Finite Group Databasebeta

← #14908604

Subgroups — #14908604

Order 2816.

580 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#467C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic
3#13070826C212yesmaximal, complemented
4#13070822C212yesmaximal, complemented
5#13070818C211yesmaximal, characteristic, complemented
6#13070814C211yesmaximal, characteristic, complemented
7#13070811C211yesmaximal, characteristic, complemented
8#13070401C212yesmaximal, complemented
9#13070334C212yesmaximal, complemented
10#13070225C211yesmaximal, characteristic
11C11×#2236C211yesmaximal, characteristic, complemented
12C2×Q16×D11C2211yescharacteristic
13C22×C8×D11C2211yescharacteristic
14D11×C22⋊Q8—21no—
15C2×#66945—21no—
16C11×#467C2211yescharacteristic
17C2×C11×#107C2211yescharacteristic
18#10622801C2211yescharacteristic
19#10622729C2211yescharacteristic
20C2×#66882C2211yescharacteristic
21#10622664—21no—
22C2×#66872—21no—
23C2×#66862C2212yes—
24#10622500C2211yescharacteristic
25#10622493—21no—
26#10622493—21no—
27#10622493C2212yes—
28#10622493C2212yes—
29D11×#107C2211yescharacteristic
30#10622426—21no—
31D11×#103—21no—
32C11×#366C2212yescomplemented
33C11×#358C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic
35#10622202C2212yescomplemented
36C22⋊(C11⋊C16)C2211yescharacteristic
37(C2×D11)⋊C16C2212yes—
38#10622143C2212yescomplemented
39#10622141C2212yescomplemented
40#10622130C2212yescomplemented
41#10622128C2212yescomplemented
42#10622127C2212yescomplemented
43C2×Q8×D11—21no—
44C22×C4×D11D411yescharacteristic
45C2×C11×Q16C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×C22⋊Q8—21no—
48C2×C11×C4⋊C4—21no—
49#66999—21no—
50C2×#4326—21no—
51C2×(C2×D11)⋊C4—41no—
52C2×C4⋊Dic11—21no—
53#66977—21no—
54C2×C4×Dic11—41no—
55C22×C11⋊C8D411yescharacteristic
56Q16×D11—24no—
57C2×Dic44C2311yescharacteristic
58C2×C8×D11—24no—
59C2×C8×D11D411yescharacteristic
60C2×C8×D11D411yescharacteristic
61C2×C8×D11C2311yescharacteristic
62C2×C8×D11C2311yescharacteristic
63#66950—21no—
64#66949—41no—
65#66945—22no—
66#66945—22no—
67#66945—41no—
68#66945—41no—
69C4⋊C4×D11—21no—
70C4⋊C4×D11—41no—
71C22⋊C4×D11—41no—
72#66931—41no—
73C2×C11×C16C2312yes—
74C11×#107—21no—
75C11×#107C2311yescharacteristic
76C11×#107C2312yes—
77C11×#103—21no—
78#66899—21no—
79#66882—21no—
80#66882C2311yescharacteristic
81#66882C2312yes—
82#66880—21no—
83C2×C11⋊C16C2312yes—
84#66874—21no—
85#66872—22no—
86#66872—22no—
87#66871—21no—
88#66862—24no—
89#33649—111nomaximal, Sylow
90C23×D11D811yescharacteristic
91C2×Q8×C11—21no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—41no—
95C22×Dic11D811yescharacteristic
96Q8×D11—42no—
97Q8×D11—42no—
98C2×C4×D11—22no—
99C2×C4×D11—22no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11D811yescharacteristic
103C2×C4×D11D811yescharacteristic
104C2×C4×D11C2×D411yescharacteristic
105C2×C4×D11C2×D411yescharacteristic
106C2×Dic22—21no—
107C2×Dic22—41no—
108C11×Q16—22no—
109C2×C8×C11—22no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C11×C22⋊C4—41no—
117C22⋊Dic11—41no—
118#4326—42no—
119(C2×D11)⋊C4—41no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—42no—
122(C2×D11)⋊C4—42no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—41no—
126C4⋊Dic11—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130C4×Dic11—42no—
131C4×Dic11—42no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8C2×D411yescharacteristic
134C2×C11⋊C8C2×D411yescharacteristic
135Dic44—22no—
136C8×D11—22no—
137C8×D11—22no—
138C8×D11—22no—
139C8×D11#4114yes—
140C11×C16—22no—
141C11⋊C16—22no—
142C2×#467—111no—
143C2×#427—111no—
144#2237—112no—
145#2237—112no—
146#2236—111no—
147#2236D1111yescharacteristic, complemented
148#2235—111no—
149#2235—111no—
150#2159—112no—
151#2141—112no—
152#2112—111no—
153C23×C11C2×D811yescharacteristic
154C22×D11—22no—
155C22×D11—22no—
156C22×D11—41no—
157C22×D11C2×D811yescharacteristic
158C22×D11C2×D811yescharacteristic
159Q8×C11—41no—
160Q8×C11—41no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—42no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—82no—
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×Dic11—22no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—82no—
174C2×Dic11C2×D811yescharacteristic
175C2×Dic11C2×D811yescharacteristic
176C4×D11—22no—
177C4×D11—21no—
178C4×D11—21no—
179C4×D11—22no—
180C4×D11—82no—
181C4×D11—82no—
182C4×D11#12312yes—
183C4×D11#13712yes—
184Dic22—41no—
185Dic22—41no—
186Dic22—82no—
187C8×C11—21no—
188C8×C11C2×#4112yes—
189C11⋊C8—21no—
190C11⋊C8#12312yes—
191C22×Q16—111no—
192C23×C8—111no—
193C2×C22⋊Q8—221no—
194C2×#117—221no—
195C2×M32—112no—
196#467—111no—
197#467—111no—
198#467—111no—
199#467—221no—
200#467—221no—
201#467C2×D1111yescharacteristic
202#427—112no—
203#427—112no—
204#427—221no—
205#427—221no—
206C2×#107—111no—
207C2×#107—111no—
208C2×#107C2×D1111yescharacteristic
209C2×#106—221no—
210C2×#103—221no—
211#367—112no—
212#367—112no—
213#366—112no—
214#366C2×D1112yescomplemented
215#358—112no—
216#358—112no—
217#358—112no—
218#358C2×D1112yescomplemented
219C22⋊C16—111no—
220C22⋊C16—112no—
221C22⋊C16C2×D1111yescharacteristic
222C22×C11—21no—
223C22×C11—21no—
224C22×C11#51012yes—
225C22×C11C22×D811yescharacteristic
226C2×D11—21no—
227C2×D11—21no—
228C2×D11—21no—
229C2×D11—21no—
230C2×D11—21no—
231C2×D11—44no—
232C2×D11#48012yes—
233C4×C11—21no—
234C4×C11—81no—
235C4×C11—82no—
236C4×C11—81no—
237C4×C11C2×#12311yescharacteristic
238C4×C11C2×#13711yescharacteristic
239Dic11—21no—
240Dic11—81no—
241Dic11—82no—
242Dic11—81no—
243Dic11#48012yes—
244C22×Q8—221no—
245C23×C4—111no—
246C2×Q16—111no—
247C2×Q16—224no—
248C2×Q16—221no—
249C2×Q16C22×D1111yescharacteristic
250C22×C8—111no—
251C22×C8—111no—
252C22×C8—111no—
253C22×C8—111no—
254C22×C8—111no—
255C22×C8—224no—
256C22×C8C22×D1111yescharacteristic
257C22⋊Q8—21no—
258C22⋊Q8—221no—
259C22⋊Q8—221no—
260C22⋊Q8—221no—
261C22⋊Q8—441no—
262C22⋊Q8—441no—
263#117—222no—
264#117—222no—
265#117—441no—
266#117—441no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—441no—
271C2×C22⋊C4—441no—
272C2×C22⋊C4—441no—
273C2×C42—441no—
274M32—224no—
275C2×C16—112no—
276C2×C16C22×D1112yes—
277#107—21no—
278#107—112no—
279#107—111no—
280#107—221no—
281#107—221no—
282#107C22×D1112yes—
283#107C22×D1111yescharacteristic
284#106—222no—
285#106—222no—
286#103—21no—
287#103—221no—
288#103—221no—
289#103—221no—
290C2×C11—22no—
291C2×C11C2×#48011yescharacteristic
292C2×C11C2×#51011yescharacteristic
293C2×C11#341411yescharacteristic
294D11—22no—
295D11—41no—
296C24—111no—
297C2×Q8—21no—
298C2×Q8—221no—
299C2×Q8—441no—
300C2×Q8—442no—
301C2×Q8—442no—
302C22×C4—41no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—441no—
311C22×C4—441no—
312C22×C4—441no—
313C22×C4D4×D1111yescharacteristic
314Q16—22no—
315Q16—222no—
316Q16—442no—
317C2×C8—22no—
318C2×C8—111no—
319C2×C8—114no—
320C2×C8—111no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8D4×D1111yescharacteristic
326C2×C8C23×D1111yescharacteristic
327C4⋊C4—21no—
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—221no—
332C4⋊C4—222no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C4⋊C4—441no—
336C4⋊C4—441no—
337C4⋊C4—441no—
338C22⋊C4—41no—
339C22⋊C4—442no—
340C22⋊C4—442no—
341C22⋊C4—441no—
342C22⋊C4—441no—
343C22⋊C4—441no—
344C42—442no—
345C42—442no—
346C16—22no—
347C16—222no—
348C11#3364911yescharacteristic, complemented, Sylow
349C23—111no—
350C23—111no—
351C23—222no—
352C23—222no—
353C23—441no—
354C23D8×D1111yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—441no—
358Q8—441no—
359Q8—882no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—111no—
367C2×C4—112no—
368C2×C4—112no—
369C2×C4—111no—
370C2×C4—222no—
371C2×C4—222no—
372C2×C4—222no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—442no—
376C2×C4—441no—
377C2×C4—441no—
378C2×C4—882no—
379C2×C4—882no—
380C2×C4—882no—
381C2×C4D8×D1111yescharacteristic
382C2×C4C2×D4×D1111yescharacteristic
383C8—21no—
384C8—112no—
385C8—221no—
386C8#41×D1112yes—
387C22—21no—
388C22—21no—
389C22—112no—
390C22—221no—
391C22—221no—
392C22—221no—
393C22—221no—
394C22—221no—
395C22—444no—
396C22#1062253112yes—
397C22C2×D8×D1111yescharacteristic
398C4—21no—
399C4—82no—
400C4—81no—
401C4—81no—
402C4—112no—
403C4—221no—
404C4—882no—
405C4—881no—
406C4—881no—
407C4D11×#12311yescharacteristic
408C4D11×#13711yescharacteristic
409C2—22no—
410C2—222no—
411C2—441no—
412C2D11×#48011yescharacteristic
413C2C2×#1062253111yescharacteristic
414C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2236C2
socleC22×C11C22×D8
prime radicalC23×D11D8
hypercenter#2236D11
hypocenterC11#33649
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2236

Complements

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

NH ≅ G/Ntype
3. #13070826C2semidirect
4. #13070822C2semidirect
5. #13070818C2semidirect
6. #13070814C2semidirect
7. #13070811C2semidirect
8. #13070401C2semidirect
9. #13070334C2semidirect
11. C11×#2236C2semidirect
32. C11×#366C22semidirect
33. C11×#358C22semidirect
35. #10622202C22semidirect
38. #10622143C22semidirect
39. #10622141C22semidirect
40. #10622130C22semidirect
41. #10622128C22semidirect
42. #10622127C22semidirect
147. #2236D11semidirect
214. #366C2×D11semidirect
218. #358C2×D11semidirect
348. C11#33649semidirect

Maximal subgroups

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

subgroupindex
D11×#4672
C2×#106224932
#130708262
#130708222
#130708182
#130708142
#130708112
#130704012
#130703342
#130702252
C11×#22362
#3364911