Finite Group Databasebeta

← #14811898

Subgroups — #14811898

Order 2816.

786 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
1#13073642C211yesmaximal, characteristic, complemented
2#13071563C211yesmaximal, characteristic
3#13069989C212yesmaximal
4#13069753C212yesmaximal
5#13069563C212yesmaximal, complemented
6#13069380C211yesmaximal, characteristic, complemented
7#13069202C212yesmaximal, complemented
8#13068744C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C2×#66945—21no—
13C2×#66941—21no—
14C2×C4×D44C2211yescharacteristic
15C2×#66922C2212yes—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66885C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66885C2212yes—
23C2×#66881C2212yes—
24#10622600—21no—
25#10622598—21no—
26#10622552C2212yes—
27#10622548C2211yescharacteristic
28#10622548C2211yescharacteristic
29C4×C4⋊Dic11C2211yescharacteristic
30C4×C4⋊Dic11C2212yes—
31#10622541C2212yes—
32#10622283—22no—
33#10622269—22no—
34C11×#336C2212yes—
35#10622189C2212yes—
36#10622189C2212yes—
37#10622189C2211yescharacteristic
38#10622189C2211yescharacteristic
39#10622189C2212yes—
40#10622189C2212yes—
41C22×D44C2311yescharacteristic
42C22×C4×D11—21no—
43C22×Dic22—22no—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C42×C11C2312yes—
50C2×C42×C11C2311yescharacteristic
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—22no—
67#66945—44no—
68#66941—44no—
69C4×D44—22no—
70C4×D44Q814yescomplemented
71#66922—24no—
72#66922—42no—
73C11×C4⋊C8—22no—
74C11×C4⋊C8—42no—
75C4×C8×C11—22no—
76C11×#95D412yes—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80#66885—22no—
81#66885—22no—
82#66885—42no—
83#66881—24no—
84#26024—111nomaximal, Sylow
85C23×D11—21no—
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11C2×D412yes—
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2411yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—22no—
95C22×Dic11—22no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44C2×Q812yes—
102C2×C4×D11—24no—
103C2×C4×D11—42no—
104C2×C4×D11—42no—
105C2×Dic22—44no—
106C2×Dic22—44no—
107C2×Dic22—82no—
108C2×C8×C11—22no—
109C2×C8×C11—21no—
110C2×C8×C11—21no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4SD1614yes—
119C42×C11—22no—
120C42×C11—22no—
121C42×C11C2×Q812yes—
122C42×C11#4112yes—
123(C2×D11)⋊C4—24no—
124(C2×D11)⋊C4—44no—
125(C2×D11)⋊C4—82no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—21no—
130C4⋊Dic11—22no—
131C4⋊Dic11—21no—
132C4⋊Dic11—22no—
133C4⋊Dic11—44no—
134C4⋊Dic11—42no—
135C4⋊Dic11—42no—
136C4⋊Dic11—81no—
137C4⋊Dic11—81no—
138C4⋊Dic11C2×Q812yes—
139C4⋊Dic11#4112yes—
140C4⋊Dic11#4112yes—
141Dic11⋊C4—44no—
142C4×Dic11—44no—
143C4×Dic11—42no—
144#2551—111no—
145#2354—111no—
146#2065—112no—
147#2023—112no—
148#1987—112no—
149#1948—111no—
150#1939D1111yescharacteristic, complemented
151#1920—112no—
152#1834—111no—
153#1802—111no—
154C4×#102—111no—
155C23×C11C22×D411yescharacteristic
156C22×D11—22no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163C2×C4×C11—22no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11C22⋊Q812yes—
171C2×C4×C11C22⋊Q812yes—
172C2×C4×C11C2×SD1614yes—
173C2×C4×C11C2×SD1612yes—
174C2×C4×C11AGL(1,ℤ/8)12yes—
175C2×C4×C11C22×Q811yescharacteristic
176C2×C4×C11C2×#4111yescharacteristic
177C2×C4×C11C2×#4111yescharacteristic
178C2×C4×C11C2×#4111yescharacteristic
179C2×C4×C11H(5,𝔽2)11yescharacteristic
180C2×C4×C112−1+411yescharacteristic
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196D44—22no—
197D44—22no—
198D44—41no—
199D44—41no—
200C4×D11—48no—
201Dic22—88no—
202C8×C11—42no—
203C8×C11—41no—
204C8×C11—41no—
205C2×C4⋊Q8—112no—
206C2×C4⋊Q8—221no—
207C2×C4×D4—111no—
208C2×#117—221no—
209C2×#106—112no—
210C2×C4⋊C8C2×D1111yescharacteristic
211C2×C4⋊C8C2×D1112yes—
212C2×#102—111no—
213C2×#102—111no—
214C2×#102—112no—
215C2×C4×C8C2×D1111yescharacteristic
216#395—222no—
217#390—112no—
218#389—112no—
219#389—221no—
220#388—222no—
221#384—111no—
222#384—111no—
223#380—221no—
224C4×C4⋊C4—112no—
225C4×C4⋊C4—111no—
226C4×C4⋊C4C2×D1111yescharacteristic
227#340—112no—
228#340—112no—
229#340—112no—
230#340—111no—
231#340—112no—
232#340—111no—
233#336C2×D1112yes—
234C22×C11C2×C22⋊Q811yescharacteristic
235C22×C11#54611yescharacteristic
236C22×C11#54811yescharacteristic
237C22×C11C22×SD1611yescharacteristic
238C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
239C22×C11#57611yescharacteristic
240C22×C11#57811yescharacteristic
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—81no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—22no—
249C4×C11—24no—
250C4×C11—42no—
251C4×C11#47614yes—
252C4×C11#53311yescharacteristic
253C4×C11#54411yescharacteristic
254C4×C11#55511yescharacteristic
255C4×C11#55611yescharacteristic
256Dic11—42no—
257Dic11—42no—
258Dic11—42no—
259Dic11—82no—
260Dic11—82no—
261C22×Q8—222no—
262C22×D4—111no—
263C23×C4—221no—
264C22×C8C22×D1111yescharacteristic
265C22×C8C22×D1112yes—
266C22×C8C22×D1111yescharacteristic
267C4⋊Q8—224no—
268C4⋊Q8—442no—
269C4⋊Q8—444no—
270C4×D4—114no—
271C4×D4—222no—
272#117—444no—
273C2×C4⋊C4—111no—
274C2×C4⋊C4—111no—
275C2×C4⋊C4—111no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—221no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—222no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4—221no—
284C2×C4⋊C4D4411yescharacteristic
285C2×C4⋊C4D4411yescharacteristic
286C2×C22⋊C4—221no—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C42—222no—
290C2×C42—221no—
291C2×C42C22×D1112yes—
292C2×C42C22×D1111yescharacteristic
293#106—224no—
294C4⋊C8—22no—
295C4⋊C8—42no—
296#102—222no—
297#102—222no—
298#102—442no—
299C4×C8—22no—
300#95—222no—
301#95—221no—
302#95—222no—
303#95D4412yes—
304C2×C11#243911yescharacteristic
305C2×C11C2×#47611yescharacteristic
306C2×C11#308311yescharacteristic
307C2×C11#329811yescharacteristic
308C2×C11#332511yescharacteristic
309C2×C11#336211yescharacteristic
310C2×C11#336711yescharacteristic
311D11—82no—
312C24—221no—
313C2×Q8—444no—
314C2×Q8—444no—
315C2×Q8—882no—
316C2×D4—112no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—224no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—442no—
329C22×C4—442no—
330C22×C4C2×D4412yes—
331C22×C4C2×D4411yescharacteristic
332C22×C4C2×D4412yes—
333C22×C4C2×D4411yescharacteristic
334C22×C4C23×D1111yescharacteristic
335C2×C8—21no—
336C2×C8—21no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—21no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—22no—
344C4⋊C4—22no—
345C4⋊C4—112no—
346C4⋊C4—112no—
347C4⋊C4—112no—
348C4⋊C4—221no—
349C4⋊C4—221no—
350C4⋊C4—221no—
351C4⋊C4—222no—
352C4⋊C4—222no—
353C4⋊C4—222no—
354C4⋊C4—222no—
355C4⋊C4—444no—
356C4⋊C4—444no—
357C4⋊C4—442no—
358C4⋊C4—442no—
359C4⋊C4—881no—
360C4⋊C4—881no—
361C4⋊C4#431414yes—
362C22⋊C4—224no—
363C22⋊C4—444no—
364C22⋊C4—882no—
365C42—22no—
366C42—22no—
367C42—444no—
368C42—442no—
369C42#434112yes—
370C42Q8×D1112yes—
371C11#2602411yescharacteristic, complemented, Sylow
372C23—222no—
373C23—441no—
374C23—441no—
375C23—441no—
376C23—441no—
377C23—441no—
378C23—441no—
379C23C22×D4411yescharacteristic
380Q8—888no—
381D4—222no—
382D4—222no—
383D4—441no—
384D4—441no—
385C2×C4—21no—
386C2×C4—22no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—448no—
402C2×C4—442no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4#6695012yes—
409C2×C4#6695012yes—
410C2×C4C2×#431414yes—
411C2×C4C2×#431412yes—
412C2×C4#6696112yes—
413C2×C4C2×#434111yescharacteristic
414C2×C4#6703711yescharacteristic
415C2×C4C2×Q8×D1111yescharacteristic
416C2×C4#6704011yescharacteristic
417C2×C4#41×D1111yescharacteristic
418C2×C4#41×D1111yescharacteristic
419C8—41no—
420C8—42no—
421C8—41no—
422C22—442no—
423C22—442no—
424C22—442no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22C2×#6695011yescharacteristic
430C22#1062308511yescharacteristic
431C22#1062310711yescharacteristic
432C22C22×#431411yescharacteristic
433C22C2×#6696111yescharacteristic
434C22#1062328311yescharacteristic
435C22#1062328411yescharacteristic
436C4—24no—
437C4—22no—
438C4—42no—
439C4—442no—
440C4—442no—
441C4—442no—
442C4—882no—
443C4—882no—
444C4#1062245514yes—
445C4#1062314711yescharacteristic
446C4#1062317211yescharacteristic
447C4#1062321911yescharacteristic
448C4#1062326011yescharacteristic
449C2—882no—
450C2#1307230511yescharacteristic
451C2C2×#1062245511yescharacteristic
452C2#1307846911yescharacteristic
453C2#1308048211yescharacteristic
454C2#1308085911yescharacteristic
455C2#1308128811yescharacteristic
456C2#1308133611yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#26024
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. #13073642C2semidirect
5. #13069563C2semidirect
6. #13069380C2semidirect
7. #13069202C2semidirect
8. #13068744C2semidirect
11. C11×#1939C2semidirect
70. C4×D44Q8semidirect
150. #1939D11semidirect
371. C11#26024semidirect

Maximal subgroups

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

subgroupindex
#130736422
#130715632
#130699892
#130697532
#130695632
#130693802
#130692022
#130687442
#130686172
C4×#668852
C11×#19392
#2602411