Finite Group Databasebeta

← #14647129

Subgroups — #14647129

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3#13066457C212yesmaximal, complemented
4#13066457C212yesmaximal, complemented
5C4×C11×#117C211yesmaximal, characteristic
6C2×C11×#117C411yescharacteristic
7C2×C11×#117C411yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C4×C11×C4⋊C4C411yescharacteristic
10C4×C11×C4⋊C4C411yescharacteristic
11C4×C11×C4⋊C4C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C4×C11×C22⋊C4—21no—
14C4×C11×C22⋊C4—21no—
15C11×#376—21no—
16C43×C11—21no—
17C2×C22⋊(C11⋊C8)—21no—
18C2×C22⋊(C11⋊C8)—21no—
19C2×C4⋊(C11⋊C8)C2212yes—
20C2×C4×C11⋊C8C2212yes—
21#10622162—21no—
22#10622162—21no—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C11×#117—22no—
27C11×#117—22no—
28C11×#117—22no—
29C11×#117C814yescomplemented
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C42×C11—21no—
37C2×C42×C11—21no—
38C2×C42×C11—22no—
39C2×C42×C11—22no—
40C2×C42×C11—21no—
41C2×C42×C11—21no—
42C2×C42×C11—21no—
43C2×C42×C11—21no—
44C2×C42×C11C2×C411yescharacteristic
45C2×C42×C11D411yescharacteristic
46C2×C42×C11D411yescharacteristic
47C2×C42×C11C2311yescharacteristic
48C22×C11⋊C8—22no—
49C22×C11⋊C8—22no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C22⋊(C11⋊C8)—24no—
55C22⋊(C11⋊C8)—42no—
56C4⋊(C11⋊C8)—22no—
57C4⋊(C11⋊C8)—22no—
58C4×C11⋊C8—22no—
59C4×C11⋊C8—22no—
60#8708—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C2×C812yes—
81C22×C4×C11M1612yes—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2×C812yes—
90C11×C4⋊C4C2×C812yes—
91C11×C4⋊C4M1612yes—
92C11×C4⋊C4M1612yes—
93C11×C22⋊C4—24no—
94C11×C22⋊C4—24no—
95C42×C11—24no—
96C42×C11—24no—
97C42×C11—21no—
98C42×C11—21no—
99C42×C11—22no—
100C42×C11—22no—
101C42×C11—42no—
102C42×C11—42no—
103C42×C11—42no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11#4112yes—
107C42×C11#4112yes—
108C2×C11⋊C8—24no—
109C2×C11⋊C8—42no—
110C2×C11⋊C8—42no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—42no—
114C4×#117D1111yescharacteristic
115#1797—111no—
116C4×C22⋊C8—111no—
117#1279—112no—
118#1279—112no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C22⋊C812yes—
126C23×C11C2×C22⋊C411yescharacteristic
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—21no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—44no—
145C2×C4×C11—41no—
146C2×C4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C22⋊C812yes—
156C2×C4×C11#10412yes—
157C2×C4×C11#11711yescharacteristic
158C2×C4×C11#11711yescharacteristic
159C2×C4×C11#12312yes—
160C2×C4×C11#12312yes—
161C2×C4×C11C22×C811yescharacteristic
162C2×C4×C11C2×M1611yescharacteristic
163C2×C4×C11C2×M1611yescharacteristic
164C2×C4×C11C2×M1611yescharacteristic
165C2×C4×C11#13512yes—
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C11⋊C8—44no—
169C11⋊C8—82no—
170C2×#117Dic1111yescharacteristic
171C2×#117Dic1111yescharacteristic
172C22×C42C2×D1111yescharacteristic
173C2×C4⋊C8—112no—
174C2×C22⋊C8—221no—
175C2×C22⋊C8—221no—
176C2×C4×C8—112no—
177C4×C4⋊C4Dic1111yescharacteristic
178C4×C4⋊C4Dic1111yescharacteristic
179C4×C4⋊C4C2×D1111yescharacteristic
180C4×C4⋊C4C2×D1111yescharacteristic
181C4×C22⋊C4—21no—
182C4×C22⋊C4—21no—
183#376—21no—
184C43—21no—
185#336—221no—
186#336—221no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11#38111yescharacteristic
195C22×C11C2×C22⋊C811yescharacteristic
196C22×C11#40711yescharacteristic
197C22×C11#41611yescharacteristic
198C22×C11#41711yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C22×C11#42111yescharacteristic
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—41no—
205C4×C11—42no—
206C4×C11—42no—
207C4×C11—42no—
208C4×C11—42no—
209C4×C11#43111yescharacteristic
210C4×C11#43111yescharacteristic
211C4×C11#43211yescharacteristic
212C4×C11#43211yescharacteristic
213C4×C11#48212yes—
214C4×C11#48512yes—
215C23×C4C2×Dic1111yescharacteristic
216C23×C4C22⋊D1111yescharacteristic
217C23×C4C22⋊D1111yescharacteristic
218C22×C8—222no—
219C22×C8—222no—
220#117—22no—
221#117—22no—
222#117—22no—
223#117C11⋊C814yescomplemented
224C2×C4⋊C4C2×Dic1111yescharacteristic
225C2×C4⋊C4C2×Dic1111yescharacteristic
226C2×C4⋊C4C2×Dic1111yescharacteristic
227C2×C4⋊C4C2×Dic1111yescharacteristic
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C42—21no—
231C2×C42—21no—
232C2×C42—22no—
233C2×C42—22no—
234C2×C42—21no—
235C2×C42—21no—
236C2×C42—21no—
237C2×C42—21no—
238C2×C42C2×Dic1111yescharacteristic
239C2×C42C22⋊D1111yescharacteristic
240C2×C42C22⋊D1111yescharacteristic
241C2×C42C22×D1111yescharacteristic
242C4⋊C8—222no—
243C4⋊C8—222no—
244C22⋊C8—224no—
245C22⋊C8—442no—
246C4×C8—222no—
247C4×C8—222no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252C2×C11—42no—
253C2×C11#147611yescharacteristic
254C2×C11#147711yescharacteristic
255C2×C11#148811yescharacteristic
256C2×C11#148911yescharacteristic
257C2×C11#181711yescharacteristic
258C2×C11#182511yescharacteristic
259C2×C11#182611yescharacteristic
260C24C22⋊Dic1111yescharacteristic
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—41no—
276C22×C4C2×C11⋊C812yes—
277C22×C4#431812yes—
278C22×C4C22⋊Dic1111yescharacteristic
279C22×C4C22⋊Dic1111yescharacteristic
280C22×C4C22⋊Dic1111yescharacteristic
281C22×C4C22×Dic1111yescharacteristic
282C22×C4C2×C22⋊D1111yescharacteristic
283C22×C4C2×C22⋊D1111yescharacteristic
284C2×C8—224no—
285C2×C8—442no—
286C2×C8—442no—
287C2×C8—442no—
288C2×C8—442no—
289C2×C8—442no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4C2×C11⋊C812yes—
295C4⋊C4C2×C11⋊C812yes—
296C4⋊C4#431812yes—
297C4⋊C4#431812yes—
298C22⋊C4—24no—
299C22⋊C4—24no—
300C42—24no—
301C42—24no—
302C42—21no—
303C42—21no—
304C42—22no—
305C42—22no—
306C42—42no—
307C42—42no—
308C42—41no—
309C42—42no—
310C42—41no—
311C42#433912yes—
312C42#433912yes—
313C11#870811yescharacteristic, complemented, Sylow
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23C22⋊(C11⋊C8)12yes—
321C23C2×C22⋊Dic1111yescharacteristic
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—44no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4C22⋊(C11⋊C8)12yes—
351C2×C4#6690112yes—
352C2×C4C22×C11⋊C811yescharacteristic
353C2×C4C2×#431811yescharacteristic
354C2×C4C2×#431811yescharacteristic
355C2×C4C2×#431811yescharacteristic
356C2×C4#6697911yescharacteristic
357C2×C4#6697911yescharacteristic
358C2×C4#6698212yes—
359C2×C4#6698212yes—
360C2×C4#6700211yescharacteristic
361C2×C4#6700312yes—
362C2×C4#6700411yescharacteristic
363C8—444no—
364C8—882no—
365C22—22no—
366C22—22no—
367C22—22no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22C2×C22⋊(C11⋊C8)11yescharacteristic
373C22#1062282011yescharacteristic
374C22#1062282411yescharacteristic
375C22#1062284511yescharacteristic
376C22#1062284611yescharacteristic
377C22C2×#6690111yescharacteristic
378C22#1062284911yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—42no—
383C4—42no—
384C4—41no—
385C4—42no—
386C4—42no—
387C4#1062253811yescharacteristic
388C4#1062253811yescharacteristic
389C4#1062253911yescharacteristic
390C4#1062253911yescharacteristic
391C4#1062260912yes—
392C4#1062261612yes—
393C2—42no—
394C2#1306699811yescharacteristic
395C2#1306700311yescharacteristic
396C2#1306705011yescharacteristic
397C2#1306705511yescharacteristic
398C2#1306868411yescharacteristic
399C2#1306871111yescharacteristic
400C2#1306871511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC4×C11×#117C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC4×#117D11
hypocenterC11#8708
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
3. #13066457C2semidirect
4. #13066457C2semidirect
29. C11×#117C8semidirect
223. #117C11⋊C8semidirect
313. C11#8708semidirect

Maximal subgroups

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

subgroupindex
#130685962
C4×C22⋊(C11⋊C8)2
#130664572
C4×C11×#1172
#870811