Finite Group Databasebeta

← #14660269

Subgroups — #14660269

Order 2816.

1634 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66898C212yesmaximal
2C2×#10622824C212yesmaximal, complemented
3C2×#10622164C212yesmaximal, complemented
4C22×C11×#123C211yesmaximal, characteristic
5C23×D4×C11C2211yescharacteristic
6C24×C4×C11C2211yescharacteristic
7C2×C11×#123—24no—
8C2×C11×#123—24no—
9C2×C11×#123—24no—
10C22×C11×C4⋊C4C412yescomplemented
11C22×C11×C22⋊C4C412yescomplemented
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C22⋊Dic11C2214yes—
14C2×#66898—24no—
15C2×#66898—28no—
16#10622824—28no—
17C2×C11⋊#95—24no—
18#10622164—24no—
19C25×C11C2×C411yescharacteristic
20C25×C11C2311yescharacteristic
21C22×D4×C11—24no—
22C22×D4×C11—22no—
23C22×D4×C11—22no—
24C22×D4×C11—24no—
25C22×D4×C11D414yes—
26C23×C4×C11—24no—
27C23×C4×C11—22no—
28C23×C4×C11—22no—
29C23×C4×C11—24no—
30C23×C4×C11C2×C412yes—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C412yes—
33C23×C4×C11D414yes—
34C23×Dic11—24no—
35C11×#123—232no—
36C2×C11×C4⋊C4—24no—
37C2×C11×C4⋊C4—24no—
38C2×C11×C4⋊C4—24no—
39C2×C11×C22⋊C4—24no—
40C2×C11×C22⋊C4—22no—
41C2×C11×C22⋊C4—22no—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—24no—
44C2×C11×C22⋊C4D414yes—
45C2×C22⋊Dic11—24no—
46C2×C22⋊Dic11—24no—
47C2×C22⋊Dic11—24no—
48C2×C22⋊Dic11—24no—
49C2×C22⋊Dic11—24no—
50C2×C22⋊Dic11D418yes—
51#66898—216no—
52C11⋊#95—216no—
53#10966—111nomaximal, Sylow
54C24×C11—21no—
55C24×C11—21no—
56C24×C11—24no—
57C24×C11—44no—
58C24×C11—44no—
59C24×C11C22⋊C412yes—
60C24×C11C22×C411yescharacteristic
61C24×C11C2×D412yes—
62C24×C11C2×D412yes—
63C24×C11C2×D412yes—
64C24×C11C2×D414yes—
65C24×C11#4114yes—
66C2×D4×C11—24no—
67C2×D4×C11—28no—
68C2×D4×C11—28no—
69C2×D4×C11—24no—
70C2×D4×C11—42no—
71C2×D4×C11—44no—
72C2×D4×C11—44no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—28no—
83C22×C4×C11—24no—
84C22×C4×C11—24no—
85C22×C4×C11—28no—
86C22×C4×C11—28no—
87C22×C4×C11—24no—
88C22×C4×C11—42no—
89C22×C4×C11—44no—
90C22×C4×C11—44no—
91C22×C4×C11—42no—
92C22×C4×C11—42no—
93C22×C4×C11—42no—
94C22×C4×C11—44no—
95C22×C4×C11C22⋊C414yes—
96C22×C4×C11C22⋊C412yes—
97C22×C4×C11C22⋊C414yes—
98C22×Dic11—28no—
99C22×Dic11—416no—
100C22×Dic11—44no—
101C22×Dic11—44no—
102C11×C4⋊C4—216no—
103C11×C22⋊C4—216no—
104C11×C22⋊C4—28no—
105C22⋊Dic11—28no—
106C22⋊Dic11—28no—
107C22⋊Dic11—44no—
108C22⋊Dic11—44no—
109C22×#123D1111yescharacteristic
110C22×#99—112no—
111C2×#381—112no—
112C2×#342—112no—
113C23×C11—28no—
114C23×C11—24no—
115C23×C11—22no—
116C23×C11—24no—
117C23×C11—48no—
118C23×C11—44no—
119C23×C11—44no—
120C23×C11—48no—
121C23×C11—44no—
122C23×C11—44no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—44no—
126C23×C11—88no—
127C23×C11C2×C22⋊C411yescharacteristic
128C23×C11C2×C22⋊C411yescharacteristic
129C23×C11C2×C22⋊C411yescharacteristic
130C23×C11C4×D414yes—
131C23×C11#12012yes—
132C23×C11#12012yes—
133C23×C11#12014yes—
134C23×C11#12114yes—
135C23×C11#12114yes—
136C23×C11#12114yes—
137C23×C11#12312yes—
138C23×C11#12312yes—
139C23×C11#12412yes—
140C23×C11#12712yes—
141D4×C11—48no—
142D4×C11—48no—
143C2×C4×C11—24no—
144C2×C4×C11—24no—
145C2×C4×C11—22no—
146C2×C4×C11—28no—
147C2×C4×C11—24no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—42no—
151C2×C4×C11—44no—
152C2×C4×C11—42no—
153C2×C4×C11—48no—
154C2×C4×C11—48no—
155C2×C4×C11—44no—
156C2×C4×C11—44no—
157C2×Dic11—416no—
158C2×Dic11—48no—
159C2×Dic11—88no—
160C2×Dic11—88no—
161C23×D4C2×D1111yescharacteristic
162C24×C4C2×D1111yescharacteristic
163C2×#123—24no—
164C2×#123—24no—
165C2×#123—24no—
166C22×C4⋊C4Dic1112yescomplemented
167C22×C22⋊C4—114no—
168C22×C22⋊C4Dic1112yescomplemented
169C22×C22⋊C4C2×D1111yescharacteristic
170C2×#99—228no—
171C2×#99—224no—
172#381—228no—
173C2×#95—224no—
174#342—224no—
175C22×C11—28no—
176C22×C11—24no—
177C22×C11—28no—
178C22×C11—24no—
179C22×C11—22no—
180C22×C11—22no—
181C22×C11—28no—
182C22×C11—42no—
183C22×C11—44no—
184C22×C11—44no—
185C22×C11—42no—
186C22×C11—42no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11—44no—
190C22×C11—84no—
191C22×C11—84no—
192C22×C11—84no—
193C22×C11#37911yescharacteristic
194C22×C11#38612yes—
195C22×C11#38612yes—
196C22×C11#39012yes—
197C22×C11#39214yes—
198C22×C11#39414yes—
199C22×C11#41014yes—
200C4×C11—44no—
201C4×C11—42no—
202C4×C11—44no—
203Dic11—88no—
204C25C2×Dic1111yescharacteristic
205C25C22×D1111yescharacteristic
206C22×D4—24no—
207C22×D4—24no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4C22⋊D1114yes—
211C23×C4—24no—
212C23×C4—24no—
213C23×C4—22no—
214C23×C4—22no—
215C23×C4—224no—
216C23×C4C2×Dic1112yes—
217C23×C4C2×Dic1111yescharacteristic
218C23×C4C2×Dic1112yes—
219C23×C4C22⋊D1114yes—
220#123—232no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—24no—
224C2×C22⋊C4—24no—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—22no—
227C2×C22⋊C4—24no—
228C2×C22⋊C4—24no—
229C2×C22⋊C4—118no—
230C2×C22⋊C4—224no—
231C2×C22⋊C4—224no—
232C2×C22⋊C4—224no—
233C2×C22⋊C4—224no—
234C2×C22⋊C4—224no—
235C2×C22⋊C4C22⋊D1114yes—
236#99—2216no—
237#95—2216no—
238C2×C11—24no—
239C2×C11—22no—
240C2×C11—22no—
241C2×C11—24no—
242C2×C11—82no—
243C2×C11#143811yescharacteristic
244C2×C11#178212yes—
245C2×C11#189914yes—
246C24—21no—
247C24—21no—
248C24—24no—
249C24—44no—
250C24—44no—
251C24C22⋊Dic1112yes—
252C24D4×D1114yes—
253C24#434114yes—
254C24C22×Dic1111yescharacteristic
255C24C2×C22⋊D1112yes—
256C24C2×C22⋊D1112yes—
257C24C2×C22⋊D1112yes—
258C2×D4—24no—
259C2×D4—24no—
260C2×D4—28no—
261C2×D4—28no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—42no—
268C22×C4—28no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—28no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—21no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—28no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—44no—
284C22×C4—44no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4—228no—
288C22×C4—4416no—
289C22×C4—444no—
290C22×C4—444no—
291C22×C4C22⋊Dic1112yes—
292C22×C4C22⋊Dic1114yes—
293C22×C4C22⋊Dic1114yes—
294C4⋊C4—216no—
295C22⋊C4—216no—
296C22⋊C4—28no—
297C22⋊C4—228no—
298C22⋊C4—228no—
299C22⋊C4—444no—
300C22⋊C4—444no—
301C11#1096611yescharacteristic, complemented, Sylow
302C23—24no—
303C23—28no—
304C23—22no—
305C23—24no—
306C23—48no—
307C23—48no—
308C23—44no—
309C23—44no—
310C23—44no—
311C23—44no—
312C23—42no—
313C23—42no—
314C23—44no—
315C23—88no—
316C23D4×Dic1114yes—
317C23#6698812yes—
318C23#6698812yes—
319C23#6698912yes—
320C23#6699012yes—
321C23#6699012yes—
322C23#6699114yes—
323C23#6699214yes—
324C23#6699214yes—
325C23#6699312yes—
326C23C2×C22⋊Dic1111yescharacteristic
327C23C2×C22⋊Dic1111yescharacteristic
328C23C2×C22⋊Dic1111yescharacteristic
329C23#6700614yes—
330D4—48no—
331D4—48no—
332C2×C4—28no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—44no—
338C2×C4—44no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—48no—
343C2×C4—48no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—4416no—
347C2×C4—448no—
348C2×C4—888no—
349C2×C4—888no—
350C22—24no—
351C22—28no—
352C22—28no—
353C22—24no—
354C22—22no—
355C22—22no—
356C22—28no—
357C22—42no—
358C22—42no—
359C22—42no—
360C22—44no—
361C22—44no—
362C22—42no—
363C22—42no—
364C22—44no—
365C22—84no—
366C22—84no—
367C22—84no—
368C22#1062283312yes—
369C22#1062283312yes—
370C22#1062283412yes—
371C22#1062283514yes—
372C22#1062283614yes—
373C22#1062285314yes—
374C22#1062286011yescharacteristic
375C4—44no—
376C4—42no—
377C4—44no—
378C4—888no—
379C2—24no—
380C2—22no—
381C2—22no—
382C2—24no—
383C2—82no—
384C2#1306685711yescharacteristic
385C2#1306853412yes—
386C2#1306907514yes—
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC24×C11C22×C4
FrattiniC25C22×D11
FittingC22×C11×#123C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D4×C11C22
cosocleC25×C11C23
hypercenterC22×#123D11
hypocenterC11#10966
LCSG ▷ C24×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
2. C2×#10622824C2semidirect
3. C2×#10622164C2semidirect
10. C22×C11×C4⋊C4C4semidirect
11. C22×C11×C22⋊C4C4semidirect
166. C22×C4⋊C4Dic11semidirect
168. C22×C22⋊C4Dic11semidirect
301. C11#10966semidirect

Maximal subgroups

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

subgroupindex
C22×#668982
C2×#106228242
C2×#106221642
C22×C11×#1232
#1096611