Finite Group Databasebeta

← #14770558

Subgroups — #14770558

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×#10623108C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069543C213yesmaximal, complemented
4#13069421C213yesmaximal, complemented
5#13068613C213yesmaximal, complemented
6C4×#66873C213yesmaximal, complemented
7Q8×C11×C4⋊C4C211yesmaximal, characteristic, complemented
8C22×#4343—21no—
9C2×C4×Q8×C11—21no—
10C2×C4×Q8×C11C2211yescharacteristic
11#10623108—24no—
12#10623108C418yescomplemented
13C2×#66948—23no—
14C2×#66927C2213yes—
15C2×C4×D44C2213yes—
16C11×#389—23no—
17C11×#384C2213yes—
18C4×C11×C4⋊C4C2213yes—
19Q8×C11⋊C8—24no—
20C2×#66873C2213yes—
21C2×#66873C2213yes—
22C2×#66873C2216yes—
23C2×C4⋊(C11⋊C8)C2213yes—
24C2×C4×C11⋊C8C2213yes—
25#10622167C2213yes—
26#10622167C2211yescharacteristic
27C22×Q8×C11D411yescharacteristic
28C2×#4343—28no—
29C2×#4343—44no—
30C2×#4343—44no—
31C22×D44—23no—
32C22×D44—23no—
33C22×D44C2313yes—
34C22×C4×D11—23no—
35C4×Q8×C11—44no—
36C4×Q8×C11C2×C414yes—
37C4×Q8×C11D414yes—
38C2×C11×C4⋊C4—23no—
39C2×C11×C4⋊C4—23no—
40C2×C11×C4⋊C4D413yes—
41C2×C11×C4⋊C4C2313yes—
42C2×C11×C4⋊C4C2311yescharacteristic
43C2×C42×C11—23no—
44C2×C42×C11C2313yes—
45C2×(C2×D11)⋊C4—23no—
46C2×C4⋊Dic11C2311yescharacteristic
47C22×C11⋊C8C2313yes—
48C22×C11⋊C8C2311yescharacteristic
49#66948—224no—
50#66927—26no—
51#66927C2×C4112yes—
52C4×D44—26no—
53C4×D44C2×C4112yes—
54C11×#95—23no—
55#66873—26no—
56#66873—26no—
57#66873—46no—
58C4⋊(C11⋊C8)—26no—
59C4×C11⋊C8—26no—
60#22540—111nomaximal, Sylow
61C23×D11—23no—
62C2×Q8×C11C22⋊C414yes—
63C2×Q8×C11D814yes—
64C2×Q8×C11SD1614yes—
65C22×C4×C11—21no—
66C22×C4×C11—23no—
67C22×C4×C11C2×D413yes—
68C22×C4×C11C2×D413yes—
69C22×C4×C11C2411yescharacteristic
70C22×Dic11—21no—
71#4343—432no—
72C2×D44—212no—
73C2×D44—212no—
74C2×D44—23no—
75C2×D44—23no—
76C2×D44—23no—
77C2×D44—23no—
78C2×D44—23no—
79C2×D44—46no—
80C2×D44—46no—
81C2×D44—83no—
82C2×D44—83no—
83C2×D44C22×C416yes—
84C2×C4×D11—212no—
85C2×C4×D11—46no—
86C2×C4×D11—46no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—23no—
89C11×C4⋊C4—23no—
90C11×C4⋊C4—46no—
91C11×C4⋊C4—83no—
92C11×C4⋊C4C22⋊C4112yes—
93C11×C4⋊C4#4112yescomplemented
94C42×C11—46no—
95C42×C11C22×C416yes—
96C42×C11C2×D416yes—
97(C2×D11)⋊C4—212no—
98C4⋊Dic11—21no—
99C4⋊Dic11C22×C412yes—
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×#550—111no—
107C2×C8×Q8—111no—
108Q8×C4⋊C4D1111yescharacteristic, complemented
109#1982—113no—
110#1957—113no—
111#1802—113no—
112C4×#102—113no—
113C23×C11C22×D411yescharacteristic
114C22×D11—26no—
115C22×D11—43no—
116C22×D11—43no—
117C22×D11—43no—
118C22×D11—43no—
119C22×D11—43no—
120C22×D11—43no—
121Q8×C11#102116yescomplemented
122C2×C4×C11—23no—
123C2×C4×C11—23no—
124C2×C4×C11—22no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—43no—
128C2×C4×C11—43no—
129C2×C4×C11—43no—
130C2×C4×C11C2×C22⋊C416yes—
131C2×C4×C11C2×C22⋊C416yes—
132C2×C4×C11C2×D816yes—
133C2×C4×C11C2×SD1616yes—
134C2×C4×C11C23×C411yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C2×#4111yescharacteristic
137C2×C4×C11C2×#4111yescharacteristic
138C2×C4×C11H(5,𝔽2)11yescharacteristic
139C2×C4×C112−1+411yescharacteristic
140C2×Dic11—22no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143D44—26no—
144D44—26no—
145D44—43no—
146D44—43no—
147D44—424no—
148D44—812no—
149C4×D11—424no—
150C11⋊C8—22no—
151C11⋊C8—43no—
152C22×#41—221no—
153#550—118no—
154#550—224no—
155C2×#127—113no—
156C2×#121—223no—
157C2×C4×Q8—21no—
158C2×C4×Q8C2×D1111yescharacteristic
159C2×C4×D4—113no—
160C8×Q8—224no—
161C2×C4⋊C8—113no—
162C2×#102—113no—
163C2×#102—113no—
164C2×#102—116no—
165C2×C4×C8—113no—
166#389—23no—
167#384C2×D1113yes—
168C4×C4⋊C4C2×D1113yes—
169#340—113no—
170#340—111no—
171C22×C11C22×C22⋊C411yescharacteristic
172C22×C11#54811yescharacteristic
173C22×C11#55011yescharacteristic
174C22×C11C22×D811yescharacteristic
175C22×C11C22×SD1611yescharacteristic
176C22×C11#57611yescharacteristic
177C22×C11#57711yescharacteristic
178C2×D11—46no—
179C2×D11—46no—
180C2×D11—46no—
181C2×D11—83no—
182C2×D11—83no—
183C2×D11—83no—
184C2×D11—83no—
185C4×C11—26no—
186C4×C11—42no—
187C4×C11—83no—
188C4×C11C2×#102112yes—
189C4×C11C4×#4111yescharacteristic
190C4×C11#52011yescharacteristic
191C4×C11#54811yescharacteristic
192C4×C11#55011yescharacteristic
193Dic11—42no—
194C2×#41—228no—
195C2×#41—444no—
196C2×#41—444no—
197C22×Q8C22⋊D1111yescharacteristic
198C22×D4—113no—
199C22×D4—223no—
200C22×D4—223no—
201C23×C4—223no—
202C22×C8—111no—
203C22×C8—113no—
204#127—1112no—
205#127—226no—
206#121—2224no—
207C4×Q8—44no—
208C4×Q8C4×D1114yes—
209C4×Q8D4414yes—
210C4×D4—1112no—
211C4×D4—226no—
212C2×C4⋊C4—23no—
213C2×C4⋊C4—23no—
214C2×C4⋊C4—111no—
215C2×C4⋊C4C22⋊D1113yes—
216C2×C4⋊C4C22×D1113yes—
217C2×C4⋊C4C22×D1111yescharacteristic
218C2×C22⋊C4—223no—
219C2×C42—23no—
220C2×C42C22×D1113yes—
221C4⋊C8—226no—
222#102—226no—
223#102—226no—
224#102—446no—
225C4×C8—226no—
226#95—23no—
227C2×C11#234111yescharacteristic
228C2×C11C22×#10211yescharacteristic
229C2×C11#289711yescharacteristic
230C2×C11#335811yescharacteristic
231C2×C11#336211yescharacteristic
232C2×C11#339111yescharacteristic
233C2×C11#339211yescharacteristic
234D11—86no—
235C24—223no—
236#41—4432no—
237C2×Q8(C2×D11)⋊C414yes—
238C2×Q8#432314yes—
239C2×Q8#432514yes—
240C2×D4—116no—
241C2×D4—2212no—
242C2×D4—2212no—
243C2×D4—223no—
244C2×D4—223no—
245C2×D4—223no—
246C2×D4—223no—
247C2×D4—223no—
248C2×D4—446no—
249C2×D4—446no—
250C2×D4—883no—
251C2×D4—883no—
252C22×C4—21no—
253C22×C4—23no—
254C22×C4—221no—
255C22×C4—2212no—
256C22×C4—446no—
257C22×C4—446no—
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—23no—
269C4⋊C4—23no—
270C4⋊C4—46no—
271C4⋊C4—83no—
272C4⋊C4—112no—
273C4⋊C4—221no—
274C4⋊C4(C2×D11)⋊C4112yes—
275C4⋊C4#434312yescomplemented
276C22⋊C4—2212no—
277C42—46no—
278C42C2×C4×D1116yes—
279C42C2×D4416yes—
280C11#2254011yescharacteristic, complemented, Sylow
281C23—226no—
282C23—443no—
283C23—443no—
284C23—443no—
285C23—443no—
286C23—443no—
287C23—443no—
288C23C22×C22⋊D1111yescharacteristic
289Q8#66873116yescomplemented
290D4—226no—
291D4—226no—
292D4—4424no—
293D4—443no—
294D4—443no—
295D4—8812no—
296C2×C4—23no—
297C2×C4—23no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—43no—
302C2×C4—43no—
303C2×C4—43no—
304C2×C4—222no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—4424no—
308C2×C4C2×(C2×D11)⋊C416yes—
309C2×C4C2×(C2×D11)⋊C416yes—
310C2×C4C2×#432316yes—
311C2×C4C2×#432516yes—
312C2×C4C22×C4×D1111yescharacteristic
313C2×C4C22×D4411yescharacteristic
314C2×C4C2×#434311yescharacteristic
315C2×C4#6704011yescharacteristic
316C2×C4#41×D1111yescharacteristic
317C2×C4#6704211yescharacteristic
318C8—222no—
319C8—443no—
320C22—446no—
321C22—446no—
322C22—446no—
323C22—883no—
324C22—883no—
325C22—883no—
326C22—883no—
327C22C22×(C2×D11)⋊C411yescharacteristic
328C22C22×#432311yescharacteristic
329C22C22×#432511yescharacteristic
330C22#1062334811yescharacteristic
331C22#1062336511yescharacteristic
332C22#1062336611yescharacteristic
333C22#1062336811yescharacteristic
334C4—26no—
335C4—42no—
336C4—83no—
337C4—442no—
338C4C2×#66873112yes—
339C4C4×#434311yescharacteristic
340C4#1062310511yescharacteristic
341C4#1062310711yescharacteristic
342C4#1062310811yescharacteristic
343C2—886no—
344C2#1307145411yescharacteristic
345C2C22×#6687311yescharacteristic
346C2#1307713911yescharacteristic
347C2#1308125111yescharacteristic
348C2#1308128711yescharacteristic
349C2#1308158811yescharacteristic
350C2#1308159311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10623108C2
cosocleC22×C4×C11C24
hypercenterQ8×C4⋊C4D11
hypocenterC11#22540
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13069543C2semidirect
4. #13069421C2semidirect
5. #13068613C2semidirect
6. C4×#66873C2semidirect
7. Q8×C11×C4⋊C4C2semidirect
12. #10623108C4semidirect
93. C11×C4⋊C4#41semidirect
105. C2×C11⋊C8#41semidirect
108. Q8×C4⋊C4D11semidirect
121. Q8×C11#102semidirect
275. C4⋊C4#4343semidirect
280. C11#22540semidirect
289. Q8#66873semidirect

Maximal subgroups

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

subgroupindex
C2×#106231082
C2×Q8×C11⋊C82
#130695432
#130694212
#130686132
C4×#668732
Q8×C11×C4⋊C42
#2254011