Finite Group Databasebeta

← #14646531

Subgroups — #14646531

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic
2C2×#10622176C212yesmaximal
3#13066846C211yesmaximal, characteristic
4#13066494C212yesmaximal
5C4×C11×C22⋊Q8C211yesmaximal, characteristic
6C2×C11×C22⋊Q8C2211yescharacteristic
7C2×C4×Q8×C11C411yescharacteristic, complemented
8C22×C42×C11C2211yescharacteristic
9C22×C4⋊Dic11—21no—
10C11×#391C411yescharacteristic, complemented
11C11×#389C411yescharacteristic, complemented
12C11×#387—21no—
13C11×#385—21no—
14C11×#380C2211yescharacteristic
15C4×C11×C4⋊C4—21no—
16C4×C11×C4⋊C4C411yescharacteristic, complemented
17C4×C11×C22⋊C4—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
49C2×C4⋊Dic11—24no—
50C2×C4⋊Dic11—42no—
51C2×C4⋊Dic11—42no—
52C22×C11⋊C8—22no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95—21no—
57C11×#95—21no—
58C11⋊#95—22no—
59C11⋊#95—22no—
60C11⋊#95—42no—
61C22⋊(C11⋊C8)—22no—
62C22⋊(C11⋊C8)—22no—
63C4⋊(C11⋊C8)—42no—
64#8578—111nomaximal, Sylow
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—21no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11C4⋊C412yescomplemented
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22⋊C411yescharacteristic
85C22×C4×C11C22⋊C411yescharacteristic
86C22×C4×C11SD1612yes—
87C22×C4×C11Q1612yes—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×Q811yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—24no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C11×C4⋊C4—21no—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—42no—
108C11×C4⋊C4C4⋊C412yescomplemented
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C42×C11—22no—
114C42×C11—22no—
115C42×C11—41no—
116C42×C11—41no—
117C42×C11—42no—
118C42×C11—42no—
119C4⋊Dic11—48no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—42no—
123C4×C22⋊Q8D1111yescharacteristic
124#1797—111no—
125C2×#328—112no—
126C4⋊#95—111no—
127#1294—112no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11C2×C22⋊C411yescharacteristic
133C23×C11#12111yescharacteristic
134C23×C11C22⋊Q811yescharacteristic
135C23×C11C2×SD1611yescharacteristic
136C23×C11C2×Q1611yescharacteristic
137C23×C11AGL(1,ℤ/8)11yescharacteristic
138C23×C11#13711yescharacteristic
139Q8×C11—42no—
140Q8×C11—42no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
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—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
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—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11#9912yes—
174C2×C4×C11#10312yes—
175C2×C4×C11#10312yes—
176C2×C4×C11#10412yes—
177C2×C4×C11C2×C4⋊C411yescharacteristic
178C2×C4×C11#11711yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11C22⋊Q811yescharacteristic
181C2×Dic11—44no—
182C2×Dic11—44no—
183C2×Dic11—44no—
184C2×Dic11—82no—
185C2×Dic11—82no—
186C2×Dic11—82no—
187C2×Dic11—82no—
188C11⋊C8—82no—
189C2×C22⋊Q8C2×D1111yescharacteristic
190C2×C4×Q8Dic1111yescharacteristic, complemented
191C22×C4⋊C4—221no—
192C22×C42C2×D1111yescharacteristic
193C2×C4⋊C8—221no—
194C2×C22⋊C8—112no—
195#391Dic1111yescharacteristic, complemented
196#389Dic1111yescharacteristic, complemented
197#387—21no—
198#385—21no—
199#380C2×D1111yescharacteristic
200C4×C4⋊C4—21no—
201C4×C4⋊C4Dic1111yescharacteristic, complemented
202C4×C22⋊C4—21no—
203C2×#95—112no—
204C2×#95—221no—
205#336—221no—
206#328—224no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11#38011yescharacteristic
220C22×C11C2×#9911yescharacteristic
221C22×C11#41011yescharacteristic
222C22×C11C2×#10311yescharacteristic
223C22×C11#41711yescharacteristic
224C22×C11C2×#10411yescharacteristic
225C22×C11#42111yescharacteristic
226C22×C11#46011yescharacteristic
227C22×C11#46211yescharacteristic
228C22×C11#47511yescharacteristic
229C22×C11#47711yescharacteristic
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—42no—
239C4×C11—42no—
240C4×C11—81no—
241C4×C11—81no—
242Dic11—84no—
243C22×Q8C2×Dic1111yescharacteristic
244C23×C4—222no—
245C23×C4C22⋊D1111yescharacteristic
246C23×C4C22⋊D1111yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C22×C8—222no—
249C22⋊Q8—21no—
250C22⋊Q8—21no—
251C22⋊Q8Dic2212yes—
252C22⋊Q8D4412yes—
253C4×Q8—42no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—224no—
258C2×C4⋊C4—442no—
259C2×C4⋊C4—442no—
260C2×C4⋊C4C2×Dic1111yescharacteristic
261C2×C4⋊C4C2×Dic1111yescharacteristic
262C2×C4⋊C4C2×Dic1111yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C42—21no—
266C2×C42—21no—
267C2×C42—42no—
268C2×C42C2×Dic1111yescharacteristic
269C2×C42C2×Dic1111yescharacteristic
270C2×C42C22⋊D1111yescharacteristic
271C2×C42C22⋊D1111yescharacteristic
272C4⋊C8—442no—
273C22⋊C8—222no—
274C22⋊C8—222no—
275#95—21no—
276#95—21no—
277#95—21no—
278#95—21no—
279#95—21no—
280#95—222no—
281#95—222no—
282#95—442no—
283C2×C11—21no—
284C2×C11—21no—
285C2×C11—21no—
286C2×C11—21no—
287C2×C11#150311yescharacteristic
288C2×C11#150411yescharacteristic
289C2×C11#151211yescharacteristic
290C2×C11#152011yescharacteristic
291C2×C11#179911yescharacteristic
292C2×C11#180311yescharacteristic
293C2×C11#180611yescharacteristic
294C24C2×C22⋊D1111yescharacteristic
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8C4⋊Dic1112yescomplemented
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—224no—
312C22×C4—442no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4#432512yes—
319C22×C4#432612yes—
320C22×C4C22⋊Dic1111yescharacteristic
321C22×C4C22⋊Dic1111yescharacteristic
322C22×C4C22⋊Dic1111yescharacteristic
323C22×C4C22⋊Dic1111yescharacteristic
324C22×C4C2×Dic2211yescharacteristic
325C22×C4C2×D4411yescharacteristic
326C22×C4#433911yescharacteristic
327C22×C4#433911yescharacteristic
328C22×C4C22×Dic1111yescharacteristic
329C22×C4C2×C22⋊D1111yescharacteristic
330C2×C8—442no—
331C2×C8—442no—
332C2×C8—442no—
333C4⋊C4—22no—
334C4⋊C4—21no—
335C4⋊C4—22no—
336C4⋊C4—41no—
337C4⋊C4—41no—
338C4⋊C4—42no—
339C4⋊C4—42no—
340C4⋊C4—448no—
341C4⋊C4C4⋊Dic1112yescomplemented
342C22⋊C4—22no—
343C22⋊C4—22no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C42—22no—
347C42—22no—
348C42—41no—
349C42—41no—
350C42—42no—
351C42—42no—
352C11#857811yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23#6697711yescharacteristic
358C23#6698311yescharacteristic
359C23C2×#432511yescharacteristic
360C23C2×#432611yescharacteristic
361C23#6700211yescharacteristic
362C23#6700411yescharacteristic
363C23C2×C22⋊Dic1111yescharacteristic
364Q8—42no—
365Q8—42no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—444no—
399C2×C4—444no—
400C2×C4—444no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4—882no—
404C2×C4—882no—
405C2×C4#6689812yes—
406C2×C4#6689912yes—
407C2×C4#6689912yes—
408C2×C4#6690112yes—
409C2×C4#6697711yescharacteristic
410C2×C4C2×C4⋊Dic1111yescharacteristic
411C2×C4#6697911yescharacteristic
412C2×C4#6698311yescharacteristic
413C8—882no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22#1062263311yescharacteristic
427C22#1062263411yescharacteristic
428C22#1062264011yescharacteristic
429C22#1062264411yescharacteristic
430C22#1062282511yescharacteristic
431C22C2×#6689811yescharacteristic
432C22C2×#6689911yescharacteristic
433C22#1062284511yescharacteristic
434C22C2×#6690111yescharacteristic
435C22#1062284911yescharacteristic
436C22#1062285311yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—22no—
445C4—42no—
446C4—42no—
447C4—81no—
448C4—81no—
449C4—884no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2#1306711511yescharacteristic
455C2#1306712011yescharacteristic
456C2#1306715411yescharacteristic
457C2#1306718811yescharacteristic
458C2#1306860411yescharacteristic
459C2#1306862111yescharacteristic
460C2#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#8578
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
10. C11×#391C4semidirect
11. C11×#389C4semidirect
16. C4×C11×C4⋊C4C4semidirect
69. C2×Q8×C11C4⋊C4semidirect
108. C11×C4⋊C4C4⋊C4semidirect
190. C2×C4×Q8Dic11semidirect
195. #391Dic11semidirect
196. #389Dic11semidirect
201. C4×C4⋊C4Dic11semidirect
298. C2×Q8C4⋊Dic11semidirect
341. C4⋊C4C4⋊Dic11semidirect
352. C11#8578semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221762
#130668462
#130664942
C4×C11×C22⋊Q82
#857811