Finite Group Databasebeta

← #14649549

Subgroups — #14649549

Order 2816.

1024 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622825C211yesmaximal, characteristic, complemented
2#13068526C211yesmaximal, characteristic, complemented
3C2×#10622175C212yesmaximal, complemented
4#13066494C212yesmaximal, complemented
5C11×#2847C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×#121C412yescomplemented
8C2×C11×#121C2211yescharacteristic
9C2×C11×#120—21no—
10C22×C22⋊Dic11—21no—
11C22×C4⋊Dic11—21no—
12C11×#386—21no—
13C11×#386—22no—
14C11×#380C412yescomplemented
15C11×#380C2211yescharacteristic
16#10622825—24no—
17C2×C11⋊#95C2212yes—
18C2×C22⋊(C11⋊C8)—22no—
19C2×C22⋊(C11⋊C8)C2212yes—
20#10622175—24no—
21C25×C11D411yescharacteristic
22C22×D4×C11—22no—
23C22×D4×C11—21no—
24C22×D4×C11C2×C411yescharacteristic
25C23×C4×C11—22no—
26C23×C4×C11—22no—
27C23×C4×C11—44no—
28C23×C4×C11C2×C412yes—
29C23×C4×C11D411yescharacteristic
30C23×C4×C11D412yes—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—22no—
33C11×#121—22no—
34C11×#121—22no—
35C11×#121—44no—
36C11×#120—42no—
37C11×#120—42no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C412yes—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—22no—
43C2×C11×C22⋊C4—21no—
44C2×C22⋊Dic11—24no—
45C2×C22⋊Dic11—42no—
46C2×C22⋊Dic11—42no—
47C2×C4⋊Dic11—24no—
48C2×C4⋊Dic11—44no—
49C22×C11⋊C8—22no—
50C11×#95—22no—
51C11×#95—21no—
52C11⋊#95—22no—
53C11⋊#95D414yescomplemented
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)—22no—
56C22⋊(C11⋊C8)—44no—
57#9155—111nomaximal, Sylow
58C24×C11—21no—
59C24×C11—21no—
60C24×C11—21no—
61C24×C11—21no—
62C24×C11—21no—
63C24×C11—42no—
64C24×C11—42no—
65C24×C11C22⋊C412yes—
66C24×C11D812yes—
67C24×C11SD1612yes—
68C24×C11C2×D411yescharacteristic
69C2×D4×C11—22no—
70C2×D4×C11—42no—
71C2×D4×C11—44no—
72C2×D4×C11—44no—
73C2×D4×C11—44no—
74C2×D4×C11—41no—
75C2×D4×C11—41no—
76C2×D4×C11—41no—
77C2×D4×C11—41no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—24no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—24no—
86C22×C4×C11—24no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—42no—
90C22×C4×C11—42no—
91C22×C4×C11—42no—
92C22×C4×C11—48no—
93C22×C4×C11—48no—
94C22×C4×C11C22⋊C412yes—
95C22×C4×C11C22×C411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D412yes—
98C22×C4×C11#4112yes—
99C22×Dic11—24no—
100C22×Dic11—44no—
101C22×Dic11—44no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—42no—
106C11×C22⋊C4—44no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—44no—
110C11×C22⋊C4—42no—
111C22⋊Dic11—48no—
112C4⋊Dic11—48no—
113C2×C11⋊C8—44no—
114C2×C11⋊C8—42no—
115#2847D1111yescharacteristic
116C2×#380—111no—
117#1779—111no—
118C2×#327—112no—
119#1294—112no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—44no—
133C23×C11—44no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—44no—
139C23×C11—44no—
140C23×C11—41no—
141C23×C11—42no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—42no—
145C23×C11#10214yes—
146C23×C11C2×C22⋊C411yescharacteristic
147C23×C11#12011yescharacteristic
148C23×C11#12311yescharacteristic
149C23×C11C2×D811yescharacteristic
150C23×C11C2×SD1611yescharacteristic
151C23×C11AGL(1,ℤ/8)11yescharacteristic
152C23×C11#13711yescharacteristic
153D4×C11—82no—
154D4×C11—88no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—24no—
160C2×C4×C11—24no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—48no—
168C2×C4×C11—48no—
169C2×C4×C11—41no—
170C2×C4×C11—42no—
171C2×C4×C11—41no—
172C2×C4×C11—42no—
173C2×C4×C11—41no—
174C2×C4×C11—42no—
175C2×C4×C11#9914yes—
176C2×C4×C11C4×D412yes—
177C2×C4×C11#12112yes—
178C2×Dic11—44no—
179C2×Dic11—44no—
180C2×Dic11—44no—
181C2×Dic11—84no—
182C2×Dic11—84no—
183C11⋊C8—82no—
184C24×C4C2×D1111yescharacteristic
185C2×#121Dic1112yescomplemented
186C2×#121C2×D1111yescharacteristic
187C2×#120—21no—
188C22×C4⋊C4—221no—
189C22×C22⋊C4—221no—
190C2×C22⋊C8—112no—
191C2×C22⋊C8—222no—
192#386—21no—
193#386—22no—
194#380—224no—
195#380Dic1112yescomplemented
196#380C2×D1111yescharacteristic
197C2×#95—112no—
198#327—224no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—24no—
208C22×C11—24no—
209C22×C11—24no—
210C22×C11—44no—
211C22×C11—44no—
212C22×C11—44no—
213C22×C11—44no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11#38611yescharacteristic
224C22×C11C2×#9912yes—
225C22×C11C2×#10211yescharacteristic
226C22×C11#41711yescharacteristic
227C22×C11#42112yes—
228C22×C11#44711yescharacteristic
229C22×C11#44811yescharacteristic
230C22×C11#48011yescharacteristic
231C22×C11#48111yescharacteristic
232C4×C11—24no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—81no—
236C4×C11—82no—
237Dic11—84no—
238C25C22⋊D1111yescharacteristic
239C22×D4—22no—
240C22×D4—21no—
241C22×D4C2×Dic1111yescharacteristic
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—44no—
245C23×C4—222no—
246C23×C4C2×Dic1112yes—
247C23×C4C22⋊D1111yescharacteristic
248C23×C4C22⋊D1112yes—
249C23×C4C22×D1111yescharacteristic
250C22×C8—222no—
251#121—22no—
252#121—22no—
253#121—44no—
254#120—42no—
255#120—42no—
256C2×C4⋊C4—224no—
257C2×C4⋊C4—444no—
258C2×C4⋊C4C2×Dic1111yescharacteristic
259C2×C4⋊C4C2×Dic1112yes—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—21no—
264C2×C22⋊C4—224no—
265C2×C22⋊C4—442no—
266C2×C22⋊C4—442no—
267C22⋊C8—222no—
268C22⋊C8—222no—
269C22⋊C8—444no—
270#95—22no—
271#95—21no—
272#95—114no—
273#95—222no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—44no—
279C2×C11—161no—
280C2×C11#151312yes—
281C2×C11#151912yes—
282C2×C11#187411yescharacteristic
283C2×C11#189711yescharacteristic
284C2×C11#189811yescharacteristic
285C24—21no—
286C24—21no—
287C24—21no—
288C24—21no—
289C24—21no—
290C24—42no—
291C24—42no—
292C24#432312yes—
293C24#432412yes—
294C24C22⋊Dic1112yes—
295C24C2×C22⋊D1111yescharacteristic
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—44no—
299C2×D4—44no—
300C2×D4—44no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—48no—
320C22×C4—48no—
321C22×C4—224no—
322C22×C4—444no—
323C22×C4—444no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4C22⋊Dic1112yes—
327C22×C4D4×D1112yes—
328C22×C4#434112yes—
329C22×C4C22×Dic1111yescharacteristic
330C22×C4C2×C22⋊D1111yescharacteristic
331C2×C8—444no—
332C2×C8—442no—
333C4⋊C4—22no—
334C4⋊C4—42no—
335C4⋊C4—448no—
336C22⋊C4—44no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—44no—
340C22⋊C4—42no—
341C22⋊C4—448no—
342C11#915511yescharacteristic, complemented, Sylow
343C23—22no—
344C23—22no—
345C23—22no—
346C23—22no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—44no—
356C23—44no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—44no—
362C23—44no—
363C23—41no—
364C23—42no—
365C23—41no—
366C23—41no—
367C23—42no—
368C23#6689614yes—
369C23C2×#432311yescharacteristic
370C23C2×#432411yescharacteristic
371C23#6698811yescharacteristic
372C23#6699011yescharacteristic
373C23#6700211yescharacteristic
374C23#6700411yescharacteristic
375C23C2×C22⋊Dic1111yescharacteristic
376D4—82no—
377D4—88no—
378D4—81no—
379D4—81no—
380D4—81no—
381D4—81no—
382C2×C4—24no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—48no—
391C2×C4—48no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—444no—
399C2×C4—444no—
400C2×C4—444no—
401C2×C4—884no—
402C2×C4—884no—
403C2×C4#6689814yes—
404C2×C4D4×Dic1112yes—
405C2×C4#6699212yes—
406C8—882no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—22no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—24no—
416C22—24no—
417C22—24no—
418C22—44no—
419C22—44no—
420C22—44no—
421C22—44no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—81no—
427C22—81no—
428C22—81no—
429C22—82no—
430C22—82no—
431C22#1062264611yescharacteristic
432C22#1062264711yescharacteristic
433C22#1062264911yescharacteristic
434C22#1062265311yescharacteristic
435C22C2×#6689611yescharacteristic
436C22C2×#6689812yes—
437C22#1062283311yescharacteristic
438C22#1062284511yescharacteristic
439C22#1062284912yes—
440C4—22no—
441C4—24no—
442C4—22no—
443C4—81no—
444C4—82no—
445C4—884no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2—44no—
451C2—161no—
452C2#1306715912yes—
453C2#1306718412yes—
454C2#1306893411yescharacteristic
455C2#1306906511yescharacteristic
456C2#1306907011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#2847C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenter#2847D11
hypocenterC11#9155
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C2×#10622825C2semidirect
2. #13068526C2semidirect
3. C2×#10622175C2semidirect
4. #13066494C2semidirect
7. C2×C11×#121C4semidirect
14. C11×#380C4semidirect
53. C11⋊#95D4semidirect
185. C2×#121Dic11semidirect
195. #380Dic11semidirect
342. C11#9155semidirect

Maximal subgroups

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

subgroupindex
C2×#106228252
#130685262
C2×#106221752
#130664942
C11×#28472
#915511