Finite Group Databasebeta

← #14670766

Subgroups — #14670766

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#13078198C211yesmaximal, characteristic
2C2×D11×#106C211yesmaximal, characteristic, complemented
3C2×#10622156C211yesmaximal, characteristic, complemented
4C2×#10622126C211yesmaximal, characteristic, complemented
5#13070226C211yesmaximal, characteristic, complemented
6#13066721C211yesmaximal, characteristic, complemented
7C11×#1386C211yesmaximal, characteristic, complemented
8C2×#66957C2211yescharacteristic
9C22×C8×D11C2211yescharacteristic
10#10623055—21no—
11C2×C4⋊C4×D11—21no—
12C2×C11×M32C2211yescharacteristic
13C11×#427C2211yescharacteristic
14C2×C11×#106C2211yescharacteristic
15C2×#66881C2211yescharacteristic
16C2×#66876C2211yescharacteristic
17#10622615—21no—
18C2×#66872—21no—
19#10622500C412yescomplemented
20#10622496C412yescomplemented
21#10622477—22no—
22D11×#106—22no—
23D11×#106—22no—
24#10622156—22no—
25(C2×D11)⋊C16—22no—
26#10622126—22no—
27C2×#4339—21no—
28C22×C4×D11—41no—
29C22×C4×D11D411yescharacteristic
30C22×C8×C11C2311yescharacteristic
31C11×#117—21no—
32C2×C11×C4⋊C4—21no—
33C2×C4⋊Dic11—21no—
34C2×Dic11⋊C4—41no—
35C22×C11⋊C8D411yescharacteristic
36C2×Dic44C2×C411yescharacteristic, complemented
37#66957—21no—
38#66957—21no—
39#66957—21no—
40#66957—21no—
41C2×D88C2×C411yescharacteristic, complemented
42C2×#4314—21no—
43C2×C8×D11—21no—
44C2×C8×D11—21no—
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47C2×C8×D11C2×C412yes—
48C2×C8×D11D412yes—
49#66950—22no—
50#66948—22no—
51C4⋊C4×D11—24no—
52C4⋊C4×D11—42no—
53#66939—41no—
54#66935—41no—
55C4×D44—42no—
56C11×M32—21no—
57C11×M32—21no—
58C2×C11×C16—21no—
59C11×#107C2×C412yescomplemented
60C11×#106—21no—
61C11×#106—21no—
62C11×#106D412yescomplemented
63#66881—21no—
64#66881D412yescomplemented
65#66876—21no—
66#66876—21no—
67C2×C11⋊C16—21no—
68#66874—22no—
69#66873—22no—
70#66872—24no—
71#13001—111nomaximal, Sylow
72C23×D11D811yescharacteristic
73C22×C4×C11—41no—
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—41no—
76C22×Dic11—41no—
77C22×Dic11D811yescharacteristic
78#4339—41no—
79#4339—41no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×D44—42no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11—44no—
89C2×C4×D11—41no—
90C2×C4×D11—84no—
91C2×C4×D11C22⋊C412yes—
92C2×C4×D11SD1612yes—
93C2×Dic22—21no—
94C2×C8×C11C22×C411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C11×C4⋊C4—22no—
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—41no—
104C42×C11—41no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—42no—
107C4⋊Dic11—22no—
108C4⋊Dic11—42no—
109C4⋊Dic11—41no—
110Dic11⋊C4—44no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8C22⋊C412yes—
114Dic44—21no—
115Dic44—21no—
116D88—21no—
117D88—21no—
118#4314—41no—
119#4314—41no—
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×#360—111no—
130#2112—111no—
131#1386—111no—
132#1386D1111yescharacteristic, complemented
133C23×C11C2×D811yescharacteristic
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—24no—
137C22×D11—41no—
138C22×D11#10212yes—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—82no—
142C2×C4×C11C2×C22⋊C411yescharacteristic
143C2×C4×C11#12011yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11C2×SD1611yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C22⋊D11—81no—
149C22⋊D11—81no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—41no—
153C2×Dic11—42no—
154C2×Dic11—82no—
155C2×Dic11#10212yes—
156D44—41no—
157D44—41no—
158D44—84no—
159C4×D11—22no—
160C4×D11—22no—
161C4×D11—22no—
162C4×D11—22no—
163C4×D11—88no—
164C4×D11—81no—
165C4×D11—81no—
166Dic22—41no—
167Dic22—41no—
168C8×C11C4×D411yescharacteristic
169C8×C11C4×D411yescharacteristic
170C8×C11#12111yescharacteristic
171C8×C11#12111yescharacteristic
172C11⋊C8—22no—
173C2×#135—111no—
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#427C2×D1111yescharacteristic
183C2×#106—111no—
184C2×#106—222no—
185C2×#106—221no—
186C2×#106—222no—
187C2×#106C2×D1111yescharacteristic
188#416—221no—
189#360—222no—
190#360—222no—
191C22⋊C16—222no—
192C22×C11—22no—
193C22×C11C2×#10211yescharacteristic
194C22×C11#44711yescharacteristic
195C22×C11#48011yescharacteristic
196C2×D11—24no—
197C2×D11—24no—
198C2×D11—22no—
199C2×D11—22no—
200C2×D11—81no—
201C2×D11—82no—
202C2×D11#36014yescomplemented
203C4×C11—82no—
204C4×C11—82no—
205C4×C11#38611yescharacteristic
206C4×C11#41711yescharacteristic
207C4×C11#44811yescharacteristic
208C4×C11#48111yescharacteristic
209Dic11—22no—
210Dic11—82no—
211Dic11—81no—
212C2×#41—221no—
213C23×C4—111no—
214C23×C4—441no—
215#135—221no—
216#135—221no—
217#135—221no—
218#135—221no—
219C2×Q16—111no—
220C2×SD16—221no—
221C2×D8—111no—
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—21no—
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#107C4×D1112yescomplemented
248#106—21no—
249#106—21no—
250#106—112no—
251#106—224no—
252#106—221no—
253#106D4412yescomplemented
254#103—222no—
255#102—222no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11#187411yescharacteristic
259C2×C11C2×#36012yes—
260D11—24no—
261D11—161no—
262C24—111no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—221no—
268C2×D4—221no—
269C2×D4—442no—
270C2×D4—441no—
271C22×C4—41no—
272C22×C4—111no—
273C22×C4—112no—
274C22×C4—112no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—444no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4—884no—
283C22×C4D4×D1111yescharacteristic
284Q16—221no—
285Q16—221no—
286SD16—441no—
287SD16—441no—
288D8—221no—
289D8—221no—
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×C8C2×D4411yescharacteristic
299C2×C8#433911yescharacteristic
300C2×C8D4×D1111yescharacteristic
301C2×C8D4×D1111yescharacteristic
302C2×C8#434311yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—22no—
305C4⋊C4—41no—
306C4⋊C4—222no—
307C4⋊C4—442no—
308C4⋊C4—444no—
309C4⋊C4—441no—
310C22⋊C4—41no—
311C22⋊C4—442no—
312C22⋊C4—442no—
313C42—41no—
314C16—41no—
315C16—441no—
316C11#1300111yescharacteristic, complemented, Sylow
317C23—112no—
318C23—224no—
319C23—221no—
320C23—221no—
321C23—441no—
322C23D8×D1111yescharacteristic
323Q8—441no—
324Q8—441no—
325D4—441no—
326D4—441no—
327D4—884no—
328D4—881no—
329D4—881no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—82no—
333C2×C4—112no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—222no—
337C2×C4—222no—
338C2×C4—222no—
339C2×C4—222no—
340C2×C4—441no—
341C2×C4—442no—
342C2×C4—888no—
343C2×C4—882no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4C22⋊C4×D1111yescharacteristic
347C2×C4#6693511yescharacteristic
348C2×C4#6694711yescharacteristic
349C2×C4SD16×D1111yescharacteristic
350C2×C4#6696711yescharacteristic
351C2×C4#6697111yescharacteristic
352C8—222no—
353C8C4×D4411yescharacteristic
354C8#6693711yescharacteristic
355C8#6694611yescharacteristic
356C8#6694811yescharacteristic
357C22—22no—
358C22—114no—
359C22—224no—
360C22—224no—
361C22—222no—
362C22—222no—
363C22—882no—
364C22—881no—
365C22D11×#10211yescharacteristic
366C22#1062238611yescharacteristic
367C22#1062249511yescharacteristic
368C4—82no—
369C4—82no—
370C4—222no—
371C4—882no—
372C4—881no—
373C4#1062227811yescharacteristic
374C4#1062241611yescharacteristic
375C4#1062241911yescharacteristic
376C4#1062247611yescharacteristic
377C2—21no—
378C2—21no—
379C2—224no—
380C2—1761no—
381C2#1306893211yescharacteristic
382C2D11×#36012yes—
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1386C2
socleC22×C11C2×#102
prime radical#13078198C2
cosocleC22×C8×C11C23
hypercenter#1386D11
hypocenterC11#13001
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
2. C2×D11×#106C2semidirect
3. C2×#10622156C2semidirect
4. C2×#10622126C2semidirect
5. #13070226C2semidirect
6. #13066721C2semidirect
7. C11×#1386C2semidirect
19. #10622500C4semidirect
20. #10622496C4semidirect
36. C2×Dic44C2×C4semidirect
41. C2×D88C2×C4semidirect
59. C11×#107C2×C4semidirect
62. C11×#106D4semidirect
64. #66881D4semidirect
132. #1386D11semidirect
202. C2×D11#360semidirect
247. #107C4×D11semidirect
253. #106D44semidirect
316. C11#13001semidirect

Maximal subgroups

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

subgroupindex
#130781982
C2×D11×#1062
C2×#106221562
C2×#106221262
#130702262
#130667212
C11×#13862
#1300111