Finite Group Databasebeta

← #14649514

Subgroups — #14649514

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
2#13068684C211yesmaximal, characteristic, complemented
3C2×#10622175C212yesmaximal
4#13066494C212yesmaximal, complemented
5C11×#2854C211yesmaximal, characteristic
6C2×C11×#123—21no—
7C2×C11×#121C2211yescharacteristic
8C22×C42×C11C2211yescharacteristic
9C22×C4⋊Dic11—21no—
10C22×C4×Dic11—21no—
11C11×#390C412yescomplemented
12C11×#389C412yescomplemented
13C11×#388—22no—
14C11×#386—21no—
15C11×#380C2211yescharacteristic
16C2×C11⋊#95C2212yes—
17C2×C22⋊(C11⋊C8)C2212yes—
18C4×C4⋊Dic11—24no—
19#10622175—24no—
20#10622162—22no—
21C22×D4×C11—21no—
22C22×D4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11—22no—
27C11×#123—42no—
28C11×#123—42no—
29C11×#121—22no—
30C11×#121—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C11×C4⋊C4C2×C412yes—
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—22no—
36C2×C11×C22⋊C4—22no—
37C2×C11×C22⋊C4—21no—
38C2×C42×C11—22no—
39C2×C42×C11—22no—
40C2×C42×C11C2×C412yes—
41C2×C42×C11D412yes—
42C2×C4⋊Dic11—24no—
43C2×C4⋊Dic11—28no—
44C2×C4×Dic11—24no—
45C2×C4×Dic11—42no—
46C2×C4×Dic11—42no—
47C22×C11⋊C8—22no—
48C11×#95—22no—
49C11×#95—21no—
50C11⋊#95—22no—
51C11⋊#95D414yes—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54#9148—111nomaximal, Sylow
55C24×C11—21no—
56C24×C11C2×D411yescharacteristic
57C2×D4×C11—22no—
58C2×D4×C11—42no—
59C2×D4×C11—41no—
60C2×D4×C11—41no—
61C2×D4×C11—41no—
62C2×D4×C11—41no—
63C2×D4×C11—41no—
64C2×D4×C11—41no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—24no—
72C22×C4×C11—22no—
73C22×C4×C11—21no—
74C22×C4×C11—42no—
75C22×C4×C11C22⋊C412yes—
76C22×C4×C11C22⋊C412yes—
77C22×C4×C11D812yes—
78C22×C4×C11SD1612yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×C4×C11#4112yes—
83C22×Dic11—28no—
84C22×Dic11—24no—
85C22×Dic11—44no—
86C22×Dic11—42no—
87C22×Dic11—42no—
88C11×C4⋊C4—22no—
89C11×C4⋊C4—42no—
90C11×C4⋊C4—44no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—44no—
94C11×C22⋊C4—44no—
95C11×C22⋊C4—42no—
96C42×C11—24no—
97C42×C11—24no—
98C4⋊Dic11—216no—
99C4×Dic11—48no—
100C2×C11⋊C8—44no—
101C2×C11⋊C8—42no—
102#2854D1111yescharacteristic
103C2×C4×C4⋊C4—111no—
104#1817—111no—
105C2×#327—112no—
106#1294—112no—
107C23×C11—22no—
108C23×C11—22no—
109C23×C11—41no—
110C23×C11—42no—
111C23×C11—41no—
112C23×C11—41no—
113C23×C11—42no—
114C23×C11C2×C22⋊C411yescharacteristic
115C23×C11#12011yescharacteristic
116C23×C11#12311yescharacteristic
117C23×C11C2×D811yescharacteristic
118C23×C11C2×SD1611yescharacteristic
119C23×C11AGL(1,ℤ/8)11yescharacteristic
120C23×C11#13711yescharacteristic
121D4×C11—82no—
122D4×C11—81no—
123D4×C11—81no—
124D4×C11—81no—
125D4×C11—81no—
126C2×C4×C11—24no—
127C2×C4×C11—24no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—22no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—22no—
135C2×C4×C11—22no—
136C2×C4×C11—22no—
137C2×C4×C11—22no—
138C2×C4×C11—42no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—42no—
142C2×C4×C11—42no—
143C2×C4×C11—41no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11#10214yes—
147C2×C4×C11#10414yes—
148C2×C4×C11C4×D412yes—
149C2×C4×C11#12112yes—
150C2×Dic11—28no—
151C2×Dic11—44no—
152C2×Dic11—48no—
153C2×Dic11—48no—
154C2×Dic11—44no—
155C11⋊C8—82no—
156C2×#123—21no—
157C2×#121C2×D1111yescharacteristic
158C22×C4⋊C4—221no—
159C22×C42—221no—
160C22×C42C2×D1111yescharacteristic
161C2×C22⋊C8—112no—
162#390Dic1112yescomplemented
163#389Dic1112yescomplemented
164#388—22no—
165#386—21no—
166#380C2×D1111yescharacteristic
167C4×C4⋊C4—224no—
168C2×#95—112no—
169#336—222no—
170#327—224no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11—21no—
175C22×C11—22no—
176C22×C11—22no—
177C22×C11—22no—
178C22×C11—22no—
179C22×C11—81no—
180C22×C11—81no—
181C22×C11—81no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11#38611yescharacteristic
185C22×C11#41012yes—
186C22×C11C2×#10211yescharacteristic
187C22×C11#41711yescharacteristic
188C22×C11C2×#10412yes—
189C22×C11#44711yescharacteristic
190C22×C11#44811yescharacteristic
191C22×C11#48011yescharacteristic
192C22×C11#48111yescharacteristic
193C4×C11—24no—
194C4×C11—24no—
195C4×C11—22no—
196C4×C11—22no—
197C4×C11—81no—
198C4×C11—82no—
199Dic11—48no—
200C22×D4—21no—
201C22×D4C2×Dic1111yescharacteristic
202C23×C4—222no—
203C23×C4C22⋊D1111yescharacteristic
204C23×C4C22⋊D1111yescharacteristic
205C23×C4C22×D1111yescharacteristic
206C22×C8—222no—
207#123—42no—
208#123—42no—
209#121—22no—
210#121—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—224no—
213C2×C4⋊C4—228no—
214C2×C4⋊C4C2×Dic1111yescharacteristic
215C2×C4⋊C4C2×Dic1112yes—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C42—22no—
221C2×C42—22no—
222C2×C42—224no—
223C2×C42—442no—
224C2×C42—442no—
225C2×C42C2×Dic1112yes—
226C2×C42C22⋊D1112yes—
227C22⋊C8—222no—
228C22⋊C8—222no—
229#95—22no—
230#95—21no—
231#95—114no—
232#95—222no—
233C2×C11—21no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—21no—
237C2×C11—161no—
238C2×C11#150212yes—
239C2×C11#150912yes—
240C2×C11#187411yescharacteristic
241C2×C11#189611yescharacteristic
242C2×C11#189911yescharacteristic
243C24—21no—
244C24C2×C22⋊D1111yescharacteristic
245C2×D4—22no—
246C2×D4—42no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—22no—
261C22×C4—21no—
262C22×C4—42no—
263C22×C4—228no—
264C22×C4—224no—
265C22×C4—444no—
266C22×C4—442no—
267C22×C4—442no—
268C22×C4#432312yes—
269C22×C4#432412yes—
270C22×C4C22⋊Dic1112yes—
271C22×C4C22⋊Dic1112yes—
272C22×C4D4×D1112yes—
273C22×C4#434112yes—
274C22×C4C22×Dic1111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C2×C8—444no—
277C2×C8—442no—
278C4⋊C4—22no—
279C4⋊C4—42no—
280C4⋊C4—44no—
281C4⋊C4—2216no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—44no—
285C22⋊C4—44no—
286C22⋊C4—42no—
287C42—24no—
288C42—24no—
289C42—448no—
290C11#914811yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—42no—
297C23—42no—
298C23C2×#432311yescharacteristic
299C23C2×#432411yescharacteristic
300C23#6698811yescharacteristic
301C23#6699011yescharacteristic
302C23#6700211yescharacteristic
303C23#6700411yescharacteristic
304C23C2×C22⋊Dic1111yescharacteristic
305D4—82no—
306D4—81no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—228no—
331C2×C4—444no—
332C2×C4—448no—
333C2×C4—448no—
334C2×C4—444no—
335C2×C4#6689614yes—
336C2×C4#6690114yes—
337C2×C4D4×Dic1112yes—
338C2×C4#6699212yes—
339C8—882no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—81no—
349C22—81no—
350C22—82no—
351C22—82no—
352C22—81no—
353C22#1062264611yescharacteristic
354C22#1062264711yescharacteristic
355C22#1062264911yescharacteristic
356C22#1062265311yescharacteristic
357C22C2×#6689611yescharacteristic
358C22#1062283311yescharacteristic
359C22#1062284511yescharacteristic
360C22C2×#6690112yes—
361C22#1062285312yes—
362C4—24no—
363C4—22no—
364C4—22no—
365C4—24no—
366C4—82no—
367C4—81no—
368C4—448no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2—21no—
373C2—161no—
374C2#1306711112yes—
375C2#1306714112yes—
376C2#1306893411yescharacteristic
377C2#1306906011yescharacteristic
378C2#1306907511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2854C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2854D11
hypocenterC11#9148
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊Dic11C2semidirect
2. #13068684C2semidirect
4. #13066494C2semidirect
11. C11×#390C4semidirect
12. C11×#389C4semidirect
162. #390Dic11semidirect
163. #389Dic11semidirect
290. C11#9148semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊Dic112
#130686842
C2×#106221752
#130664942
C11×#28542
#914811