Finite Group Databasebeta

← #14649351

Subgroups — #14649351

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622539C211yesmaximal, characteristic
2#13076955C211yesmaximal, characteristic
3C2×#10622090C212yesmaximal
4#13066495C212yesmaximal
5C11×#1434C211yesmaximal, characteristic
6C22×C42×C11C2211yescharacteristic
7C2×#66977C2211yescharacteristic
8C2×C11×#95—21no—
9C2×C11×#95—21no—
10C2×C11×#95C2212yes—
11#10622825C2211yescharacteristic
12#10622824—21no—
13#10622823—21no—
14C2×C22⋊(C11⋊C8)C2212yes—
15#10622546—21no—
16#10622546—21no—
17#10622542C411yescharacteristic, complemented
18#10622542C411yescharacteristic, complemented
19#10622541C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21#10622539—24no—
22C2×C4⋊(C11⋊C8)—21no—
23C2×#66867—21no—
24#10622090—24no—
25C23×C4×C11—22no—
26C23×C4×C11D411yescharacteristic
27C23×C4×C11D411yescharacteristic
28C23×C4×C11C2311yescharacteristic
29C22×Dic22C2×C411yescharacteristic
30C2×C42×C11—22no—
31C2×C42×C11—22no—
32C2×C42×C11C2×C411yescharacteristic
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11D411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11—21no—
37C2×C22⋊Dic11—21no—
38C2×C4⋊Dic11C2×C411yescharacteristic
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41#66977—22no—
42#66977—22no—
43C2×Dic11⋊C4—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C22×C11⋊C8—22no—
47C11×#95—24no—
48C11×#95—22no—
49C11×#95—22no—
50C11×#95—42no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)D414yes—
60C4⋊(C11⋊C8)—24no—
61#66867—24no—
62#9116—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—24no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—42no—
75C22×C4×C11—42no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11—42no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D412yes—
87C22×C4×C11#4112yes—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×Dic22—22no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C42×C11—22no—
96C42×C11—22no—
97C42×C11—21no—
98C42×C11—21no—
99C42×C11—21no—
100C42×C11—21no—
101C22⋊Dic11—42no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104C4⋊Dic11—22no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107Dic11⋊C4—42no—
108Dic11⋊C4—42no—
109Dic11⋊C4—41no—
110Dic11⋊C4—41no—
111C2×C11⋊C8—24no—
112C2×C11⋊C8—42no—
113C2×C11⋊C8—42no—
114C2×#432—111no—
115#2855—111no—
116C2×#328—112no—
117#1434D1111yescharacteristic
118#1294—112no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11C2×C22⋊C411yescharacteristic
124C23×C11#12112yes—
125C23×C11AGL(1,ℤ/8)11yescharacteristic
126C23×C11#13711yescharacteristic
127C23×C11#13712yes—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—42no—
144C2×C4×C11—42no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—82no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11#10412yes—
156C2×C4×C11C4×D412yes—
157C2×C4×C11#12011yescharacteristic
158C2×C4×C11#12311yescharacteristic
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—41no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171Dic22—82no—
172C11⋊C8—44no—
173C2×C22⋊Q8—111no—
174C22×C42C2×D1111yescharacteristic
175#432—224no—
176C2×C4⋊C8—221no—
177C2×C22⋊C8—112no—
178C2×#97—221no—
179#391—111no—
180#391—111no—
181#389—111no—
182#389—111no—
183#387—221no—
184#387—221no—
185#385—221no—
186#381—221no—
187#380—111no—
188C2×#95—21no—
189C2×#95—21no—
190C2×#95C2×D1112yes—
191#328—224no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—22no—
200C22×C11#38611yescharacteristic
201C22×C11#41011yescharacteristic
202C22×C11#41011yescharacteristic
203C22×C11#41711yescharacteristic
204C22×C11#41911yescharacteristic
205C22×C11C2×#10411yescharacteristic
206C22×C11#42111yescharacteristic
207C22×C11#46812yes—
208C22×C11#47012yes—
209C4×C11—22no—
210C4×C11—22no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—41no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11—84no—
217Dic11—81no—
218Dic11—81no—
219Dic11—81no—
220Dic11—81no—
221C22×Q8—111no—
222C23×C4—22no—
223C23×C4C22⋊D1111yescharacteristic
224C23×C4C22⋊D1111yescharacteristic
225C23×C4C22×D1111yescharacteristic
226C22×C8—222no—
227C22⋊Q8—222no—
228C22⋊Q8—222no—
229C2×C4⋊C4—111no—
230C2×C4⋊C4—111no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C22⋊C4—221no—
237C2×C42—22no—
238C2×C42—22no—
239C2×C42C4×D1111yescharacteristic
240C2×C42C4×D1111yescharacteristic
241C2×C42D4411yescharacteristic
242C2×C42D4411yescharacteristic
243C4⋊C8—224no—
244C22⋊C8—114no—
245C22⋊C8—222no—
246#97—224no—
247#95—24no—
248#95—22no—
249#95—22no—
250#95—42no—
251#95—221no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95—221no—
257#95—221no—
258C2×C11—22no—
259C2×C11—22no—
260C2×C11#150611yescharacteristic
261C2×C11#150911yescharacteristic
262C2×C11#151211yescharacteristic
263C2×C11#151511yescharacteristic
264C2×C11#187111yescharacteristic
265C2×C11#189411yescharacteristic
266C2×C11#189911yescharacteristic
267C24C2×C22⋊D1111yescharacteristic
268C2×Q8—222no—
269C2×Q8—441no—
270C2×Q8—441no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—42no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4(C2×D11)⋊C411yescharacteristic
293C22×C4(C2×D11)⋊C411yescharacteristic
294C22×C4(C2×D11)⋊C411yescharacteristic
295C22×C4C2×C4×D1111yescharacteristic
296C22×C4C2×D4411yescharacteristic
297C22×C4D4×D1112yes—
298C22×C4#434112yes—
299C2×C8—224no—
300C2×C8—442no—
301C2×C8—442no—
302C4⋊C4—222no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—442no—
306C4⋊C4—442no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C22⋊C4—441no—
310C22⋊C4—442no—
311C22⋊C4—441no—
312C42—22no—
313C42—22no—
314C42—21no—
315C42—21no—
316C42—21no—
317C42—21no—
318C11#911611yescharacteristic, complemented, Sylow
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23C2×(C2×D11)⋊C411yescharacteristic
324C23#6698511yescharacteristic
325C23#6699212yes—
326C23#6699511yescharacteristic
327C23#6700412yes—
328Q8—882no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—44no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—82no—
355C2×C4—82no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—441no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4#6686912yes—
369C2×C4(C22⋊D11)⋊C412yes—
370C2×C4#6693511yescharacteristic
371C2×C4#6693911yescharacteristic
372C8—444no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—22no—
381C22C2×#6686911yescharacteristic
382C22#1062257111yescharacteristic
383C22#1062257911yescharacteristic
384C22#1062261711yescharacteristic
385C22#1062261811yescharacteristic
386C22#1062261911yescharacteristic
387C22#1062261911yescharacteristic
388C22#1062265512yes—
389C22#1062266512yes—
390C4—21no—
391C4—22no—
392C4—21no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—84no—
398C4—881no—
399C4—881no—
400C4—881no—
401C4—881no—
402C2—22no—
403C2—22no—
404C2#1306712711yescharacteristic
405C2#1306713911yescharacteristic
406C2#1306715211yescharacteristic
407C2#1306716611yescharacteristic
408C2#1306891611yescharacteristic
409C2#1306904711yescharacteristic
410C2#1306907211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1434C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1434D11
hypocenterC11#9116
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1434

Complements

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

NH ≅ G/Ntype
17. #10622542C4semidirect
18. #10622542C4semidirect
19. #10622541C4semidirect
20. #10622541C4semidirect
318. C11#9116semidirect

Maximal subgroups

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

subgroupindex
C2×#106225392
#130769552
C2×#106220902
#130664952
C11×#14342
#911611