Finite Group Databasebeta

← #14652918

Subgroups — #14652918

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic, complemented
2C2×#10622176C212yesmaximal, complemented
3C2×#10622175C212yesmaximal
4#13066843C211yesmaximal, characteristic, complemented
5C11×#2850C211yesmaximal, characteristic
6C2×C11×#124C411yescharacteristic, complemented
7C2×C11×C22⋊Q8C2211yescharacteristic
8C2×C11×#121C2211yescharacteristic
9C22×C42×C11C2211yescharacteristic
10C11×#391C411yescharacteristic, complemented
11C11×#390C411yescharacteristic, complemented
12C11×#388—21no—
13C11×#388—21no—
14C11×#386—21no—
15C11×#386—21no—
16C11×#382C411yescharacteristic, complemented
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#10622175—24no—
24#10622162—21no—
25C22×Q8×C11C2×C411yescharacteristic
26C22×D4×C11—21no—
27C22×D4×C11C2×C411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—22no—
32C11×#124—42no—
33C11×C22⋊Q8—22no—
34C11×C22⋊Q8—22no—
35C11×#121—22no—
36C11×#121—22no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—42no—
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C22×C11⋊C8—22no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—22no—
57C11⋊#95—42no—
58C11⋊#95—42no—
59C11⋊#95D414yes—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62C4⋊(C11⋊C8)—42no—
63#9716—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C2×Q8×C11—22no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×D4×C11—22no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C22×C4×C11—22no—
77C22×C4×C11—21no—
78C22×C4×C11—21no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11#4112yes—
96C22×Dic11—24no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11—22no—
115C42×C11—22no—
116C42×C11—41no—
117C42×C11—41no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—42no—
121#2850D1111yescharacteristic
122#1797—111no—
123C2×#328—112no—
124C2×#327—112no—
125#1434—111no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—41no—
131C23×C11—41no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11C2×C22⋊C411yescharacteristic
138C23×C11#12112yes—
139C23×C11#13512yes—
140C23×C11AGL(1,ℤ/8)11yescharacteristic
141C23×C11#13711yescharacteristic
142Q8×C11—82no—
143D4×C11—82no—
144D4×C11—82no—
145D4×C11—82no—
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—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—44no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
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—41no—
174C2×C4×C11—41no—
175C2×C4×C11#9912yes—
176C2×C4×C11C4×D412yes—
177C2×C4×C11#12411yescharacteristic
178C2×C4×C11#12711yescharacteristic
179C2×Dic11—44no—
180C2×Dic11—44no—
181C2×Dic11—44no—
182C2×Dic11—82no—
183C2×Dic11—82no—
184C2×Dic11—82no—
185C2×Dic11—82no—
186C11⋊C8—82no—
187C2×#124Dic1111yescharacteristic, complemented
188C2×C22⋊Q8C2×D1111yescharacteristic
189C2×#121C2×D1111yescharacteristic
190C22×C42C2×D1111yescharacteristic
191C2×C4⋊C8—221no—
192C2×C22⋊C8—112no—
193#391Dic1111yescharacteristic, complemented
194#390Dic1111yescharacteristic, complemented
195#388—21no—
196#388—21no—
197#386—21no—
198#386—21no—
199#382Dic1111yescharacteristic, complemented
200C2×#95—112no—
201C2×#95—221no—
202C2×#95—221no—
203#336—221no—
204#328—224no—
205#327—224no—
206C22×C11—22no—
207C22×C11—22no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11#39011yescharacteristic
222C22×C11C2×#9911yescharacteristic
223C22×C11#41011yescharacteristic
224C22×C11#41611yescharacteristic
225C22×C11#41711yescharacteristic
226C22×C11#42111yescharacteristic
227C22×C11#42111yescharacteristic
228C22×C11#46312yes—
229C22×C11#46412yes—
230C4×C11—22no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—22no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—41no—
237C4×C11—81no—
238C4×C11—81no—
239C4×C11—81no—
240Dic11—84no—
241C22×Q8C2×Dic1111yescharacteristic
242C22×D4—21no—
243C22×D4C2×Dic1111yescharacteristic
244C23×C4—222no—
245C23×C4C22⋊D1111yescharacteristic
246C23×C4C22⋊D1111yescharacteristic
247C23×C4C22×D1111yescharacteristic
248C22×C8—222no—
249#124—42no—
250C22⋊Q8—22no—
251C22⋊Q8—22no—
252#121—22no—
253#121—22no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C2×Dic1111yescharacteristic
256C2×C4⋊C4C2×Dic1111yescharacteristic
257C2×C22⋊C4—21no—
258C2×C22⋊C4—21no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C42—42no—
264C2×C42C2×Dic1111yescharacteristic
265C2×C42C2×Dic1111yescharacteristic
266C2×C42C22⋊D1111yescharacteristic
267C2×C42C22⋊D1111yescharacteristic
268C4⋊C8—442no—
269C22⋊C8—222no—
270C22⋊C8—222no—
271#95—21no—
272#95—21no—
273#95—21no—
274#95—21no—
275#95—114no—
276#95—222no—
277#95—442no—
278#95—442no—
279C2×C11—22no—
280C2×C11—22no—
281C2×C11—161no—
282C2×C11#151211yescharacteristic
283C2×C11#151311yescharacteristic
284C2×C11#151611yescharacteristic
285C2×C11#152111yescharacteristic
286C2×C11#196311yescharacteristic
287C2×C11#196411yescharacteristic
288C2×C11#198311yescharacteristic
289C24—21no—
290C24C2×C22⋊D1111yescharacteristic
291C2×Q8—22no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—41no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—224no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4C22⋊Dic1111yescharacteristic
321C22×C4C22⋊Dic1111yescharacteristic
322C22×C4C22⋊Dic1111yescharacteristic
323C22×C4C22⋊Dic1111yescharacteristic
324C22×C4D4×D1112yes—
325C22×C4#434112yes—
326C22×C4C22×Dic1111yescharacteristic
327C22×C4C2×C22⋊D1111yescharacteristic
328C2×C8—442no—
329C2×C8—442no—
330C2×C8—442no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—41no—
334C4⋊C4—41no—
335C22⋊C4—42no—
336C22⋊C4—42no—
337C22⋊C4—42no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—22no—
343C42—22no—
344C42—41no—
345C42—41no—
346C11#971611yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23#6699112yes—
359C23#6700211yescharacteristic
360C23#6700312yes—
361C23#6700411yescharacteristic
362C23C2×C22⋊Dic1111yescharacteristic
363Q8—82no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—21no—
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—21no—
381C2×C4—21no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—42no—
386C2×C4—42no—
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—444no—
397C2×C4—444no—
398C2×C4—444no—
399C2×C4—882no—
400C2×C4—882no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4#6689812yes—
404C2×C4D4×Dic1112yes—
405C2×C4#6698911yescharacteristic
406C2×C4#6699311yescharacteristic
407C8—882no—
408C22—22no—
409C22—22no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—22no—
415C22—22no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—81no—
420C22—81no—
421C22—81no—
422C22—81no—
423C22#1062266712yes—
424C22#1062267012yes—
425C22C2×#6689811yescharacteristic
426C22#1062283411yescharacteristic
427C22#1062284511yescharacteristic
428C22#1062284611yescharacteristic
429C22#1062284911yescharacteristic
430C22#1062284911yescharacteristic
431C22#1062285311yescharacteristic
432C4—21no—
433C4—22no—
434C4—21no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—884no—
443C2—22no—
444C2—22no—
445C2—161no—
446C2#1306715411yescharacteristic
447C2#1306715911yescharacteristic
448C2#1306717211yescharacteristic
449C2#1306719311yescharacteristic
450C2#1306944911yescharacteristic
451C2#1306945311yescharacteristic
452C2#1306954911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2850C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2850D11
hypocenterC11#9716
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2850

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
2. C2×#10622176C2semidirect
4. #13066843C2semidirect
6. C2×C11×#124C4semidirect
10. C11×#391C4semidirect
11. C11×#390C4semidirect
16. C11×#382C4semidirect
187. C2×#124Dic11semidirect
193. #391Dic11semidirect
194. #390Dic11semidirect
199. #382Dic11semidirect
346. C11#9716semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221762
C2×#106221752
#130668432
C11×#28502
#971611