Finite Group Databasebeta

← #14770486

Subgroups — #14770486

Order 2816.

1428 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069410C213yesmaximal, complemented
4#13069409C213yesmaximal, complemented
5#13068593C213yesmaximal, complemented
6C4×(C2×D11)⋊C8C213yesmaximal, complemented
7C2×C8×Q8×C11C211yesmaximal, characteristic, complemented
8C22×#4343C411yescharacteristic
9C2×C4×Q8×C11C2211yescharacteristic
10C2×Q8×Dic11C411yescharacteristic
11C4×#4343—24no—
12C4×#4343—24no—
13C2×#66946C413yes—
14C2×#66945C413yes—
15C2×C4×D44C2213yes—
16C2×C42×D11C2213yes—
17C8×Q8×C11—24no—
18C2×C11×C4⋊C8C2213yes—
19C2×C4×C8×C11C2213yes—
20C2×(C2×D11)⋊C8C2213yes—
21C2×(C2×D11)⋊C8C2213yes—
22C2×(C2×D11)⋊C8C2216yes—
23Q8×C11⋊C8—24no—
24C2×C4⋊(C11⋊C8)C2213yes—
25C2×C4×C11⋊C8C2213yes—
26#10622188C2213yes—
27#10622188C2211yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic
29C2×#4343—24no—
30C2×#4343—24no—
31C2×#4343C818yescomplemented
32C22×D44C2×C413yes—
33C22×C4×D11C2×C413yes—
34C22×C4×D11C2×C413yes—
35C22×C4×D11C2313yes—
36C22×C8×C11C2313yes—
37C22×C8×C11C2311yescharacteristic
38C4×Q8×C11D414yes—
39C4×Q8×C11D414yes—
40C2×C11×C4⋊C4C2×C413yes—
41C2×C42×C11C2313yes—
42Q8×Dic11—24no—
43C2×(C2×D11)⋊C4C2×C416yes—
44C2×C4⋊Dic11C2×C413yes—
45C2×C4×Dic11C2×C413yes—
46C2×C4×Dic11C2×C413yes—
47C2×C4×Dic11C2311yescharacteristic
48C22×C11⋊C8C2313yes—
49C22×C11⋊C8C2311yescharacteristic
50#66946—212no—
51#66945—212no—
52C4×D44—26no—
53C4×D44—26no—
54C42×D11—26no—
55C42×D11—26no—
56C11×C4⋊C8—26no—
57C4×C8×C11—26no—
58(C2×D11)⋊C8—26no—
59(C2×D11)⋊C8—26no—
60(C2×D11)⋊C8—46no—
61C4⋊(C11⋊C8)—26no—
62C4×C11⋊C8—26no—
63#22530—111nomaximal, Sylow
64C23×D11C22×C413yes—
65C2×Q8×C11C22⋊C414yes—
66C2×Q8×C11C2×C814yes—
67C2×Q8×C11M1614yes—
68C22×C4×C11C22×C413yes—
69C22×C4×C11C22×C413yes—
70C22×C4×C11C2411yescharacteristic
71C22×Dic11C22×C413yes—
72C22×Dic11C22×C411yescharacteristic
73C22×Dic11C22×C411yescharacteristic
74#4343—232no—
75C2×D44—26no—
76C2×D44—26no—
77C2×D44C2×C8112yes—
78C2×C4×D11—26no—
79C2×C4×D11—26no—
80C2×C4×D11—26no—
81C2×C4×D11—26no—
82C2×C4×D11—23no—
83C2×C4×D11—23no—
84C2×C4×D11—23no—
85C2×C4×D11—23no—
86C2×C4×D11—23no—
87C2×C4×D11—23no—
88C2×C4×D11—43no—
89C2×C4×D11C2×C8112yes—
90C2×C8×C11—21no—
91C2×C8×C11—23no—
92C2×C8×C11—23no—
93C2×C8×C11—23no—
94C2×C8×C11—21no—
95C2×C8×C11#4112yescomplemented
96C11×C4⋊C4C22⋊C4112yes—
97C42×C11C2×D416yes—
98C42×C11C2×D416yes—
99(C2×D11)⋊C4—212no—
100C4⋊Dic11—26no—
101C4×Dic11—26no—
102C4×Dic11—26no—
103C4×Dic11—21no—
104C4×Dic11—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—23no—
107C2×C11⋊C8—23no—
108C2×C11⋊C8—23no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8#4112yescomplemented
111C2×C4×#41—111no—
112C2×C8×Q8—111no—
113C2×C8×Q8D1111yescharacteristic, complemented
114#1954—113no—
115#1954—113no—
116#1797—113no—
117C4×C22⋊C8—113no—
118C23×C11C23×C411yescharacteristic
119C22×D11—23no—
120C22×D11—23no—
121C22×D11—23no—
122C22×D11—23no—
123C22×D11—23no—
124C22×D11—23no—
125C22×D11C22×C816yes—
126Q8×C11C22⋊C8116yescomplemented
127C2×C4×C11—23no—
128C2×C4×C11—23no—
129C2×C4×C11C2×C22⋊C416yes—
130C2×C4×C11C2×C22⋊C416yes—
131C2×C4×C11C22×C816yes—
132C2×C4×C11C2×M1616yes—
133C2×C4×C11C22×D411yescharacteristic
134C2×C4×C11C22×D411yescharacteristic
135C2×C4×C11C2×#4111yescharacteristic
136C2×C4×C11C2×#4111yescharacteristic
137C2×C4×C11H(5,𝔽2)11yescharacteristic
138C2×C4×C112−1+411yescharacteristic
139C2×Dic11—21no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11—23no—
144C2×Dic11—23no—
145C2×Dic11—23no—
146C2×Dic11C22×C812yes—
147C2×Dic11#13112yes—
148D44—224no—
149C4×D11—224no—
150C4×D11—412no—
151C4×D11—43no—
152C4×D11—43no—
153C4×D11—43no—
154C4×D11—43no—
155C8×C11—22no—
156C8×C11—43no—
157C11⋊C8—22no—
158C11⋊C8—43no—
159C22×#41—111no—
160C4×#41—224no—
161C4×#41—224no—
162C2×C4×Q8—111no—
163C2×C4×Q8C2×D1111yescharacteristic
164C2×C4×D4—113no—
165C2×C4×D4—113no—
166C2×#117—113no—
167C22×C42—113no—
168C8×Q8—24no—
169C8×Q8—224no—
170C2×C4⋊C8—113no—
171C2×C4⋊C8C2×D1113yes—
172C2×C22⋊C8—113no—
173C2×C22⋊C8—113no—
174C2×C22⋊C8—116no—
175C2×C4×C8—113no—
176C2×C4×C8C2×D1113yes—
177#336—113no—
178#336—111no—
179C22×C11C22×C22⋊C411yescharacteristic
180C22×C11C4×#4111yescharacteristic
181C22×C11#52011yescharacteristic
182C22×C11C23×C811yescharacteristic
183C22×C11C22×M1611yescharacteristic
184C22×C11C2×#13111yescharacteristic
185C22×C11#56811yescharacteristic
186C2×D11—26no—
187C2×D11—26no—
188C2×D11—26no—
189C2×D11—43no—
190C2×D11—43no—
191C2×D11—43no—
192C2×D11—43no—
193C4×C11—26no—
194C4×C11C2×C22⋊C8112yes—
195C4×C11#54811yescharacteristic
196C4×C11#54811yescharacteristic
197C4×C11#55011yescharacteristic
198C4×C11#55011yescharacteristic
199Dic11—22no—
200Dic11—22no—
201Dic11—43no—
202C2×#41—118no—
203C2×#41—224no—
204C2×#41—224no—
205C22×Q8C4×D1111yescharacteristic
206C22×D4—113no—
207C23×C4—113no—
208C23×C4—113no—
209C23×C4—113no—
210C22×C8—111no—
211C22×C8—113no—
212C22×C8C22×D1113yes—
213C22×C8C22×D1111yescharacteristic
214C4×Q8—224no—
215C4×Q8D4414yes—
216C4×Q8C22⋊D1114yes—
217C4×D4—2212no—
218C4×D4—226no—
219C4×D4—226no—
220#117—2212no—
221C2×C4⋊C4—113no—
222C2×C4⋊C4C4×D1113yes—
223C2×C22⋊C4—116no—
224C2×C42—113no—
225C2×C42—113no—
226C2×C42—111no—
227C2×C42—226no—
228C2×C42—226no—
229C2×C42C22×D1113yes—
230C4⋊C8—26no—
231C4⋊C8—226no—
232C22⋊C8—226no—
233C22⋊C8—226no—
234C22⋊C8—446no—
235C4×C8—26no—
236C4×C8—226no—
237C2×C11#234111yescharacteristic
238C2×C11C22×C22⋊C811yescharacteristic
239C2×C11#288011yescharacteristic
240C2×C11C8×#4111yescharacteristic
241C2×C11#297111yescharacteristic
242C2×C11#298811yescharacteristic
243C2×C11#299111yescharacteristic
244D11—46no—
245C24—113no—
246#41—2232no—
247C2×Q8C8×D1114yes—
248C2×Q8#431314yes—
249C2×Q8(C2×D11)⋊C414yes—
250C2×D4—1112no—
251C2×D4—226no—
252C2×D4—226no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—1112no—
256C22×C4—113no—
257C22×C4—226no—
258C22×C4—226no—
259C22×C4—226no—
260C22×C4—226no—
261C22×C4—223no—
262C22×C4—223no—
263C22×C4—223no—
264C22×C4—223no—
265C22×C4—223no—
266C22×C4—223no—
267C22×C4—443no—
268C22×C4C2×C4×D1113yes—
269C22×C4C2×C4×D1113yes—
270C22×C4C23×D1111yescharacteristic
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—23no—
274C2×C8—23no—
275C2×C8—23no—
276C2×C8—112no—
277C2×C8—221no—
278C2×C8—221no—
279C2×C8—223no—
280C2×C8—223no—
281C2×C8—223no—
282C2×C8#434312yescomplemented
283C4⋊C4—226no—
284C4⋊C4(C2×D11)⋊C4112yes—
285C22⋊C4—2212no—
286C42—226no—
287C42—226no—
288C42—221no—
289C42—221no—
290C42C2×D4416yes—
291C42C2×C22⋊D1116yes—
292C11#2253011yescharacteristic, complemented, Sylow
293C23—116no—
294C23—223no—
295C23—223no—
296C23—223no—
297C23—223no—
298C23—223no—
299C23—223no—
300C23C22×C4×D1111yescharacteristic
301Q8(C2×D11)⋊C8116yescomplemented
302D4—2224no—
303C2×C4—23no—
304C2×C4—23no—
305C2×C4—112no—
306C2×C4—112no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—2224no—
312C2×C4—223no—
313C2×C4—223no—
314C2×C4—223no—
315C2×C4—4412no—
316C2×C4—443no—
317C2×C4—443no—
318C2×C4—443no—
319C2×C4—443no—
320C2×C4C2×C8×D1116yes—
321C2×C4C2×#431316yes—
322C2×C4C2×(C2×D11)⋊C416yes—
323C2×C4C2×(C2×D11)⋊C416yes—
324C2×C4C22×D4411yescharacteristic
325C2×C4C2×#434311yescharacteristic
326C2×C4#6704011yescharacteristic
327C2×C4#41×D1111yescharacteristic
328C2×C4#6704211yescharacteristic
329C2×C4C22×C22⋊D1111yescharacteristic
330C8—22no—
331C8—43no—
332C8—222no—
333C8—443no—
334C22—226no—
335C22—226no—
336C22—226no—
337C22—443no—
338C22—443no—
339C22—443no—
340C22—443no—
341C22C4×#434311yescharacteristic
342C22#1062310511yescharacteristic
343C22C22×C8×D1111yescharacteristic
344C22C22×#431311yescharacteristic
345C22D11×#13111yescharacteristic
346C22#1062328111yescharacteristic
347C22C22×(C2×D11)⋊C411yescharacteristic
348C4—26no—
349C4—222no—
350C4—222no—
351C4—443no—
352C4C2×(C2×D11)⋊C8112yes—
353C4#1062310711yescharacteristic
354C4#1062310811yescharacteristic
355C4#1062334811yescharacteristic
356C4#1062336511yescharacteristic
357C2—446no—
358C2#1307145411yescharacteristic
359C2C22×(C2×D11)⋊C811yescharacteristic
360C2#1307706311yescharacteristic
361C2C8×#434311yescharacteristic
362C2#1307763511yescharacteristic
363C2#1307772611yescharacteristic
364C2#1307774711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C23×C8
FittingC2×C8×Q8×C11C2
socleC23×C11C23×C4
prime radicalC22×#4343C4
cosocleC22×C4×C11C24
hypercenterC2×C8×Q8D11
hypocenterC11#22530
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C8×Q8

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13069410C2semidirect
4. #13069409C2semidirect
5. #13068593C2semidirect
6. C4×(C2×D11)⋊C8C2semidirect
7. C2×C8×Q8×C11C2semidirect
31. C2×#4343C8semidirect
95. C2×C8×C11#41semidirect
110. C2×C11⋊C8#41semidirect
113. C2×C8×Q8D11semidirect
126. Q8×C11C22⋊C8semidirect
282. C2×C8#4343semidirect
292. C11#22530semidirect
301. Q8(C2×D11)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
C2×Q8×C11⋊C82
#130694102
#130694092
#130685932
C4×(C2×D11)⋊C82
C2×C8×Q8×C112
#2253011