Finite Group Databasebeta

← #14644261

Subgroups — #14644261

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3C2×#10622092C211yesmaximal, characteristic, complemented
4C2×C8×C11⋊C8C211yesmaximal, characteristic, complemented
5C11⋊#1273C211yesmaximal, characteristic, complemented
6C11⋊#1273C211yesmaximal, characteristic, complemented
7C2×C11×#431C211yesmaximal, characteristic
8C22×C42×C11C2211yescharacteristic
9C11×#431—22no—
10C11×#431—22no—
11C2×C11×C4⋊C8C412yes—
12C2×C11×C22⋊C8C412yes—
13C2×C4×C8×C11C2211yescharacteristic
14C2×C4×C8×C11C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C412yes—
16C2×C22⋊(C11⋊C8)C412yes—
17C2×C4×C11⋊C8C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20C2×C4×C11⋊C8C2211yescharacteristic
21#10622162C412yes—
22#10622162C412yes—
23#10622092—22no—
24C8×C11⋊C8—22no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2×C411yescharacteristic
27C23×C4×C11C2×C411yescharacteristic
28C22×C8×C11C2×C412yes—
29C22×C8×C11C2×C412yes—
30C2×C42×C11—21no—
31C2×C42×C11—21no—
32C2×C42×C11—21no—
33C2×C42×C11—21no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11C2×C411yescharacteristic
37C2×C42×C11C2311yescharacteristic
38C22×C11⋊C8C2×C412yes—
39C22×C11⋊C8C2×C412yes—
40C22×C11⋊C8C2×C412yes—
41C22×C11⋊C8C2×C412yes—
42C11×C4⋊C8—24no—
43C11×C22⋊C8—24no—
44C4×C8×C11—21no—
45C4×C8×C11—21no—
46C4×C8×C11D412yes—
47C4×C8×C11D412yes—
48C22⋊(C11⋊C8)—24no—
49C22⋊(C11⋊C8)C818yescomplemented
50C4×C11⋊C8—21no—
51C4×C11⋊C8—21no—
52C4×C11⋊C8—21no—
53C4×C11⋊C8—21no—
54C4×C11⋊C8—21no—
55C4×C11⋊C8—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58#8148—111nomaximal, Sylow
59C24×C11C4211yescharacteristic
60C22×C4×C11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—22no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11C4211yescharacteristic
72C22×C4×C11C4211yescharacteristic
73C22×C4×C11C4211yescharacteristic
74C22×C4×C11C2×C814yes—
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C22×C411yescharacteristic
77C22×C4×C11C22×C411yescharacteristic
78C2×C8×C11—22no—
79C2×C8×C11—22no—
80C2×C8×C11—22no—
81C2×C8×C11—22no—
82C2×C8×C11—22no—
83C2×C8×C11C22⋊C414yes—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11—21no—
87C42×C11—21no—
88C42×C11—21no—
89C42×C11—21no—
90C42×C11C2×D411yescharacteristic
91C42×C11C2×D411yescharacteristic
92C42×C11#4111yescharacteristic
93C42×C11#4111yescharacteristic
94C2×C11⋊C8—22no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—22no—
97C2×C11⋊C8—22no—
98C2×C11⋊C8—22no—
99C2×C11⋊C8—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8C2×C814yes—
104C2×C11⋊C8C2×C814yes—
105C2×C11⋊C8M1614yes—
106C2×#431D1111yescharacteristic
107C4×C22⋊C8—111no—
108C4×C22⋊C8—111no—
109C2×#322—111no—
110C2×C82—111no—
111#1273—111no—
112#1273—111no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11—21no—
119C23×C11C4×C812yes—
120C23×C11C2×C4211yescharacteristic
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—24no—
124C2×C4×C11—24no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—42no—
132C2×C4×C11—42no—
133C2×C4×C11—42no—
134C2×C4×C11—42no—
135C2×C4×C11C4×C812yes—
136C2×C4×C11C2×C22⋊C411yescharacteristic
137C2×C4×C11#11711yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11C4×D411yescharacteristic
141C2×C4×C11C4×D411yescharacteristic
142C2×C4×C11C22×C812yes—
143C2×C4×C11C2×M1612yes—
144C2×C4×C11#13112yes—
145C2×C4×C11#13112yes—
146C2×C4×C11#13112yes—
147C2×C4×C11#13112yes—
148C8×C11—24no—
149C8×C11—42no—
150C11⋊C8—24no—
151C11⋊C8—24no—
152C11⋊C8—24no—
153C11⋊C8—42no—
154C22×C42C2×D1111yescharacteristic
155#431—22no—
156#431—22no—
157C2×C4⋊C8Dic1112yes—
158C2×C22⋊C8—112no—
159C2×C22⋊C8—112no—
160C2×C22⋊C8Dic1112yes—
161C2×C4×C8—111no—
162C2×C4×C8—111no—
163C2×C4×C8—111no—
164C2×C4×C8—111no—
165C2×C4×C8C2×D1111yescharacteristic
166C2×C4×C8C2×D1111yescharacteristic
167#336—112no—
168#336—112no—
169#322—222no—
170C82—222no—
171C22×C11—22no—
172C22×C11—22no—
173C22×C11—22no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11C4×C22⋊C411yescharacteristic
179C22×C11C2×C4×C811yescharacteristic
180C22×C11C4×M1611yescharacteristic
181C22×C11#40511yescharacteristic
182C22×C11#40511yescharacteristic
183C22×C11#40511yescharacteristic
184C22×C11#40511yescharacteristic
185C4×C11—22no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11#40812yes—
189C4×C11#43312yes—
190C4×C11C8×D412yes—
191C4×C11C8×D412yes—
192C4×C11#43512yes—
193C4×C11#43612yes—
194C23×C4C4×D1111yescharacteristic
195C23×C4C4×D1111yescharacteristic
196C23×C4C2×Dic1111yescharacteristic
197C22×C8—112no—
198C22×C8—112no—
199C22×C8—112no—
200C22×C8—112no—
201C22×C8C2×Dic1112yes—
202C22×C8C2×Dic1112yes—
203C2×C42—21no—
204C2×C42—21no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42C4×D1111yescharacteristic
208C2×C42C4×D1111yescharacteristic
209C2×C42C2×Dic1111yescharacteristic
210C2×C42C22×D1111yescharacteristic
211C4⋊C8—24no—
212C22⋊C8—24no—
213C22⋊C8—118no—
214C22⋊C8—224no—
215C4×C8—21no—
216C4×C8—21no—
217C4×C8—221no—
218C4×C8—221no—
219C4×C8—221no—
220C4×C8—221no—
221C4×C8—221no—
222C4×C8—221no—
223C4×C8—221no—
224C4×C8—221no—
225C4×C8C22⋊D1112yes—
226C4×C8C22⋊D1112yes—
227C2×C11—42no—
228C2×C11C8×M1611yescharacteristic
229C2×C11#145011yescharacteristic
230C2×C11#145311yescharacteristic
231C2×C11#145411yescharacteristic
232C2×C11#175011yescharacteristic
233C2×C11C8×C22⋊C411yescharacteristic
234C2×C11#175311yescharacteristic
235C24C4×Dic1111yescharacteristic
236C22×C4—22no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4C8×D1114yes—
248C22×C4C4×Dic1111yescharacteristic
249C22×C4C4×Dic1111yescharacteristic
250C22×C4C4×Dic1111yescharacteristic
251C22×C4C2×C4×D1111yescharacteristic
252C22×C4C2×C4×D1111yescharacteristic
253C22×C4C22×Dic1111yescharacteristic
254C2×C8—22no—
255C2×C8—22no—
256C2×C8—22no—
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—114no—
260C2×C8—114no—
261C2×C8—114no—
262C2×C8—222no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8—222no—
266C2×C8—222no—
267C2×C8—222no—
268C2×C8—222no—
269C2×C8—222no—
270C2×C8—222no—
271C2×C8C22⋊Dic1114yes—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42#433911yescharacteristic
279C42#433911yescharacteristic
280C42C2×C22⋊D1111yescharacteristic
281C42C2×C22⋊D1111yescharacteristic
282C11#814811yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C8×Dic1112yes—
290C23C2×C4×Dic1111yescharacteristic
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—24no—
294C2×C4—24no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4C8×Dic1112yes—
306C2×C4C2×C8×D1112yes—
307C2×C4#6695412yes—
308C2×C4M16×D1112yes—
309C2×C4#6696012yes—
310C2×C4#6697911yescharacteristic
311C2×C4C4×C22⋊D1111yescharacteristic
312C2×C4C4×C22⋊D1111yescharacteristic
313C2×C4C4×C22⋊D1111yescharacteristic
314C2×C4C4×C22⋊D1111yescharacteristic
315C2×C4#6700112yes—
316C2×C4#6700112yes—
317C2×C4C2×C22⋊Dic1111yescharacteristic
318C8—24no—
319C8—42no—
320C8—224no—
321C8—224no—
322C8—224no—
323C8—442no—
324C22—22no—
325C22—22no—
326C22—22no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22#1062261011yescharacteristic
332C22#1062261011yescharacteristic
333C22C2×C8×Dic1111yescharacteristic
334C22#1062271411yescharacteristic
335C22M16×Dic1111yescharacteristic
336C22#1062273511yescharacteristic
337C22C4×C22⋊Dic1111yescharacteristic
338C4—22no—
339C4—41no—
340C4—41no—
341C4#1062261312yes—
342C4C8×C22⋊D1112yes—
343C4C8×C22⋊D1112yes—
344C4#1062274012yes—
345C4#1062274112yes—
346C4#1062284712yes—
347C2—42no—
348C2#1306689711yescharacteristic
349C2#1306690011yescharacteristic
350C2#1306691111yescharacteristic
351C2#1306691611yescharacteristic
352C2#1306838211yescharacteristic
353C2C8×C22⋊Dic1111yescharacteristic
354C2#1306839711yescharacteristic
subgroupG/H
center, FrattiniC2×C42C22×D11
commutatorC22×C11C2×C4×C8
FittingC2×C11×#431C2
socleC23×C11C2×C42
prime radicalC24×C11C42
cosocleC2×C42×C11C23
hypercenterC2×#431D11
hypocenterC11#8148
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. C2×#10622092C2semidirect
4. C2×C8×C11⋊C8C2semidirect
5. C11⋊#1273C2semidirect
6. C11⋊#1273C2semidirect
49. C22⋊(C11⋊C8)C8semidirect
282. C11#8148semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊(C11⋊C8)2
C2×#106220922
C2×C8×C11⋊C82
C11⋊#12732
C2×C11×#4312
#814811