Finite Group Databasebeta

← #14771447

Subgroups — #14771447

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#13071491C211yesmaximal, characteristic
3#13071483C211yesmaximal, characteristic
4#13069359C212yesmaximal, complemented
5#13069202C212yesmaximal, complemented
6#13069195C212yesmaximal, complemented
7#13068707C211yesmaximal, characteristic
8#13068703C211yesmaximal, characteristic
9#13068645C211yesmaximal, characteristic
10#13068513C212yesmaximal, complemented
11C11×#1752C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C2×#66930—21no—
16C2×C11×C22⋊C8C2211yescharacteristic
17C2×C11×#97C2212yes—
18C4×C11×C22⋊C4C2211yescharacteristic
19#10622825C2211yescharacteristic
20#10622825C2211yescharacteristic
21C2×#66882C2212yes—
22C2×#66881C418yescomplemented
23C2×#66881C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27#10622556—21no—
28#10622555—21no—
29C22⋊C4×Dic11—21no—
30C4×C4⋊Dic11C2212yes—
31C4×C4⋊Dic11C2212yes—
32#10622541C2212yes—
33#10622541C2212yes—
34#10622267—22no—
35#10622266—22no—
36C11×#336C2212yes—
37#10622189C2212yes—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×C8×C11—24no—
46C22×C8×C11C2×C414yes—
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C22⋊C4D411yescharacteristic
51C2×C11×C22⋊C4D411yescharacteristic
52C2×C42×C11C2312yes—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—21no—
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⋊Dic11C2312yes—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11—22no—
71#66930—44no—
72C11×C22⋊C8—22no—
73C11×#97—24no—
74C11×#95D412yes—
75C11⋊#95—21no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81#66882—24no—
82#66881C2×C414yes—
83#66881C2×C414yes—
84#66881C2×C414yes—
85#66881C2×C414yes—
86#22615—111nomaximal, Sylow
87C24×C11C2×D411yescharacteristic
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11C22×C412yes—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
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—22no—
103C22×Dic11—22no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C22×Dic11—82no—
107C2×C8×C11—28no—
108C2×C8×C11—22no—
109C2×C8×C11—22no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11C22×C412yes—
113C2×C8×C11C22×C412yes—
114C2×C8×C11#4114yes—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C42×C11—22no—
118C42×C11—22no—
119C22⋊Dic11—42no—
120C22⋊Dic11—42no—
121C4⋊Dic11—24no—
122C4⋊Dic11—24no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11C22×C412yes—
132C4⋊Dic11C22×C412yes—
133C4⋊Dic11C22×C412yes—
134C4⋊Dic11C22×C412yes—
135Dic11⋊C4—44no—
136Dic11⋊C4—82no—
137C4×Dic11—44no—
138C4×Dic11—82no—
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#1808—111no—
148#1776—112no—
149#1752D1111yescharacteristic
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—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11C4×D412yes—
167C2×C4×C11C23×C411yescharacteristic
168C2×C4×C11C2×#4111yescharacteristic
169C2×C4×C11C2×#4112yes—
170C2×C4×C112−1+412yes—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—48no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—84no—
189C8×C11—22no—
190C8×C11—42no—
191C8×C11#11714yescomplemented
192C23×C8C2×D1111yescharacteristic
193C2×#117—221no—
194C22×C4⋊C4—111no—
195C22×C4⋊C4—111no—
196C2×#107—112no—
197C2×#106—111no—
198C2×#106—111no—
199C2×#106—111no—
200C2×#106—111no—
201C2×#106—118no—
202C2×C22⋊C8C2×D1111yescharacteristic
203C2×#97C2×D1112yes—
204#389—112no—
205#389—112no—
206#387—222no—
207#387—222no—
208#381—221no—
209#380—111no—
210#380—111no—
211#380—221no—
212C4×C4⋊C4—112no—
213C4×C4⋊C4—112no—
214C4×C22⋊C4—221no—
215C4×C22⋊C4C2×D1111yescharacteristic
216#340—112no—
217#340—112no—
218#340—112no—
219#340—112no—
220#340—112no—
221#336C2×D1112yes—
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—42no—
234C4×C11—42no—
235C4×C11C2×#11711yescharacteristic
236C4×C11#51911yescharacteristic
237C4×C11#55212yes—
238Dic11—42no—
239Dic11—42no—
240Dic11—42no—
241Dic11—42no—
242Dic11—82no—
243Dic11—82no—
244C23×C4—221no—
245C23×C4—221no—
246C23×C4C22×D1111yescharacteristic
247C22×C8—24no—
248C22×C8C4×D1114yes—
249C22×C8C22×D1112yes—
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—112no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—221no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—222no—
267C2×C22⋊C4—221no—
268C2×C22⋊C4—221no—
269C2×C22⋊C4D4411yescharacteristic
270C2×C22⋊C4D4411yescharacteristic
271C2×C42—222no—
272C2×C42—222no—
273C2×C42C22×D1112yes—
274#107—224no—
275#106—114no—
276#106—114no—
277#106—114no—
278#106—114no—
279C22⋊C8—22no—
280#97—24no—
281#95—222no—
282#95—222no—
283#95—222no—
284#95—221no—
285#95—221no—
286#95—222no—
287#95D4412yes—
288C2×C11—24no—
289C2×C11#234411yescharacteristic
290C2×C11C2×#44011yescharacteristic
291C2×C11#294911yescharacteristic
292C2×C11#334412yes—
293C2×C11#334512yes—
294C24C2×D4411yescharacteristic
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—224no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4—224no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—442no—
306C22×C4—442no—
307C22×C4—882no—
308C22×C4C2×C4×D1112yes—
309C22×C4C2×D4412yes—
310C22×C4C2×D4412yes—
311C22×C4C2×D4411yescharacteristic
312C22×C4#433912yes—
313C22×C4C23×D1111yescharacteristic
314C2×C8—22no—
315C2×C8—28no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8C2×C4×D1112yes—
320C2×C8C2×C4×D1112yes—
321C2×C8#434114yes—
322C4⋊C4—112no—
323C4⋊C4—112no—
324C4⋊C4—112no—
325C4⋊C4—112no—
326C4⋊C4—224no—
327C4⋊C4—224no—
328C4⋊C4—221no—
329C4⋊C4—221no—
330C4⋊C4—221no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C4⋊C4—222no—
335C4⋊C4—222no—
336C4⋊C4—444no—
337C4⋊C4—882no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C42—22no—
343C42—22no—
344C42—444no—
345C42—882no—
346C11#2261511yescharacteristic, complemented, Sylow
347C23—22no—
348C23—22no—
349C23C4×D4412yes—
350C23#6696112yes—
351C23#6696212yes—
352C23C22×D4411yescharacteristic
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—222no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—441no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4—448no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—884no—
381C2×C4C4×D4412yes—
382C2×C4C22×C4×D1111yescharacteristic
383C2×C4C2×#433911yescharacteristic
384C2×C4C2×#434112yes—
385C2×C4#6704312yes—
386C8—22no—
387C8—42no—
388C8#6693014yescomplemented
389C22—24no—
390C22—22no—
391C22—22no—
392C22—24no—
393C22#1062232314yes—
394C22C2×C4×D4411yescharacteristic
395C22#1062308612yes—
396C22C2×#6696111yescharacteristic
397C22C2×#6696211yescharacteristic
398C22#1062328212yes—
399C4—22no—
400C4—42no—
401C4—42no—
402C4—442no—
403C4—442no—
404C4—442no—
405C4—442no—
406C4—882no—
407C4—882no—
408C4C2×#6693011yescharacteristic
409C4#1062304711yescharacteristic
410C4#1062307212yes—
411C2—24no—
412C2#1307148311yescharacteristic
413C2C2×#1062232311yescharacteristic
414C2#1307747711yescharacteristic
415C2#1308107312yes—
416C2#1308108812yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1752C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1752D11
hypocenterC11#22615
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1752

Complements

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

NH ≅ G/Ntype
4. #13069359C2semidirect
5. #13069202C2semidirect
6. #13069195C2semidirect
10. #13068513C2semidirect
22. C2×#66881C4semidirect
191. 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
#130714912
#130714832
#130693592
#130692022
#130691952
#130687072
#130687032
#130686452
#130685132
C11×#17522
#2261511