Finite Group Databasebeta

← #14646521

Subgroups — #14646521

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2C2×#10622176C212yesmaximal
3#13066843C211yesmaximal, characteristic
4#13066494C212yesmaximal
5C4×C11×C22⋊Q8C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C2×C4×Q8×C11C411yescharacteristic, complemented
8C22×C42×C11C2211yescharacteristic
9C11×#391C411yescharacteristic, complemented
10C11×#389C411yescharacteristic, complemented
11C11×#387—21no—
12C11×#385—21no—
13C11×#380C2211yescharacteristic
14C4×C11×C4⋊C4—21no—
15C4×C11×C4⋊C4C411yescharacteristic, complemented
16C4×C11×C22⋊C4—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C4⋊(C11⋊C8)—21no—
22#10622176—24no—
23#10622162—21no—
24C22×Q8×C11C2×C411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C23×Dic11—22no—
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8D412yes—
32C11×C22⋊Q8Q812yes—
33C4×Q8×C11—42no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C42×C11—21no—
43C2×C42×C11—21no—
44C2×C42×C11—42no—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11D411yescharacteristic
48C2×C42×C11D411yescharacteristic
49C22×C11⋊C8—22no—
50C11×#95—21no—
51C11×#95—21no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11⋊#95—24no—
56C11⋊#95—22no—
57C11⋊#95—22no—
58C11⋊#95—42no—
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)—22no—
61C4⋊(C11⋊C8)—42no—
62#8576—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—41no—
66C2×Q8×C11—41no—
67C2×Q8×C11C4⋊C412yes—
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×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
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×D411yescharacteristic
87C22×C4×C11C2×Q811yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C22×Dic11—24no—
91C22×Dic11—42no—
92C22×Dic11—42no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C11×C4⋊C4—21no—
98C11×C4⋊C4—22no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—42no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C4⋊C4—42no—
104C11×C4⋊C4C4⋊C412yes—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—22no—
107C11×C22⋊C4—42no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—41no—
111C42×C11—41no—
112C42×C11—42no—
113C42×C11—42no—
114C2×C11⋊C8—42no—
115C2×C11⋊C8—42no—
116C2×C11⋊C8—42no—
117C4×C22⋊Q8D1111yescharacteristic
118#1797—111no—
119C2×#328—112no—
120#1434—111no—
121#1294—112no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11C2×C22⋊C411yescharacteristic
127C23×C11#12111yescharacteristic
128C23×C11C22⋊Q811yescharacteristic
129C23×C11#13512yes—
130C23×C11#13712yes—
131Q8×C11—42no—
132Q8×C11—42no—
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—22no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—44no—
154C2×C4×C11—44no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
165C2×C4×C11#9912yes—
166C2×C4×C11#10412yes—
167C2×C4×C11C2×C4⋊C411yescharacteristic
168C2×C4×C11#11711yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11C22⋊Q811yescharacteristic
171C2×Dic11—44no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11—82no—
175C2×Dic11—82no—
176C2×Dic11—82no—
177C2×Dic11—82no—
178C11⋊C8—82no—
179C2×C22⋊Q8C2×D1111yescharacteristic
180C2×C4×Q8Dic1111yescharacteristic, complemented
181C22×C42C2×D1111yescharacteristic
182C2×C4⋊C8—221no—
183C2×C22⋊C8—112no—
184#391Dic1111yescharacteristic, complemented
185#389Dic1111yescharacteristic, complemented
186#387—21no—
187#385—21no—
188#380C2×D1111yescharacteristic
189C4×C4⋊C4—21no—
190C4×C4⋊C4Dic1111yescharacteristic, complemented
191C4×C22⋊C4—21no—
192C2×#95—112no—
193C2×#95—221no—
194C2×#95—221no—
195#336—221no—
196#328—224no—
197C22×C11—21no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11#38011yescharacteristic
206C22×C11C2×#9911yescharacteristic
207C22×C11#41011yescharacteristic
208C22×C11#41611yescharacteristic
209C22×C11#41911yescharacteristic
210C22×C11C2×#10411yescharacteristic
211C22×C11#42111yescharacteristic
212C22×C11#46412yes—
213C22×C11#47912yes—
214C4×C11—21no—
215C4×C11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—22no—
219C4×C11—22no—
220C4×C11—42no—
221C4×C11—42no—
222C4×C11—41no—
223C4×C11—41no—
224C4×C11—81no—
225C4×C11—81no—
226Dic11—84no—
227C22×Q8C2×Dic1111yescharacteristic
228C23×C4—222no—
229C23×C4C22⋊D1111yescharacteristic
230C23×C4C22⋊D1111yescharacteristic
231C23×C4C22×D1111yescharacteristic
232C22×C8—222no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8Dic2212yes—
236C22⋊Q8D4412yes—
237C4×Q8—42no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4C2×Dic1111yescharacteristic
242C2×C4⋊C4C2×Dic1111yescharacteristic
243C2×C4⋊C4C2×Dic1111yescharacteristic
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—42no—
249C2×C42C2×Dic1111yescharacteristic
250C2×C42C2×Dic1111yescharacteristic
251C2×C42C22⋊D1111yescharacteristic
252C2×C42C22⋊D1111yescharacteristic
253C4⋊C8—442no—
254C22⋊C8—222no—
255C22⋊C8—222no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—224no—
262#95—222no—
263#95—222no—
264#95—442no—
265C2×C11—22no—
266C2×C11—22no—
267C2×C11#150111yescharacteristic
268C2×C11#150611yescharacteristic
269C2×C11#151111yescharacteristic
270C2×C11#152111yescharacteristic
271C2×C11#179911yescharacteristic
272C2×C11#180511yescharacteristic
273C2×C11#180611yescharacteristic
274C24C2×C22⋊D1111yescharacteristic
275C2×Q8—21no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8C4⋊Dic1112yes—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—41no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—224no—
292C22×C4—442no—
293C22×C4—442no—
294C22×C4—442no—
295C22×C4—442no—
296C22×C4—442no—
297C22×C4—442no—
298C22×C4C22⋊Dic1111yescharacteristic
299C22×C4C22⋊Dic1111yescharacteristic
300C22×C4C22⋊Dic1111yescharacteristic
301C22×C4C22⋊Dic1111yescharacteristic
302C22×C4C2×Dic2211yescharacteristic
303C22×C4C2×D4411yescharacteristic
304C22×C4#433911yescharacteristic
305C22×C4#433911yescharacteristic
306C22×C4C22×Dic1111yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308C2×C8—442no—
309C2×C8—442no—
310C2×C8—442no—
311C4⋊C4—22no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—42no—
318C4⋊C4C4⋊Dic1112yes—
319C22⋊C4—22no—
320C22⋊C4—22no—
321C22⋊C4—42no—
322C42—22no—
323C42—22no—
324C42—41no—
325C42—41no—
326C42—42no—
327C42—42no—
328C11#857611yescharacteristic, complemented, Sylow
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23#6697711yescharacteristic
334C23#6698311yescharacteristic
335C23#6699512yes—
336C23#6700312yes—
337C23C2×C22⋊Dic1111yescharacteristic
338Q8—42no—
339Q8—42no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—444no—
373C2×C4—444no—
374C2×C4—444no—
375C2×C4—882no—
376C2×C4—882no—
377C2×C4—882no—
378C2×C4—882no—
379C2×C4#6689812yes—
380C2×C4#6690112yes—
381C2×C4#6697711yescharacteristic
382C2×C4C2×C4⋊Dic1111yescharacteristic
383C2×C4#6697911yescharacteristic
384C2×C4#6698311yescharacteristic
385C8—882no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22—22no—
394C22#1062263512yes—
395C22#1062264112yes—
396C22#1062282511yescharacteristic
397C22C2×#6689811yescharacteristic
398C22#1062283811yescharacteristic
399C22#1062284611yescharacteristic
400C22C2×#6690111yescharacteristic
401C22#1062284911yescharacteristic
402C22#1062285311yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—21no—
407C4—22no—
408C4—22no—
409C4—42no—
410C4—42no—
411C4—41no—
412C4—41no—
413C4—81no—
414C4—81no—
415C4—884no—
416C2—22no—
417C2—22no—
418C2#1306710711yescharacteristic
419C2#1306712811yescharacteristic
420C2#1306714911yescharacteristic
421C2#1306719311yescharacteristic
422C2#1306860411yescharacteristic
423C2#1306863111yescharacteristic
424C2#1306863611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC4×C22⋊Q8D11
hypocenterC11#8576
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
7. C2×C4×Q8×C11C4semidirect
9. C11×#391C4semidirect
10. C11×#389C4semidirect
15. C4×C11×C4⋊C4C4semidirect
180. C2×C4×Q8Dic11semidirect
184. #391Dic11semidirect
185. #389Dic11semidirect
190. C4×C4⋊C4Dic11semidirect
328. C11#8576semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221762
#130668432
#130664942
C4×C11×C22⋊Q82
#857611