Finite Group Databasebeta

← #14772046

Subgroups — #14772046

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1M16×D44C212yesmaximal
2C2×#10622301C211yesmaximal, characteristic
3C2×#10622506C212yesmaximal, complemented
4#13069391C212yesmaximal, complemented
5#13068822C214yesmaximal, complemented
6#13068788C211yesmaximal, characteristic, complemented
7#13068655C212yesmaximal, complemented
8C4×C11×#108C211yesmaximal, characteristic, complemented
9C2×M16×D11C2214yes—
10C22×#4313C2212yes—
11C2×C4×D44C2211yescharacteristic
12C2×C11×#108C2211yescharacteristic
13C2×C11×#108C2211yescharacteristic
14C4×C11×M16C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16#10622739C2214yes—
17C2×#66886C2214yes—
18C2×(C2×D11)⋊C8C2212yes—
19C2×#66883C2212yes—
20C2×#66883C2212yes—
21#10622537C2212yes—
22C2×C4⋊(C11⋊C8)C2211yescharacteristic
23#10622506—28no—
24#10622319—24no—
25#10622301—22no—
26#10622301C414yes—
27#10622301C414yes—
28C8×D44—22no—
29C11×#341C2212yes—
30#10622196C2214yes—
31C22×D44Q811yescharacteristic
32C22×C4×D11C2312yes—
33C2×C11×M16C2312yes—
34C2×C11×M16C2312yes—
35C22×C8×C11C2311yescharacteristic
36C22×C8×C11C2311yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C2×(C2×D11)⋊C4Q812yes—
39C2×C4⋊Dic11Q811yescharacteristic
40C2×#4318C2314yes—
41C22×C11⋊C8C2312yes—
42M16×D11—28no—
43M16×D11—44no—
44C2×#4313—24no—
45C2×#4313—24no—
46C2×#4313—24no—
47C2×#4313C2×C418yes—
48C2×C8×D11—24no—
49C4×D44C2×C412yes—
50C4×D44C2×C412yes—
51C4×D44D412yes—
52C4×D44D412yes—
53C11×#108—22no—
54C11×#108D414yescomplemented
55C11×#97—22no—
56C4×C8×C11—22no—
57C4×C8×C11C2×C412yes—
58C4×C8×C11C2×C412yes—
59#66886—28no—
60(C2×D11)⋊C8—24no—
61(C2×D11)⋊C8—24no—
62(C2×D11)⋊C8C2×C418yes—
63#66883—24no—
64#66883—42no—
65C4⋊(C11⋊C8)—22no—
66C4⋊(C11⋊C8)—22no—
67C4⋊(C11⋊C8)C2×C412yes—
68C4⋊(C11⋊C8)C2×C412yes—
69#22669—111nomaximal, Sylow
70C23×D11C2×Q812yes—
71C22×C4×C11C2×Q811yescharacteristic
72C22×C4×C11C2×Q811yescharacteristic
73C22×C4×C11C2411yescharacteristic
74C22×Dic11C2×Q812yes—
75C2×D44—42no—
76C2×D44C4⋊C412yes—
77C2×D44C4⋊C412yes—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—22no—
81C2×C4×D11—22no—
82C2×C4×D11C22×C414yes—
83C2×C4×D11C2×D414yes—
84C11×M16—22no—
85C11×M16—22no—
86C11×M16—22no—
87C11×M16C2×D414yes—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—21no—
91C2×C8×C11—21no—
92C2×C8×C11C22×C412yes—
93C2×C8×C11C22×C412yes—
94C2×C8×C11C2×D412yes—
95C2×C8×C11#4112yes—
96C42×C11C22×C411yescharacteristic
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100(C2×D11)⋊C4C4⋊C414yes—
101(C2×D11)⋊C4C4⋊C414yes—
102C4⋊Dic11C4⋊C412yes—
103C4⋊Dic11C4⋊C412yes—
104#4318—24no—
105#4318—24no—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—24no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8C22×C414yes—
110#4313—216no—
111#4313—48no—
112C8×D11—48no—
113D4×M16—112no—
114C2×#436—111no—
115C2×#430—112no—
116#1950—112no—
117#1855—114no—
118#1848—111no—
119#1811—112no—
120C4×#108D1111yescharacteristic, complemented
121C23×C11C22×Q811yescharacteristic
122C22×D11—22no—
123C22×D11—22no—
124C22×D11—42no—
125C22×D11—42no—
126C22×D11C2×C4⋊C414yes—
127C2×C4×C11—22no—
128C2×C4×C11—41no—
129C2×C4×C11C2×C4⋊C411yescharacteristic
130C2×C4×C11C2×C4⋊C411yescharacteristic
131C2×C4×C11C2×C4⋊C411yescharacteristic
132C2×C4×C11C2×C4⋊C411yescharacteristic
133C2×C4×C11C23×C411yescharacteristic
134C2×C4×C11C22×D411yescharacteristic
135C2×C4×C11C22×D411yescharacteristic
136C2×C4×C11C2×#4111yescharacteristic
137C2×C4×C11H(5,𝔽2)11yescharacteristic
138C2×C4×C112−1+411yescharacteristic
139C2×Dic11—22no—
140C2×Dic11—22no—
141C2×Dic11C2×C4⋊C414yes—
142D44—24no—
143D44—42no—
144C4×D11—24no—
145C4×D11—24no—
146C4×D11—24no—
147C4×D11—24no—
148C8×C11—22no—
149C8×C11—24no—
150C8×C11—42no—
151C8×C11C4×D414yes—
152C11⋊C8—24no—
153C11⋊C8—44no—
154C22×M16—112no—
155C22×M16—114no—
156C2×C4×D4—111no—
157#436—114no—
158#436—114no—
159#436—222no—
160#435—224no—
161C8×D4—222no—
162#430—228no—
163C2×#108—114no—
164C2×#108—112no—
165C2×#108—112no—
166C2×#108C2×D1111yescharacteristic
167C2×#108C2×D1111yescharacteristic
168#423—112no—
169C2×C4⋊C8—111no—
170#407—114no—
171C2×C22⋊C8—112no—
172C4×M16C2×D1112yes—
173C2×C4×C8C2×D1111yescharacteristic
174#341—114no—
175#341C2×D1112yes—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11C22×C4⋊C411yescharacteristic
179C22×C11D4×Q811yescharacteristic
180C22×C11#55411yescharacteristic
181C2×D11—24no—
182C2×D11—24no—
183C2×D11—24no—
184C2×D11—82no—
185C2×D11—82no—
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11#43012yescomplemented
190C4×C11C2×C4×D411yescharacteristic
191C4×C11#52011yescharacteristic
192C4×C11D4211yescharacteristic
193C4×C11#54711yescharacteristic
194Dic11—24no—
195C22×D4—111no—
196C23×C4—112no—
197C2×M16—118no—
198C2×M16—114no—
199C2×M16—224no—
200C2×M16—224no—
201C2×M16—224no—
202C2×M16—228no—
203C2×M16—444no—
204C2×M16C22×D1112yes—
205C2×M16C22×D1112yes—
206C22×C8—112no—
207C22×C8—224no—
208C22×C8C22×D1111yescharacteristic
209C22×C8C22×D1111yescharacteristic
210C4×D4—112no—
211C4×D4—112no—
212C4×D4—112no—
213C4×D4—112no—
214C2×C4⋊C4—111no—
215C2×C22⋊C4—112no—
216C2×C42C22×D1111yescharacteristic
217#108—22no—
218#108—228no—
219#108—224no—
220#108—442no—
221#108D4414yescomplemented
222C4⋊C8—112no—
223C4⋊C8—112no—
224C4⋊C8—222no—
225C4⋊C8—222no—
226C22⋊C8—118no—
227C22⋊C8—224no—
228C22⋊C8—224no—
229#97—22no—
230C4×C8—22no—
231C4×C8C4×D1112yes—
232C4×C8C4×D1112yes—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11D4×C4⋊C411yescharacteristic
236C2×C11C2×#43011yescharacteristic
237C2×C11#291611yescharacteristic
238D11—44no—
239C24—112no—
240C2×D4—112no—
241C2×D4—112no—
242C2×D4—442no—
243C22×C4—112no—
244C22×C4—114no—
245C22×C4—114no—
246C22×C4—222no—
247C22×C4—222no—
248C22×C4—222no—
249C22×C4—222no—
250C22×C4Q8×D1111yescharacteristic
251C22×C4Q8×D1111yescharacteristic
252C22×C4C23×D1111yescharacteristic
253M16—22no—
254M16—22no—
255M16—22no—
256M16—2216no—
257M16—224no—
258M16—224no—
259M16—448no—
260M16C2×D4414yes—
261C2×C8—22no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—22no—
265C2×C8—114no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8—224no—
269C2×C8—448no—
270C2×C8C2×C4×D1112yes—
271C2×C8C2×C4×D1112yes—
272C2×C8C2×D4412yes—
273C2×C8#433912yes—
274C4⋊C4—112no—
275C4⋊C4—112no—
276C22⋊C4—114no—
277C22⋊C4—114no—
278C42C2×C4×D1111yescharacteristic
279C42C2×C4×D1111yescharacteristic
280C42D4×D1111yescharacteristic
281C42D4×D1111yescharacteristic
282C11#2266911yescharacteristic, complemented, Sylow
283C23—114no—
284C23—222no—
285C23—222no—
286C23—442no—
287C23—442no—
288C23C2×Q8×D1111yescharacteristic
289D4—224no—
290D4—442no—
291C2×C4—22no—
292C2×C4—41no—
293C2×C4—114no—
294C2×C4—222no—
295C2×C4—222no—
296C2×C4—224no—
297C2×C4—224no—
298C2×C4—224no—
299C2×C4—224no—
300C2×C4C4⋊C4×D1111yescharacteristic
301C2×C4C4⋊C4×D1111yescharacteristic
302C2×C4C4⋊C4×D1111yescharacteristic
303C2×C4C4⋊C4×D1111yescharacteristic
304C2×C4C22×C4×D1111yescharacteristic
305C2×C4C22×D4411yescharacteristic
306C2×C4C2×#433911yescharacteristic
307C2×C4C2×D4×D1111yescharacteristic
308C2×C4#6704211yescharacteristic
309C2×C4#6704311yescharacteristic
310C8—22no—
311C8—24no—
312C8—42no—
313C8—224no—
314C8—444no—
315C8C4×D4414yes—
316C22—21no—
317C22—21no—
318C22—224no—
319C22—224no—
320C22—224no—
321C22—882no—
322C22—882no—
323C22C2×C4⋊C4×D1111yescharacteristic
324C22Q8×D4411yescharacteristic
325C22#1062311011yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—224no—
330C4#1062250612yescomplemented
331C4C2×C4×D4411yescharacteristic
332C4#1062305411yescharacteristic
333C4D4×D4411yescharacteristic
334C4#1062308211yescharacteristic
335C2—21no—
336C2—21no—
337C2—444no—
338C2C4⋊C4×D4411yescharacteristic
339C2C2×#1062250611yescharacteristic
340C2#1307722411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#108C2
socleC22×C11C22×C4⋊C4
prime radicalC22×D44Q8
cosocleC22×C4×C11C24
hypercenterC4×#108D11
hypocenterC11#22669
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#108

Complements

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

NH ≅ G/Ntype
3. C2×#10622506C2semidirect
4. #13069391C2semidirect
5. #13068822C2semidirect
6. #13068788C2semidirect
7. #13068655C2semidirect
8. C4×C11×#108C2semidirect
54. C11×#108D4semidirect
120. C4×#108D11semidirect
189. C4×C11#430semidirect
221. #108D44semidirect
282. C11#22669semidirect
330. C4#10622506semidirect

Maximal subgroups

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

subgroupindex
M16×D442
C2×#106223012
C2×#106225062
#130693912
#130688222
#130687882
#130686552
C4×C11×#1082
#2266911