Finite Group Databasebeta

← #14771466

Subgroups — #14771466

Order 2816.

866 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66871C211yesmaximal, characteristic
2#13071487C211yesmaximal, characteristic
3#13071485C211yesmaximal, characteristic
4#13069353C212yesmaximal, complemented
5#13069211C212yesmaximal, complemented
6#13069206C212yesmaximal, complemented
7#13068703C211yesmaximal, characteristic
8#13068639C211yesmaximal, characteristic
9#13068512C212yesmaximal, complemented
10#13068395C211yesmaximal, characteristic
11C11×#1823C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C2×#66979—21no—
14C22×C4⋊Dic11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×#66930—21no—
17C2×C11×C22⋊C8C2211yescharacteristic
18C11×#380C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622824—21no—
21C4×C22⋊Dic11C2211yescharacteristic
22C2×#66879C2212yes—
23#10622598C2212yes—
24#10622594—22no—
25C4⋊C4×Dic11C2212yes—
26C4⋊C4×Dic11C2212yes—
27#10622586C2212yes—
28C2×#66872C2212yes—
29C2×#66871C418yescomplemented
30C2×#66871C2211yescharacteristic
31C2×#66871C2211yescharacteristic
32C2×#66871C2211yescharacteristic
33C2×#66871C2211yescharacteristic
34#10622556—21no—
35#10622267—22no—
36C11×#340C2212yes—
37C11×#340C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C23×Dic11—21no—
45C22×C8×C11C2312yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4C2×C414yes—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11D411yescharacteristic
55C2×C22⋊Dic11D411yescharacteristic
56#66979—44no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11C2×C414yes—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11C2312yes—
68C22×C11⋊C8—24no—
69C22×C11⋊C8C2×C414yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72#66930—44no—
73C11×C22⋊C8—22no—
74C11×#95—21no—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95D412yes—
81#66879—24no—
82#66872—24no—
83#66871C2×C414yes—
84#66871C2×C414yes—
85#66871C2×C414yes—
86#66871C2×C414yes—
87#22617—111nomaximal, Sylow
88C24×C11C2×D411yescharacteristic
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—24no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4112yes—
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—24no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—42no—
106C22×Dic11—42no—
107C22×Dic11C2×D412yes—
108C22×Dic11C2×D412yes—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C11×C4⋊C4—24no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4C22×C412yes—
118C11×C4⋊C4C22×C412yes—
119C11×C22⋊C4—42no—
120C22⋊Dic11—22no—
121C22⋊Dic11—22no—
122C22⋊Dic11—42no—
123C4⋊Dic11—24no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—44no—
129C4⋊Dic11C22×C412yes—
130C4⋊Dic11C22×C412yes—
131Dic11⋊C4—44no—
132C4×Dic11—22no—
133C4×Dic11—22no—
134C4×Dic11—44no—
135C4×Dic11—44no—
136C2×C11⋊C8—28no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8C22×C412yes—
139C2×C11⋊C8C22×C412yes—
140C2×C11⋊C8#4114yes—
141C22×#107—111no—
142#2344—111no—
143#2344—111no—
144#1943—112no—
145#1921—112no—
146#1921—112no—
147#1823—111no—
148#1823D1111yescharacteristic
149#1807—111no—
150#1776—112no—
151#1752—111no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11C4×D412yes—
155C23×C11AGL(1,ℤ/8)12yes—
156C23×C11AGL(1,ℤ/8)12yes—
157C23×C11C22×D411yescharacteristic
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—24no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—48no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11C4×D412yes—
173C2×C4×C11C23×C411yescharacteristic
174C2×C4×C11C2×#4111yescharacteristic
175C2×C4×C11C2×#4112yes—
176C2×C4×C112−1+412yes—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—22no—
182C2×Dic11—22no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—48no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C8×C11—42no—
194C11⋊C8—22no—
195C11⋊C8#11714yescomplemented
196C23×C8—111no—
197C2×#117—221no—
198C2×#117—221no—
199C22×C4⋊C4—111no—
200C22×C4⋊C4C2×D1111yescharacteristic
201C2×#107—111no—
202C2×#107—111no—
203C2×#107—111no—
204C2×#107—111no—
205C2×#107—118no—
206C2×#106—112no—
207C2×C22⋊C8C2×D1111yescharacteristic
208C2×#97—112no—
209#389—112no—
210#389—112no—
211#387—222no—
212#387—222no—
213#381—221no—
214#381—221no—
215#380—111no—
216#380C2×D1111yescharacteristic
217C4×C4⋊C4—112no—
218C4×C4⋊C4—112no—
219C4×C22⋊C4—111no—
220#340—112no—
221#340—112no—
222#340—112no—
223#340C2×D1112yes—
224#340C2×D1112yes—
225#336—112no—
226C22×C11—24no—
227C22×C11—24no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11#44214yes—
231C22×C11C2×C4×D411yescharacteristic
232C22×C11#54712yes—
233C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
235C22×C11#57812yes—
236C4×C11—22no—
237C4×C11—42no—
238C4×C11—42no—
239C4×C11—82no—
240C4×C11C2×#11711yescharacteristic
241C4×C11#51911yescharacteristic
242C4×C11#55212yes—
243Dic11—42no—
244Dic11—42no—
245Dic11—42no—
246Dic11—42no—
247Dic11—82no—
248C23×C4—21no—
249C23×C4—221no—
250C23×C4C22×D1111yescharacteristic
251C22×C8—111no—
252C22×C8—114no—
253C22×C8—111no—
254C22×C8—224no—
255C22×C8C22×D1112yes—
256#117—444no—
257#117—444no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—114no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—111no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4C4×D1114yes—
269C2×C4⋊C4C22×D1112yes—
270C2×C4⋊C4C22×D1111yescharacteristic
271C2×C4⋊C4C22×D1111yescharacteristic
272C2×C22⋊C4—21no—
273C2×C22⋊C4—111no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—221no—
276C2×C42—112no—
277C2×C42—222no—
278C2×C42—222no—
279#107—114no—
280#107—114no—
281#107—114no—
282#107—114no—
283#106—224no—
284C22⋊C8—22no—
285#97—224no—
286#95—21no—
287#95—112no—
288#95—222no—
289#95—222no—
290#95—222no—
291#95—222no—
292#95—221no—
293C2×C11—24no—
294C2×C11#234411yescharacteristic
295C2×C11C2×#44211yescharacteristic
296C2×C11#295011yescharacteristic
297C2×C11#334312yes—
298C2×C11#334312yes—
299C24D4×D1111yescharacteristic
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—24no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—112no—
309C22×C4—112no—
310C22×C4—224no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—222no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4C2×C4×D1112yes—
317C22×C4D4×D1111yescharacteristic
318C22×C4#434112yes—
319C22×C4C23×D1111yescharacteristic
320C2×C8—22no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—112no—
324C2×C8—114no—
325C2×C8—112no—
326C2×C8—228no—
327C2×C8—222no—
328C4⋊C4—24no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—112no—
334C4⋊C4—112no—
335C4⋊C4—224no—
336C4⋊C4—221no—
337C4⋊C4—221no—
338C4⋊C4—222no—
339C4⋊C4—222no—
340C4⋊C4—444no—
341C4⋊C4—444no—
342C4⋊C4C2×C4×D1112yes—
343C4⋊C4C2×C4×D1112yes—
344C22⋊C4—42no—
345C22⋊C4—222no—
346C22⋊C4—222no—
347C22⋊C4—442no—
348C42—222no—
349C42—222no—
350C42—444no—
351C42—444no—
352C11#2261711yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23(C22⋊D11)⋊C412yes—
356C23#6696412yes—
357C23#6696712yes—
358C23C2×D4×D1111yescharacteristic
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—22no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—48no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—222no—
374C2×C4—222no—
375C2×C4—222no—
376C2×C4—222no—
377C2×C4—222no—
378C2×C4—222no—
379C2×C4—222no—
380C2×C4—222no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4—441no—
385C2×C4—448no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4(C22⋊D11)⋊C412yes—
390C2×C4C22×C4×D1111yescharacteristic
391C2×C4C2×#434111yescharacteristic
392C2×C4#41×D1112yes—
393C2×C4#6704312yes—
394C8—42no—
395C8—114no—
396C8—222no—
397C22—22no—
398C22—24no—
399C22—24no—
400C22—22no—
401C22#1062239814yes—
402C22C2×(C22⋊D11)⋊C411yescharacteristic
403C22#1062318612yes—
404C22C2×#6696411yescharacteristic
405C22C2×#6696711yescharacteristic
406C22#1062331012yes—
407C4—22no—
408C4—42no—
409C4—42no—
410C4—82no—
411C4—442no—
412C4—442no—
413C4—442no—
414C4—442no—
415C4—882no—
416C4#1062304711yescharacteristic
417C4D11×#11711yescharacteristic
418C4#1062318112yes—
419C2—24no—
420C2#1307148011yescharacteristic
421C2C2×#1062239811yescharacteristic
422C2#1307748011yescharacteristic
423C2#1308105412yes—
424C2#1308106012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1823C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1823D11
hypocenterC11#22617
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13069353C2semidirect
5. #13069211C2semidirect
6. #13069206C2semidirect
9. #13068512C2semidirect
29. C2×#66871C4semidirect
195. C11⋊C8#117semidirect
352. C11#22617semidirect

Maximal subgroups

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

subgroupindex
C22×#668712
#130714872
#130714852
#130693532
#130692112
#130692062
#130687032
#130686392
#130685122
#130683952
C11×#18232
#2261711