Finite Group Databasebeta

← #14660335

Subgroups — #14660335

Order 2816.

1946 conjugacy classes of subgroups; only the 259 normal subgroups are shown.

normal subgroups only

This group has 1946 conjugacy classes of subgroups — too many to draw. Only its 259 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×#66898C214yesmaximal, complemented
2#13066839C212yesmaximal, complemented
3C22×C11×#121C211yesmaximal, characteristic
4C23×D4×C11C411yescharacteristic, complemented
5C23×D4×C11C2212yes—
6C24×C4×C11C2211yescharacteristic
7C2×C11×#121—28no—
8C2×C11×#121—24no—
9C22×C11×C4⋊C4C411yescharacteristic, complemented
10C22×C11×C22⋊C4C412yescomplemented
11C22×C22⋊Dic11C2214yes—
12C2×#66898—28no—
13C2×#66898—216no—
14C2×C11⋊#95—24no—
15C25×C11C2×C412yes—
16C25×C11C2311yescharacteristic
17C22×D4×C11—24no—
18C22×D4×C11—28no—
19C22×D4×C11—24no—
20C22×D4×C11—24no—
21C22×D4×C11—28no—
22C22×D4×C11—22no—
23C22×D4×C11—44no—
24C22×D4×C11D418yes—
25C23×C4×C11—24no—
26C23×C4×C11—44no—
27C23×C4×C11C2×C412yes—
28C23×C4×C11C2×C411yescharacteristic
29C23×C4×C11C2×C411yescharacteristic
30C23×C4×C11D414yes—
31C23×Dic11—24no—
32C11×#121—232no—
33C2×C11×C4⋊C4—24no—
34C2×C11×C4⋊C4—22no—
35C2×C11×C22⋊C4—24no—
36C2×C11×C22⋊C4—24no—
37C2×C11×C22⋊C4—24no—
38C2×C22⋊Dic11—28no—
39C2×C22⋊Dic11—28no—
40C2×C22⋊Dic11—24no—
41C2×C22⋊Dic11D418yescomplemented
42#66898—232no—
43C11⋊#95—48no—
44#10980—111nomaximal, Sylow
45C24×C11—22no—
46C24×C11—22no—
47C24×C11—28no—
48C24×C11—42no—
49C24×C11—42no—
50C24×C11—44no—
51C24×C11—44no—
52C24×C11C22⋊C414yes—
53C24×C11C22×C411yescharacteristic
54C24×C11C2×D412yes—
55C24×C11C2×D414yes—
56C24×C11C2×D414yes—
57C24×C11#4114yes—
58C2×D4×C11—28no—
59C2×D4×C11—28no—
60C2×D4×C11—216no—
61C2×D4×C11—216no—
62C2×D4×C11—28no—
63C2×D4×C11—416no—
64C2×D4×C11—44no—
65C2×D4×C11—44no—
66C2×D4×C11—48no—
67C2×D4×C11—48no—
68C2×D4×C11—44no—
69C2×D4×C11—44no—
70C2×D4×C11—44no—
71C2×D4×C11—44no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—28no—
78C22×C4×C11—28no—
79C22×C4×C11—28no—
80C22×C4×C11—42no—
81C22×C4×C11—44no—
82C22×C4×C11—416no—
83C22×C4×C11C22⋊C412yes—
84C22×C4×C11C22⋊C414yes—
85C22×C4×C11C22⋊C412yes—
86C22×Dic11—28no—
87C22×Dic11—48no—
88C22×Dic11—48no—
89C22×Dic11—44no—
90C22×Dic11—44no—
91C11×C4⋊C4—28no—
92C11×C22⋊C4—216no—
93C22⋊Dic11—216no—
94C22⋊Dic11—48no—
95C22×#121D1111yescharacteristic
96C22×#99—114no—
97C22⋊#95—112no—
98C23×C11—24no—
99C23×C11—22no—
100C23×C11—24no—
101C23×C11—22no—
102C23×C11—24no—
103C23×C11—28no—
104C23×C11—44no—
105C23×C11—48no—
106C23×C11—44no—
107C23×C11—48no—
108C23×C11—44no—
109C23×C11—44no—
110C23×C11—44no—
111C23×C11—44no—
112C23×C11—44no—
113C23×C11—44no—
114C23×C11—44no—
115C23×C11—44no—
116C23×C11—816no—
117C23×C11C2×C22⋊C412yes—
118C23×C11C2×C22⋊C411yescharacteristic
119C23×C11C4×D414yes—
120C23×C11#12014yes—
121C23×C11#12014yes—
122C23×C11#12114yes—
123C23×C11#12118yes—
124C23×C11#12314yes—
125C23×C11#12412yes—
126C23×C11#12712yes—
127D4×C11—416no—
128D4×C11—416no—
129D4×C11—416no—
130C2×C4×C11—28no—
131C2×C4×C11—22no—
132C2×C4×C11—22no—
133C2×C4×C11—22no—
134C2×C4×C11—24no—
135C2×C4×C11—28no—
136C2×C4×C11—24no—
137C2×C4×C11—416no—
138C2×C4×C11—44no—
139C2×C4×C11—44no—
140C2×C4×C11—44no—
141C2×C4×C11#9914yescomplemented
142C2×Dic11—416no—
143C2×Dic11—48no—
144C2×Dic11—88no—
145C2×Dic11—84no—
146C2×Dic11—84no—
147C23×D4Dic1111yescharacteristic, complemented
148C23×D4C2×D1112yes—
149C24×C4C2×D1111yescharacteristic
150C2×#121—28no—
151C2×#121—24no—
152C22×C4⋊C4Dic1111yescharacteristic, complemented
153C22×C22⋊C4—114no—
154C22×C22⋊C4Dic1112yescomplemented
155C2×#99—2216no—
156C2×#99—228no—
157C2×#95—224no—
158C22×C11—28no—
159C22×C11—28no—
160C22×C11—24no—
161C22×C11—24no—
162C22×C11—22no—
163C22×C11—24no—
164C22×C11—22no—
165C22×C11—24no—
166C22×C11—44no—
167C22×C11—48no—
168C22×C11—44no—
169C22×C11—44no—
170C22×C11—44no—
171C22×C11—44no—
172C22×C11—88no—
173C22×C11—88no—
174C22×C11—88no—
175C22×C11#37911yescharacteristic
176C22×C11#38614yes—
177C22×C11#39012yes—
178C22×C11#39214yes—
179C22×C11#39414yes—
180C22×C11C2×#9912yes—
181C22×C11#41012yes—
182C4×C11—24no—
183C4×C11—44no—
184C4×C11—42no—
185Dic11—88no—
186C25C2×Dic1112yes—
187C25C22×D1111yescharacteristic
188C22×D4—24no—
189C22×D4—28no—
190C22×D4—28no—
191C22×D4—24no—
192C22×D4—24no—
193C22×D4—22no—
194C22×D4—44no—
195C22×D4C22⋊D1118yes—
196C23×C4—24no—
197C23×C4—44no—
198C23×C4—224no—
199C23×C4C2×Dic1112yes—
200C23×C4C2×Dic1111yescharacteristic
201C23×C4C2×Dic1111yescharacteristic
202C23×C4C22⋊D1114yes—
203#121—232no—
204C2×C4⋊C4—24no—
205C2×C4⋊C4—22no—
206C2×C22⋊C4—24no—
207C2×C22⋊C4—24no—
208C2×C22⋊C4—24no—
209C2×C22⋊C4—118no—
210C2×C22⋊C4—228no—
211C2×C22⋊C4—228no—
212C2×C22⋊C4—224no—
213#99—2232no—
214#95—448no—
215C2×C11—24no—
216C2×C11—24no—
217C2×C11—24no—
218C2×C11—84no—
219C2×C11#143811yescharacteristic
220C2×C11#178111yescharacteristic
221C2×C11#178211yescharacteristic
222C2×C11#196414yes—
223C24—22no—
224C24—22no—
225C24—28no—
226C24—42no—
227C24—42no—
228C24—44no—
229C24—44no—
230C24C22⋊Dic1114yes—
231C24D4×D1114yes—
232C24#434114yes—
233C24C22×Dic1111yescharacteristic
234C24C2×C22⋊D1112yes—
235C24C2×C22⋊D1114yes—
236C2×D4—28no—
237C2×D4—28no—
238C2×D4—28no—
239C2×D4—216no—
240C2×D4—216no—
241C2×D4—416no—
242C2×D4—44no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—48no—
247C2×D4—48no—
248C2×D4—44no—
249C2×D4—44no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—28no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—28no—
257C22×C4—28no—
258C22×C4—42no—
259C22×C4—44no—
260C22×C4—416no—
261C22×C4—228no—
262C22×C4—448no—
263C22×C4—448no—
264C22×C4—444no—
265C22×C4—444no—
266C22×C4C22⋊Dic1114yes—
267C22×C4C22⋊Dic1112yes—
268C22×C4C22⋊Dic1112yes—
269C4⋊C4—28no—
270C22⋊C4—216no—
271C22⋊C4—2216no—
272C22⋊C4—448no—
273C11#1098011yescharacteristic, complemented, Sylow
274C23—24no—
275C23—22no—
276C23—24no—
277C23—22no—
278C23—24no—
279C23—28no—
280C23—44no—
281C23—48no—
282C23—48no—
283C23—44no—
284C23—44no—
285C23—44no—
286C23—44no—
287C23—44no—
288C23—44no—
289C23—44no—
290C23—44no—
291C23—44no—
292C23—816no—
293C23D4×Dic1114yes—
294C23#6698814yes—
295C23#6698912yes—
296C23#6699014yes—
297C23#6699114yes—
298C23#6699218yes—
299C23#6699312yes—
300C23C2×C22⋊Dic1112yes—
301C23C2×C22⋊Dic1111yescharacteristic
302C23#6700614yes—
303D4—416no—
304D4—416no—
305D4—416no—
306C2×C4—28no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—28no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—416no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—4416no—
318C2×C4—448no—
319C2×C4—888no—
320C2×C4—884no—
321C2×C4—884no—
322C2×C4#6689814yescomplemented
323C22—28no—
324C22—24no—
325C22—28no—
326C22—24no—
327C22—22no—
328C22—24no—
329C22—24no—
330C22—22no—
331C22—44no—
332C22—44no—
333C22—48no—
334C22—44no—
335C22—44no—
336C22—44no—
337C22—88no—
338C22—88no—
339C22—88no—
340C22C2×#6689812yes—
341C22#1062283314yes—
342C22#1062283412yes—
343C22#1062283514yes—
344C22#1062283614yes—
345C22#1062285312yes—
346C22#1062286011yescharacteristic
347C4—24no—
348C4—44no—
349C4—42no—
350C4—888no—
351C2—24no—
352C2—24no—
353C2—24no—
354C2—84no—
355C2#1306685711yescharacteristic
356C2#1306853111yescharacteristic
357C2#1306853411yescharacteristic
358C2#1306945314yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC25C22×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C2×C22⋊C4
cosocleC25×C11C23
hypercenterC22×#121D11
hypocenterC11#10980
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66898C2semidirect
2. #13066839C2semidirect
4. C23×D4×C11C4semidirect
9. C22×C11×C4⋊C4C4semidirect
10. C22×C11×C22⋊C4C4semidirect
41. C2×C22⋊Dic11D4semidirect
141. C2×C4×C11#99semidirect
147. C23×D4Dic11semidirect
152. C22×C4⋊C4Dic11semidirect
154. C22×C22⋊C4Dic11semidirect
273. C11#10980semidirect
322. C2×C4#66898semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
#130668392
C22×C11×#1212
#1098011