Finite Group Databasebeta

← #14646278

Subgroups — #14646278

Order 2816.

754 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 754 conjugacy classes of subgroups — too many to draw. Only its 107 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×#10623065C211yesmaximal, characteristic
2#13068699C211yesmaximal, characteristic, complemented
3#13067148C212yesmaximal, complemented
4#13067144C212yesmaximal
5C11×#1820C211yesmaximal, characteristic, complemented
6C2×C11×#117C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66977C2211yescharacteristic
9#10623065—24no—
10#10623065—24no—
11C2×#66951—21no—
12C2×#66949—21no—
13C2×#66938—21no—
14C2×#66936—21no—
15C2×#66928C411yescharacteristic, complemented
16C2×C4×D44C411yescharacteristic, complemented
17C2×#66922C411yescharacteristic, complemented
18C2×C4×Dic22C411yescharacteristic, complemented
19C11×#381C2212yes—
20#10622820C2212yes—
21C11×#342—21no—
22C11×#342—21no—
23#10622168—21no—
24#10622168—21no—
25#10622090—24no—
26#10622089—24no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C22×Dic22—21no—
32C22×Dic22C2×C411yescharacteristic
33C11×#117—22no—
34C11×#117—22no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C22⋊C4—22no—
38C2×C11×C22⋊C4D411yescharacteristic
39C2×C11×C22⋊C4D411yescharacteristic
40C2×C42×C11C2×C411yescharacteristic
41C2×C42×C11C2×C411yescharacteristic
42C2×C22⋊Dic11—21no—
43#66983—22no—
44#66983D414yes—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—21no—
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11C2×C411yescharacteristic
51C2×C4⋊Dic11C2×C411yescharacteristic
52#66977—22no—
53#66977D414yes—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×C4×Dic11—21no—
57C2×#4318—22no—
58#66951—28no—
59#66949—28no—
60#66938—28no—
61#66936—28no—
62#66928—22no—
63#66928—22no—
64C4×D44—22no—
65C4×D44—22no—
66#66922—22no—
67#66922—22no—
68C4×Dic22—22no—
69C4×Dic22—22no—
70C11×#95—22no—
71C11×#95—22no—
72C22⋊(C11⋊C8)—22no—
73C22⋊(C11⋊C8)—22no—
74#8519—111nomaximal, Sylow
75C24×C11C2×D411yescharacteristic
76C23×D11—21no—
77C22×C4×C11—42no—
78C22×C4×C11—42no—
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22⋊C411yescharacteristic
82C22×C4×C11C22⋊C411yescharacteristic
83C22×C4×C11C22×C411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D412yes—
86C22×C4×C11C2×D412yes—
87C2×C22⋊D11—24no—
88C2×C22⋊D11—82no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C2×D44—21no—
93C2×D44—42no—
94C2×D44C22⋊C412yes—
95C2×C4×D11—24no—
96C2×C4×D11—82no—
97C2×Dic22—24no—
98C2×Dic22—21no—
99C2×Dic22—42no—
100C2×Dic22—82no—
101C2×Dic22C22⋊C412yes—
102C11×C4⋊C4—22no—
103C11×C4⋊C4—22no—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C11×C22⋊C4—44no—
107C42×C11—21no—
108C42×C11—21no—
109C42×C11—21no—
110C42×C11—21no—
111C22⋊Dic11—24no—
112(C2×D11)⋊C4—24no—
113(C2×D11)⋊C4—24no—
114(C2×D11)⋊C4—24no—
115(C2×D11)⋊C4—24no—
116C4⋊Dic11—24no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11C22⋊C412yes—
120C4⋊Dic11C22⋊C412yes—
121Dic11⋊C4—24no—
122Dic11⋊C4—24no—
123C4×Dic11—24no—
124#4318—44no—
125C2×C11⋊C8—42no—
126C2×#542—111no—
127#1822—111no—
128#1820D1111yescharacteristic, complemented
129#1511—112no—
130#1510—112no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11C2×C22⋊C411yescharacteristic
135C23×C11#12012yes—
136C22×D11—22no—
137C22×D11—42no—
138C22×D11—42no—
139C22×D11—42no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—42no—
147C2×C4×C11—42no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—82no—
153C2×C4×C11—82no—
154C2×C4×C11—82no—
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11C2×C22⋊C411yescharacteristic
157C2×C4×C11#12012yes—
158C22⋊D11—84no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—22no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—42no—
165D44—42no—
166D44—42no—
167C4×D11—84no—
168Dic22—42no—
169Dic22—42no—
170Dic22—84no—
171C11⋊C8—82no—
172#542—224no—
173#542—224no—
174C2×C4⋊Q8—111no—
175C2×#126—221no—
176C2×#124—111no—
177C2×#124—221no—
178C2×#123—221no—
179C2×C22⋊Q8—111no—
180C2×C22⋊Q8—221no—
181C2×#121—111no—
182C2×C4×Q8—111no—
183C2×C4×D4—111no—
184C2×#117C2×D1111yescharacteristic
185#407—112no—
186#381C2×D1112yes—
187#343—221no—
188#343—221no—
189#342—21no—
190#342—21no—
191#328—224no—
192#327—224no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11—22no—
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—82no—
199C22×C11#37911yescharacteristic
200C22×C11#41012yes—
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—84no—
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—22no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11—41no—
211C4×C11—41no—
212C4×C11—162no—
213Dic11—42no—
214Dic11—42no—
215Dic11—42no—
216C22×Q8—111no—
217C22×Q8—221no—
218C22×D4—111no—
219C22×D4—221no—
220C23×C4—221no—
221C23×C4C22×D1111yescharacteristic
222C2×M16—222no—
223C4⋊Q8—222no—
224C4⋊Q8—222no—
225#126—228no—
226#124—222no—
227#124—222no—
228#124—228no—
229#123—228no—
230C22⋊Q8—114no—
231C22⋊Q8—228no—
232C22⋊Q8—222no—
233#121—114no—
234#121—222no—
235C4×Q8—222no—
236C4×Q8—222no—
237C4×D4—222no—
238C4×D4—222no—
239#117—22no—
240#117—22no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—221no—
245C2×C4⋊C4—221no—
246C2×C4⋊C4D4411yescharacteristic
247C2×C4⋊C4D4411yescharacteristic
248C2×C22⋊C4—22no—
249C2×C22⋊C4—221no—
250C2×C22⋊C4—221no—
251C2×C22⋊C4—221no—
252C2×C22⋊C4—221no—
253C2×C22⋊C4—221no—
254C2×C22⋊C4C22⋊D1111yescharacteristic
255C2×C22⋊C4C22⋊D1111yescharacteristic
256C2×C42—221no—
257C2×C42C4×D1111yescharacteristic
258C2×C42C4×D1111yescharacteristic
259C22⋊C8—222no—
260C22⋊C8—222no—
261#95—22no—
262#95—22no—
263C2×C11—22no—
264C2×C11—42no—
265C2×C11#178211yescharacteristic
266C2×C11#179511yescharacteristic
267C2×C11#179611yescharacteristic
268D11—82no—
269C24—221no—
270C24C2×C22⋊D1111yescharacteristic
271C2×Q8—112no—
272C2×Q8—224no—
273C2×Q8—221no—
274C2×Q8—442no—
275C2×Q8—882no—
276C2×D4—112no—
277C2×D4—224no—
278C2×D4—221no—
279C2×D4—442no—
280C2×D4—882no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—224no—
284C22×C4—221no—
285C22×C4—221no—
286C22×C4—221no—
287C22×C4—882no—
288C22×C4(C2×D11)⋊C411yescharacteristic
289C22×C4(C2×D11)⋊C411yescharacteristic
290C22×C4(C2×D11)⋊C411yescharacteristic
291C22×C4(C2×D11)⋊C411yescharacteristic
292C22×C4C2×C4×D1111yescharacteristic
293C22×C4C2×D4411yescharacteristic
294C22×C4D4×D1112yes—
295C22×C4D4×D1112yes—
296M16—444no—
297C2×C8—442no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—112no—
301C4⋊C4—112no—
302C4⋊C4—224no—
303C4⋊C4—224no—
304C4⋊C4—221no—
305C4⋊C4—221no—
306C4⋊C4—224no—
307C22⋊C4—22no—
308C22⋊C4—22no—
309C22⋊C4—44no—
310C22⋊C4—224no—
311C22⋊C4—224no—
312C22⋊C4—224no—
313C22⋊C4—224no—
314C22⋊C4—224no—
315C42—21no—
316C42—21no—
317C42—21no—
318C42—21no—
319C42—224no—
320C11#851911yescharacteristic, complemented, Sylow
321C23—22no—
322C23—41no—
323C23—41no—
324C23—222no—
325C23—442no—
326C23—442no—
327C23—442no—
328C23C2×(C2×D11)⋊C411yescharacteristic
329C23#6699012yes—
330Q8—442no—
331Q8—442no—
332Q8—884no—
333D4—442no—
334D4—442no—
335D4—884no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—82no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—222no—
352C2×C4—222no—
353C2×C4—222no—
354C2×C4—442no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—884no—
358C2×C4C22⋊C4×D1111yescharacteristic
359C2×C4C22⋊C4×D1111yescharacteristic
360C2×C4#6693512yes—
361C8—882no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—82no—
368C22—442no—
369C22—442no—
370C22—442no—
371C22—884no—
372C22#1062256811yescharacteristic
373C22#1062261912yes—
374C4—22no—
375C4—21no—
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—162no—
382C4—442no—
383C4—442no—
384C4—442no—
385C2—22no—
386C2—42no—
387C2—882no—
388C2#1306853311yescharacteristic
389C2#1306858411yescharacteristic
390C2#1306858911yescharacteristic
subgroupG/H
centerC22#10622568
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1820C2
socleC22×C11#379
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1820D11
hypocenterC11#8519
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #13068699C2semidirect
3. #13067148C2semidirect
5. C11×#1820C2semidirect
15. C2×#66928C4semidirect
16. C2×C4×D44C4semidirect
17. C2×#66922C4semidirect
18. C2×C4×Dic22C4semidirect
128. #1820D11semidirect
320. C11#8519semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130686992
#130671482
#130671442
C11×#18202
#851911