Finite Group Databasebeta

← #14745787

Subgroups — #14745787

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081356C212yesmaximal
2#13081048C211yesmaximal, characteristic
3#13068225C211yesmaximal, characteristic, complemented
4#13068200C212yesmaximal, complemented
5#13068012C211yesmaximal, characteristic
6#13068010C211yesmaximal, characteristic, complemented
7#13067837C212yesmaximal, complemented
8#13067787C212yesmaximal
9#13067513C211yesmaximal, characteristic, complemented
10C8×#4325C211yesmaximal, characteristic
11Q8×C11×Q16C211yesmaximal, characteristic, complemented
12Q82×C11C2212yes—
13#10623115C2212yes—
14C11×#500—21no—
15C11×#500C2211yescharacteristic
16C11×#477—22no—
17C11×#477C2212yes—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×Q16—21no—
20C4×C11×Q16C2211yescharacteristic
21#10622801—21no—
22#10622707—22no—
23#10622706C2212yes—
24#10622702—22no—
25#10622697C2212yes—
26#10622694C2212yes—
27#10622644C2212yes—
28#10622643—22no—
29#10622641—22no—
30C4×#4325C2211yescharacteristic
31#10622637C2212yes—
32#10622633C2212yes—
33#10622493—21no—
34#10622427—22no—
35C8×D44C2211yescharacteristic
36#10622295C2211yescharacteristic
37#10622184C2212yes—
38Q8⋊(C11⋊C8)C2212yes—
39Q8⋊(C11⋊C8)C2211yescharacteristic
40#10622124C2212yes—
41#10622121C2211yescharacteristic
42#10622118C2211yescharacteristic
43#10622096C2211yescharacteristic
44C8×C11⋊C8C2211yescharacteristic
45C2×C11×Q16D411yescharacteristic
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—42no—
49C11×C4⋊Q8C2312yes—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11C2312yes—
53C4×Q8×C11C2311yescharacteristic
54#66999—22no—
55C2×#4326—22no—
56C2×#4325D411yescharacteristic
57C2×C8×D11—21no—
58#66951—42no—
59#66945—22no—
60#66928—22no—
61C4×D44C2311yescharacteristic
62#66922C2312yes—
63C4×Dic22—22no—
64C11×#107—21no—
65C11×#107—21no—
66C11×#107—22no—
67C11×#107D411yescharacteristic
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2311yescharacteristic
70C11×#103—22no—
71C11×#103D412yes—
72C4×C8×C11—21no—
73C4×C8×C11C2311yescharacteristic
74#66899—22no—
75#66899—42no—
76#66899D411yescharacteristic
77(C2×D11)⋊C8—21no—
78#66882—21no—
79#66882—21no—
80#66874—22no—
81#66874—22no—
82#66874—22no—
83#66873—22no—
84#66873D411yescharacteristic
85#66872—22no—
86#66872—22no—
87#66872D411yescharacteristic
88C4⋊(C11⋊C8)—22no—
89C4⋊(C11⋊C8)C2311yescharacteristic
90C4⋊(C11⋊C8)C2312yes—
91#66867—22no—
92C4×C11⋊C8C2311yescharacteristic
93C4×C11⋊C8C2311yescharacteristic
94#19940—111nomaximal, Sylow
95C2×Q8×C11—22no—
96C2×Q8×C11—42no—
97C2×Q8×C11C2×D412yes—
98C2×Q8×C11C2×D411yescharacteristic
99C2×D44C2×D411yescharacteristic
100C2×C4×D11—21no—
101C2×Dic22—22no—
102C11×Q16—22no—
103C2×C8×C11—21no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C11×C4⋊C4—22no—
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—42no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4C2×D411yescharacteristic
113C11×C4⋊C4C2×D412yes—
114C42×C11—22no—
115C42×C11—21no—
116C42×C11—42no—
117C42×C11C2411yescharacteristic
118#4326—44no—
119#4325—22no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—42no—
122(C2×D11)⋊C4—42no—
123C4⋊Dic11—22no—
124C4⋊Dic11—22no—
125C4⋊Dic11C2×D411yescharacteristic
126Dic11⋊C4—42no—
127C4×Dic11—42no—
128C2×C11⋊C8—22no—
129C2×C11⋊C8—21no—
130C2×C11⋊C8—21no—
131C2×C11⋊C8C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C8×D11—42no—
134Q8×Q16D1111yescharacteristic, complemented
135#3369—112no—
136#3342—111no—
137#1710—111no—
138#1704—112no—
139#1675—111no—
140#1674—111no—
141#1645—112no—
142#1638—112no—
143#1591—111no—
144C8×SD16—111no—
145C22×D11—21no—
146Q8×C11—21no—
147Q8×C11—22no—
148Q8×C11—22no—
149Q8×C11—82no—
150Q8×C11—162no—
151Q8×C11#13512yes—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—21no—
156C2×C4×C11—42no—
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11H(5,𝔽2)11yescharacteristic
160C2×Dic11—21no—
161C2×Dic11—42no—
162D44—21no—
163D44—21no—
164C4×D11—41no—
165C4×D11—41no—
166Dic22—42no—
167Dic22—42no—
168C8×C11—21no—
169C8×C11—41no—
170C8×C11#13712yes—
171C11⋊C8—21no—
172C11⋊C8—21no—
173C11⋊C8—41no—
174C11⋊C8—42no—
175C11⋊C8—41no—
176Q82C2×D1112yes—
177#556—112no—
178#500—21no—
179#500—111no—
180#500C2×D1111yescharacteristic
181#489—222no—
182#487—112no—
183#487—112no—
184#485—222no—
185#477—22no—
186#477C2×D1112yes—
187#476—112no—
188#475—112no—
189#475—222no—
190#467—221no—
191#464—222no—
192#462—112no—
193#446—112no—
194C8×Q8C2×D1111yescharacteristic
195#441—222no—
196C4×Q16—21no—
197C4×Q16C2×D1111yescharacteristic
198C4×SD16—111no—
199C8×D4—111no—
200#427—221no—
201#335—111no—
202#334—111no—
203#333—112no—
204#332—112no—
205Q8⋊C8—111no—
206Q8⋊C8—112no—
207D4⋊C8—111no—
208C82—111no—
209C22×C11D4211yescharacteristic
210C2×D11—41no—
211C2×D11—41no—
212C2×D11—41no—
213C4×C11—22no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—42no—
217C4×C11—41no—
218C4×C11—82no—
219C4×C11C2×#13511yescharacteristic
220C4×C11C2×#13711yescharacteristic
221C4×C11#57811yescharacteristic
222C4×C11#57811yescharacteristic
223Dic11—41no—
224Dic11—82no—
225C2×Q16—222no—
226C2×Q16C22⋊D1111yescharacteristic
227C2×SD16—111no—
228C22×C8—221no—
229C4⋊Q8—22no—
230C4⋊Q8—22no—
231C4⋊Q8—42no—
232C4⋊Q8—112no—
233C4⋊Q8C22×D1112yes—
234#126—442no—
235#124—222no—
236C22⋊Q8—222no—
237C4×Q8—22no—
238C4×Q8—22no—
239C4×Q8—222no—
240C4×Q8C22×D1111yescharacteristic
241C4×Q8C22×D1112yes—
242C4×D4—111no—
243#117—222no—
244#107—21no—
245#107—21no—
246#107—22no—
247#107—221no—
248#107—221no—
249#107C22⋊D1111yescharacteristic
250#106—111no—
251#106—222no—
252#106—222no—
253C4⋊C8—21no—
254C4⋊C8—112no—
255C4⋊C8—111no—
256C4⋊C8—222no—
257C4⋊C8C22×D1111yescharacteristic
258#103—22no—
259#103—111no—
260#103—222no—
261#103—222no—
262#103—222no—
263#103—222no—
264#103—442no—
265#103C22⋊D1112yes—
266#102—111no—
267#102—222no—
268C22⋊C8—221no—
269#97—222no—
270C4×C8—21no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8C22×D1111yescharacteristic
274C2×C11#327611yescharacteristic
275C2×C11#328511yescharacteristic
276C2×C11#329011yescharacteristic
277D11—81no—
278C2×Q8—22no—
279C2×Q8—42no—
280C2×Q8—222no—
281C2×Q8D4×D1111yescharacteristic
282C2×Q8C2×C22⋊D1112yes—
283C2×D4—111no—
284C22×C4—221no—
285Q16—22no—
286Q16—444no—
287SD16—222no—
288C2×C8—21no—
289C2×C8—111no—
290C2×C8—111no—
291C2×C8—222no—
292C2×C8—221no—
293C2×C8—221no—
294C2×C8—442no—
295C2×C8C2×C22⋊D1111yescharacteristic
296C2×C8C2×C22⋊D1111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—111no—
304C4⋊C4—222no—
305C4⋊C4—222no—
306C4⋊C4—442no—
307C4⋊C4D4×D1111yescharacteristic
308C4⋊C4C2×C22⋊D1112yes—
309C22⋊C4—221no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C42—22no—
313C42—21no—
314C42—42no—
315C42—442no—
316C42C23×D1111yescharacteristic
317C11#1994011yescharacteristic, complemented, Sylow
318C23—221no—
319Q8—21no—
320Q8—22no—
321Q8—22no—
322Q8—82no—
323Q8—162no—
324Q8—442no—
325Q8—442no—
326Q8#6697212yes—
327D4—221no—
328D4—221no—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—221no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4C2×D4×D1111yescharacteristic
339C2×C4#6703711yescharacteristic
340C2×C4C22×C22⋊D1111yescharacteristic
341C8—21no—
342C8—41no—
343C8—221no—
344C8—221no—
345C8—441no—
346C8—442no—
347C8—441no—
348C8#6699512yes—
349C22—441no—
350C22—441no—
351C22—441no—
352C22D4×C22⋊D1111yescharacteristic
353C4—22no—
354C4—21no—
355C4—41no—
356C4—42no—
357C4—42no—
358C4—82no—
359C4—441no—
360C4—882no—
361C4C2×#6697211yescharacteristic
362C4#1062329711yescharacteristic
363C4C2×#6699511yescharacteristic
364C4#1062336911yescharacteristic
365C2—881no—
366C2#1308026211yescharacteristic
367C2#1308035711yescharacteristic
368C2#1308039811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×Q16C2
socleC22×C11D42
prime radicalC2×D44C2×D4
hypercenterQ8×Q16D11
hypocenterC11#19940
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ Q8×Q16

Complements

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

NH ≅ G/Ntype
3. #13068225C2semidirect
4. #13068200C2semidirect
6. #13068010C2semidirect
7. #13067837C2semidirect
9. #13067513C2semidirect
11. Q8×C11×Q16C2semidirect
134. Q8×Q16D11semidirect
317. C11#19940semidirect

Maximal subgroups

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

subgroupindex
#130813562
#130810482
#130682252
#130682002
#130680122
#130680102
#130678372
#130677872
#130675132
C8×#43252
Q8×C11×Q162
#1994011