Finite Group Databasebeta

← #14643233

Subgroups — #14643233

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622446C211yesmaximal, characteristic
2C2×D11×C4⋊C8C211yesmaximal, characteristic
3C2×C4×#4313C211yesmaximal, characteristic
4#13066451C211yesmaximal, characteristic, complemented
5#13066450C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C11×#1277C211yesmaximal, characteristic, complemented
8C22×#4313C412yes—
9C22×C8×D11—21no—
10C2×C42×D11C2211yescharacteristic
11C2×C11×C4⋊C8C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C4×C8×C11C2211yescharacteristic
14C2×(C2×D11)⋊C8—21no—
15C2×#66879C412yes—
16C2×Dic11⋊C8—21no—
17C2×C8×Dic11—21no—
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622446—22no—
22#10622446C414yes—
23D11×C4⋊C8—22no—
24D11×C4⋊C8C414yes—
25C4×#4313—22no—
26C4×#4313—22no—
27C22×C4×D11C2×C411yescharacteristic
28C22×C4×D11D411yescharacteristic
29C22×C4×D11Q811yescharacteristic
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11C2×C412yes—
33C2×C42×C11C2311yescharacteristic
34C2×C4×Dic11C2×C411yescharacteristic
35C2×C4×Dic11D411yescharacteristic
36C2×C4×Dic11Q811yescharacteristic
37C22×C11⋊C8—21no—
38C22×C11⋊C8—21no—
39C22×C11⋊C8C2×C412yes—
40C2×#4313—24no—
41C2×#4313—24no—
42C2×#4313C818yescomplemented
43C2×C8×D11—24no—
44C2×C8×D11—42no—
45C2×C8×D11—42no—
46C42×D11C2×C412yes—
47C42×D11C2×C412yes—
48C42×D11D412yes—
49C42×D11D412yes—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8C2×C412yes—
53C11×C4⋊C8C2×C412yes—
54C4×C8×C11—21no—
55C4×C8×C11—21no—
56(C2×D11)⋊C8—24no—
57#66879—24no—
58Dic11⋊C8—24no—
59C8×Dic11—24no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)C2×C412yes—
63C4⋊(C11⋊C8)C2×C412yes—
64C4×C11⋊C8—21no—
65C4×C11⋊C8—21no—
66#7873—111nomaximal, Sylow
67C23×D11C4⋊C411yescharacteristic
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×Q811yescharacteristic
71C22×Dic11C4⋊C411yescharacteristic
72C22×Dic11C4⋊C411yescharacteristic
73C22×Dic11C4⋊C411yescharacteristic
74C2×C4×D11—21no—
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×C4×D11—42no—
79C2×C4×D11C4212yes—
80C2×C4×D11C22⋊C412yes—
81C2×C4×D11C22⋊C412yes—
82C2×C4×D11C22⋊C412yes—
83C2×C4×D11C4⋊C412yes—
84C2×C4×D11C4⋊C412yes—
85C2×C4×D11C2×C814yes—
86C2×C4×D11M1614yes—
87C2×C8×C11—22no—
88C2×C8×C11—22no—
89C2×C8×C11—22no—
90C2×C8×C11—22no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11—41no—
94C2×C8×C11—41no—
95C2×C8×C11C2×C814yescomplemented
96C42×C11C22×C411yescharacteristic
97C42×C11C22×C411yescharacteristic
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C4×Dic11C4212yes—
101C4×Dic11C22⋊C412yes—
102C4×Dic11C22⋊C412yes—
103C4×Dic11C22⋊C412yes—
104C4×Dic11C4⋊C412yes—
105C4×Dic11C4⋊C412yes—
106C2×C11⋊C8—22no—
107C2×C11⋊C8—22no—
108C2×C11⋊C8—22no—
109C2×C11⋊C8—22no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8C2×C814yescomplemented
115#4313—216no—
116C8×D11—48no—
117C2×#431—111no—
118C22×C4⋊C8—111no—
119C2×C4×M16—111no—
120#1277—111no—
121#1277—111no—
122#1277—111no—
123#1277D1111yescharacteristic, complemented
124C23×C11C2×C4⋊C411yescharacteristic
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—22no—
128C22×D11#9512yes—
129C22×D11C4⋊C814yes—
130C2×C4×C11—22no—
131C2×C4×C11C2×C4211yescharacteristic
132C2×C4×C11C2×C22⋊C411yescharacteristic
133C2×C4×C11C2×C22⋊C411yescharacteristic
134C2×C4×C11C2×C22⋊C411yescharacteristic
135C2×C4×C11C2×C4⋊C411yescharacteristic
136C2×C4×C11C2×C4⋊C411yescharacteristic
137C2×C4×C11C22×C812yes—
138C2×C4×C11C2×M1612yes—
139C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C11#13711yescharacteristic
142C2×C4×C11#13711yescharacteristic
143C2×Dic11—21no—
144C2×Dic11—21no—
145C2×Dic11—22no—
146C2×Dic11#9512yes—
147C2×Dic11#9512yes—
148C2×Dic11#9512yes—
149C2×Dic11C4⋊C814yes—
150C4×D11—22no—
151C4×D11—22no—
152C4×D11—22no—
153C4×D11—22no—
154C4×D11—42no—
155C4×D11—42no—
156C4×D11C4×C814yes—
157C4×D11#9714yes—
158C4×D11C22⋊C818yes—
159C8×C11—24no—
160C8×C11—42no—
161C8×C11—42no—
162C11⋊C8—24no—
163C11⋊C8—42no—
164C11⋊C8—42no—
165C22×M16—112no—
166C23×C8—221no—
167C22×C42—111no—
168#431—114no—
169#431—222no—
170C2×C4⋊C8—111no—
171C2×C4⋊C8—111no—
172C2×C4⋊C8—114no—
173C2×C4⋊C8—222no—
174C2×C4⋊C8—221no—
175C2×C4⋊C8C2×D1111yescharacteristic
176C2×C4⋊C8C2×D1111yescharacteristic
177C2×C22⋊C8—221no—
178C4×M16—222no—
179C4×M16—222no—
180C2×#97—112no—
181C2×C4×C8—111no—
182C2×C4×C8—221no—
183C2×C4×C8C2×D1111yescharacteristic
184C22×C11C2×#9511yescharacteristic
185C22×C11C2×C4⋊C812yes—
186C22×C11#42811yescharacteristic
187C22×C11#42811yescharacteristic
188C22×C11#43012yes—
189C2×D11—24no—
190C2×D11—24no—
191C2×D11—22no—
192C2×D11—22no—
193C2×D11#33614yes—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11C2×C4×C811yescharacteristic
197C4×C11C2×#9711yescharacteristic
198C4×C11C2×C22⋊C812yes—
199C4×C11#41711yescharacteristic
200C4×C11#41711yescharacteristic
201C4×C11#41811yescharacteristic
202C4×C11#41911yescharacteristic
203Dic11—22no—
204Dic11—22no—
205Dic11#33614yes—
206C23×C4—111no—
207C23×C4—111no—
208C23×C4—111no—
209C2×M16—118no—
210C2×M16—224no—
211C2×M16—224no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—112no—
215C22×C8—224no—
216C22×C8—221no—
217C22×C8—221no—
218C22×C8—442no—
219C22×C8—442no—
220C22×C8C4×D1112yes—
221C2×C42—111no—
222C2×C42—111no—
223C2×C42—111no—
224C2×C42—112no—
225C2×C42—112no—
226C2×C42—112no—
227C2×C42—112no—
228C2×C42C22×D1111yescharacteristic
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—112no—
232C4⋊C8—112no—
233C4⋊C8—224no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8C4×D1112yes—
237C4⋊C8C4×D1112yes—
238C22⋊C8—224no—
239#97—224no—
240C4×C8—21no—
241C4×C8—21no—
242C4×C8—224no—
243C4×C8—221no—
244C4×C8—221no—
245C2×C11#156512yes—
246C2×C11#156512yes—
247C2×C11C2×#33611yescharacteristic
248C2×C11#173611yescharacteristic
249C2×C11#173811yescharacteristic
250D11—24no—
251C24—111no—
252C22×C4—111no—
253C22×C4—112no—
254C22×C4—112no—
255C22×C4—114no—
256C22×C4—114no—
257C22×C4—111no—
258C22×C4—111no—
259C22×C4—112no—
260C22×C4—112no—
261C22×C4—112no—
262C22×C4—112no—
263C22×C4—221no—
264C22×C4—221no—
265C22×C4—221no—
266C22×C4—221no—
267C22×C4—442no—
268C22×C4C2×C4×D1111yescharacteristic
269C22×C4D4×D1111yescharacteristic
270C22×C4Q8×D1111yescharacteristic
271M16—2216no—
272C2×C8—22no—
273C2×C8—22no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—114no—
281C2×C8—222no—
282C2×C8—222no—
283C2×C8—222no—
284C2×C8—222no—
285C2×C8—448no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—441no—
290C2×C8C8×D1114yescomplemented
291C42—112no—
292C42—112no—
293C42—112no—
294C42—112no—
295C42—112no—
296C42—112no—
297C42C2×C4×D1111yescharacteristic
298C42C2×C4×D1111yescharacteristic
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C11#787311yescharacteristic, complemented, Sylow
302C23—112no—
303C23—114no—
304C23—221no—
305C23—221no—
306C23—222no—
307C23C4⋊C4×D1111yescharacteristic
308C2×C4—22no—
309C2×C4—112no—
310C2×C4—114no—
311C2×C4—114no—
312C2×C4—114no—
313C2×C4—118no—
314C2×C4—112no—
315C2×C4—112no—
316C2×C4—221no—
317C2×C4—221no—
318C2×C4—222no—
319C2×C4—222no—
320C2×C4—222no—
321C2×C4—222no—
322C2×C4—222no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4C42×D1111yescharacteristic
326C2×C4C22⋊C4×D1111yescharacteristic
327C2×C4C22⋊C4×D1111yescharacteristic
328C2×C4C22⋊C4×D1111yescharacteristic
329C2×C4C4⋊C4×D1111yescharacteristic
330C2×C4C4⋊C4×D1111yescharacteristic
331C2×C4C2×C8×D1112yes—
332C2×C4M16×D1112yes—
333C2×C4#6696411yescharacteristic
334C2×C4#6696711yescharacteristic
335C2×C4#6696811yescharacteristic
336C2×C4#6697111yescharacteristic
337C8—24no—
338C8—42no—
339C8—42no—
340C8—224no—
341C8—442no—
342C8—442no—
343C22—114no—
344C22—222no—
345C22—222no—
346C22—224no—
347C22—224no—
348C22D11×#9511yescharacteristic
349C22D11×C4⋊C812yes—
350C22#1062247411yescharacteristic
351C22#1062249411yescharacteristic
352C22#1062250612yes—
353C4—21no—
354C4—21no—
355C4—114no—
356C4—222no—
357C4—222no—
358C4C4×C8×D1111yescharacteristic
359C4D11×#9711yescharacteristic
360C4D11×C22⋊C812yes—
361C4#1062238311yescharacteristic
362C4#1062238411yescharacteristic
363C4#1062241511yescharacteristic
364C4#1062241611yescharacteristic
365C2—224no—
366C2#1306736512yes—
367C2#1306736712yes—
368C2D11×#33611yescharacteristic
369C2#1306833411yescharacteristic
370C2#1306834111yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC4×C11C2×C4×C8
FrattiniC2×C42C22×D11
FittingC11×#1277C2
socleC23×C11C2×C4⋊C4
prime radicalC23×D11C4⋊C4
cosocleC2×C42×C11C23
hypercenter#1277D11
hypocenterC11#7873
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
4. #13066451C2semidirect
5. #13066450C2semidirect
6. #13066450C2semidirect
7. C11×#1277C2semidirect
42. C2×#4313C8semidirect
95. C2×C8×C11C2×C8semidirect
114. C2×C11⋊C8C2×C8semidirect
123. #1277D11semidirect
290. C2×C8C8×D11semidirect
301. C11#7873semidirect

Maximal subgroups

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

subgroupindex
C2×#106224462
C2×D11×C4⋊C82
C2×C4×#43132
#130664512
#130664502
C11×#12772
#787311