Finite Group Databasebeta

← #14644673

Subgroups — #14644673

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66977C211yesmaximal, characteristic
2#13068378C211yesmaximal, characteristic
3C2×#10622090C212yesmaximal
4#13066495C212yesmaximal
5C4×C11×#95C211yesmaximal, characteristic
6C22×C42×C11—21no—
7C22×C42×C11C2211yescharacteristic
8C2×#66977C2211yescharacteristic
9C2×C4×Dic22C411yescharacteristic, complemented
10C2×C11×#95—21no—
11C2×C11×#95C2212yes—
12#10622825C2211yescharacteristic
13#10622823—21no—
14C4×C22⋊Dic11—21no—
15C2×C22⋊(C11⋊C8)C2212yes—
16C4×C4⋊Dic11C411yescharacteristic, complemented
17#10622546—21no—
18C4×Dic11⋊C4—21no—
19#10622542C411yescharacteristic, complemented
20#10622541C411yescharacteristic, complemented
21C2×#66867—21no—
22#10622162—21no—
23#10622090C418yescomplemented
24C23×C4×C11—22no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×Dic22C2×C411yescharacteristic
29C2×C42×C11—24no—
30C2×C42×C11—42no—
31C2×C42×C11—42no—
32C2×C42×C11—42no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×C4⋊Dic11C2×C411yescharacteristic
42#66977—22no—
43#66977C2×C414yes—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×Dic11⋊C4—21no—
47C2×C4×Dic11—21no—
48C2×C4×Dic11—21no—
49C22×C11⋊C8—22no—
50C4×Dic22—42no—
51C11×#95—24no—
52C11×#95—22no—
53C11×#95C2×C414yes—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)C2×C414yes—
61#66867—42no—
62#8219—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—24no—
69C22×C4×C11—24no—
70C22×C4×C11—24no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
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×C11C22×C412yes—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4112yes—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×Dic22—21no—
93C2×Dic22—41no—
94C2×Dic22—41no—
95C2×Dic22C4212yescomplemented
96C42×C11—22no—
97C42×C11—22no—
98C42×C11—41no—
99C42×C11—41no—
100C42×C11—48no—
101C22⋊Dic11—24no—
102C22⋊Dic11—41no—
103C22⋊Dic11—41no—
104C4⋊Dic11—21no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107C4⋊Dic11C4212yescomplemented
108Dic11⋊C4—24no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111C4×Dic11—42no—
112C4×Dic11—42no—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C4×C22⋊Q8—111no—
117#1749—111no—
118C2×#328—112no—
119C4×#95D1111yescharacteristic
120#1294—112no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11C2×C22⋊C411yescharacteristic
126C23×C11C4×D412yes—
127C23×C11AGL(1,ℤ/8)11yescharacteristic
128C23×C11#13711yescharacteristic
129C23×C11#13712yes—
130C2×C4×C11—24no—
131C2×C4×C11—24no—
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—28no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11#9912yes—
156C2×C4×C11#10412yes—
157C2×C4×C11#10412yes—
158C2×C4×C11C2×C4211yescharacteristic
159C2×C4×C11#11711yescharacteristic
160C2×C4×C11C4×D412yes—
161C2×Dic11—22no—
162C2×Dic11—22no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173Dic22—42no—
174Dic22—42no—
175C11⋊C8—44no—
176C2×C22⋊Q8—111no—
177C2×C4×Q8—111no—
178C22×C42—21no—
179C22×C42C2×D1111yescharacteristic
180C2×C22⋊C8—112no—
181C2×#97—221no—
182#391—111no—
183#389—111no—
184#387—221no—
185#385—221no—
186#380—111no—
187C4×C4⋊C4—111no—
188C4×C4⋊C4—221no—
189C4×C22⋊C4—221no—
190C2×#95—21no—
191C2×#95C2×D1112yes—
192#336—221no—
193#328—118no—
194C22×C11—22no—
195C22×C11—22no—
196C22×C11—21no—
197C22×C11—21no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11C4×C22⋊C411yescharacteristic
203C22×C11C2×#9911yescharacteristic
204C22×C11#41011yescharacteristic
205C22×C11#41711yescharacteristic
206C22×C11#41911yescharacteristic
207C22×C11C2×#10411yescharacteristic
208C22×C11C2×#10411yescharacteristic
209C22×C11#44012yes—
210C22×C11#44112yes—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—22no—
214C4×C11—22no—
215C4×C11—22no—
216C4×C11—22no—
217C4×C11—48no—
218C4×C11—41no—
219Dic11—42no—
220Dic11—42no—
221Dic11—81no—
222Dic11—81no—
223C22×Q8—111no—
224C23×C4—22no—
225C23×C4C22⋊D1111yescharacteristic
226C23×C4C22⋊D1111yescharacteristic
227C23×C4C22×D1111yescharacteristic
228C22×C8—222no—
229C22⋊Q8—114no—
230C22⋊Q8—222no—
231C4×Q8—442no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—111no—
234C2×C4⋊C4—111no—
235C2×C4⋊C4—221no—
236C2×C4⋊C4—221no—
237C2×C4⋊C4—221no—
238C2×C22⋊C4—221no—
239C2×C22⋊C4—221no—
240C2×C42—24no—
241C2×C42—42no—
242C2×C42—42no—
243C2×C42—42no—
244C2×C42—221no—
245C2×C42—221no—
246C2×C42C4×D1111yescharacteristic
247C2×C42C4×D1111yescharacteristic
248C2×C42D4411yescharacteristic
249C2×C42D4411yescharacteristic
250C22⋊C8—114no—
251C22⋊C8—222no—
252#97—442no—
253#95—24no—
254#95—22no—
255#95—221no—
256#95—221no—
257#95—221no—
258#95—221no—
259#95—221no—
260#95C4×D1114yes—
261C2×C11—22no—
262C2×C11—22no—
263C2×C11#150411yescharacteristic
264C2×C11#150611yescharacteristic
265C2×C11#150811yescharacteristic
266C2×C11#150911yescharacteristic
267C2×C11C4×#9911yescharacteristic
268C2×C11C4×#10411yescharacteristic
269C2×C11#176311yescharacteristic
270C24C2×C22⋊D1111yescharacteristic
271C2×Q8—112no—
272C2×Q8—221no—
273C2×Q8—441no—
274C2×Q8—441no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—221no—
292C22×C4—221no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4(C2×D11)⋊C411yescharacteristic
296C22×C4(C2×D11)⋊C411yescharacteristic
297C22×C4(C2×D11)⋊C411yescharacteristic
298C22×C4(C2×D11)⋊C411yescharacteristic
299C22×C4C2×C4×D1111yescharacteristic
300C22×C4C2×C4×D1112yes—
301C22×C4C2×D4411yescharacteristic
302C22×C4#433912yes—
303C2×C8—224no—
304C2×C8—442no—
305C2×C8—442no—
306C4⋊C4—112no—
307C4⋊C4—221no—
308C4⋊C4—224no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—442no—
312C4⋊C4—442no—
313C22⋊C4—224no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C42—22no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42—48no—
321C42—442no—
322C42—442no—
323C11#821911yescharacteristic, complemented, Sylow
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23C2×(C2×D11)⋊C411yescharacteristic
329C23C4×C22⋊D1112yes—
330C23#6698511yescharacteristic
331C23#6699511yescharacteristic
332C23#6700412yes—
333Q8—442no—
334Q8—442no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—28no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—222no—
361C2×C4—222no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4#6686912yes—
373C2×C4#6686912yes—
374C2×C4#6687012yes—
375C2×C4C42×D1111yescharacteristic
376C2×C4#6692511yescharacteristic
377C2×C4C4×D4412yes—
378C8—444no—
379C22—21no—
380C22—21no—
381C22—22no—
382C22—22no—
383C22—22no—
384C22—21no—
385C22—21no—
386C22—22no—
387C22C2×#6686911yescharacteristic
388C22C2×#6686911yescharacteristic
389C22C4×(C2×D11)⋊C411yescharacteristic
390C22C2×#6687011yescharacteristic
391C22#1062257911yescharacteristic
392C22#1062261711yescharacteristic
393C22#1062261911yescharacteristic
394C22#1062263112yes—
395C22#1062264312yes—
396C4—22no—
397C4—22no—
398C4—22no—
399C4—21no—
400C4—21no—
401C4—22no—
402C4—48no—
403C4—41no—
404C4—442no—
405C4—442no—
406C4—881no—
407C4—881no—
408C2—22no—
409C2—22no—
410C2#1306711811yescharacteristic
411C2#1306712711yescharacteristic
412C2#1306713511yescharacteristic
413C2#1306713911yescharacteristic
414C2C4×#6687011yescharacteristic
415C2C4×#6686911yescharacteristic
416C2#1306844911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC4×C11×#95C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4×#95D11
hypocenterC11#8219
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
9. C2×C4×Dic22C4semidirect
16. C4×C4⋊Dic11C4semidirect
19. #10622542C4semidirect
20. #10622541C4semidirect
23. #10622090C4semidirect
95. C2×Dic22C42semidirect
107. C4⋊Dic11C42semidirect
323. C11#8219semidirect

Maximal subgroups

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

subgroupindex
C4×#669772
#130683782
C2×#106220902
#130664952
C4×C11×#952
#821911