Finite Group Databasebeta

← #14645371

Subgroups — #14645371

Order 2816.

852 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068715C212yesmaximal, complemented
2C4×#66898C211yesmaximal, characteristic, complemented
3#13067132C212yesmaximal, complemented
4#13066954C211yesmaximal, characteristic, complemented
5C2×C11×#553C211yesmaximal, characteristic
6C11×#553—24no—
7C11×#553—24no—
8C2×C11×#126—21no—
9C2×C11×#125C411yescharacteristic, complemented
10C2×C11×#123—21no—
11C2×C11×#121—21no—
12C2×C11×#121C411yescharacteristic, complemented
13C2×C11×#121C2211yescharacteristic
14C2×C4×D4×C11—21no—
15C2×C4×D4×C11C411yescharacteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C411yescharacteristic, complemented
19C2×#66898—21no—
20C4×C22⋊Dic11C2212yes—
21#10622820C2212yes—
22#10622175—24no—
23#10622170—24no—
24#10622166—21no—
25#10622164—21no—
26#10622163—21no—
27C22×D4×C11—21no—
28C22×D4×C11—21no—
29C22×D4×C11C2×C411yescharacteristic
30C22×D4×C11D411yescharacteristic
31C23×C4×C11—21no—
32C23×C4×C11—21no—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C11×#126—28no—
36C11×#125—22no—
37C11×#125—22no—
38C11×#123—28no—
39C11×#121—28no—
40C11×#121—22no—
41C11×#121—22no—
42C11×#121—22no—
43C11×#121D414yes—
44C4×D4×C11—28no—
45C4×D4×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C4×D4×C11—22no—
49C11×#117—22no—
50C11×#117D414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4D411yescharacteristic
65C2×C11×C22⋊C4D411yescharacteristic
66C2×C42×C11—21no—
67C2×C42×C11C2×C411yescharacteristic
68C2×C22⋊Dic11—22no—
69C2×C4×Dic11—22no—
70C2×#4318—22no—
71#66898—24no—
72C11⋊#95—22no—
73C22⋊(C11⋊C8)—22no—
74C22⋊(C11⋊C8)—22no—
75#8362—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11C22⋊C411yescharacteristic
78C24×C11C2×D411yescharacteristic
79C2×D4×C11—24no—
80C2×D4×C11—22no—
81C2×D4×C11—22no—
82C2×D4×C11—24no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—42no—
88C2×D4×C11—82no—
89C2×D4×C11C22⋊C412yes—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11—82no—
100C22×C4×C11—82no—
101C22×C4×C11C22⋊C411yescharacteristic
102C22×C4×C11C22⋊C411yescharacteristic
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22×C411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×Dic11—42no—
109C11×C4⋊C4—24no—
110C11×C4⋊C4—24no—
111C11×C4⋊C4—24no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4C22⋊C412yes—
117C11×C4⋊C4C22⋊C412yes—
118C11×C4⋊C4C22⋊C412yes—
119C11×C22⋊C4—24no—
120C11×C22⋊C4—24no—
121C11×C22⋊C4—24no—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—24no—
124C11×C22⋊C4—22no—
125C42×C11—21no—
126C42×C11—21no—
127C42×C11—24no—
128C22⋊Dic11—24no—
129C22⋊Dic11—42no—
130C4×Dic11—44no—
131#4318—44no—
132C2×C11⋊C8—42no—
133C2×#553D1111yescharacteristic
134#1826—112no—
135C4×#99—111no—
136#1507—112no—
137#1465—111no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—21no—
142C23×C11—22no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—42no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11#10412yes—
152C23×C11C2×C22⋊C411yescharacteristic
153C23×C11#12012yes—
154D4×C11—42no—
155D4×C11—44no—
156D4×C11—48no—
157D4×C11—42no—
158D4×C11—84no—
159C2×C4×C11—24no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—22no—
163C2×C4×C11—21no—
164C2×C4×C11—22no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—42no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—84no—
180C2×C4×C11—84no—
181C2×C4×C11C2×C22⋊C411yescharacteristic
182C2×C4×C11C2×C22⋊C411yescharacteristic
183C2×C4×C11#12012yes—
184C2×Dic11—44no—
185C2×Dic11—82no—
186C2×Dic11—82no—
187C11⋊C8—82no—
188#553—24no—
189#553—24no—
190C2×#126—21no—
191C2×#125Dic1111yescharacteristic, complemented
192C2×#123—21no—
193C2×#121—21no—
194C2×#121Dic1111yescharacteristic, complemented
195C2×#121C2×D1111yescharacteristic
196C2×C4×D4—21no—
197C2×C4×D4Dic1111yescharacteristic, complemented
198C2×C4×D4C2×D1111yescharacteristic
199C2×#117C2×D1111yescharacteristic
200C22×C4⋊C4Dic1111yescharacteristic, complemented
201C2×#99—221no—
202#407—112no—
203C4×C22⋊C4—112no—
204#342—221no—
205#339—224no—
206#327—224no—
207#324—221no—
208#323—221no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—22no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—41no—
218C22×C11—41no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—82no—
225C22×C11—82no—
226C22×C11#37911yescharacteristic
227C22×C11C2×#10411yescharacteristic
228C22×C11#42111yescharacteristic
229C4×C11—21no—
230C4×C11—22no—
231C4×C11—42no—
232C4×C11—42no—
233C4×C11—41no—
234C4×C11—41no—
235C4×C11—41no—
236C4×C11—42no—
237C4×C11#41012yes—
238Dic11—84no—
239C22×D4—21no—
240C22×D4—21no—
241C22×D4C2×Dic1111yescharacteristic
242C22×D4C22⋊D1111yescharacteristic
243C23×C4—21no—
244C23×C4—21no—
245C23×C4C2×Dic1111yescharacteristic
246C23×C4C22×D1111yescharacteristic
247C2×M16—222no—
248#126—28no—
249#125—22no—
250#125—22no—
251#123—28no—
252#121—28no—
253#121—22no—
254#121—22no—
255#121—22no—
256#121C22⋊D1114yes—
257C4×D4—28no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262#117—22no—
263#117C22⋊D1114yes—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4C2×Dic1111yescharacteristic
270C2×C4⋊C4C2×Dic1111yescharacteristic
271C2×C4⋊C4C2×Dic1111yescharacteristic
272C2×C4⋊C4C22⋊D1111yescharacteristic
273C2×C22⋊C4—21no—
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4—222no—
278C2×C22⋊C4C22⋊D1111yescharacteristic
279C2×C22⋊C4C22⋊D1111yescharacteristic
280C2×C42—21no—
281C2×C42—222no—
282C2×C42C2×Dic1111yescharacteristic
283#99—224no—
284C22⋊C8—222no—
285C22⋊C8—222no—
286#95—222no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—42no—
290C2×C11—42no—
291C2×C11—82no—
292C2×C11#178211yescharacteristic
293C2×C11#178911yescharacteristic
294C2×C11#179511yescharacteristic
295C24—21no—
296C24C22⋊Dic1111yescharacteristic
297C24C2×C22⋊D1111yescharacteristic
298C2×D4—24no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—24no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—42no—
305C2×D4—42no—
306C2×D4—42no—
307C2×D4—82no—
308C2×D4C22⋊Dic1112yes—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—24no—
313C22×C4—24no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—42no—
318C22×C4—82no—
319C22×C4—82no—
320C22×C4—442no—
321C22×C4C22⋊Dic1111yescharacteristic
322C22×C4C22⋊Dic1111yescharacteristic
323C22×C4C22⋊Dic1111yescharacteristic
324C22×C4C22×Dic1111yescharacteristic
325C22×C4C2×C22⋊D1112yes—
326C22×C4C2×C22⋊D1112yes—
327C22×C4C2×C22⋊D1111yescharacteristic
328M16—444no—
329C2×C8—442no—
330C4⋊C4—24no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4C22⋊Dic1112yes—
338C4⋊C4C22⋊Dic1112yes—
339C4⋊C4C22⋊Dic1112yes—
340C22⋊C4—24no—
341C22⋊C4—24no—
342C22⋊C4—24no—
343C22⋊C4—22no—
344C22⋊C4—24no—
345C22⋊C4—22no—
346C22⋊C4—224no—
347C22⋊C4—442no—
348C42—21no—
349C42—21no—
350C42—24no—
351C42—444no—
352C11#836211yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—22no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23—41no—
362C23—42no—
363C23—42no—
364C23—41no—
365C23—41no—
366C23#6690112yes—
367C23C2×C22⋊Dic1111yescharacteristic
368C23#6700612yes—
369D4—42no—
370D4—44no—
371D4—48no—
372D4—42no—
373D4—84no—
374C2×C4—24no—
375C2×C4—22no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—84no—
395C2×C4—84no—
396C2×C4—444no—
397C2×C4—882no—
398C2×C4—882no—
399C2×C4C2×C22⋊Dic1111yescharacteristic
400C2×C4C2×C22⋊Dic1111yescharacteristic
401C2×C4#6700612yes—
402C8—882no—
403C22—21no—
404C22—21no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—42no—
410C22—42no—
411C22—41no—
412C22—41no—
413C22—42no—
414C22—42no—
415C22—42no—
416C22—81no—
417C22—81no—
418C22—82no—
419C22—82no—
420C22C2×#6690111yescharacteristic
421C22#1062284911yescharacteristic
422C22#1062286011yescharacteristic
423C4—22no—
424C4—21no—
425C4—41no—
426C4—42no—
427C4—42no—
428C4—42no—
429C4—41no—
430C4—41no—
431C4—884no—
432C4#1062285312yes—
433C2—21no—
434C2—21no—
435C2—42no—
436C2—42no—
437C2—82no—
438C2#1306853411yescharacteristic
439C2#1306856011yescharacteristic
440C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#553C2
socleC22×C11#379
cosocleC23×C4×C11C23
hypercenterC2×#553D11
hypocenterC11#8362
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. #13068715C2semidirect
2. C4×#66898C2semidirect
3. #13067132C2semidirect
4. #13066954C2semidirect
9. C2×C11×#125C4semidirect
12. C2×C11×#121C4semidirect
15. C2×C4×D4×C11C4semidirect
18. C22×C11×C4⋊C4C4semidirect
191. C2×#125Dic11semidirect
194. C2×#121Dic11semidirect
197. C2×C4×D4Dic11semidirect
200. C22×C4⋊C4Dic11semidirect
352. C11#8362semidirect

Maximal subgroups

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

subgroupindex
#130687152
C4×#668982
#130671322
#130669542
C2×C11×#5532
#836211