Finite Group Databasebeta

← #14660235

Subgroups — #14660235

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622752C212yesmaximal
2#13071104C211yesmaximal, characteristic
3#13068349C211yesmaximal, characteristic, complemented
4C2×#10622193C212yesmaximal, complemented
5C11×#2873C211yesmaximal, characteristic, complemented
6C22×#4339C2211yescharacteristic
7C22×C11×M16C2212yes—
8C2×C11×#117C2211yescharacteristic
9C2×#66979C2212yes—
10C22×C4×Dic11C2211yescharacteristic
11C11×#405—24no—
12C4×C11×M16—22no—
13#10622752—24no—
14#10622752C418yescomplemented
15C2×#66889—24no—
16#10622601C412yescomplemented
17#10622587C412yescomplemented
18#10622571—22no—
19C4×(C2×D11)⋊C4—22no—
20#10622193—24no—
21#10622164—22no—
22C23×C4×C11C2311yescharacteristic
23C22×C22⋊D11—21no—
24C23×Dic11—21no—
25C2×#4339—22no—
26C2×#4339—22no—
27C2×#4339—22no—
28C2×#4339—22no—
29C2×#4339—22no—
30C2×#4339C2×C414yes—
31C22×D44C2×C411yescharacteristic
32C22×C4×D11—21no—
33C22×Dic22C2×C411yescharacteristic
34C2×C11×M16—22no—
35C2×C11×M16—22no—
36C2×C11×M16—22no—
37C2×C11×M16C2×C414yes—
38C2×C11×M16D414yes—
39C2×C11×M16D414yes—
40C22×C8×C11—22no—
41C11×#117—22no—
42C11×#117—22no—
43C2×C11×C4⋊C4C2×C412yes—
44C2×C11×C22⋊C4D412yes—
45C2×C42×C11D412yes—
46C2×C22⋊Dic11—22no—
47C2×(C2×D11)⋊C4—24no—
48#66979—22no—
49#66979—22no—
50#66979—22no—
51#66979C2×C414yes—
52C2×C4⋊Dic11—22no—
53C2×C4×Dic11—22no—
54C2×C4×Dic11—22no—
55C2×C4×Dic11—22no—
56C2×C4×Dic11—21no—
57C2×C4×Dic11C2×C412yes—
58C11×#97—24no—
59C4×C8×C11—24no—
60C11⋊#95—24no—
61#66889—216no—
62#10959—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C23×D11—21no—
65C22×C4×C11C22⋊C414yes—
66C22×C4×C11C22×C412yes—
67C22×C4×C11C22×C411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D412yes—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4112yes—
72C22×C4×C11#4112yes—
73C22×C4×C11#4112yes—
74C2×C22⋊D11—24no—
75C2×C22⋊D11—42no—
76C2×C22⋊D11—41no—
77C2×C22⋊D11—41no—
78C22×Dic11—21no—
79C22×Dic11—22no—
80C22×Dic11—44no—
81C22×Dic11—42no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84#4339—24no—
85#4339—24no—
86#4339—24no—
87#4339—24no—
88#4339—42no—
89#4339—42no—
90#4339—42no—
91#4339—42no—
92C2×D44—21no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44C4212yes—
96C2×C4×D11—24no—
97C2×C4×D11—41no—
98C2×C4×D11—42no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22C4212yes—
104C11×M16—24no—
105C11×M16—24no—
106C11×M16—24no—
107C11×M16C22⋊C418yescomplemented
108C2×C8×C11—24no—
109C2×C8×C11—24no—
110C2×C8×C11—24no—
111C11×C4⋊C4—24no—
112C11×C22⋊C4—24no—
113C42×C11—22no—
114C42×C11—22no—
115C22⋊Dic11—24no—
116C22⋊Dic11—42no—
117(C2×D11)⋊C4—48no—
118C4⋊Dic11—24no—
119C4⋊Dic11—42no—
120C4×Dic11—24no—
121C4×Dic11—24no—
122C4×Dic11—42no—
123C4×Dic11—42no—
124C2×#421—112no—
125#2873D1111yescharacteristic, complemented
126#2297—111no—
127#1740—111no—
128C2×#339—112no—
129C23×C11—42no—
130C23×C11C2×C22⋊C411yescharacteristic
131C23×C11C4×D412yes—
132C23×C11#12112yes—
133C23×C11#12411yescharacteristic
134C23×C11#12711yescharacteristic
135C22×D11—22no—
136C22×D11—44no—
137C22×D11—41no—
138C22×D11—41no—
139C2×C4×C11—24no—
140C2×C4×C11—44no—
141C2×C4×C11C2×C4211yescharacteristic
142C2×C4×C11C2×C22⋊C412yes—
143C2×C4×C11#11712yes—
144C2×C4×C11#11711yescharacteristic
145C2×C4×C11C4×D412yes—
146C2×C4×C11C4×D412yes—
147C2×C4×C11C4×D412yes—
148C2×C4×C11C4×D412yes—
149C2×C4×C11C4×D412yes—
150C2×C4×C11#12011yescharacteristic
151C2×C4×C11#12112yes—
152C2×C4×C11#12112yes—
153C2×C4×C11#12312yes—
154C2×C4×C11#12311yescharacteristic
155C2×C4×C11#12412yes—
156C2×C4×C11#12612yes—
157C22⋊D11—44no—
158C22⋊D11—44no—
159C2×Dic11—24no—
160C2×Dic11—22no—
161C2×Dic11—42no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—41no—
165C2×Dic11—42no—
166C2×Dic11—41no—
167C2×Dic11—44no—
168C2×Dic11—84no—
169D44—24no—
170D44—42no—
171C4×D11—44no—
172C4×D11—44no—
173Dic22—24no—
174Dic22—42no—
175C8×C11—28no—
176C22×#41—111no—
177C22×M16C2×D1112yes—
178C2×#117—112no—
179C2×#117C2×D1111yescharacteristic
180C22×C42—111no—
181#421—118no—
182#421—224no—
183C2×#104—224no—
184#405—24no—
185C4×M16—22no—
186#391—112no—
187#390—112no—
188#386—222no—
189C4×C22⋊C4—222no—
190#342—222no—
191#339—224no—
192C22×C11—22no—
193C22×C11—24no—
194C22×C11—42no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11C4×C22⋊C411yescharacteristic
198C22×C11#38611yescharacteristic
199C22×C11#38812yes—
200C22×C11#39012yes—
201C22×C11#39011yescharacteristic
202C2×D11—44no—
203C2×D11—42no—
204C2×D11—82no—
205C2×D11—82no—
206C4×C11—44no—
207C4×C11C4×C22⋊C412yes—
208C4×C11#38612yes—
209C4×C11#38812yes—
210C4×C11#38812yes—
211Dic11—44no—
212Dic11—42no—
213Dic11—84no—
214C2×#41—114no—
215C2×#41—222no—
216C2×#41—222no—
217C2×#41—222no—
218C2×#41—222no—
219C2×#41—222no—
220C22×Q8—111no—
221C22×D4—111no—
222C22×D4—221no—
223C23×C4—221no—
224C23×C4—221no—
225C23×C4C22×D1111yescharacteristic
226C2×M16—22no—
227C2×M16—22no—
228C2×M16—22no—
229C2×M16C4×D1114yes—
230C2×M16D4414yes—
231C2×M16C22⋊D1114yes—
232C22×C8—22no—
233#117—22no—
234#117—22no—
235#117—114no—
236#117—222no—
237#117—222no—
238#117—222no—
239C2×C4⋊C4—222no—
240C2×C4⋊C4C4×D1112yes—
241C2×C22⋊C4—222no—
242C2×C22⋊C4—224no—
243C2×C22⋊C4D4412yes—
244C2×C42—112no—
245C2×C42—222no—
246C2×C42—222no—
247C2×C42—222no—
248C2×C42—221no—
249C2×C42C22⋊D1112yes—
250#104—2216no—
251#97—24no—
252C4×C8—24no—
253#95—224no—
254C2×C11—21no—
255C2×C11—22no—
256C2×C11—21no—
257C2×C11—22no—
258C2×C11#143711yescharacteristic
259C2×C11#188412yes—
260D11—82no—
261C24—221no—
262C24C2×D4411yescharacteristic
263#41—224no—
264#41—224no—
265#41—224no—
266#41—224no—
267#41—442no—
268#41—442no—
269#41—442no—
270#41—442no—
271C2×Q8—112no—
272C2×Q8—221no—
273C2×Q8—222no—
274C2×Q8—222no—
275C2×D4—112no—
276C2×D4—224no—
277C2×D4—221no—
278C2×D4—222no—
279C2×D4—222no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—442no—
283C22×C4—221no—
284C22×C4—222no—
285C22×C4—224no—
286C22×C4—444no—
287C22×C4—441no—
288C22×C4—441no—
289C22×C4—441no—
290C22×C4—442no—
291C22×C4—441no—
292C22×C4—442no—
293C22×C4(C2×D11)⋊C414yes—
294C22×C4C2×C4×D1111yescharacteristic
295C22×C4C2×C4×D1112yes—
296C22×C4C2×D4412yes—
297C22×C4#433912yes—
298C22×C4#433912yes—
299C22×C4#433912yes—
300C22×C4C2×C22⋊D1112yes—
301C22×C4C2×C22⋊D1111yescharacteristic
302M16—24no—
303M16—24no—
304M16—24no—
305M16(C2×D11)⋊C418yescomplemented
306C2×C8—24no—
307C2×C8—24no—
308C2×C8—24no—
309C4⋊C4—24no—
310C4⋊C4—224no—
311C4⋊C4—442no—
312C22⋊C4—24no—
313C22⋊C4—224no—
314C22⋊C4—448no—
315C22⋊C4—442no—
316C42—22no—
317C42—22no—
318C42—224no—
319C42—224no—
320C42—442no—
321C42—442no—
322C11#1095911yescharacteristic, complemented, Sylow
323C23—42no—
324C23—222no—
325C23—444no—
326C23—441no—
327C23—441no—
328C23C4×D4412yes—
329C23#6692711yescharacteristic
330C23#6692811yescharacteristic
331C23C2×(C2×D11)⋊C411yescharacteristic
332C23#6698312yes—
333Q8—224no—
334Q8—442no—
335D4—224no—
336D4—444no—
337D4—444no—
338D4—442no—
339C2×C4—24no—
340C2×C4—44no—
341C2×C4—224no—
342C2×C4—222no—
343C2×C4—442no—
344C2×C4—444no—
345C2×C4—444no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4—441no—
349C2×C4—444no—
350C2×C4—444no—
351C2×C4—444no—
352C2×C4—884no—
353C2×C4C42×D1111yescharacteristic
354C2×C4#6692512yes—
355C2×C4#6692511yescharacteristic
356C2×C4C4×D4412yes—
357C2×C4C4×D4412yes—
358C2×C4#6692812yes—
359C2×C4#6692912yes—
360C2×C4C2×(C2×D11)⋊C412yes—
361C2×C4C4×C22⋊D1112yes—
362C2×C4C4×C22⋊D1112yes—
363C2×C4C4×C22⋊D1112yes—
364C2×C4#6698211yescharacteristic
365C2×C4#6698212yes—
366C2×C4#6698312yes—
367C2×C4#6698312yes—
368C2×C4#6700611yescharacteristic
369C8—28no—
370C22—22no—
371C22—24no—
372C22—41no—
373C22—41no—
374C22—42no—
375C22—444no—
376C22—442no—
377C22—882no—
378C22—882no—
379C22C4×(C2×D11)⋊C411yescharacteristic
380C22#1062255211yescharacteristic
381C22#1062255212yes—
382C22#1062255312yes—
383C22#1062282611yescharacteristic
384C4—44no—
385C4—444no—
386C4—442no—
387C4—884no—
388C4C4×(C2×D11)⋊C412yes—
389C4#1062255312yes—
390C4#1062255312yes—
391C4#1062282612yes—
392C2—21no—
393C2—22no—
394C2—21no—
395C2—22no—
396C2—882no—
397C2#1306685411yescharacteristic
398C2#1306899912yes—
subgroupG/H
centerC2×C4#67006
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#2873C2
socleC22×C11#386
prime radicalC22×#4339C22
cosocleC23×C4×C11C23
hypercenter#2873D11
hypocenterC11#10959
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2873

Complements

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

NH ≅ G/Ntype
3. #13068349C2semidirect
4. C2×#10622193C2semidirect
5. C11×#2873C2semidirect
14. #10622752C4semidirect
16. #10622601C4semidirect
17. #10622587C4semidirect
107. C11×M16C22⋊C4semidirect
125. #2873D11semidirect
305. M16(C2×D11)⋊C4semidirect
322. C11#10959semidirect

Maximal subgroups

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

subgroupindex
C2×#106227522
#130711042
#130683492
C2×#106221932
C11×#28732
#1095911