Finite Group Databasebeta

← #14772048

Subgroups — #14772048

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622765C211yesmaximal, characteristic
2C2×D8×Dic11C211yesmaximal, characteristic
3D4×Dic11⋊C4C212yesmaximal, complemented
4#13069354C211yesmaximal, characteristic, complemented
5#13069352C211yesmaximal, characteristic, complemented
6#13068877C212yesmaximal, complemented
7#13068875C212yesmaximal, complemented
8#13068771C211yesmaximal, characteristic, complemented
9#13068614C212yesmaximal, complemented
10#13068484C211yesmaximal, characteristic, complemented
11C2×C11×#442C211yesmaximal, characteristic
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11C2212yes—
14C2×D4×Dic11C2212yes—
15C2×D4×Dic11C2212yes—
16C22×Dic11⋊C4—22no—
17C11×#442—24no—
18C2×C11×#106C2211yescharacteristic
19C2×C11×#102C2212yes—
20C2×C11×#97C2211yescharacteristic
21C2×#66896C2212yes—
22C2×#66896C2212yes—
23#10622823—22no—
24#10622765—24no—
25D8×Dic11C418yescomplemented
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31#10622589C2212yes—
32#10622586C2212yes—
33C2×#66872C2212yes—
34#10622559—22no—
35#10622555—22no—
36C4×Dic11⋊C4C2211yescharacteristic
37#10622541C2212yes—
38#10622189C2212yes—
39#10622188C2211yescharacteristic
40#10622167C2212yes—
41#10622162C2211yescharacteristic
42C22×D4×C11C2312yes—
43C23×C4×C11—22no—
44C23×Dic11—22no—
45C23×Dic11—22no—
46C2×C11×D8C2×C414yes—
47C2×C11×D8D414yes—
48C2×C11×D8Q814yes—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C4×D4×C11—24no—
52C4×D4×C11—42no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57C2×C22⋊Dic11—22no—
58D4×Dic11—24no—
59D4×Dic11—24no—
60D4×Dic11—42no—
61D4×Dic11C2×C418yescomplemented
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—48no—
69C2×Dic11⋊C4D412yes—
70C2×C4×Dic11C2311yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C11×#106—22no—
75C11×#102—24no—
76C11×#97—22no—
77#66896—24no—
78#66896C2×C418yescomplemented
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95D412yes—
82#66882C2×C414yescomplemented
83#66881—22no—
84#66879—22no—
85Dic11⋊C8—22no—
86C8×Dic11C2×C414yescomplemented
87#66872—42no—
88#22670—111nomaximal, Sylow
89C24×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11C22×C414yes—
94C2×D4×C11C2×D414yes—
95C2×D4×C11C2×Q814yes—
96C22×C4×C11—22no—
97C22×C4×C11—44no—
98C22×C4×C11—44no—
99C22×C4×C11—82no—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—28no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—44no—
106C22×Dic11—44no—
107C22×Dic11—44no—
108C22×Dic11—44no—
109C22×Dic11—82no—
110C22×Dic11C2×D412yes—
111C22×Dic11C2×D411yescharacteristic
112C22×Dic11C2×D411yescharacteristic
113C11×D8C4⋊C4116yescomplemented
114C2×C8×C11—21no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11C22×C412yes—
118C2×C8×C11C2×D412yes—
119C2×C8×C11C2×Q812yes—
120C11×C4⋊C4—22no—
121C11×C4⋊C4—22no—
122C11×C22⋊C4—44no—
123C42×C11—21no—
124C42×C11—21no—
125C22⋊Dic11—28no—
126C22⋊Dic11—44no—
127C4⋊Dic11—22no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11C22×C414yes—
131Dic11⋊C4—24no—
132Dic11⋊C4—44no—
133Dic11⋊C4—44no—
134Dic11⋊C4—44no—
135Dic11⋊C4—82no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138C4×Dic11C22×C412yes—
139C4×Dic11#4112yes—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—21no—
144C2×C11⋊C8—21no—
145C2×C11⋊C8C22×C412yes—
146C2×#442—111no—
147C2×#442D1111yescharacteristic
148C2×C4×D8—111no—
149D4×C4⋊C4—112no—
150#1943—111no—
151#1943—111no—
152#1864—112no—
153#1864—112no—
154#1844—111no—
155#1802—112no—
156#1770—111no—
157C23×C11—24no—
158C23×C11—24no—
159C23×C11—24no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11C22×D411yescharacteristic
165D4×C11—24no—
166D4×C11—24no—
167D4×C11—24no—
168D4×C11C2×C4⋊C418yescomplemented
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—88no—
176C2×C4×C11C23×C411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11C22×Q811yescharacteristic
179C2×C4×C11C2×#4111yescharacteristic
180C2×C4×C11H(5,𝔽2)11yescharacteristic
181C2×C4×C112−1+411yescharacteristic
182C2×Dic11—22no—
183C2×Dic11—24no—
184C2×Dic11—22no—
185C2×Dic11—22no—
186C2×Dic11—22no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—416no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—88no—
194C2×Dic11C4×D412yes—
195C2×Dic11C4×D412yes—
196C2×Dic11AGL(1,ℤ/8)14yes—
197C8×C11—41no—
198C8×C11C2×C4⋊C414yescomplemented
199C11⋊C8—22no—
200C11⋊C8—41no—
201C22×D8C2×D1111yescharacteristic
202C2×C4×D4—112no—
203C2×C4×D4—112no—
204C2×C4×D4C2×D1112yes—
205C22×C4⋊C4—222no—
206#442—24no—
207#442—224no—
208C4×D8—118no—
209C2×#107—111no—
210C2×#106—111no—
211C2×#106—112no—
212C2×#106C2×D1111yescharacteristic
213C2×C4⋊C8—111no—
214C2×#102—112no—
215C2×#102—112no—
216C2×#102C2×D1112yes—
217C2×#97—111no—
218C2×#97C2×D1111yescharacteristic
219C2×C4×C8—111no—
220#389—112no—
221#389—112no—
222#385—222no—
223#385—222no—
224#384—112no—
225#380—222no—
226C4×C4⋊C4—111no—
227#340—112no—
228#340—112no—
229#336—111no—
230#336—111no—
231C22×C11—28no—
232C22×C11—44no—
233C22×C11—44no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11—44no—
238C22×C11C2×C4×D411yescharacteristic
239C22×C11D4211yescharacteristic
240C22×C11D4×Q811yescharacteristic
241C22×C11C2×AGL(1,ℤ/8)12yes—
242C22×C11#57712yes—
243C4×C11—42no—
244C4×C11—82no—
245C4×C11C22×C4⋊C411yescharacteristic
246C4×C11#52011yescharacteristic
247C4×C11#54711yescharacteristic
248C4×C11#55411yescharacteristic
249Dic11—22no—
250Dic11—44no—
251Dic11—42no—
252Dic11—82no—
253Dic11#44214yescomplemented
254C22×D4C22×D1112yes—
255C23×C4—22no—
256C23×C4—222no—
257C23×C4—222no—
258C2×D8Dic2214yes—
259C2×D8C4×D1114yes—
260C2×D8C22⋊D1114yes—
261C22×C8—111no—
262C22×C8—111no—
263C22×C8C22×D1111yescharacteristic
264C22×C8C22×D1111yescharacteristic
265C4×D4—24no—
266C4×D4—42no—
267C4×D4—118no—
268C4×D4—224no—
269C4×D4—224no—
270C4×D4—442no—
271C2×C4⋊C4—112no—
272C2×C4⋊C4—112no—
273C2×C4⋊C4—112no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4—222no—
276C2×C4⋊C4—222no—
277C2×C4⋊C4—222no—
278C2×C4⋊C4—448no—
279C2×C4⋊C4C22×D1112yes—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4—222no—
283C2×C42—111no—
284C2×C42—111no—
285C2×C42C22×D1111yescharacteristic
286#107—114no—
287#106—22no—
288#106—222no—
289#106—442no—
290C4⋊C8—222no—
291#102—24no—
292#102—118no—
293#102—224no—
294#97—22no—
295#97—222no—
296C4×C8—114no—
297#95—112no—
298#95—222no—
299#95—222no—
300C2×C11—48no—
301C2×C11D4×C4⋊C411yescharacteristic
302C2×C11C2×#44211yescharacteristic
303C2×C11#295211yescharacteristic
304C2×C11#327212yes—
305C2×C11#338412yes—
306C24—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4C2×Dic2214yes—
311C2×D4C2×C4×D1114yes—
312C2×D4C2×C22⋊D1114yes—
313C22×C4—22no—
314C22×C4—44no—
315C22×C4—44no—
316C22×C4—82no—
317C22×C4—111no—
318C22×C4—111no—
319C22×C4—112no—
320C22×C4—228no—
321C22×C4—222no—
322C22×C4—222no—
323C22×C4—444no—
324C22×C4—444no—
325C22×C4—444no—
326C22×C4—444no—
327C22×C4—882no—
328C22×C4D4×D1112yes—
329C22×C4C23×D1111yescharacteristic
330D8Dic11⋊C4116yescomplemented
331C2×C8—21no—
332C2×C8—21no—
333C2×C8—21no—
334C2×C8—112no—
335C2×C8—221no—
336C2×C8—221no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8C2×Dic2212yes—
341C2×C8C2×C4×D1112yes—
342C2×C8C2×C22⋊D1112yes—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—114no—
346C4⋊C4—224no—
347C4⋊C4—222no—
348C4⋊C4—222no—
349C4⋊C4—222no—
350C4⋊C4—444no—
351C4⋊C4—444no—
352C4⋊C4—444no—
353C4⋊C4—882no—
354C22⋊C4—44no—
355C22⋊C4—228no—
356C22⋊C4—444no—
357C42—21no—
358C42—21no—
359C42—112no—
360C42—112no—
361C42—221no—
362C42—221no—
363C11#2267011yescharacteristic, complemented, Sylow
364C23—24no—
365C23—24no—
366C23—24no—
367C23—42no—
368C23—42no—
369C23—42no—
370C23—42no—
371C23C2×D4×D1111yescharacteristic
372D4—24no—
373D4—24no—
374D4—24no—
375D4C2×Dic11⋊C418yescomplemented
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—88no—
383C2×C4—114no—
384C2×C4—112no—
385C2×C4—112no—
386C2×C4—222no—
387C2×C4—222no—
388C2×C4—222no—
389C2×C4—224no—
390C2×C4—222no—
391C2×C4—4416no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—442no—
396C2×C4—442no—
397C2×C4—888no—
398C2×C4C22×Dic2211yescharacteristic
399C2×C4C22×C4×D1111yescharacteristic
400C2×C4#6703711yescharacteristic
401C2×C4#41×D1111yescharacteristic
402C2×C4#6704311yescharacteristic
403C2×C4C22×C22⋊D1111yescharacteristic
404C8—41no—
405C8—222no—
406C8—441no—
407C8C2×Dic11⋊C414yescomplemented
408C22—28no—
409C22—44no—
410C22—44no—
411C22—44no—
412C22—44no—
413C22—44no—
414C22—44no—
415C22D4×Dic2211yescharacteristic
416C22C4×D4×D1111yescharacteristic
417C22D11×AGL(1,ℤ/8)12yes—
418C22#1062330612yes—
419C22D4×C22⋊D1111yescharacteristic
420C4—42no—
421C4—82no—
422C4—114no—
423C4—222no—
424C4—442no—
425C4—444no—
426C4—882no—
427C4#1062307011yescharacteristic
428C4#1062307711yescharacteristic
429C4C22×Dic11⋊C411yescharacteristic
430C4#1062335511yescharacteristic
431C2—48no—
432C2D4×Dic11⋊C411yescharacteristic
433C2D11×#44211yescharacteristic
434C2#1307749811yescharacteristic
435C2#1308021012yes—
436C2#1308151612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
cosocleC22×C4×C11C24
hypercenterC2×#442D11
hypocenterC11#22670
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
3. D4×Dic11⋊C4C2semidirect
4. #13069354C2semidirect
5. #13069352C2semidirect
6. #13068877C2semidirect
7. #13068875C2semidirect
8. #13068771C2semidirect
9. #13068614C2semidirect
10. #13068484C2semidirect
25. D8×Dic11C4semidirect
61. D4×Dic11C2×C4semidirect
78. #66896C2×C4semidirect
82. #66882C2×C4semidirect
86. C8×Dic11C2×C4semidirect
113. C11×D8C4⋊C4semidirect
168. D4×C11C2×C4⋊C4semidirect
198. C8×C11C2×C4⋊C4semidirect
253. Dic11#442semidirect
330. D8Dic11⋊C4semidirect
363. C11#22670semidirect
375. D4C2×Dic11⋊C4semidirect
407. C8C2×Dic11⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106227652
C2×D8×Dic112
D4×Dic11⋊C42
#130693542
#130693522
#130688772
#130688752
#130687712
#130686142
#130684842
C2×C11×#4422
#2267011