Finite Group Databasebeta

← #14642015

Subgroups — #14642015

Order 2816.

730 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071106C211yesmaximal, characteristic
2#13068310C211yesmaximal, characteristic, complemented
3#13066441C212yesmaximal, complemented
4#13066436C212yesmaximal, complemented
5C11×#1728C211yesmaximal, characteristic, complemented
6C22×#4339C411yescharacteristic
7C22×C11×M16—21no—
8C22×C42×C11C2211yescharacteristic
9C2×#66979C411yescharacteristic
10C22×#4318—21no—
11#10622826—21no—
12#10622826—21no—
13#10622552C411yescharacteristic
14#10622552C2211yescharacteristic
15C4×(C2×D11)⋊C4—21no—
16C4×(C2×D11)⋊C4—21no—
17#10622542C411yescharacteristic
18#10622542C2211yescharacteristic
19C11×#336—21no—
20C11×#336C2212yes—
21#10622162—21no—
22#10622162C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C2×#4339—22no—
28C2×#4339—22no—
29C2×#4339—42no—
30C2×#4339—42no—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22C2×C411yescharacteristic
34C2×C11×M16—24no—
35C2×C11×M16—42no—
36C2×C11×M16—42no—
37C22×C8×C11—22no—
38C2×C42×C11—42no—
39C2×C42×C11C2×C411yescharacteristic
40C2×C42×C11D411yescharacteristic
41C2×C42×C11D411yescharacteristic
42C2×C42×C11C2311yescharacteristic
43C2×C22⋊Dic11—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48#66979—42no—
49C2×C4⋊Dic11C2×C411yescharacteristic
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4×Dic11—21no—
52C2×#4318—24no—
53C2×#4318—42no—
54C2×#4318—42no—
55C22×C11⋊C8—22no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60#7631—111nomaximal, Sylow
61C24×C11C22⋊C411yescharacteristic
62C23×D11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—22no—
65C22×C4×C11—22no—
66C22×C4×C11—22no—
67C22×C4×C11—22no—
68C22×C4×C11—22no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22×C411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C2×C22⋊D11—24no—
82C2×C22⋊D11—42no—
83C2×C22⋊D11—42no—
84C22×Dic11—21no—
85C22×Dic11—21no—
86C22×Dic11—21no—
87#4339—48no—
88#4339—48no—
89C2×D44—21no—
90C2×D44—41no—
91C2×D44—41no—
92C2×D44M1612yescomplemented
93C2×C4×D11—24no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×Dic22—21no—
97C2×Dic22—41no—
98C2×Dic22—41no—
99C2×Dic22M1612yescomplemented
100C11×M16—48no—
101C2×C8×C11—24no—
102C2×C8×C11—42no—
103C2×C8×C11—42no—
104C42×C11—41no—
105C42×C11—41no—
106C42×C11—41no—
107C42×C11—41no—
108C22⋊Dic11—42no—
109(C2×D11)⋊C4—42no—
110(C2×D11)⋊C4—42no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4×Dic11—42no—
118#4318—48no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—42no—
122#2297—111no—
123#1728—111no—
124#1728D1111yescharacteristic, complemented
125#1272—112no—
126#1270—112no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11#9912yes—
134C23×C11C2×C22⋊C411yescharacteristic
135C22×D11—22no—
136C22×D11—41no—
137C22×D11—41no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—24no—
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#10012yes—
161C2×C4×C11#10412yes—
162C2×C4×C11#10412yes—
163C2×C4×C11C2×M1611yescharacteristic
164C2×C4×C11C2×M1611yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11#13711yescharacteristic
168C2×C4×C11#13711yescharacteristic
169C22⋊D11—48no—
170C2×Dic11—22no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179D44—42no—
180D44—42no—
181C4×D11—48no—
182Dic22—42no—
183Dic22—42no—
184C8×C11—44no—
185C11⋊C8—44no—
186C22×#41—111no—
187C22×M16—21no—
188C22×M16—221no—
189C2×#117—111no—
190C22×C42C2×D1111yescharacteristic
191#391—111no—
192#391—111no—
193#390—111no—
194#390—111no—
195#386—221no—
196#386—221no—
197C4×C22⋊C4—221no—
198C4×C22⋊C4—221no—
199#336—21no—
200#336—112no—
201#336—221no—
202#336C2×D1112yes—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11#40711yescharacteristic
211C22×C11C2×#9911yescharacteristic
212C22×C11C2×#10011yescharacteristic
213C22×C11#41711yescharacteristic
214C22×C11#41711yescharacteristic
215C22×C11C2×#10411yescharacteristic
216C22×C11C2×#10411yescharacteristic
217C2×D11—42no—
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—81no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—81no—
224C4×C11—22no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—22no—
228C4×C11—22no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233Dic11—42no—
234Dic11—81no—
235Dic11—81no—
236C2×#41—222no—
237C2×#41—222no—
238C2×#41—442no—
239C2×#41—442no—
240C22×Q8—111no—
241C22×D4—111no—
242C22×D4—221no—
243C23×C4—221no—
244C23×C4C4×D1111yescharacteristic
245C23×C4D4411yescharacteristic
246C23×C4C22⋊D1111yescharacteristic
247C2×M16—24no—
248C2×M16—42no—
249C2×M16—42no—
250C2×M16—224no—
251C2×M16—442no—
252C2×M16—442no—
253C22×C8—22no—
254C22×C8—222no—
255#117—442no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C42—42no—
264C2×C42—221no—
265C2×C42C4×D1111yescharacteristic
266C2×C42D4411yescharacteristic
267C2×C42C22⋊D1111yescharacteristic
268C2×C42C22×D1111yescharacteristic
269#95—221no—
270#95—221no—
271#95—221no—
272#95—221no—
273C2×C11—42no—
274C2×C11#146211yescharacteristic
275C2×C11#148911yescharacteristic
276C2×C11#148911yescharacteristic
277C2×C11#150411yescharacteristic
278C2×C11#150411yescharacteristic
279C2×C11#152511yescharacteristic
280C2×C11#156011yescharacteristic
281D11—82no—
282C24—221no—
283C24(C2×D11)⋊C411yescharacteristic
284#41—448no—
285#41—448no—
286C2×Q8—112no—
287C2×Q8—221no—
288C2×Q8—441no—
289C2×Q8—441no—
290C2×D4—112no—
291C2×D4—224no—
292C2×D4—221no—
293C2×D4—441no—
294C2×D4—441no—
295C2×D4—442no—
296C2×D4—442no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—224no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4(C2×D11)⋊C411yescharacteristic
316C22×C4(C2×D11)⋊C411yescharacteristic
317C22×C4(C2×D11)⋊C411yescharacteristic
318C22×C4C2×C4×D1111yescharacteristic
319C22×C4C2×D4411yescharacteristic
320C22×C4C2×C22⋊D1111yescharacteristic
321M16—48no—
322M16—448no—
323C2×C8—24no—
324C2×C8—42no—
325C2×C8—42no—
326C2×C8—224no—
327C2×C8—442no—
328C2×C8—442no—
329C4⋊C4—441no—
330C4⋊C4—441no—
331C22⋊C4—442no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C22⋊C4—441no—
338C42—41no—
339C42—41no—
340C42—41no—
341C42—41no—
342C42—442no—
343C11#763111yescharacteristic, complemented, Sylow
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—222no—
351C23—441no—
352C23—441no—
353C23—441no—
354C23—441no—
355C23—441no—
356C23—441no—
357C23#6687012yes—
358C23C2×(C2×D11)⋊C411yescharacteristic
359Q8—442no—
360Q8—442no—
361D4—442no—
362D4—442no—
363D4—448no—
364C2×C4—24no—
365C2×C4—24no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—24no—
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—222no—
383C2×C4—448no—
384C2×C4—441no—
385C2×C4—441no—
386C2×C4—441no—
387C2×C4—441no—
388C2×C4—441no—
389C2×C4—441no—
390C2×C4—441no—
391C2×C4—441no—
392C2×C4#6686912yes—
393C2×C4#6688712yes—
394C2×C4#6688912yes—
395C2×C4M16×D1111yescharacteristic
396C2×C4M16×D1111yescharacteristic
397C2×C4#6696111yescharacteristic
398C2×C4#6696211yescharacteristic
399C2×C4#6698511yescharacteristic
400C2×C4#6699511yescharacteristic
401C8—44no—
402C8—444no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—442no—
411C22—442no—
412C22—442no—
413C22—881no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22C2×#6686911yescharacteristic
418C22C2×#6687011yescharacteristic
419C22#1062257911yescharacteristic
420C22#1062273911yescharacteristic
421C22C2×#6688711yescharacteristic
422C22#1062274611yescharacteristic
423C22C2×#6688911yescharacteristic
424C4—21no—
425C4—22no—
426C4—21no—
427C4—21no—
428C4—22no—
429C4—21no—
430C4—22no—
431C4—21no—
432C4—21no—
433C4—442no—
434C4—881no—
435C4—881no—
436C2—42no—
437C2—882no—
438C2#1306694211yescharacteristic
439C2#1306705311yescharacteristic
440C2#1306705611yescharacteristic
441C2#1306711811yescharacteristic
442C2#1306712111yescharacteristic
443C2#1306720711yescharacteristic
444C2#1306734911yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1728C2
socleC23×C11C2×C22⋊C4
prime radicalC22×#4339C4
cosocleC2×C42×C11C23
hypercenter#1728D11
hypocenterC11#7631
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
2. #13068310C2semidirect
3. #13066441C2semidirect
4. #13066436C2semidirect
5. C11×#1728C2semidirect
92. C2×D44M16semidirect
99. C2×Dic22M16semidirect
124. #1728D11semidirect
343. C11#7631semidirect

Maximal subgroups

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

subgroupindex
#130711062
#130683102
#130664412
#130664362
C11×#17282
#763111