Finite Group Databasebeta

← #14645136

Subgroups — #14645136

Order 2816.

874 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 874 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C22×#66951C211yesmaximal, characteristic
2#13068682C212yesmaximal, complemented
3C2×#10622166C211yesmaximal, characteristic, complemented
4C2×#10622106C212yesmaximal
5C2×C11×#324C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C22×(C2×D11)⋊C4C411yescharacteristic
8C22×(C2×D11)⋊C4C411yescharacteristic
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C22×C4⋊Dic11C411yescharacteristic
11C22×Dic11⋊C4C411yescharacteristic
12C22×C4×Dic11C2211yescharacteristic
13C2×#66951—22no—
14C2×#66951—22no—
15C2×#66951—24no—
16C2×#66951—24no—
17C2×C11×C22⋊C8C2212yes—
18C2×C22⋊(C11⋊C8)C2212yes—
19C11×#324—22no—
20#10622188—24no—
21#10622166—22no—
22#10622106—24no—
23C24×D11C2×C411yescharacteristic
24C23×C4×C11C2×C411yescharacteristic
25C23×C4×C11C2×C411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C23×Dic11C2×C411yescharacteristic
28C23×Dic11C2×C411yescharacteristic
29C23×Dic11C2×C411yescharacteristic
30C22×C8×C11—22no—
31C2×C11×C4⋊C4—22no—
32C2×C11×C4⋊C4—22no—
33C2×C11×C4⋊C4D412yes—
34C2×C11×C4⋊C4D412yes—
35C2×(C2×D11)⋊C4—22no—
36C2×(C2×D11)⋊C4—22no—
37C2×(C2×D11)⋊C4—22no—
38C2×(C2×D11)⋊C4—22no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—22no—
43C2×(C2×D11)⋊C4—22no—
44C2×(C2×D11)⋊C4D414yes—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—22no—
47C2×C4⋊Dic11—22no—
48C2×Dic11⋊C4—22no—
49C2×Dic11⋊C4—22no—
50C2×Dic11⋊C4—22no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—22no—
53C2×C4×Dic11—21no—
54C2×C4×Dic11D414yes—
55C22×C11⋊C8—22no—
56#66951—216no—
57#66951—216no—
58C11×C22⋊C8—22no—
59C11×C22⋊C8—22no—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62#8309—111nomaximal, Sylow
63C24×C11C22×C411yescharacteristic
64C23×D11—21no—
65C23×D11—21no—
66C23×D11—22no—
67C23×D11—22no—
68C23×D11—42no—
69C23×D11—42no—
70C23×D11C22⋊C412yes—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11C22⋊C412yes—
80C22×C4×C11C22⋊C412yes—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11C2×D411yescharacteristic
85C22×Dic11—21no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11C22⋊C412yes—
96C22×Dic11C22⋊C412yes—
97C22×Dic11C22⋊C412yes—
98C2×C8×C11—44no—
99C2×C8×C11—42no—
100C11×C4⋊C4—24no—
101C11×C4⋊C4—24no—
102(C2×D11)⋊C4—28no—
103(C2×D11)⋊C4—28no—
104(C2×D11)⋊C4—24no—
105(C2×D11)⋊C4—24no—
106C4⋊Dic11—28no—
107Dic11⋊C4—28no—
108C4×Dic11—24no—
109C4×Dic11—24no—
110C2×C11⋊C8—44no—
111C2×C11⋊C8—42no—
112C22×#126—111no—
113#1817—112no—
114C2×#324—111no—
115C2×#324D1111yescharacteristic, complemented
116C2×#323—112no—
117C23×C11—22no—
118C23×C11—22no—
119C23×C11C2×C22⋊C411yescharacteristic
120C23×C11C2×C22⋊C411yescharacteristic
121C23×C11C2×C22⋊C411yescharacteristic
122C23×C11#13112yes—
123C23×C11#13112yes—
124C22×D11—22no—
125C22×D11—24no—
126C22×D11—42no—
127C22×D11—42no—
128C22×D11—41no—
129C22×D11—41no—
130C22×D11—42no—
131C22×D11—42no—
132C22×D11—42no—
133C22×D11—42no—
134C22×D11—42no—
135C22×D11—84no—
136C22×D11—84no—
137C2×C4×C11—24no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—41no—
143C2×C4×C11—42no—
144C2×C4×C11—41no—
145C2×C4×C11—42no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11#12012yes—
151C2×C4×C11#12012yes—
152C2×Dic11—22no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—24no—
156C2×Dic11—24no—
157C2×Dic11—42no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165C8×C11—82no—
166C11⋊C8—82no—
167C2×#126—224no—
168C2×#126—224no—
169C2×#126—222no—
170C2×#126—222no—
171C22×C4⋊C4—111no—
172C22×C4⋊C4—111no—
173C22×C4⋊C4C2×D1111yescharacteristic
174C22×C22⋊C4—111no—
175C22×C22⋊C4—111no—
176C22×C22⋊C4—111no—
177C22×C42—111no—
178C2×C22⋊C8—112no—
179C2×C22⋊C8C2×D1112yes—
180#336—224no—
181#324—22no—
182#324—222no—
183#323—224no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#37911yescharacteristic
191C22×C11#40811yescharacteristic
192C22×C11#40811yescharacteristic
193C22×C11#40812yes—
194C22×C11#40812yes—
195C22×C11#41012yes—
196C22×C11#41312yes—
197C2×D11—42no—
198C2×D11—42no—
199C2×D11—42no—
200C2×D11—82no—
201C2×D11—82no—
202C2×D11—84no—
203C2×D11—84no—
204C4×C11—22no—
205C4×C11—22no—
206C4×C11—42no—
207C4×C11—42no—
208Dic11—42no—
209Dic11—42no—
210Dic11—42no—
211C25—111no—
212C23×C4—111no—
213C23×C4—111no—
214C23×C4—111no—
215C23×C4C4×D1111yescharacteristic
216C23×C4C4×D1111yescharacteristic
217C23×C4C22×D1111yescharacteristic
218C22×C8—22no—
219C22×C8—222no—
220#126—2216no—
221#126—2216no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—222no—
225C2×C4⋊C4—222no—
226C2×C4⋊C4—222no—
227C2×C4⋊C4—222no—
228C2×C4⋊C4—222no—
229C2×C4⋊C4—222no—
230C2×C4⋊C4D4412yes—
231C2×C4⋊C4C22⋊D1112yes—
232C2×C22⋊C4—114no—
233C2×C22⋊C4—222no—
234C2×C22⋊C4—222no—
235C2×C22⋊C4—222no—
236C2×C22⋊C4—222no—
237C2×C22⋊C4—222no—
238C2×C22⋊C4—222no—
239C2×C22⋊C4—221no—
240C2×C22⋊C4—222no—
241C2×C22⋊C4—221no—
242C2×C42—114no—
243C2×C42—221no—
244C2×C42—222no—
245C2×C42—221no—
246C22⋊C8—22no—
247C22⋊C8—22no—
248C22⋊C8—222no—
249C22⋊C8—222no—
250C2×C11—21no—
251C2×C11—21no—
252C2×C11—22no—
253C2×C11#147314yes—
254C2×C11#178011yescharacteristic
255C2×C11#178211yescharacteristic
256C2×C11#178511yescharacteristic
257D11—82no—
258C24—112no—
259C24—221no—
260C24—221no—
261C24—222no—
262C24—222no—
263C24—442no—
264C24—442no—
265C24C2×C4×D1111yescharacteristic
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—42no—
274C22×C4—112no—
275C22×C4—112no—
276C22×C4—112no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—222no—
281C22×C4—222no—
282C22×C4—221no—
283C22×C4—221no—
284C22×C4—221no—
285C22×C4—442no—
286C22×C4—442no—
287C22×C4(C2×D11)⋊C412yes—
288C22×C4(C2×D11)⋊C412yes—
289C22×C4C2×D4411yescharacteristic
290C22×C4D4×D1112yes—
291C22×C4D4×D1112yes—
292C22×C4C2×C22⋊D1111yescharacteristic
293C2×C8—44no—
294C2×C8—42no—
295C2×C8—444no—
296C2×C8—442no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—228no—
300C4⋊C4—228no—
301C22⋊C4—228no—
302C22⋊C4—228no—
303C22⋊C4—224no—
304C22⋊C4—224no—
305C42—224no—
306C42—224no—
307C11#830911yescharacteristic, complemented, Sylow
308C23—22no—
309C23—22no—
310C23—222no—
311C23—224no—
312C23—442no—
313C23—442no—
314C23—442no—
315C23—442no—
316C23—441no—
317C23—441no—
318C23—442no—
319C23—442no—
320C23—442no—
321C23—884no—
322C23—884no—
323C23C22⋊C4×D1111yescharacteristic
324C23C22⋊C4×D1111yescharacteristic
325C23#6695412yes—
326C23#6696012yes—
327C23C2×(C2×D11)⋊C411yescharacteristic
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—222no—
342C2×C4—222no—
343C2×C4—222no—
344C2×C4—224no—
345C2×C4—224no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—442no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4#6693512yes—
355C2×C4#6699012yes—
356C8—82no—
357C8—882no—
358C22—24no—
359C22—24no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—442no—
365C22—442no—
366C22—442no—
367C22—884no—
368C22—882no—
369C22—882no—
370C22—884no—
371C22#1062234012yes—
372C22#1062234012yes—
373C22#1062235312yes—
374C22#1062236412yes—
375C22#1062256811yescharacteristic
376C22#1062272311yescharacteristic
377C22#1062274211yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—442no—
383C4—442no—
384C4—442no—
385C2—21no—
386C2—21no—
387C2—22no—
388C2—882no—
389C2#1306698414yes—
390C2#1306852711yescharacteristic
391C2#1306853211yescharacteristic
392C2#1306854311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#324C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC23×C4×C11C23
hypercenterC2×#324D11
hypocenterC11#8309
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13068682C2semidirect
3. C2×#10622166C2semidirect
5. C2×C11×#324C2semidirect
115. C2×#324D11semidirect
307. C11#8309semidirect

Maximal subgroups

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

subgroupindex
C22×#669512
#130686822
C2×#106221662
C2×#106221062
C2×C11×#3242
#830911