Finite Group Databasebeta

← #14770562

Subgroups — #14770562

Order 2816.

1430 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
2Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13069544C213yesmaximal, complemented
4#13069423C213yesmaximal, complemented
5#13068616C213yesmaximal, complemented
6C4×#66896C213yesmaximal, complemented
7C2×C11×#550C211yesmaximal, characteristic
8C22×C11×#41—21no—
9C11×#550—24no—
10C11×#550C418yescomplemented
11C2×C11×#127C2213yes—
12C2×C11×#121—23no—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2213yes—
15C2×Q8×Dic11—21no—
16C2×#66896C2213yes—
17C2×#66896C2213yes—
18C2×#66896C2216yes—
19Q8×C11⋊C8—24no—
20#10622598—23no—
21#10622548C2213yes—
22C4×C4⋊Dic11C2213yes—
23C2×C4⋊(C11⋊C8)C2213yes—
24C2×C4×C11⋊C8C2213yes—
25#10622167C2213yes—
26#10622167C2211yescharacteristic
27C2×C11×#41—28no—
28C2×C11×#41—44no—
29C2×C11×#41—44no—
30C22×Q8×C11D411yescharacteristic
31C22×D4×C11—23no—
32C22×D4×C11—23no—
33C22×D4×C11C2313yes—
34C23×C4×C11—23no—
35C11×#127—26no—
36C11×#127C2×C4112yes—
37C11×#121—224no—
38C4×Q8×C11C2×C414yes—
39C4×Q8×C11D414yes—
40C4×D4×C11—26no—
41C4×D4×C11C2×C4112yes—
42C2×C11×C4⋊C4D413yes—
43C2×C11×C4⋊C4C2311yescharacteristic
44C2×C11×C22⋊C4—23no—
45C2×C42×C11C2313yes—
46Q8×Dic11—44no—
47C2×C4⋊Dic11—23no—
48C2×C4⋊Dic11—23no—
49C2×C4⋊Dic11C2313yes—
50C2×C4⋊Dic11C2311yescharacteristic
51C2×C4×Dic11—23no—
52C22×C11⋊C8C2313yes—
53C22×C11⋊C8C2311yescharacteristic
54#66896—26no—
55#66896—26no—
56#66896—46no—
57C11⋊#95—23no—
58C4⋊(C11⋊C8)—26no—
59C4×C11⋊C8—26no—
60#22540—111nomaximal, Sylow
61C24×C11—23no—
62C11×#41—432no—
63C2×Q8×C11C22⋊C414yes—
64C2×Q8×C11D814yes—
65C2×Q8×C11SD1614yes—
66C2×D4×C11—212no—
67C2×D4×C11—212no—
68C2×D4×C11—23no—
69C2×D4×C11—23no—
70C2×D4×C11—23no—
71C2×D4×C11—23no—
72C2×D4×C11—23no—
73C2×D4×C11—46no—
74C2×D4×C11—46no—
75C2×D4×C11—83no—
76C2×D4×C11—83no—
77C2×D4×C11C22×C416yes—
78C22×C4×C11—21no—
79C22×C4×C11—212no—
80C22×C4×C11—46no—
81C22×C4×C11—46no—
82C22×C4×C11C2×D413yes—
83C22×C4×C11C2×D413yes—
84C22×C4×C11C2411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—23no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4C22⋊C4112yes—
89C11×C4⋊C4C22×C412yes—
90C11×C22⋊C4—212no—
91C42×C11C22×C416yes—
92C42×C11C2×D416yes—
93C4⋊Dic11—23no—
94C4⋊Dic11—23no—
95C4⋊Dic11—21no—
96C4⋊Dic11—46no—
97C4⋊Dic11—83no—
98C4⋊Dic11#4112yescomplemented
99C4×Dic11—46no—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—23no—
102C2×C11⋊C8—23no—
103C2×C11⋊C8—23no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8#4112yescomplemented
106C2×#550D1111yescharacteristic
107C2×C8×Q8—111no—
108Q8×C4⋊C4—111no—
109#1982—113no—
110#1957—113no—
111#1802—113no—
112C4×#102—113no—
113C23×C11—26no—
114C23×C11—43no—
115C23×C11—43no—
116C23×C11—43no—
117C23×C11—43no—
118C23×C11—43no—
119C23×C11—43no—
120C23×C11C22×D411yescharacteristic
121Q8×C11#102116yescomplemented
122D4×C11—26no—
123D4×C11—26no—
124D4×C11—43no—
125D4×C11—43no—
126D4×C11—424no—
127D4×C11—812no—
128C2×C4×C11—23no—
129C2×C4×C11—23no—
130C2×C4×C11—22no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—424no—
134C2×C4×C11C2×C22⋊C416yes—
135C2×C4×C11C2×C22⋊C416yes—
136C2×C4×C11C2×D816yes—
137C2×C4×C11C2×SD1616yes—
138C2×C4×C11C23×C411yescharacteristic
139C2×C4×C11C22×D411yescharacteristic
140C2×C4×C11C2×#4111yescharacteristic
141C2×C4×C11C2×#4111yescharacteristic
142C2×C4×C11H(5,𝔽2)11yescharacteristic
143C2×C4×C112−1+411yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—43no—
148C2×Dic11—43no—
149C2×Dic11—43no—
150C11⋊C8—22no—
151C11⋊C8—43no—
152C22×#41—21no—
153#550—24no—
154#550Dic1118yescomplemented
155C2×#127C2×D1113yes—
156C2×#121—23no—
157C2×C4×Q8—221no—
158C2×C4×Q8C2×D1111yescharacteristic
159C2×C4×D4C2×D1113yes—
160C8×Q8—224no—
161C2×C4⋊C8—113no—
162C2×#102—113no—
163C2×#102—113no—
164C2×#102—116no—
165C2×C4×C8—113no—
166#389—223no—
167#384—113no—
168C4×C4⋊C4—113no—
169#340—113no—
170#340—111no—
171C22×C11—46no—
172C22×C11—46no—
173C22×C11—46no—
174C22×C11—83no—
175C22×C11—83no—
176C22×C11—83no—
177C22×C11—83no—
178C22×C11C22×C22⋊C411yescharacteristic
179C22×C11#54811yescharacteristic
180C22×C11#55011yescharacteristic
181C22×C11C22×D811yescharacteristic
182C22×C11C22×SD1611yescharacteristic
183C22×C11#57611yescharacteristic
184C22×C11#57711yescharacteristic
185C4×C11—26no—
186C4×C11—42no—
187C4×C11C2×#102112yes—
188C4×C11C4×#4111yescharacteristic
189C4×C11#52011yescharacteristic
190C4×C11#54811yescharacteristic
191C4×C11#55011yescharacteristic
192Dic11—42no—
193Dic11—83no—
194C2×#41—28no—
195C2×#41—44no—
196C2×#41—44no—
197C22×Q8C22⋊D1111yescharacteristic
198C22×D4—23no—
199C22×D4—23no—
200C22×D4C22×D1113yes—
201C23×C4—23no—
202C22×C8—111no—
203C22×C8—113no—
204#127—26no—
205#127C2×Dic11112yes—
206#121—224no—
207C4×Q8—444no—
208C4×Q8C2×Dic1114yes—
209C4×Q8C22⋊D1114yes—
210C4×D4—26no—
211C4×D4C2×Dic11112yes—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—113no—
214C2×C4⋊C4—223no—
215C2×C4⋊C4—223no—
216C2×C4⋊C4C22⋊D1113yes—
217C2×C4⋊C4C22×D1111yescharacteristic
218C2×C22⋊C4—23no—
219C2×C42—223no—
220C2×C42C22×D1113yes—
221C4⋊C8—226no—
222#102—226no—
223#102—226no—
224#102—446no—
225C4×C8—226no—
226#95—223no—
227C2×C11—86no—
228C2×C11#234111yescharacteristic
229C2×C11C22×#10211yescharacteristic
230C2×C11#289711yescharacteristic
231C2×C11#335811yescharacteristic
232C2×C11#336211yescharacteristic
233C2×C11#339111yescharacteristic
234C2×C11#339211yescharacteristic
235C24—23no—
236#41—432no—
237C2×Q8#432314yes—
238C2×Q8#432414yes—
239C2×Q8C22⋊Dic1114yes—
240C2×D4—212no—
241C2×D4—212no—
242C2×D4—23no—
243C2×D4—23no—
244C2×D4—23no—
245C2×D4—23no—
246C2×D4—23no—
247C2×D4—46no—
248C2×D4—46no—
249C2×D4—83no—
250C2×D4—83no—
251C2×D4C22×Dic1116yes—
252C22×C4—21no—
253C22×C4—212no—
254C22×C4—46no—
255C22×C4—46no—
256C22×C4—221no—
257C22×C4—223no—
258C22×C4C2×C22⋊D1113yes—
259C22×C4C2×C22⋊D1113yes—
260C22×C4C23×D1111yescharacteristic
261C2×C8—112no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—223no—
265C2×C8—223no—
266C2×C8—223no—
267C4⋊C4—21no—
268C4⋊C4—112no—
269C4⋊C4—221no—
270C4⋊C4—223no—
271C4⋊C4—223no—
272C4⋊C4—446no—
273C4⋊C4—883no—
274C4⋊C4C22⋊Dic11112yes—
275C4⋊C4C22×Dic1112yes—
276C22⋊C4—212no—
277C42—446no—
278C42C22×Dic1116yes—
279C42C2×C22⋊D1116yes—
280C11#2254011yescharacteristic, complemented, Sylow
281C23—26no—
282C23—43no—
283C23—43no—
284C23—43no—
285C23—43no—
286C23—43no—
287C23—43no—
288C23C22×C22⋊D1111yescharacteristic
289Q8#66896116yescomplemented
290D4—26no—
291D4—26no—
292D4—424no—
293D4—43no—
294D4—43no—
295D4—812no—
296C2×C4—23no—
297C2×C4—23no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—424no—
302C2×C4—222no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—443no—
306C2×C4—443no—
307C2×C4—443no—
308C2×C4C2×#432316yes—
309C2×C4C2×#432416yes—
310C2×C4C2×C22⋊Dic1116yes—
311C2×C4C2×C22⋊Dic1116yes—
312C2×C4#41×D1111yescharacteristic
313C2×C4#41×D1111yescharacteristic
314C2×C4#6704211yescharacteristic
315C2×C4#6704311yescharacteristic
316C2×C4C23×Dic1111yescharacteristic
317C2×C4C22×C22⋊D1111yescharacteristic
318C8—222no—
319C8—443no—
320C22—46no—
321C22—46no—
322C22—46no—
323C22—83no—
324C22—83no—
325C22—83no—
326C22—83no—
327C22C22×#432311yescharacteristic
328C22C22×#432411yescharacteristic
329C22#1062336211yescharacteristic
330C22#1062336511yescharacteristic
331C22#1062336611yescharacteristic
332C22#1062336711yescharacteristic
333C22C22×C22⋊Dic1111yescharacteristic
334C4—26no—
335C4—42no—
336C4—442no—
337C4—883no—
338C4C2×#66896112yes—
339C4#41×Dic1111yescharacteristic
340C4#1062335811yescharacteristic
341C4#1062336211yescharacteristic
342C4#1062336511yescharacteristic
343C2—86no—
344C2#1307145711yescharacteristic
345C2C22×#6689611yescharacteristic
346C2#1307714211yescharacteristic
347C2#1308124711yescharacteristic
348C2#1308128311yescharacteristic
349C2#1308158811yescharacteristic
350C2#1308159711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#550C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#550D11
hypocenterC11#22540
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C11⋊C8C2semidirect
2. Q8×C4⋊Dic11C2semidirect
3. #13069544C2semidirect
4. #13069423C2semidirect
5. #13068616C2semidirect
6. C4×#66896C2semidirect
10. C11×#550C4semidirect
98. C4⋊Dic11#41semidirect
105. C2×C11⋊C8#41semidirect
121. Q8×C11#102semidirect
154. #550Dic11semidirect
280. C11#22540semidirect
289. Q8#66896semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C11⋊C82
Q8×C4⋊Dic112
#130695442
#130694232
#130686162
C4×#668962
C2×C11×#5502
#2254011