
174C8×Q8—221no—
175C8×D4—223no—
176#431—113no—
177#424—223no—
178#423—113no—
179C2×C4⋊C8—113no—
180C2×C4×C8—113no—
181Q8⋊C8—111no—
182Q8⋊C8—113no—
183Q8⋊C8—113no—
184Q8⋊C8—113no—
185Q8⋊C8—116no—
186C22×C11—23no—
187C22×C11—23no—
188C22×C11C2×#10316yes—
189C22×C11C22×C22⋊C411yescharacteristic
190C4×C11—23no—
191C4×C11—22no—
192C4×C11—21no—
193C4×C11—23no—
194C4×C11—43no—
195C4×C11—41no—
196C4×C11—43no—
197C4×C11C2×#10316yes—
198C4×C11C2×#13111yescharacteristic
199C4×C11#56811yescharacteristic
200C4×C11C22×SD1611yescharacteristic
201C4×C11C22×Q1611yescharacteristic
202C2×#41C22⋊D1111yescharacteristic
203C22×Q8C2×Dic1113yes—
204#131—444no—
205C2×M16—223no—
206C22×C8—223no—
207C22×C8—223no—
208C4⋊Q8—23no—
209C4⋊Q8—23no—
210C4⋊Q8C2×Dic1113yes—
211C4⋊Q8C2×Dic1113yes—
212#125—23no—
213#125—23no—
214#125—23no—
215C22⋊Q8—23no—
216C22⋊Q8—26no—
217C22⋊Q8—26no—
218C22⋊Q8C2×Dic1116yes—
219C4×Q8—21no—
220C4×Q8—21no—
221C4×Q8—23no—
222C4×Q8—23no—
223C4×Q8—23no—
224C4×Q8C2×Dic1113yes—
225C4×Q8C2×Dic1113yes—
226C4×Q8C2×Dic1111yescharacteristic
227C4×Q8C22⋊D1111yescharacteristic
228C4×Q8C22×D1111yescharacteristic
229C4×Q8C22×D1113yes—
230C4×D4—23no—
231C4×D4—23no—
232C4×D4C2×Dic1113yes—
233C4×D4C22⋊D1113yes—
234#117—23no—
235#117C22⋊D1113yes—
236C2×C4⋊C4—23no—
237C2×C4⋊C4C2×Dic1113yes—
238C2×C42—23no—
239C2×C42C22×D1113yes—
240C4⋊C8—111no—
241C4⋊C8—113no—
242C4⋊C8—223no—
243C4⋊C8—223no—
244C4⋊C8—223no—
245C22⋊C8—223no—
246C4×C8—111no—
247C4×C8—113no—
248C4×C8—223no—
249C2×C11—26no—
250C2×C11#288011yescharacteristic
251C2×C11C22×#10311yescharacteristic
252C2×C11#290111yescharacteristic
253#41#432514yes—
254#41#432614yes—
255C2×Q8—23no—
256C2×Q8—23no—
257C2×Q8—26no—
258C2×Q8—43no—
259C2×Q8C22⋊Dic1111yescharacteristic
260C2×Q8C22×Dic1113yes—
261C2×Q8C22×Dic1111yescharacteristic
262C2×D4C22⋊Dic1113yes—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4C22×Dic1113yes—
266C22×C4C2×C22⋊D1113yes—
267C22×C4C2×C22⋊D1113yes—
268M16—446no—
269C2×C8—221no—
270C2×C8—223no—
271C2×C8—221no—
272C2×C8—223no—
273C2×C8—446no—
274C2×C8—446no—
275C4⋊C4—23no—
276C4⋊C4—23no—
277C4⋊C4—23no—
278C4⋊C4—23no—
279C4⋊C4—23no—
280C4⋊C4—23no—
281C4⋊C4—26no—
282C4⋊C4—21no—
283C4⋊C4—23no—
284C4⋊C4C22⋊Dic1113yes—
285C4⋊C4C22⋊Dic1113yes—
286C4⋊C4C22×Dic1111yescharacteristic
287C4⋊C4C22×Dic1113yes—
288C22⋊C4—26no—
289C22⋊C4C22⋊Dic1116yes—
290C42—23no—
291C42—23no—
292C42—21no—
293C42—23no—
294C42C22×Dic1113yes—
295C42C2×C22⋊D1113yes—
296C42C2×C22⋊D1113yes—
297C42C23×D1111yescharacteristic
298C11#1750911yescharacteristic, complemented, Sylow
299C23C2×C22⋊Dic1113yes—
300Q8—21no—
301Q8—23no—
302Q8—23no—
303Q8—46no—
304Q8—83no—
305Q8#6689914yes—
306Q8#6700112yescomplemented
307D4#66899112yes—
308C2×C4—21no—
309C2×C4—23no—
310C2×C4—23no—
311C2×C4—21no—
312C2×C4—23no—
313C2×C4—23no—
314C2×C4—43no—
315C2×C4—46no—
316C2×C4—83no—
317C2×C4C2×#432516yes—
318C2×C4C2×#432616yes—
319C2×C4C2×C22⋊Dic1113yes—
320C2×C4C2×C22⋊Dic1113yes—
321C2×C4C2×C22⋊Dic1113yes—
322C2×C4C23×Dic1111yescharacteristic
323C2×C4C22×C22⋊D1111yescharacteristic
324C2×C4C22×C22⋊D1111yescharacteristic
325C8—222no—
326C8—443no—
327C8—441no—
328C8—443no—
329C22—23no—
330C22—23no—
331C22C2×#6689916yes—
332C22C22×C22⋊Dic1111yescharacteristic
333C4—23no—
334C4—22no—
335C4—21no—
336C4—23no—
337C4—43no—
338C4—41no—
339C4—43no—
340C4C2×#6689916yes—
341C4C22×#432511yescharacteristic
342C4C22×#432611yescharacteristic
343C4C2×#6700111yescharacteristic
344C4#1062335011yescharacteristic
345C2—26no—
346C2#1307706511yescharacteristic
347C2C22×#6689911yescharacteristic
348C2#1307716311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingQ8×C11×#41C2
socleC22×C11C22×C22⋊C4
prime radicalC2×C11×#41D4
cosocleC42×C11C24
hypercenterQ8×#41D11
hypocenterC11#17509
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
3. #13067071C2semidirect
4. #13067045C2semidirect
5. #13067019C2semidirect
6. C2×Q8⋊(C11⋊C8)C2semidirect
139. Q8×C11#131semidirect
298. C11#17509semidirect
306. Q8#67001semidirect

Maximal subgroups

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

subgroupindex
#41×C11⋊C82
#130771842
#130670712
#130670452
#130670192
C2×Q8⋊(C11⋊C8)2
Q8×C11×#412
#1750911