Finite Group Databasebeta

← #14645402

Subgroups — #14645402

Order 2816.

744 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 744 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×#10623115C211yesmaximal, characteristic
2C4×#66900C211yesmaximal, characteristic, complemented
3#13067215C212yesmaximal
4#13067062C212yesmaximal, complemented
5C11×#1467C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C11C2211yescharacteristic
7C2×#66999—21no—
8#10623115—24no—
9#10623115—24no—
10C2×#66951—21no—
11C2×#66951—21no—
12C2×#66945—21no—
13C2×#66928C411yescharacteristic
14C2×#66928C2211yescharacteristic
15C2×C4×D44C411yescharacteristic
16C2×#66922C411yescharacteristic
17C2×C4×Dic22C411yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#432C2212yes—
20C2×#66900—21no—
21C4×#4318C2212yes—
22C11×#324—21no—
23C11×#324—21no—
24#10622168—21no—
25#10622122—24no—
26#10622102—24no—
27C22×Q8×C11D411yescharacteristic
28C22×D44C2×C411yescharacteristic
29C22×C4×D11—21no—
30C22×Dic22C2×C411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C4×Q8×C11—22no—
33C4×Q8×C11—22no—
34C2×C11×C4⋊C4D411yescharacteristic
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C42×C11C2×C411yescharacteristic
38C2×C42×C11C2×C411yescharacteristic
39C2×C42×C11C2311yescharacteristic
40#66999—28no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—21no—
52C2×C4×Dic11—21no—
53C2×#4318—22no—
54#66951—28no—
55#66951—28no—
56#66945—28no—
57#66928—22no—
58#66928—22no—
59#66928—22no—
60#66928D414yes—
61C4×D44—22no—
62C4×D44—22no—
63#66922—22no—
64#66922—22no—
65C4×Dic22—22no—
66C4×Dic22—22no—
67C4×Dic22—22no—
68C4×Dic22D414yes—
69C11×C4⋊C8—22no—
70C11×C22⋊C8—22no—
71C11×#97—22no—
72#66900—24no—
73#66867—22no—
74C4×C11⋊C8—22no—
75#8368—111nomaximal, Sylow
76C23×D11—21no—
77C2×Q8×C11—22no—
78C2×Q8×C11—22no—
79C2×Q8×C11—41no—
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22⋊C411yescharacteristic
84C22×C4×C11C22×C411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C2×D44—21no—
91C2×D44—42no—
92C2×D44C22⋊C412yes—
93C2×C4×D11—24no—
94C2×C4×D11—42no—
95C2×C4×D11—42no—
96C2×Dic22—21no—
97C2×Dic22—21no—
98C2×Dic22—42no—
99C2×Dic22—42no—
100C2×Dic22C22⋊C412yes—
101C2×Dic22C22⋊C412yes—
102C2×C8×C11—42no—
103C11×C4⋊C4—22no—
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C42×C11—21no—
107C42×C11—21no—
108C42×C11—21no—
109C42×C11—21no—
110C42×C11C2×D412yes—
111C42×C11C2×D412yes—
112(C2×D11)⋊C4—24no—
113(C2×D11)⋊C4—24no—
114(C2×D11)⋊C4—24no—
115(C2×D11)⋊C4—24no—
116(C2×D11)⋊C4—24no—
117C4⋊Dic11—24no—
118C4⋊Dic11—24no—
119C4⋊Dic11—21no—
120C4⋊Dic11C22⋊C412yes—
121Dic11⋊C4—24no—
122Dic11⋊C4—24no—
123C4×Dic11—24no—
124C4×Dic11—24no—
125#4318—24no—
126#4318—42no—
127C2×C11⋊C8—42no—
128C2×#556—111no—
129C4×#101—111no—
130#1527—112no—
131#1491—112no—
132#1467D1111yescharacteristic, complemented
133C23×C11C2×C22⋊C411yescharacteristic
134C22×D11—22no—
135C22×D11—42no—
136C22×D11—42no—
137C22×D11—41no—
138C22×D11—41no—
139Q8×C11—44no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—22no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11#10412yes—
154C2×C4×C11C2×C22⋊C411yescharacteristic
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11#12012yes—
157C2×C4×C11#12012yes—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—42no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—41no—
165D44—42no—
166D44—42no—
167C4×D11—48no—
168Dic22—24no—
169Dic22—42no—
170Dic22—42no—
171Dic22—42no—
172C8×C11—82no—
173C11⋊C8—44no—
174#556—224no—
175#556—224no—
176C2×C4⋊Q8—111no—
177C2×#126—221no—
178C2×#126—221no—
179C2×#124—111no—
180C2×#124—111no—
181C2×C22⋊Q8—221no—
182C2×C4×Q8—111no—
183C2×C4×Q8—111no—
184C2×C4×Q8C2×D1111yescharacteristic
185C2×C4×D4—111no—
186C2×#117—221no—
187#432C2×D1112yes—
188C2×#101—221no—
189C4×M16—112no—
190#343—221no—
191#329—224no—
192Q8⋊C8—224no—
193#324—21no—
194#324—21no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11#37911yescharacteristic
198C22×C11C2×#10411yescharacteristic
199C22×C11#42111yescharacteristic
200C2×D11—42no—
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—82no—
204C2×D11—82no—
205C4×C11—22no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11#41312yes—
213Dic11—42no—
214Dic11—42no—
215Dic11—42no—
216C22×Q8—111no—
217C22×Q8—111no—
218C22×Q8D4411yescharacteristic
219C22×D4—111no—
220C23×C4—221no—
221C2×M16—222no—
222C4⋊Q8—222no—
223C4⋊Q8—222no—
224#126—228no—
225#126—228no—
226#124—114no—
227#124—222no—
228#124—222no—
229#124—222no—
230C22⋊Q8—228no—
231C4×Q8—22no—
232C4×Q8—22no—
233C4×Q8—114no—
234C4×Q8—222no—
235C4×Q8—222no—
236C4×Q8—222no—
237C4×D4—222no—
238C4×D4—222no—
239#117—228no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—221no—
242C2×C4⋊C4—221no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4D4411yescharacteristic
246C2×C4⋊C4C22⋊D1111yescharacteristic
247C2×C4⋊C4C22⋊D1111yescharacteristic
248C2×C22⋊C4—221no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C42—221no—
254C2×C42—221no—
255C2×C42C4×D1111yescharacteristic
256C2×C42C4×D1111yescharacteristic
257C2×C42C22×D1111yescharacteristic
258C4⋊C8—22no—
259#101—224no—
260C22⋊C8—22no—
261#97—22no—
262#97—222no—
263C4×C8—222no—
264C2×C11—21no—
265C2×C11—21no—
266C2×C11#178511yescharacteristic
267C2×C11#178911yescharacteristic
268C2×C11#179611yescharacteristic
269D11—82no—
270C24—221no—
271C2×Q8—22no—
272C2×Q8—22no—
273C2×Q8—41no—
274C2×Q8—112no—
275C2×Q8—112no—
276C2×Q8—221no—
277C2×Q8—221no—
278C2×Q8—442no—
279C2×Q8—442no—
280C2×D4—112no—
281C2×D4—221no—
282C2×D4—442no—
283C22×C4—224no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—442no—
288C22×C4—442no—
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4(C2×D11)⋊C411yescharacteristic
293C22×C4C2×C4×D1111yescharacteristic
294C22×C4C2×D4411yescharacteristic
295C22×C4C2×C22⋊D1111yescharacteristic
296M16—224no—
297M16—442no—
298C2×C8—42no—
299C2×C8—442no—
300C4⋊C4—22no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—112no—
304C4⋊C4—224no—
305C4⋊C4—224no—
306C4⋊C4—224no—
307C4⋊C4—221no—
308C4⋊C4—224no—
309C22⋊C4—224no—
310C22⋊C4—224no—
311C22⋊C4—224no—
312C22⋊C4—224no—
313C22⋊C4—224no—
314C42—21no—
315C42—21no—
316C42—21no—
317C42—21no—
318C42—224no—
319C42—224no—
320C42D4×D1112yes—
321C42D4×D1112yes—
322C11#836811yescharacteristic, complemented, Sylow
323C23—222no—
324C23—442no—
325C23—442no—
326C23—441no—
327C23—441no—
328C23C2×(C2×D11)⋊C411yescharacteristic
329Q8—44no—
330Q8—224no—
331Q8—442no—
332Q8—442no—
333Q8—442no—
334D4—442no—
335D4—442no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—222no—
350C2×C4—222no—
351C2×C4—222no—
352C2×C4—448no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4#6688912yes—
358C2×C4C22⋊C4×D1111yescharacteristic
359C2×C4C22⋊C4×D1111yescharacteristic
360C2×C4#6693512yes—
361C2×C4#6699012yes—
362C8—82no—
363C8—444no—
364C22—21no—
365C22—21no—
366C22—442no—
367C22—442no—
368C22—442no—
369C22—882no—
370C22—882no—
371C22#1062256811yescharacteristic
372C22C2×#6688911yescharacteristic
373C22#1062275211yescharacteristic
374C4—22no—
375C4—22no—
376C4—22no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—442no—
382C4—442no—
383C4—442no—
384C4#1062236412yes—
385C2—21no—
386C2—21no—
387C2—882no—
388C2#1306854311yescharacteristic
389C2#1306855911yescharacteristic
390C2#1306858911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1467C2
socleC22×C11#379
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1467D11
hypocenterC11#8368
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. C4×#66900C2semidirect
4. #13067062C2semidirect
5. C11×#1467C2semidirect
132. #1467D11semidirect
322. C11#8368semidirect

Maximal subgroups

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

subgroupindex
C2×#106231152
C4×#669002
#130672152
#130670622
C11×#14672
#836811