Finite Group Databasebeta

← #14647754

Subgroups — #14647754

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068808C212yesmaximal, complemented
2C2×#10622163C211yesmaximal, characteristic
3#13066861C211yesmaximal, characteristic
4#13066494C212yesmaximal, complemented
5C11×#2315C211yesmaximal, characteristic
6C22×C11×C22⋊C4—21no—
7C22×C11×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic11—21no—
9C22×C4⋊Dic11C2211yescharacteristic
10C11×#385—22no—
11C11×#385—22no—
12C11×#380—21no—
13C11×#380C2212yes—
14C2×C11⋊#95—21no—
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2212yes—
17C2×#66872—22no—
18#10622167—22no—
19#10622163C414yescomplemented
20C25×C11D411yescharacteristic
21C23×C4×C11—21no—
22C23×C4×C11—21no—
23C23×C4×C11D411yescharacteristic
24C23×C4×C11C2311yescharacteristic
25C23×Dic11—21no—
26C23×Dic11—21no—
27C2×C11×C4⋊C4—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4D412yes—
30C2×C11×C4⋊C4D412yes—
31C2×C11×C22⋊C4—22no—
32C2×C11×C22⋊C4—22no—
33C2×C11×C22⋊C4—22no—
34C2×C11×C22⋊C4—22no—
35C2×C11×C22⋊C4—42no—
36C2×C11×C22⋊C4—42no—
37C2×C11×C22⋊C4C2×C412yes—
38C2×C11×C22⋊C4Q812yes—
39C2×C22⋊Dic11—42no—
40C2×C22⋊Dic11—42no—
41C2×C22⋊Dic11—42no—
42C2×C4⋊Dic11—22no—
43C2×C4⋊Dic11—42no—
44C22×C11⋊C8—22no—
45C11×#95—22no—
46C11×#95—22no—
47C11⋊#95—22no—
48C11⋊#95—42no—
49C22⋊(C11⋊C8)—22no—
50C22⋊(C11⋊C8)C2×C414yescomplemented
51#66872—44no—
52#8854—111nomaximal, Sylow
53C24×C11—21no—
54C24×C11—21no—
55C24×C11—21no—
56C24×C11—21no—
57C24×C11—41no—
58C24×C11—41no—
59C24×C11—41no—
60C24×C11—41no—
61C24×C11C4⋊C412yes—
62C24×C11SD1612yes—
63C24×C11SD1612yes—
64C24×C11C2×D411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—42no—
74C22×C4×C11—42no—
75C22×C4×C11—81no—
76C22×C4×C11—81no—
77C22×C4×C11—81no—
78C22×C4×C11—81no—
79C22×C4×C11C4⋊C412yes—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11#4112yes—
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11—41no—
87C22×Dic11—41no—
88C22×Dic11—41no—
89C22×Dic11—41no—
90C22×Dic11—41no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11—41no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C11×C4⋊C4—42no—
99C11×C4⋊C4—42no—
100C11×C4⋊C4—81no—
101C11×C4⋊C4—81no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C11×C22⋊C4—44no—
105C11×C22⋊C4—42no—
106C11×C22⋊C4—42no—
107C22⋊Dic11—48no—
108C4⋊Dic11—24no—
109C4⋊Dic11—42no—
110C2×C11⋊C8—24no—
111C2×C11⋊C8—42no—
112C2×C11⋊C8—42no—
113#2315D1111yescharacteristic
114#1853—112no—
115C2×#323—111no—
116#1439—111no—
117#1294—112no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—22no—
123C23×C11—22no—
124C23×C11—22no—
125C23×C11—22no—
126C23×C11—22no—
127C23×C11—22no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—81no—
139C23×C11—81no—
140C23×C11—81no—
141C23×C11—81no—
142C23×C11—81no—
143C23×C11—81no—
144C23×C11#10614yescomplemented
145C23×C11C2×C4⋊C411yescharacteristic
146C23×C11#12011yescharacteristic
147C23×C11#12311yescharacteristic
148C23×C11C2×SD1611yescharacteristic
149C23×C11C2×SD1611yescharacteristic
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C23×C11#13711yescharacteristic
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—81no—
168C2×C4×C11—84no—
169C2×C4×C11—84no—
170C2×C4×C11C4×D412yes—
171C2×C4×C11C22⋊Q812yes—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11—81no—
182C2×Dic11—81no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C11⋊C8—44no—
187C22×C4⋊C4—111no—
188C22×C22⋊C4—21no—
189C22×C22⋊C4—221no—
190C22×C22⋊C4C2×D1111yescharacteristic
191C2×#106—222no—
192C2×C22⋊C8—112no—
193#385—22no—
194#385—22no—
195#380—21no—
196#380C2×D1112yes—
197C2×#95—111no—
198C2×#95—221no—
199#340—222no—
200#323—114no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—21no—
205C22×C11—21no—
206C22×C11—21no—
207C22×C11—21no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—24no—
214C22×C11—44no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—42no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—82no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11#38511yescharacteristic
225C22×C11C2×#10611yescharacteristic
226C22×C11#42811yescharacteristic
227C22×C11#44811yescharacteristic
228C22×C11#45011yescharacteristic
229C22×C11#45311yescharacteristic
230C22×C11#45511yescharacteristic
231C22×C11B(4,𝔽2)11yescharacteristic
232C22×C11#45811yescharacteristic
233C22×C11#48111yescharacteristic
234C22×C11#48311yescharacteristic
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—42no—
238C4×C11—82no—
239C4×C11—82no—
240Dic11—82no—
241Dic11—82no—
242C25C22⋊D1111yescharacteristic
243C23×C4—21no—
244C23×C4—21no—
245C23×C4—221no—
246C23×C4—221no—
247C23×C4C22⋊D1111yescharacteristic
248C23×C4C22×D1111yescharacteristic
249C22×C8—222no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4—442no—
254C2×C4⋊C4C22⋊D1112yes—
255C2×C4⋊C4C22⋊D1112yes—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—42no—
261C2×C22⋊C4—42no—
262C2×C22⋊C4—442no—
263C2×C22⋊C4—442no—
264C2×C22⋊C4—442no—
265C2×C22⋊C4Dic2212yes—
266C2×C22⋊C4C4×D1112yes—
267#106—444no—
268C22⋊C8—114no—
269C22⋊C8—222no—
270#95—22no—
271#95—22no—
272#95—222no—
273#95—442no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—44no—
279C2×C11#159611yescharacteristic
280C2×C11#160111yescharacteristic
281C2×C11#160811yescharacteristic
282C2×C11#161311yescharacteristic
283C2×C11#185311yescharacteristic
284C2×C11#185611yescharacteristic
285C2×C11#186711yescharacteristic
286C24—21no—
287C24—21no—
288C24—21no—
289C24—21no—
290C24—41no—
291C24—41no—
292C24—41no—
293C24—41no—
294C24Dic11⋊C412yes—
295C24#432412yes—
296C24#432512yes—
297C24C2×C22⋊D1111yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—81no—
309C22×C4—81no—
310C22×C4—81no—
311C22×C4—81no—
312C22×C4—222no—
313C22×C4—222no—
314C22×C4—441no—
315C22×C4—441no—
316C22×C4—441no—
317C22×C4—441no—
318C22×C4—441no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4Dic11⋊C412yes—
327C22×C4C2×Dic2211yescharacteristic
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4#433912yes—
330C22×C4C2×C22⋊D1112yes—
331C2×C8—224no—
332C2×C8—442no—
333C2×C8—442no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—81no—
337C4⋊C4—81no—
338C4⋊C4—224no—
339C4⋊C4—442no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—44no—
343C22⋊C4—42no—
344C22⋊C4—42no—
345C22⋊C4—448no—
346C11#885411yescharacteristic, complemented, Sylow
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—22no—
356C23—22no—
357C23—42no—
358C23—42no—
359C23—42no—
360C23—42no—
361C23—42no—
362C23—42no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—81no—
368C23—81no—
369C23—81no—
370C23—81no—
371C23—81no—
372C23—81no—
373C23#6687214yescomplemented
374C23C2×Dic11⋊C411yescharacteristic
375C23#6698211yescharacteristic
376C23#6698511yescharacteristic
377C23C2×#432411yescharacteristic
378C23C2×#432511yescharacteristic
379C23#6699511yescharacteristic
380C23#6700611yescharacteristic
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—81no—
397C2×C4—84no—
398C2×C4—84no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4—881no—
411C2×C4—881no—
412C2×C4—881no—
413C2×C4#6697712yes—
414C2×C4C4×C22⋊D1112yes—
415C8—444no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—24no—
429C22—44no—
430C22—42no—
431C22—42no—
432C22—42no—
433C22—42no—
434C22—42no—
435C22—42no—
436C22—82no—
437C22—82no—
438C22—82no—
439C22C2×#6687211yescharacteristic
440C22#1062257711yescharacteristic
441C22#1062258111yescharacteristic
442C22#1062258411yescharacteristic
443C22#1062282311yescharacteristic
444C22#1062283111yescharacteristic
445C22#1062284011yescharacteristic
446C22#1062285411yescharacteristic
447C22#1062285511yescharacteristic
448C22#1062285611yescharacteristic
449C22#1062285711yescharacteristic
450C4—22no—
451C4—22no—
452C4—42no—
453C4—82no—
454C4—82no—
455C4—882no—
456C4—882no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—44no—
462C2#1306753911yescharacteristic
463C2#1306756811yescharacteristic
464C2#1306760711yescharacteristic
465C2#1306763611yescharacteristic
466C2#1306880911yescharacteristic
467C2#1306882611yescharacteristic
468C2#1306889711yescharacteristic
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2315C2
socleC23×C11#120
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenter#2315D11
hypocenterC11#8854
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2315

Complements

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

NH ≅ G/Ntype
1. #13068808C2semidirect
4. #13066494C2semidirect
19. #10622163C4semidirect
50. C22⋊(C11⋊C8)C2×C4semidirect
144. C23×C11#106semidirect
346. C11#8854semidirect
373. C23#66872semidirect

Maximal subgroups

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

subgroupindex
#130688082
C2×#106221632
#130668612
#130664942
C11×#23152
#885411