Finite Group Databasebeta

← #14771453

Subgroups — #14771453

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66881C211yesmaximal, characteristic
2#13071495C211yesmaximal, characteristic
3#13071487C211yesmaximal, characteristic
4#13069357C212yesmaximal, complemented
5#13069200C212yesmaximal, complemented
6#13069193C212yesmaximal, complemented
7#13068704C211yesmaximal, characteristic
8#13068700C211yesmaximal, characteristic
9#13068515C212yesmaximal, complemented
10#13068392C211yesmaximal, characteristic
11C11×#1808C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×#66930—21no—
16C2×C11×#107C2212yes—
17C11×#380C2211yescharacteristic
18C11×#380C2211yescharacteristic
19C4×C22⋊Dic11C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×#66881C418yescomplemented
22C2×#66881C2211yescharacteristic
23C2×#66881C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×#66879C2212yes—
27C4⋊C4×Dic11C2212yes—
28C4⋊C4×Dic11C2212yes—
29#10622586C2212yes—
30#10622586C2212yes—
31#10622556—21no—
32#10622555—21no—
33C22⋊C4×Dic11—21no—
34#10622267—22no—
35#10622266—22no—
36C11×#340C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×C8×C11—24no—
46C22×C8×C11C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C22⋊Dic11D411yescharacteristic
54C2×C22⋊Dic11D411yescharacteristic
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11C2×C414yes—
60C2×C4⋊Dic11C2×C414yes—
61C2×C4⋊Dic11C2311yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2312yes—
71#66930—44no—
72C11×#107—24no—
73C11×#95—21no—
74C11×#95—21no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—22no—
79C11⋊#95D412yes—
80C22⋊(C11⋊C8)—22no—
81#66881C2×C414yes—
82#66881C2×C414yes—
83#66881C2×C414yes—
84#66881C2×C414yes—
85#66879—24no—
86#22615—111nomaximal, Sylow
87C24×C11C2×D411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11C22×C412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4112yes—
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—82no—
105C22×Dic11C2×D412yes—
106C22×Dic11C2×D412yes—
107C2×C8×C11—28no—
108C2×C8×C11—22no—
109C2×C8×C11C22×C412yes—
110C2×C8×C11C22×C412yes—
111C2×C8×C11#4114yes—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—42no—
118C22⋊Dic11—22no—
119C22⋊Dic11—22no—
120C4⋊Dic11—24no—
121C4⋊Dic11—24no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11C22×C412yes—
127C4⋊Dic11C22×C412yes—
128C4⋊Dic11C22×C412yes—
129C4⋊Dic11C22×C412yes—
130Dic11⋊C4—44no—
131Dic11⋊C4—82no—
132C4×Dic11—22no—
133C4×Dic11—22no—
134C4×Dic11—44no—
135C4×Dic11—82no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C22×#106—111no—
140#2345—111no—
141#2344—111no—
142#1944—112no—
143#1920—112no—
144#1919—112no—
145#1824—111no—
146#1823—111no—
147#1808D1111yescharacteristic
148#1776—112no—
149#1752—111no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11C4×D412yes—
153C23×C11AGL(1,ℤ/8)12yes—
154C23×C11#13712yes—
155C23×C11C22×D411yescharacteristic
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
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×C11C4×D412yes—
167C2×C4×C11C23×C411yescharacteristic
168C2×C4×C11C2×#4112yes—
169C2×C4×C11C2×#4111yescharacteristic
170C2×C4×C112−1+412yes—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—22no—
177C2×Dic11—22no—
178C2×Dic11—22no—
179C2×Dic11—22no—
180C2×Dic11—22no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—48no—
188C2×Dic11—84no—
189C8×C11—22no—
190C8×C11#11714yescomplemented
191C11⋊C8—42no—
192C23×C8C2×D1111yescharacteristic
193C2×#117—221no—
194C22×C4⋊C4—111no—
195C22×C4⋊C4—111no—
196C2×#107C2×D1112yes—
197C2×#106—111no—
198C2×#106—111no—
199C2×#106—111no—
200C2×#106—111no—
201C2×#106—118no—
202C2×C22⋊C8—111no—
203C2×#97—112no—
204#389—112no—
205#389—112no—
206#387—222no—
207#387—222no—
208#381—221no—
209#380—221no—
210#380C2×D1111yescharacteristic
211#380C2×D1111yescharacteristic
212C4×C4⋊C4—112no—
213C4×C4⋊C4—112no—
214C4×C22⋊C4—111no—
215C4×C22⋊C4—221no—
216#340—112no—
217#340—112no—
218#340—112no—
219#340—112no—
220#340C2×D1112yes—
221#336—112no—
222C22×C11—24no—
223C22×C11—24no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11#44014yes—
227C22×C11C2×C4×D411yescharacteristic
228C22×C11#54712yes—
229C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
230C22×C11C2×#13711yescharacteristic
231C22×C11#57712yes—
232C4×C11—22no—
233C4×C11—82no—
234C4×C11—82no—
235C4×C11C2×#11711yescharacteristic
236C4×C11#51911yescharacteristic
237C4×C11#55212yes—
238Dic11—42no—
239Dic11—42no—
240Dic11—42no—
241Dic11—42no—
242Dic11—42no—
243Dic11—42no—
244C23×C4—221no—
245C23×C4—221no—
246C23×C4C22×D1111yescharacteristic
247C22×C8—24no—
248C22×C8—112no—
249C22×C8C4×D1114yes—
250C22×C8C22×D1111yescharacteristic
251C22×C8C22×D1111yescharacteristic
252#117—444no—
253C2×C4⋊C4—114no—
254C2×C4⋊C4—114no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4C22×D1112yes—
266C2×C4⋊C4C22×D1112yes—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C42—112no—
272C2×C42—222no—
273C2×C42—222no—
274#107—24no—
275#106—114no—
276#106—114no—
277#106—114no—
278#106—114no—
279C22⋊C8—222no—
280#97—224no—
281#95—21no—
282#95—21no—
283#95—112no—
284#95—222no—
285#95—222no—
286#95—222no—
287#95—222no—
288C2×C11—24no—
289C2×C11#234411yescharacteristic
290C2×C11C2×#44011yescharacteristic
291C2×C11#294911yescharacteristic
292C2×C11#334412yes—
293C2×C11#334512yes—
294C24D4×D1111yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—112no—
300C22×C4—112no—
301C22×C4—224no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306C22×C4—224no—
307C22×C4—442no—
308C22×C4—442no—
309C22×C4—882no—
310C22×C4C2×C4×D1112yes—
311C22×C4D4×D1111yescharacteristic
312C22×C4#434312yes—
313C22×C4C23×D1111yescharacteristic
314C2×C8—22no—
315C2×C8—28no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8C2×C4×D1112yes—
320C2×C8C2×C4×D1112yes—
321C2×C8#434114yes—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—22no—
326C4⋊C4—112no—
327C4⋊C4—112no—
328C4⋊C4—112no—
329C4⋊C4—112no—
330C4⋊C4—224no—
331C4⋊C4—224no—
332C4⋊C4—221no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C4⋊C4—221no—
336C4⋊C4—444no—
337C4⋊C4—882no—
338C22⋊C4—42no—
339C22⋊C4—42no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C42—222no—
343C42—222no—
344C42—444no—
345C42—882no—
346C11#2261511yescharacteristic, complemented, Sylow
347C23—22no—
348C23—22no—
349C23#6694612yes—
350C23#6696412yes—
351C23#6697112yes—
352C23C2×D4×D1111yescharacteristic
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—448no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—884no—
381C2×C4#6694612yes—
382C2×C4C22×C4×D1111yescharacteristic
383C2×C4C2×#434112yes—
384C2×C4C2×#434311yescharacteristic
385C2×C4#6704312yes—
386C8—22no—
387C8—442no—
388C8#6693014yescomplemented
389C22—24no—
390C22—22no—
391C22—22no—
392C22—24no—
393C22#1062250214yes—
394C22C2×#6694611yescharacteristic
395C22#1062314212yes—
396C22C2×#6696411yescharacteristic
397C22C2×#6697111yescharacteristic
398C22#1062330112yes—
399C4—22no—
400C4—82no—
401C4—82no—
402C4—442no—
403C4—442no—
404C4—442no—
405C4—442no—
406C4—442no—
407C4—442no—
408C4C2×#6693011yescharacteristic
409C4#1062304711yescharacteristic
410C4#1062317312yes—
411C2—24no—
412C2#1307148711yescharacteristic
413C2C2×#1062250211yescharacteristic
414C2#1307747411yescharacteristic
415C2#1308107712yes—
416C2#1308109212yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1808C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1808D11
hypocenterC11#22615
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1808

Complements

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

NH ≅ G/Ntype
4. #13069357C2semidirect
5. #13069200C2semidirect
6. #13069193C2semidirect
9. #13068515C2semidirect
21. C2×#66881C4semidirect
190. C8×C11#117semidirect
346. C11#22615semidirect
388. C8#66930semidirect

Maximal subgroups

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

subgroupindex
C22×#668812
#130714952
#130714872
#130693572
#130692002
#130691932
#130687042
#130687002
#130685152
#130683922
C11×#18082
#2261511