Finite Group Databasebeta

← #14648299

Subgroups — #14648299

Order 2816.

628 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66977C211yesmaximal, characteristic
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
3C2×#10622122C212yesmaximal, complemented
4#13066455C212yesmaximal, complemented
5C2×C11×#431C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C411yescharacteristic
8C2×C4×Dic22C2211yescharacteristic
9C11×#431—24no—
10C2×C11×C4⋊C8C2212yes—
11C2×C11×C22⋊C8—21no—
12C2×C4×C8×C11—21no—
13#10622825C411yescharacteristic
14#10622823—21no—
15C4×C22⋊Dic11—21no—
16C2×C22⋊(C11⋊C8)—21no—
17C4×C4⋊Dic11C2211yescharacteristic
18#10622546—21no—
19C4×Dic11⋊C4—21no—
20#10622542C411yescharacteristic
21#10622541C411yescharacteristic
22C2×C4×C11⋊C8C2212yes—
23#10622162—21no—
24#10622122—24no—
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C22×C8×C11—22no—
30C2×C42×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11C2311yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41#66977—22no—
42#66977C814yescomplemented
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×C4×Dic11—21no—
47C2×C4×Dic11—21no—
48C22×C11⋊C8—22no—
49C4×Dic22—22no—
50C4×Dic22—22no—
51C11×C4⋊C8—22no—
52C11×C4⋊C8D414yes—
53C11×C22⋊C8—24no—
54C4×C8×C11—24no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—24no—
61C4×C11⋊C8—22no—
62C4×C11⋊C8—22no—
63#8938—111nomaximal, Sylow
64C24×C11C22⋊C411yescharacteristic
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—21no—
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C2×C812yes—
78C22×C4×C11M1612yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C2×Dic22—22no—
87C2×Dic22—21no—
88C2×Dic22—22no—
89C2×Dic22C2×C812yes—
90C2×C8×C11—24no—
91C2×C8×C11—42no—
92C2×C8×C11—42no—
93C42×C11—22no—
94C42×C11—21no—
95C42×C11—22no—
96C42×C11—21no—
97C42×C11C2×D412yes—
98C42×C11#4112yes—
99C22⋊Dic11—24no—
100C22⋊Dic11—42no—
101C4⋊Dic11—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11—22no—
104C4⋊Dic11C2×C812yes—
105Dic11⋊C4—24no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108C4×Dic11—41no—
109C4×Dic11—41no—
110C4×Dic11—42no—
111C2×C11⋊C8—24no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—42no—
114C2×#431D1111yescharacteristic
115C4×C22⋊Q8—111no—
116C4×C22⋊C8—111no—
117C2×Q8⋊C8—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—24no—
134C2×C4×C11—24no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—44no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11C22⋊C812yes—
142C2×C4×C11#10412yes—
143C2×C4×C11C4×D412yes—
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12112yes—
146C2×C4×C11#12311yescharacteristic
147C2×C4×C11C22×C811yescharacteristic
148C2×C4×C11C2×M1611yescharacteristic
149C2×C4×C11#13112yes—
150C2×C4×C11#13512yes—
151C2×C4×C11#13712yes—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164Dic22—24no—
165Dic22—42no—
166C8×C11—44no—
167C11⋊C8—44no—
168C2×C22⋊Q8—111no—
169C2×C4×Q8—111no—
170C22×C42C2×D1111yescharacteristic
171#431—24no—
172C2×C4⋊C8C2×D1112yes—
173C2×C22⋊C8—21no—
174C2×C22⋊C8—221no—
175C2×C4×C8—21no—
176C2×C4×C8—112no—
177#391—111no—
178#389—111no—
179#387—221no—
180#385—221no—
181#380—111no—
182C4×C4⋊C4—111no—
183C4×C4⋊C4—221no—
184C4×C22⋊C4—221no—
185#336—221no—
186Q8⋊C8—224no—
187C22×C11—22no—
188C22×C11—22no—
189C22×C11—22no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11#38611yescharacteristic
195C22×C11C2×C22⋊C811yescharacteristic
196C22×C11#40811yescharacteristic
197C22×C11#41611yescharacteristic
198C22×C11#41911yescharacteristic
199C22×C11C2×#10411yescharacteristic
200C22×C11#42111yescharacteristic
201C4×C11—22no—
202C4×C11—22no—
203C4×C11—22no—
204C4×C11—41no—
205C4×C11C8×D412yes—
206C4×C11#43512yes—
207C4×C11#45212yes—
208C4×C11#48512yes—
209Dic11—42no—
210Dic11—42no—
211Dic11—81no—
212Dic11—81no—
213C22×Q8—111no—
214C23×C4C4×D1111yescharacteristic
215C23×C4D4411yescharacteristic
216C23×C4C22⋊D1111yescharacteristic
217C22×C8—22no—
218C22×C8—222no—
219C22⋊Q8—114no—
220C22⋊Q8—222no—
221C4×Q8—222no—
222C4×Q8—222no—
223C2×C4⋊C4—111no—
224C2×C4⋊C4—111no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4—221no—
227C2×C4⋊C4—221no—
228C2×C4⋊C4—221no—
229C2×C22⋊C4—221no—
230C2×C22⋊C4—221no—
231C2×C42—22no—
232C2×C42—22no—
233C2×C42—221no—
234C2×C42—221no—
235C2×C42C4×D1111yescharacteristic
236C2×C42D4411yescharacteristic
237C2×C42C22⋊D1111yescharacteristic
238C2×C42C22×D1111yescharacteristic
239C4⋊C8—22no—
240C4⋊C8C22⋊D1114yes—
241C22⋊C8—24no—
242C22⋊C8—224no—
243C4×C8—24no—
244C4×C8—222no—
245C4×C8—222no—
246#95—221no—
247#95—221no—
248#95—221no—
249#95—221no—
250#95—221no—
251C2×C11—42no—
252C2×C11#147611yescharacteristic
253C2×C11#147911yescharacteristic
254C2×C11#148211yescharacteristic
255C2×C11#148511yescharacteristic
256C2×C11#186911yescharacteristic
257C2×C11#187111yescharacteristic
258C2×C11#187311yescharacteristic
259C24(C2×D11)⋊C411yescharacteristic
260C2×Q8—112no—
261C2×Q8—221no—
262C2×Q8—222no—
263C2×Q8—222no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4C8×D1112yes—
278C22×C4#431312yes—
279C22×C4(C2×D11)⋊C411yescharacteristic
280C22×C4(C2×D11)⋊C411yescharacteristic
281C22×C4(C2×D11)⋊C411yescharacteristic
282C22×C4C2×C4×D1111yescharacteristic
283C22×C4C2×D4411yescharacteristic
284C22×C4C2×C22⋊D1111yescharacteristic
285C2×C8—24no—
286C2×C8—42no—
287C2×C8—42no—
288C2×C8—224no—
289C2×C8—442no—
290C2×C8—442no—
291C4⋊C4—112no—
292C4⋊C4—224no—
293C4⋊C4—221no—
294C4⋊C4—222no—
295C4⋊C4—222no—
296C4⋊C4—442no—
297C4⋊C4—442no—
298C22⋊C4—224no—
299C22⋊C4—442no—
300C42—22no—
301C42—21no—
302C42—22no—
303C42—21no—
304C42—441no—
305C42—442no—
306C42—441no—
307C42#433912yes—
308C42C2×C22⋊D1112yes—
309C11#893811yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23(C2×D11)⋊C812yes—
317C23C2×(C2×D11)⋊C411yescharacteristic
318Q8—224no—
319Q8—442no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4(C2×D11)⋊C812yes—
347C2×C4#6688912yes—
348C2×C4C2×C8×D1111yescharacteristic
349C2×C4C2×#431311yescharacteristic
350C2×C4#6695412yes—
351C2×C4C4×C22⋊D1112yes—
352C2×C4#6698211yescharacteristic
353C2×C4#6698312yes—
354C2×C4#6700312yes—
355C2×C4#6700412yes—
356C2×C4#6700611yescharacteristic
357C8—44no—
358C8—444no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22#1062261511yescharacteristic
367C22#1062261711yescharacteristic
368C22C2×(C2×D11)⋊C811yescharacteristic
369C22#1062272311yescharacteristic
370C22C2×#6688911yescharacteristic
371C22#1062275211yescharacteristic
372C22#1062282611yescharacteristic
373C4—22no—
374C4—22no—
375C4—22no—
376C4—41no—
377C4—442no—
378C4—442no—
379C4—881no—
380C4—881no—
381C4#1062260912yes—
382C4C8×C22⋊D1112yes—
383C4#1062272412yes—
384C4#1062285212yes—
385C2—42no—
386C2#1306699611yescharacteristic
387C2#1306701011yescharacteristic
388C2#1306702211yescharacteristic
389C2#1306703611yescharacteristic
390C2#1306890811yescharacteristic
391C2#1306891811yescharacteristic
392C2#1306892811yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C11×#431C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C22⋊C4
cosocleC2×C42×C11C23
hypercenterC2×#431D11
hypocenterC11#8938
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. C2×#10622122C2semidirect
4. #13066455C2semidirect
42. #66977C8semidirect
309. C11#8938semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
C4×C22⋊(C11⋊C8)2
C2×#106221222
#130664552
C2×C11×#4312
#893811