Finite Group Databasebeta

← #14647751

Subgroups — #14647751

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#13071230C211yesmaximal, characteristic
2#13068806C212yesmaximal, complemented
3#13066861C211yesmaximal, characteristic
4#13066496C212yesmaximal, complemented
5C2×C11×#323C211yesmaximal, characteristic
6C22×C11×C22⋊C4C2211yescharacteristic
7C22×C22⋊Dic11—21no—
8C22×C22⋊Dic11—21no—
9C22×C4⋊Dic11C2211yescharacteristic
10C2×C11×C22⋊C8C2212yes—
11#10622825—21no—
12#10622825C2212yes—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2211yescharacteristic
15C2×#66882—22no—
16#10622563—22no—
17#10622563—22no—
18C11×#323C414yescomplemented
19#10622189—22no—
20C25×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—21no—
24C23×Dic11—21no—
25C23×Dic11—21no—
26C23×Dic11—21no—
27C22×C8×C11—22no—
28C2×C11×C22⋊C4—22no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4C2×C412yes—
31C2×C11×C22⋊C4Q812yes—
32C2×C22⋊Dic11—22no—
33C2×C22⋊Dic11—22no—
34C2×C22⋊Dic11—42no—
35C2×C22⋊Dic11—42no—
36C2×C22⋊Dic11—42no—
37C2×C22⋊Dic11—42no—
38C2×C22⋊Dic11—42no—
39C2×C4⋊Dic11—22no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—42no—
43C2×C4⋊Dic11D412yes—
44C2×C4⋊Dic11D412yes—
45C11×C22⋊C8—22no—
46C11×C22⋊C8C2×C414yescomplemented
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—22no—
50C11⋊#95—42no—
51#66882—44no—
52#8853—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×C11D812yes—
63C24×C11Q1612yes—
64C24×C11C2×D411yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—41no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11—41no—
71C22×C4×C11C4⋊C412yes—
72C22×C4×C11C22×C411yescharacteristic
73C22×C4×C11C2×D412yes—
74C22×C4×C11C2×Q811yescharacteristic
75C22×C4×C11#4112yes—
76C22×Dic11—22no—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C22×Dic11—41no—
81C22×Dic11—41no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11—42no—
85C22×Dic11—42no—
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—81no—
95C22×Dic11—81no—
96C22×Dic11—81no—
97C22×Dic11—81no—
98C2×C8×C11—24no—
99C2×C8×C11—42no—
100C2×C8×C11—42no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C22⋊Dic11—44no—
104C22⋊Dic11—48no—
105C22⋊Dic11—42no—
106C22⋊Dic11—42no—
107C4⋊Dic11—24no—
108C4⋊Dic11—42no—
109C4⋊Dic11—42no—
110C4⋊Dic11—42no—
111C4⋊Dic11—81no—
112C4⋊Dic11—81no—
113#2315—111no—
114#1852—112no—
115C2×#323D1111yescharacteristic
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#10714yescomplemented
145C23×C11C2×C4⋊C411yescharacteristic
146C23×C11#12011yescharacteristic
147C23×C11#12311yescharacteristic
148C23×C11C2×D811yescharacteristic
149C23×C11C2×Q1611yescharacteristic
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—81no—
162C2×C4×C11C4×D412yes—
163C2×C4×C11C22⋊Q812yes—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—81no—
177C2×Dic11—81no—
178C2×Dic11—81no—
179C2×Dic11—81no—
180C2×Dic11—81no—
181C2×Dic11—84no—
182C2×Dic11—84no—
183C2×Dic11—81no—
184C2×Dic11—81no—
185C2×Dic11—81no—
186C8×C11—44no—
187C22×C4⋊C4—111no—
188C22×C22⋊C4—221no—
189C22×C22⋊C4—221no—
190C22×C22⋊C4C2×D1111yescharacteristic
191C2×#107—222no—
192C2×C22⋊C8C2×D1112yes—
193#385—222no—
194#385—222no—
195#380—112no—
196#380—221no—
197C2×#95—111no—
198C2×#95—221no—
199#340—222no—
200#323Dic1114yescomplemented
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×#10711yescharacteristic
226C22×C11#42811yescharacteristic
227C22×C11#44711yescharacteristic
228C22×C11#45111yescharacteristic
229C22×C11#45311yescharacteristic
230C22×C11#45511yescharacteristic
231C22×C11B(4,𝔽2)11yescharacteristic
232C22×C11#45811yescharacteristic
233C22×C11#48011yescharacteristic
234C22×C11#48411yescharacteristic
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—42no—
238Dic11—82no—
239Dic11—82no—
240Dic11—82no—
241Dic11—82no—
242C25D4411yescharacteristic
243C23×C4—221no—
244C23×C4—221no—
245C23×C4—221no—
246C23×C4—221no—
247C23×C4D4411yescharacteristic
248C23×C4C22×D1111yescharacteristic
249C22×C8—22no—
250C2×C4⋊C4—112no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—222no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—442no—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—222no—
259C2×C22⋊C4—222no—
260C2×C22⋊C4—442no—
261C2×C22⋊C4—442no—
262C2×C22⋊C4—442no—
263C2×C22⋊C4—442no—
264C2×C22⋊C4—442no—
265C2×C22⋊C4Dic2212yes—
266C2×C22⋊C4C2×Dic1112yes—
267#107—444no—
268C22⋊C8—22no—
269C22⋊C8C2×Dic1114yescomplemented
270#95—222no—
271#95—222no—
272#95—222no—
273#95—442no—
274C2×C11—21no—
275C2×C11—21no—
276C2×C11—21no—
277C2×C11—21no—
278C2×C11—44no—
279C2×C11#159511yescharacteristic
280C2×C11#160211yescharacteristic
281C2×C11#160711yescharacteristic
282C2×C11#161411yescharacteristic
283C2×C11#185211yescharacteristic
284C2×C11#185611yescharacteristic
285C2×C11#186711yescharacteristic
286C24—21no—
287C24—21no—
288C24—21no—
289C24—21no—
290C24—41no—
291C24—41no—
292C24—41no—
293C24—41no—
294C24D8812yes—
295C24Dic4412yes—
296C24C4⋊Dic1112yes—
297C24C2×D4411yescharacteristic
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—222no—
305C22×C4—222no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—441no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—441no—
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—881no—
323C22×C4—881no—
324C22×C4—881no—
325C22×C4—881no—
326C22×C4C4⋊Dic1112yes—
327C22×C4C2×Dic2211yescharacteristic
328C22×C4D4×D1112yes—
329C22×C4#434112yes—
330C22×C4C22×Dic1111yescharacteristic
331C2×C8—24no—
332C2×C8—42no—
333C2×C8—42no—
334C4⋊C4—224no—
335C4⋊C4—442no—
336C4⋊C4—442no—
337C4⋊C4—442no—
338C4⋊C4—881no—
339C4⋊C4—881no—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—444no—
343C22⋊C4—448no—
344C22⋊C4—442no—
345C22⋊C4—442no—
346C11#885311yescharacteristic, 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#6688214yescomplemented
374C23#6693511yescharacteristic
375C23#6693911yescharacteristic
376C23C2×D8811yescharacteristic
377C23C2×Dic4411yescharacteristic
378C23#6696111yescharacteristic
379C23#6696211yescharacteristic
380C23C2×C4⋊Dic1111yescharacteristic
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—81no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4—442no—
403C2×C4—881no—
404C2×C4—881no—
405C2×C4—881no—
406C2×C4—881no—
407C2×C4—881no—
408C2×C4—884no—
409C2×C4—884no—
410C2×C4—881no—
411C2×C4—881no—
412C2×C4—881no—
413C2×C4#6693112yes—
414C2×C4D4×Dic1112yes—
415C8—44no—
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—
439C22#1062233511yescharacteristic
440C22#1062234511yescharacteristic
441C22#1062234911yescharacteristic
442C22#1062235211yescharacteristic
443C22#1062235411yescharacteristic
444C22#1062235511yescharacteristic
445C22#1062235911yescharacteristic
446C22#1062236011yescharacteristic
447C22#1062256311yescharacteristic
448C22C2×#6688211yescharacteristic
449C22#1062273411yescharacteristic
450C4—22no—
451C4—22no—
452C4—42no—
453C4—882no—
454C4—882no—
455C4—882no—
456C4—882no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—44no—
462C2#1306753611yescharacteristic
463C2#1306757511yescharacteristic
464C2#1306760411yescharacteristic
465C2#1306764311yescharacteristic
466C2#1306880611yescharacteristic
467C2#1306882811yescharacteristic
468C2#1306889911yescharacteristic
subgroupG/H
centerC23#66935
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#323C2
socleC23×C11#120
prime radicalC25×C11D4
cosocleC23×C4×C11C23
hypercenterC2×#323D11
hypocenterC11#8853
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. #13068806C2semidirect
4. #13066496C2semidirect
18. C11×#323C4semidirect
46. C11×C22⋊C8C2×C4semidirect
144. C23×C11#107semidirect
200. #323Dic11semidirect
269. C22⋊C8C2×Dic11semidirect
346. C11#8853semidirect
373. C23#66882semidirect

Maximal subgroups

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

subgroupindex
#130712302
#130688062
#130668612
#130664962
C2×C11×#3232
#885311