Finite Group Databasebeta

← #14908429

Subgroups — #14908429

Order 2816.

598 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079127C211yesmaximal, characteristic, complemented
2C4×D8×D11C211yesmaximal, characteristic
3#13070772C212yesmaximal, complemented
4#13070771C212yesmaximal, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070754C211yesmaximal, characteristic, complemented
7#13070753C211yesmaximal, characteristic, complemented
8#13070403C212yesmaximal, complemented
9#13070370C211yesmaximal, characteristic, complemented
10#13070330C212yesmaximal
11C11×#2226C211yesmaximal, characteristic, complemented
12C2×D8×D11C2211yescharacteristic
13#10623259—21no—
14C4×D4×D11—21no—
15C11×#500C2211yescharacteristic, complemented
16C4×C11×D8C2211yescharacteristic
17D8×Dic11C2211yescharacteristic
18#10622692—21no—
19C4×#4323—21no—
20C2×#66862C2212yes—
21#10622493—21no—
22#10622493C2212yes—
23D11×#107C2211yescharacteristic
24#10622491—21no—
25#10622491C2212yescomplemented
26#10622485C2211yescharacteristic
27D11×#102—21no—
28#10622369—21no—
29C4×D88C2211yescharacteristic
30C4×C8×D11C2211yescharacteristic
31#10622295C2211yescharacteristic, complemented
32C11×#367C2212yescomplemented
33C11×C4⋊C16C2211yescharacteristic, complemented
34C11×#357C2212yes—
35#10622200C2212yes—
36#10622147C2212yes—
37#10622142C2212yescomplemented
38Dic11⋊C16C2212yescomplemented
39#10622129C2212yes—
40#10622128C2212yescomplemented
41#10622127C2212yescomplemented
42C4⋊(C11⋊C16)C2211yescharacteristic, complemented
43C2×D4×D11—21no—
44C22×C4×D11—41no—
45C2×C11×D8C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C4×D4×C11—21no—
48#66999—41no—
49Q8×Dic11—41no—
50D4×Dic11—21no—
51C2×#4323—21no—
52C4×C22⋊D11—41no—
53D8×D11—22no—
54D8×D11Q814yescomplemented
55C2×D88C2311yescharacteristic
56C2×C8×D11D411yescharacteristic
57C2×C8×D11C2311yescharacteristic
58#66950—41no—
59#66946—21no—
60#66945—22no—
61C4⋊C4×D11—21no—
62#66943—22no—
63#66940—41no—
64(C22⋊D11)⋊C4—41no—
65C22⋊C4×D11—41no—
66C4×D44—21no—
67C42×D11D411yescharacteristic
68#66922—21no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#107C2311yescharacteristic
73C11×#102—21no—
74C4×C8×C11C2311yescharacteristic
75#66896—21no—
76#66885—21no—
77#66882—21no—
78#66882C2312yes—
79#66882C2311yescharacteristic
80C8×Dic11D411yescharacteristic
81C8×Dic11C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83#66873—21no—
84#66872—22no—
85#66872—22no—
86#66871—21no—
87C4×C11⋊C8D411yescharacteristic
88#66862—24no—
89#33627—111nomaximal, Sylow
90C23×D11—41no—
91C2×Q8×C11—41no—
92C2×D4×C11—21no—
93C22×C4×C11—41no—
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96D4×D11—24no—
97D4×D11—42no—
98C2×D44—21no—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×C4×D11—84no—
103C2×C4×D11D811yescharacteristic
104C2×C4×D11D811yescharacteristic
105C2×C4×D11C2×D411yescharacteristic
106C2×Dic22—41no—
107C11×D8—21no—
108C11×D8C2×Q812yes—
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2411yescharacteristic
111C11×C4⋊C4—21no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C42×C11C2×D411yescharacteristic
116C22⋊Dic11—41no—
117#4323—24no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—42no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—42no—
127C4×Dic11—42no—
128C4×Dic11D811yescharacteristic
129C4×Dic11D811yescharacteristic
130C4×Dic11C2×D411yescharacteristic
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133D88—21no—
134D88C2×Q812yes—
135C8×D11—22no—
136C8×D11C2×Q812yes—
137C8×D11#4112yes—
138C11×C16—22no—
139C11⋊C16—22no—
140#3160—111no—
141C2×C4×D8—111no—
142#2228—112no—
143#2228—112no—
144#2226—111no—
145#2226D1111yescharacteristic, complemented
146#2224—111no—
147#2224—111no—
148#2159—112no—
149#2150—111no—
150#2140—112no—
151C23×C11—41no—
152C22×D11—41no—
153C22×D11—44no—
154C22×D11—82no—
155C22×D11—82no—
156C22×D11C2×D811yescharacteristic
157Q8×C11—82no—
158D4×C11—22no—
159D4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—41no—
162C2×C4×C11—82no—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C22⋊D11—44no—
167C2×Dic11—42no—
168C2×Dic11—41no—
169C2×Dic11—82no—
170C2×Dic11C2×D811yescharacteristic
171C2×Dic11C2×D811yescharacteristic
172C2×Dic11C2×D811yescharacteristic
173D44—22no—
174D44—41no—
175C4×D11—22no—
176C4×D11—41no—
177C4×D11—82no—
178C4×D11—82no—
179C4×D11—82no—
180C4×D11C22⋊Q812yes—
181C4×D11#13712yes—
182Dic22—82no—
183C8×C11—21no—
184C8×C11C22×Q811yescharacteristic
185C8×C11C2×#4111yescharacteristic
186C11⋊C8—21no—
187C11⋊C8C22⋊Q812yes—
188C22×D8—111no—
189#533—221no—
190C2×C4×D4—221no—
191C2×M32—112no—
192#500—111no—
193#500C2×D1111yescharacteristic, complemented
194#499—112no—
195#499—221no—
196#498—221no—
197C4×D8—111no—
198C4×D8—111no—
199C4×D8—111no—
200C4×D8—221no—
201C4×D8—221no—
202C4×D8C2×D1111yescharacteristic
203#427—112no—
204#427—221no—
205C2×#107—111no—
206C2×#102—221no—
207C2×C4×C8—111no—
208#367—112no—
209#367C2×D1112yescomplemented
210#366—112no—
211#366—112no—
212C4⋊C16—112no—
213C4⋊C16—111no—
214C4⋊C16C2×D1111yescharacteristic, complemented
215#357—112no—
216#357—112no—
217#357—112no—
218#357C2×D1112yes—
219C22×C11—42no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11C22×D811yescharacteristic
223C2×D11—21no—
224C2×D11—21no—
225C2×D11—42no—
226C2×D11—88no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11#47412yes—
230C4×C11—21no—
231C4×C11—81no—
232C4×C11—82no—
233C4×C11#50912yes—
234C4×C11C2×C22⋊Q811yescharacteristic
235C4×C11C2×#13711yescharacteristic
236Dic11—21no—
237Dic11—21no—
238Dic11—82no—
239Dic11—81no—
240Dic11#47412yes—
241C22×D4—221no—
242C23×C4—441no—
243C2×D8—114no—
244C2×D8—111no—
245C2×D8—222no—
246C2×D8—221no—
247C2×D8C22×D1111yescharacteristic
248C22×C8—111no—
249C22×C8—111no—
250C4⋊Q8—21no—
251C4⋊Q8—221no—
252#125—222no—
253C22⋊Q8—441no—
254C22⋊Q8—441no—
255C4×Q8—441no—
256C4×Q8—441no—
257C4×D4—21no—
258C4×D4—221no—
259C4×D4—221no—
260C4×D4—221no—
261C4×D4—441no—
262C4×D4—441no—
263#117—222no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—441no—
266C2×C42—111no—
267M32—224no—
268C2×C16—112no—
269C2×C16C22×D1112yes—
270#107—21no—
271#107—112no—
272#107—111no—
273#107—221no—
274#107—221no—
275#107C22×D1112yes—
276#107C22×D1111yescharacteristic
277#106—222no—
278#106—222no—
279#102—21no—
280#102—221no—
281#102—221no—
282#102—221no—
283C4×C8—111no—
284C4×C8—111no—
285C4×C8—111no—
286C4×C8C22×D1111yescharacteristic
287C2×C11—82no—
288C2×C11C2×#47411yescharacteristic
289C2×C11C2×#50911yescharacteristic
290C2×C11#341411yescharacteristic
291D11—22no—
292D11—82no—
293C24—441no—
294C2×Q8—41no—
295C2×Q8—441no—
296C2×D4—21no—
297C2×D4—224no—
298C2×D4—221no—
299C2×D4—442no—
300C2×D4—441no—
301C22×C4—41no—
302C22×C4—111no—
303C22×C4—111no—
304C22×C4—111no—
305C22×C4—441no—
306C22×C4—441no—
307C22×C4—441no—
308C22×C4—441no—
309C22×C4—884no—
310D8—21no—
311D8—112no—
312D8—224no—
313D8—221no—
314D8Q8×D1112yes—
315C2×C8—111no—
316C2×C8—112no—
317C2×C8—112no—
318C2×C8—111no—
319C2×C8—222no—
320C2×C8D4×D1111yescharacteristic
321C2×C8C23×D1111yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—22no—
324C4⋊C4—41no—
325C4⋊C4—221no—
326C4⋊C4—222no—
327C4⋊C4—441no—
328C4⋊C4—442no—
329C4⋊C4—442no—
330C4⋊C4—441no—
331C22⋊C4—41no—
332C22⋊C4—441no—
333C22⋊C4—442no—
334C22⋊C4—441no—
335C22⋊C4—441no—
336C42—111no—
337C42—111no—
338C42—111no—
339C42—442no—
340C42D4×D1111yescharacteristic
341C16—22no—
342C16—222no—
343C11#3362711yescharacteristic, complemented, Sylow
344C23—41no—
345C23—111no—
346C23—444no—
347C23—441no—
348C23—882no—
349C23—882no—
350Q8—82no—
351Q8—882no—
352D4—22no—
353D4—41no—
354D4—222no—
355D4—444no—
356D4—441no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—82no—
360C2×C4—111no—
361C2×C4—112no—
362C2×C4—112no—
363C2×C4—111no—
364C2×C4—111no—
365C2×C4—222no—
366C2×C4—441no—
367C2×C4—442no—
368C2×C4—441no—
369C2×C4—882no—
370C2×C4—882no—
371C2×C4—882no—
372C2×C4—882no—
373C2×C4D8×D1111yescharacteristic
374C2×C4D8×D1111yescharacteristic
375C2×C4C2×D4×D1111yescharacteristic
376C8—21no—
377C8—112no—
378C8—221no—
379C8C2×Q8×D1111yescharacteristic
380C8#41×D1111yescharacteristic
381C22—42no—
382C22—81no—
383C22—81no—
384C22—112no—
385C22—221no—
386C22—221no—
387C22—442no—
388C22—888no—
389C22—881no—
390C22—881no—
391C22C2×D8×D1111yescharacteristic
392C4—21no—
393C4—81no—
394C4—82no—
395C4—112no—
396C4—221no—
397C4—221no—
398C4—881no—
399C4—882no—
400C4#1062252712yes—
401C4D11×C22⋊Q811yescharacteristic
402C4D11×#13711yescharacteristic
403C2—82no—
404C2—222no—
405C2—882no—
406C2D11×#47411yescharacteristic
407C2C2×#1062252711yescharacteristic
408C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
prime radicalC2×D8×D11C22
hypercenter#2226D11
hypocenterC11#33627
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #13079127C2semidirect
3. #13070772C2semidirect
4. #13070771C2semidirect
5. #13070760C2semidirect
6. #13070754C2semidirect
7. #13070753C2semidirect
8. #13070403C2semidirect
9. #13070370C2semidirect
11. C11×#2226C2semidirect
15. C11×#500C22semidirect
25. #10622491C22semidirect
31. #10622295C22semidirect
32. C11×#367C22semidirect
33. C11×C4⋊C16C22semidirect
37. #10622142C22semidirect
38. Dic11⋊C16C22semidirect
40. #10622128C22semidirect
41. #10622127C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
54. D8×D11Q8semidirect
145. #2226D11semidirect
193. #500C2×D11semidirect
209. #367C2×D11semidirect
214. C4⋊C16C2×D11semidirect
343. C11#33627semidirect

Maximal subgroups

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

subgroupindex
#130791272
C4×D8×D112
#130707722
#130707712
#130707602
#130707542
#130707532
#130704032
#130703702
#130703302
C11×#22262
#3362711