Finite Group Databasebeta

← #14670764

Subgroups — #14670764

Order 2816.

572 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078193C211yesmaximal, characteristic
2C2×D11×#106C211yesmaximal, characteristic, complemented
3C2×#10622204C211yesmaximal, characteristic, complemented
4#13070226C211yesmaximal, characteristic, complemented
5#13066723C211yesmaximal, characteristic, complemented
6#13066722C211yesmaximal, characteristic, complemented
7C2×C11×#360C211yesmaximal, characteristic, complemented
8C2×C11×#135C2211yescharacteristic
9#10623359—21no—
10C22×C8×D11C2211yescharacteristic
11C2×C4⋊C4×D11—21no—
12C2×C11×M32C2211yescharacteristic
13C2×C11×#106C2211yescharacteristic
14#10622846—21no—
15#10622801C412yescomplemented
16#10622784—22no—
17#10622770C412yescomplemented
18#10622719C2211yescharacteristic
19C2×#66881C2211yescharacteristic
20C2×#66876C2211yescharacteristic
21C2×#66872—21no—
22D11×#106—22no—
23D11×#106—22no—
24C11×#360—22no—
25#10622204—22no—
26(C2×D11)⋊C16—22no—
27C2×C11×#41—21no—
28C22×C4×D11—41no—
29C22×C4×D11D411yescharacteristic
30C11×#135—21no—
31C11×#135—21no—
32C11×#135—21no—
33C11×#135—21no—
34C2×C11×Q16C2×C411yescharacteristic, complemented
35C2×C11×SD16—21no—
36C2×C11×D8C2×C411yescharacteristic, complemented
37C22×C8×C11C2311yescharacteristic
38C2×C11×C4⋊C4—21no—
39#66999—22no—
40#66991—22no—
41#66990—41no—
42#66988—41no—
43C4×C22⋊D11—42no—
44#66979—21no—
45C2×C4⋊Dic11—21no—
46C2×Dic11⋊C4—41no—
47C22×C11⋊C8D411yescharacteristic
48C2×C8×D11—21no—
49C2×C8×D11—21no—
50C2×C8×D11—21no—
51C2×C8×D11—21no—
52C2×C8×D11C2×C412yes—
53C2×C8×D11D412yes—
54C4⋊C4×D11—24no—
55C4⋊C4×D11—42no—
56C11×M32—21no—
57C11×M32—21no—
58C2×C11×C16—21no—
59C11×#106—21no—
60C11×#106D412yescomplemented
61#66899—22no—
62#66896—22no—
63#66882C2×C412yescomplemented
64#66881—21no—
65#66881—21no—
66#66881D412yescomplemented
67#66876—21no—
68#66876—21no—
69C2×C11⋊C16—21no—
70#66872—24no—
71#13001—111nomaximal, Sylow
72C23×D11D811yescharacteristic
73C11×#41—41no—
74C11×#41—41no—
75C11×#41—41no—
76C11×#41—41no—
77C2×Q8×C11—21no—
78C2×D4×C11—21no—
79C2×D4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11C2×D411yescharacteristic
83C2×C22⋊D11—42no—
84C22×Dic11—41no—
85C22×Dic11D811yescharacteristic
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11—21no—
90C2×C4×D11—44no—
91C2×C4×D11—84no—
92C2×C4×D11C22⋊C412yes—
93C2×C4×D11SD1612yes—
94C11×Q16—21no—
95C11×Q16—21no—
96C11×SD16—41no—
97C11×SD16—41no—
98C11×D8—21no—
99C11×D8—21no—
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11#4111yescharacteristic
105C2×C8×C11#4111yescharacteristic
106C11×C4⋊C4—22no—
107C11×C4⋊C4—41no—
108C22⋊Dic11—42no—
109C22⋊Dic11—41no—
110(C2×D11)⋊C4—42no—
111C4⋊Dic11—22no—
112C4⋊Dic11—22no—
113C4⋊Dic11—41no—
114Dic11⋊C4—44no—
115Dic11⋊C4—42no—
116C4×Dic11—41no—
117C2×C11⋊C8—21no—
118C2×C11⋊C8—21no—
119C2×C11⋊C8C22⋊C412yes—
120C8×D11—22no—
121C8×D11—22no—
122C8×D11—22no—
123C8×D11—22no—
124C11×C16—41no—
125C11⋊C16—41no—
126#3050—111no—
127C22×#106—111no—
128C2×#360—111no—
129C2×#360D1111yescharacteristic, complemented
130#2112—111no—
131#1386—111no—
132#1386—111no—
133C23×C11—41no—
134C23×C11C2×D811yescharacteristic
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—24no—
138C22×D11#10212yes—
139Q8×C11—41no—
140Q8×C11—41no—
141D4×C11—41no—
142D4×C11—41no—
143D4×C11—81no—
144D4×C11—81no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—82no—
148C2×C4×C11—81no—
149C2×C4×C11—81no—
150C2×C4×C11C2×C22⋊C411yescharacteristic
151C2×C4×C11#12011yescharacteristic
152C2×C4×C11#12311yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C11#13711yescharacteristic
156C22⋊D11—84no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11—82no—
162C2×Dic11#10212yes—
163C4×D11—22no—
164C4×D11—22no—
165C4×D11—22no—
166C4×D11—22no—
167C4×D11—88no—
168C8×C11C4×D411yescharacteristic
169C8×C11C4×D411yescharacteristic
170C8×C11#12111yescharacteristic
171C8×C11#12111yescharacteristic
172C11⋊C8—22no—
173C2×#135C2×D1111yescharacteristic
174C23×C8—111no—
175#525—221no—
176C22×C4⋊C4—221no—
177C2×M32—111no—
178C2×M32C2×D1111yescharacteristic
179#467—112no—
180#466—112no—
181#465—222no—
182#427—111no—
183C2×#106—111no—
184C2×#106—222no—
185C2×#106—221no—
186C2×#106—222no—
187C2×#106C2×D1111yescharacteristic
188#416—221no—
189#360—22no—
190#360—222no—
191C22⋊C16—222no—
192C22×C11—22no—
193C22×C11—81no—
194C22×C11—82no—
195C22×C11C2×#10211yescharacteristic
196C22×C11#44711yescharacteristic
197C22×C11#48011yescharacteristic
198C2×D11—24no—
199C2×D11—24no—
200C2×D11—22no—
201C2×D11—22no—
202C2×D11#36014yescomplemented
203C4×C11—82no—
204C4×C11—81no—
205C4×C11#38611yescharacteristic
206C4×C11#41711yescharacteristic
207C4×C11#44811yescharacteristic
208C4×C11#48111yescharacteristic
209Dic11—22no—
210Dic11—82no—
211Dic11—82no—
212C2×#41—21no—
213C23×C4—111no—
214C23×C4—441no—
215#135—21no—
216#135—21no—
217#135—21no—
218#135—21no—
219C2×Q16C4×D1111yescharacteristic, complemented
220C2×SD16—21no—
221C2×D8C4×D1111yescharacteristic, complemented
222C22×C8—111no—
223C22×C8—112no—
224C22×C8—112no—
225C22×C8—221no—
226C22×C8—221no—
227C22×C8—221no—
228C22×C8—221no—
229C22×C8C22×D1111yescharacteristic
230#123—441no—
231C22⋊Q8—222no—
232#121—222no—
233#120—441no—
234C4×D4—442no—
235#117—221no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—224no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—442no—
240C2×C4⋊C4—441no—
241M32—21no—
242M32—21no—
243M32—221no—
244M32—221no—
245C2×C16—21no—
246C2×C16—221no—
247#107—112no—
248#106—21no—
249#106—112no—
250#106—224no—
251#106—221no—
252#106—221no—
253#106C22⋊D1112yescomplemented
254#103—222no—
255#102—222no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—161no—
259C2×C11#187411yescharacteristic
260C2×C11C2×#36012yes—
261D11—24no—
262C24—111no—
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267C2×Q8—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—442no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—111no—
274C22×C4—112no—
275C22×C4—112no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—444no—
281C22×C4—441no—
282C22×C4—884no—
283C22×C4D4×D1111yescharacteristic
284Q16—21no—
285Q16—21no—
286SD16—41no—
287SD16—41no—
288D8—21no—
289D8—21no—
290C2×C8—112no—
291C2×C8—221no—
292C2×C8—221no—
293C2×C8—222no—
294C2×C8—222no—
295C2×C8—222no—
296C2×C8—222no—
297C2×C8C2×C4×D1111yescharacteristic
298C2×C8#433911yescharacteristic
299C2×C8D4×D1111yescharacteristic
300C2×C8D4×D1111yescharacteristic
301C2×C8#434111yescharacteristic
302C2×C8C2×C22⋊D1111yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—222no—
306C4⋊C4—222no—
307C4⋊C4—442no—
308C4⋊C4—444no—
309C4⋊C4—441no—
310C22⋊C4—442no—
311C22⋊C4—442no—
312C22⋊C4—441no—
313C42—441no—
314C16—41no—
315C16—441no—
316C11#1300111yescharacteristic, complemented, Sylow
317C23—41no—
318C23—112no—
319C23—224no—
320C23—221no—
321C23—221no—
322C23D8×D1111yescharacteristic
323Q8—41no—
324Q8—41no—
325D4—41no—
326D4—41no—
327D4—81no—
328D4—81no—
329D4—884no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—112no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—222no—
341C2×C4—222no—
342C2×C4—442no—
343C2×C4—442no—
344C2×C4—888no—
345C2×C4—882no—
346C2×C4C22⋊C4×D1111yescharacteristic
347C2×C4#6693611yescharacteristic
348C2×C4#6696411yescharacteristic
349C2×C4SD16×D1111yescharacteristic
350C2×C4#6696811yescharacteristic
351C2×C4#6699011yescharacteristic
352C8—222no—
353C8(C22⋊D11)⋊C411yescharacteristic
354C8#6693711yescharacteristic
355C8C4×C22⋊D1111yescharacteristic
356C8#6699111yescharacteristic
357C22—22no—
358C22—82no—
359C22—81no—
360C22—114no—
361C22—224no—
362C22—224no—
363C22—222no—
364C22—222no—
365C22D11×#10211yescharacteristic
366C22#1062238711yescharacteristic
367C22#1062276911yescharacteristic
368C4—82no—
369C4—81no—
370C4—222no—
371C4—882no—
372C4—882no—
373C4#1062238411yescharacteristic
374C4#1062239011yescharacteristic
375C4#1062256911yescharacteristic
376C4#1062278311yescharacteristic
377C2—21no—
378C2—21no—
379C2—161no—
380C2—224no—
381C2#1306893011yescharacteristic
382C2D11×#36012yes—
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#360C2
socleC22×C11C2×#102
prime radical#13078193C2
cosocleC22×C8×C11C23
hypercenterC2×#360D11
hypocenterC11#13001
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#360

Complements

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

NH ≅ G/Ntype
2. C2×D11×#106C2semidirect
3. C2×#10622204C2semidirect
4. #13070226C2semidirect
5. #13066723C2semidirect
6. #13066722C2semidirect
7. C2×C11×#360C2semidirect
15. #10622801C4semidirect
17. #10622770C4semidirect
34. C2×C11×Q16C2×C4semidirect
36. C2×C11×D8C2×C4semidirect
60. C11×#106D4semidirect
63. #66882C2×C4semidirect
66. #66881D4semidirect
129. C2×#360D11semidirect
202. C2×D11#360semidirect
219. C2×Q16C4×D11semidirect
221. C2×D8C4×D11semidirect
253. #106C22⋊D11semidirect
316. C11#13001semidirect

Maximal subgroups

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

subgroupindex
#130781932
C2×D11×#1062
C2×#106222042
#130702262
#130667232
#130667222
C2×C11×#3602
#1300111