Finite Group Databasebeta

← #14647160

Subgroups — #14647160

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068526C211yesmaximal, characteristic
2#13066839C211yesmaximal, characteristic
3#13066494C212yesmaximal, complemented
4#13066494C212yesmaximal, complemented
5C11×#2280C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×#117C411yescharacteristic, complemented
8C2×C11×#117C411yescharacteristic, complemented
9C22×C22⋊Dic11—21no—
10C11×#381—21no—
11C11×#380C411yescharacteristic, complemented
12C11×#380C411yescharacteristic, complemented
13C11×#380C2211yescharacteristic
14C11×#380C2211yescharacteristic
15C11×#379—21no—
16C4×C11×C22⋊C4—21no—
17C4×C11×C22⋊C4—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)—21no—
21C2×C22⋊(C11⋊C8)—21no—
22C2×C22⋊(C11⋊C8)C2212yes—
23C25×C11D411yescharacteristic
24C23×C4×C11—24no—
25C23×C4×C11—42no—
26C23×C4×C11—42no—
27C23×C4×C11C2×C411yescharacteristic
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—22no—
34C11×#117—42no—
35C11×#117—42no—
36C2×C11×C4⋊C4C2×C411yescharacteristic
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×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—21no—
47C2×C42×C11—21no—
48C2×C22⋊Dic11—24no—
49C2×C22⋊Dic11—42no—
50C2×C22⋊Dic11—42no—
51C22×C11⋊C8—22no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—24no—
57C11⋊#95—42no—
58C22⋊(C11⋊C8)—24no—
59C22⋊(C11⋊C8)—42no—
60C22⋊(C11⋊C8)—42no—
61#8715—111nomaximal, Sylow
62C24×C11—22no—
63C24×C11—22no—
64C24×C11—21no—
65C24×C11—21no—
66C24×C11—22no—
67C24×C11—22no—
68C24×C11—41no—
69C24×C11—41no—
70C24×C11C22⋊C411yescharacteristic
71C24×C11C22⋊C411yescharacteristic
72C24×C11C2×D411yescharacteristic
73C22×C4×C11—22no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—416no—
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11C22⋊C411yescharacteristic
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4114yes—
100C22×Dic11—24no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C22×Dic11—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—42no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C42×C11—42no—
119C42×C11—42no—
120C22⋊Dic11—48no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8—42no—
124#2280D1111yescharacteristic
125#1779—111no—
126C22⋊#95—111no—
127#1294—112no—
128#1294—112no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—24no—
134C23×C11—24no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—44no—
148C23×C11—44no—
149C23×C11—44no—
150C23×C11—44no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—42no—
154C23×C11—42no—
155C23×C11#9912yes—
156C23×C11#10412yes—
157C23×C11C2×C22⋊C411yescharacteristic
158C23×C11#12312yes—
159C23×C11#13512yes—
160C23×C11AGL(1,ℤ/8)11yescharacteristic
161C23×C11#13711yescharacteristic
162C2×C4×C11—28no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—44no—
173C2×C4×C11—44no—
174C2×C4×C11—44no—
175C2×C4×C11—44no—
176C2×C4×C11—44no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11#9912yes—
190C2×C4×C11#11712yes—
191C2×C4×C11#12312yes—
192C2×Dic11—44no—
193C2×Dic11—44no—
194C2×Dic11—44no—
195C2×Dic11—82no—
196C2×Dic11—82no—
197C2×Dic11—82no—
198C2×Dic11—82no—
199C11⋊C8—82no—
200C24×C4C2×D1111yescharacteristic
201C2×#117Dic1111yescharacteristic, complemented
202C2×#117Dic1111yescharacteristic, complemented
203C22×C22⋊C4—221no—
204C2×C22⋊C8—112no—
205C2×C22⋊C8—221no—
206C2×C22⋊C8—221no—
207#381—21no—
208#380Dic1111yescharacteristic, complemented
209#380Dic1111yescharacteristic, complemented
210#380C2×D1111yescharacteristic
211#380C2×D1111yescharacteristic
212#379—21no—
213C4×C22⋊C4—21no—
214C4×C22⋊C4—21no—
215C2×#95—112no—
216C2×#95—221no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—22no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—48no—
232C22×C11—48no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11#38111yescharacteristic
242C22×C11C2×#9911yescharacteristic
243C22×C11C2×#9911yescharacteristic
244C22×C11#41611yescharacteristic
245C22×C11#41711yescharacteristic
246C22×C11C2×#10411yescharacteristic
247C22×C11#42111yescharacteristic
248C22×C11#48212yes—
249C22×C11#48512yes—
250C4×C11—22no—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—41no—
254C4×C11—81no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11—81no—
258Dic11—84no—
259C25C22⋊D1111yescharacteristic
260C23×C4—24no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—222no—
264C23×C4C2×Dic1111yescharacteristic
265C23×C4C2×Dic1111yescharacteristic
266C23×C4C22⋊D1111yescharacteristic
267C23×C4C22⋊D1111yescharacteristic
268C23×C4C22⋊D1111yescharacteristic
269C23×C4C22×D1111yescharacteristic
270C22×C8—222no—
271#117—42no—
272#117—42no—
273C2×C4⋊C4C2×Dic1111yescharacteristic
274C2×C4⋊C4C2×Dic1111yescharacteristic
275C2×C4⋊C4C2×Dic1111yescharacteristic
276C2×C4⋊C4C2×Dic1111yescharacteristic
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—224no—
284C2×C22⋊C4—442no—
285C2×C22⋊C4—442no—
286C2×C42—21no—
287C2×C42—21no—
288C22⋊C8—224no—
289C22⋊C8—442no—
290C22⋊C8—442no—
291#95—21no—
292#95—21no—
293#95—21no—
294#95—21no—
295#95—224no—
296#95—442no—
297C2×C11—22no—
298C2×C11—22no—
299C2×C11—42no—
300C2×C11—42no—
301C2×C11#150111yescharacteristic
302C2×C11#150411yescharacteristic
303C2×C11#151311yescharacteristic
304C2×C11#151611yescharacteristic
305C2×C11#181911yescharacteristic
306C2×C11#182511yescharacteristic
307C2×C11#182611yescharacteristic
308C24—22no—
309C24—22no—
310C24—21no—
311C24—21no—
312C24—22no—
313C24—22no—
314C24—41no—
315C24—41no—
316C24C22⋊Dic1111yescharacteristic
317C24C22⋊Dic1111yescharacteristic
318C24C2×C22⋊D1111yescharacteristic
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—416no—
341C22×C4—224no—
342C22×C4—442no—
343C22×C4—442no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4C22⋊Dic1111yescharacteristic
349C22×C4C22⋊Dic1111yescharacteristic
350C22×C4#433914yes—
351C22×C4C22×Dic1111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353C2×C8—442no—
354C2×C8—442no—
355C2×C8—442no—
356C4⋊C4—41no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—41no—
360C22⋊C4—42no—
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—42no—
364C22⋊C4—41no—
365C22⋊C4—42no—
366C22⋊C4—41no—
367C22⋊C4—448no—
368C42—42no—
369C42—42no—
370C11#871511yescharacteristic, complemented, Sylow
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—24no—
376C23—24no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—44no—
390C23—44no—
391C23—44no—
392C23—44no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23#6689812yes—
398C23#6690112yes—
399C23#6698212yes—
400C23#6700211yescharacteristic
401C23#6700312yes—
402C23#6700411yescharacteristic
403C23C2×C22⋊Dic1111yescharacteristic
404C2×C4—28no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—444no—
432C2×C4—444no—
433C2×C4—444no—
434C2×C4—882no—
435C2×C4—882no—
436C2×C4—882no—
437C2×C4—882no—
438C2×C4#6689812yes—
439C2×C4#6697912yes—
440C2×C4#6698212yes—
441C8—882no—
442C22—22no—
443C22—21no—
444C22—21no—
445C22—22no—
446C22—21no—
447C22—21no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—48no—
457C22—48no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22#1062260912yes—
467C22#1062261612yes—
468C22#1062282411yescharacteristic
469C22C2×#6689811yescharacteristic
470C22C2×#6689811yescharacteristic
471C22#1062284511yescharacteristic
472C22#1062284611yescharacteristic
473C22C2×#6690111yescharacteristic
474C22#1062284911yescharacteristic
475C4—22no—
476C4—22no—
477C4—22no—
478C4—41no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—884no—
484C2—22no—
485C2—22no—
486C2—42no—
487C2—42no—
488C2#1306710711yescharacteristic
489C2#1306712011yescharacteristic
490C2#1306715911yescharacteristic
491C2#1306717211yescharacteristic
492C2#1306869011yescharacteristic
493C2#1306871111yescharacteristic
494C2#1306871511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2280C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#2280D11
hypocenterC11#8715
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2280

Complements

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

NH ≅ G/Ntype
3. #13066494C2semidirect
4. #13066494C2semidirect
7. C2×C11×#117C4semidirect
8. C2×C11×#117C4semidirect
11. C11×#380C4semidirect
12. C11×#380C4semidirect
201. C2×#117Dic11semidirect
202. C2×#117Dic11semidirect
208. #380Dic11semidirect
209. #380Dic11semidirect
370. C11#8715semidirect

Maximal subgroups

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

subgroupindex
#130685262
#130668392
#130664942
C11×#22802
#871511