Finite Group Databasebeta

← #13071627

Subgroups — #13071627

Order 1408.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66992C211yesmaximal, characteristic
2C2×D4×Dic11C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C22×Dic11⋊C4C211yesmaximal, characteristic, complemented
5C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
6C11×#386C211yesmaximal, characteristic, complemented
7#10622571C211yesmaximal, characteristic, complemented
8#10622570C211yesmaximal, characteristic, complemented
9#10622559C211yesmaximal, characteristic, complemented
10#10622558C211yesmaximal, characteristic, complemented
11C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12#10622282C211yesmaximal, characteristic, complemented
13#10622281C211yesmaximal, characteristic, complemented
14#10622262C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C23×Dic11C2211yescharacteristic
21C23×Dic11C2211yescharacteristic
22C23×Dic11C2211yescharacteristic
23C22×C4×D11C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C11×C22⋊C4C2211yescharacteristic
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×C22⋊Dic11C2211yescharacteristic
30#66992C418yescomplemented
31D4×Dic11—24no—
32C4×C22⋊D11—24no—
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×C4⋊Dic11C2211yescharacteristic
38C2×Dic11⋊C4—24no—
39C2×Dic11⋊C4C2211yescharacteristic
40C2×Dic11⋊C4C2211yescharacteristic
41C2×Dic11⋊C4C2211yescharacteristic
42C2×Dic11⋊C4C2211yescharacteristic
43C2×Dic11⋊C4C2211yescharacteristic
44C2×Dic11⋊C4C2211yescharacteristic
45C2×C4×Dic11C2211yescharacteristic
46C2×C4×Dic11C2211yescharacteristic
47C2×C4×Dic11C2211yescharacteristic
48C2×C4×Dic11C2211yescharacteristic
49(C22⋊D11)⋊C4—24no—
50C11×#95C2211yescharacteristic
51C11×#95C2211yescharacteristic
52C11⋊#95C2211yescharacteristic
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C24×C11C2311yescharacteristic
57C24×C11C2311yescharacteristic
58C23×D11C2311yescharacteristic
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11C2×C414yescomplemented
62C22×C4×C11—22no—
63C22×C4×C11—22no—
64C22×C4×C11—41no—
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C22×C4×C11C2311yescharacteristic
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—22no—
71C2×C22⋊D11—22no—
72C2×C22⋊D11—22no—
73C2×C22⋊D11—22no—
74C2×C22⋊D11C2×C414yescomplemented
75C2×C22⋊D11C2×C414yescomplemented
76C22×Dic11—22no—
77C22×Dic11—22no—
78C22×Dic11—22no—
79C22×Dic11—22no—
80C22×Dic11—22no—
81C22×Dic11—22no—
82C22×Dic11—41no—
83C22×Dic11—41no—
84C22×Dic11C2×C414yescomplemented
85C22×Dic11C2311yescharacteristic
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C2×C4×D11—22no—
93C2×C4×D11—22no—
94C2×C4×D11—41no—
95C11×C22⋊C4—22no—
96C11×C22⋊C4—22no—
97C11×C22⋊C4—41no—
98C22⋊Dic11—22no—
99C22⋊Dic11C2×C414yescomplemented
100C22⋊Dic11D414yescomplemented
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4C2×C414yescomplemented
105C4⋊Dic11—22no—
106Dic11⋊C4—22no—
107Dic11⋊C4—22no—
108Dic11⋊C4—22no—
109Dic11⋊C4—22no—
110Dic11⋊C4C2×C414yescomplemented
111Dic11⋊C4D414yescomplemented
112C4×Dic11—22no—
113C4×Dic11—22no—
114C4×Dic11—22no—
115C4×Dic11—22no—
116#2361—111nomaximal, Sylow
117C23×C11—21no—
118C23×C11—21no—
119C23×C11—21no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11C22×C412yes—
128C23×C11C22×C412yes—
129C23×C11C2×D412yes—
130C23×C11#4112yes—
131C23×C11C2411yescharacteristic
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11C22×C412yes—
139D4×C11—28no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—44no—
154C2×C4×C11C22×C412yes—
155C2×C4×C11C2×D412yes—
156C22⋊D11—28no—
157C22⋊D11—28no—
158C2×Dic11—21no—
159C2×Dic11—21no—
160C2×Dic11—21no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—21no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—28no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11C22×C412yes—
175C2×Dic11C22×C412yes—
176C2×Dic11C22×C412yes—
177C2×Dic11C2×D412yes—
178C2×Dic11C2×D412yes—
179C2×Dic11C2×D412yes—
180C2×Dic11C2×D412yes—
181C2×Dic11#4112yes—
182C4×D11—44no—
183C2×#121—111no—
184C2×C4×D4—111no—
185C2×C4×D4—111no—
186C2×C4×D4—111no—
187C22×C4⋊C4—111no—
188#390—111no—
189#389—111no—
190#388—111no—
191#388—111no—
192#386—111no—
193#386D1111yescharacteristic, complemented
194#385—111no—
195#385—111no—
196C4×C4⋊C4—111no—
197C4×C22⋊C4—111no—
198C22×C11—22no—
199C22×C11—22no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—41no—
208C22×C11—41no—
209C22×C11—41no—
210C22×C11—41no—
211C22×C11C4×D414yescomplemented
212C22×C11C23×C411yescharacteristic
213C22×C11C22×D411yescharacteristic
214C22×C11C22×D411yescharacteristic
215C22×C11C2×#4111yescharacteristic
216C22×C11C2×#4111yescharacteristic
217C22×C11H(5,𝔽2)11yescharacteristic
218C22×C112−1+411yescharacteristic
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—41no—
223C2×D11—41no—
224C2×D11—41no—
225C2×D11—41no—
226C4×C11—22no—
227C4×C11—22no—
228C4×C11—41no—
229C4×C11—41no—
230C4×C11—41no—
231Dic11—22no—
232Dic11—22no—
233Dic11—22no—
234Dic11—22no—
235Dic11—22no—
236Dic11—41no—
237Dic11C4×D414yescomplemented
238C22×D4—111no—
239C22×D4—111no—
240C22×D4C2×D1111yescharacteristic
241C23×C4—111no—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4—111no—
245C23×C4C2×D1111yescharacteristic
246#121—118no—
247C4×D4—224no—
248C4×D4—224no—
249C4×D4—224no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—224no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4C2×D1111yescharacteristic
266C2×C22⋊C4C2×D1111yescharacteristic
267C2×C22⋊C4C2×D1111yescharacteristic
268C2×C42—111no—
269C2×C42—111no—
270C2×C42—111no—
271C2×C42—111no—
272#95—111no—
273#95—111no—
274#95—111no—
275#95—111no—
276#95C2×D1111yescharacteristic
277#95C2×D1111yescharacteristic
278C2×C11—24no—
279C2×C11—42no—
280C2×C11C2×C4×D411yescharacteristic
281C2×C11C2×C4×D411yescharacteristic
282C2×C11#52011yescharacteristic
283C2×C11D4211yescharacteristic
284C2×C11#54711yescharacteristic
285C2×C11#54811yescharacteristic
286C2×C11#55311yescharacteristic
287D11—42no—
288C24—111no—
289C24C22×D1111yescharacteristic
290C24C22×D1111yescharacteristic
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—114no—
294C2×D4—114no—
295C2×D4—222no—
296C2×D4—222no—
297C2×D4—222no—
298C2×D4—222no—
299C2×D4C4×D1114yescomplemented
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—41no—
303C22×C4—111no—
304C22×C4—114no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—222no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4C22×D1111yescharacteristic
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1111yescharacteristic
325C22×C4C22×D1111yescharacteristic
326C22×C4C22×D1111yescharacteristic
327C4⋊C4—114no—
328C4⋊C4—114no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—222no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—114no—
338C22⋊C4—114no—
339C22⋊C4—114no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—441no—
344C42—222no—
345C42—222no—
346C42—222no—
347C42—222no—
348C11#236111yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—112no—
360C23—221no—
361C23—221no—
362C23—221no—
363C23—221no—
364C23—221no—
365C23—221no—
366C23C2×C4×D1112yes—
367C23C2×C4×D1112yes—
368C23D4×D1112yes—
369C23#434112yes—
370C23C23×D1111yescharacteristic
371D4—28no—
372D4—228no—
373D4—228no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—44no—
388C2×C4—112no—
389C2×C4—112no—
390C2×C4—112no—
391C2×C4—112no—
392C2×C4—112no—
393C2×C4—112no—
394C2×C4—112no—
395C2×C4—112no—
396C2×C4—228no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—221no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—444no—
411C2×C4—444no—
412C2×C4—444no—
413C2×C4C2×C4×D1112yes—
414C2×C4D4×D1112yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—222no—
429C22—222no—
430C22—222no—
431C22—441no—
432C22—441no—
433C22—441no—
434C22—441no—
435C22(C22⋊D11)⋊C414yescomplemented
436C22C22×C4×D1111yescharacteristic
437C22C2×D4×D1111yescharacteristic
438C22C2×D4×D1111yescharacteristic
439C22C2×#434111yescharacteristic
440C22#6703711yescharacteristic
441C22#41×D1111yescharacteristic
442C22#6704311yescharacteristic
443C4—22no—
444C4—22no—
445C4—41no—
446C4—41no—
447C4—41no—
448C4—114no—
449C4—222no—
450C4—222no—
451C4—222no—
452C4—222no—
453C4—222no—
454C4—441no—
455C2—24no—
456C2—42no—
457C2—442no—
458C2C2×(C22⋊D11)⋊C411yescharacteristic
459C2C4×D4×D1111yescharacteristic
460C2#1062307711yescharacteristic
461C2#1062312111yescharacteristic
462C2#1062312911yescharacteristic
463C2#1062313211yescharacteristic
464C2#1062318611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutatorC22×C11C23×C4
FittingC11×#386C2
socle, cosocleC23×C11C24
prime radicalC2×#66992C2
hypercenter#386D11
hypocenterC11#2361
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic11C2semidirect
3. C2×C4×C22⋊D11C2semidirect
4. C22×Dic11⋊C4C2semidirect
5. C2×(C22⋊D11)⋊C4C2semidirect
6. C11×#386C2semidirect
7. #10622571C2semidirect
8. #10622570C2semidirect
9. #10622559C2semidirect
10. #10622558C2semidirect
11. C22⋊C4×Dic11C2semidirect
12. #10622282C2semidirect
13. #10622281C2semidirect
14. #10622262C2semidirect
15. #10622260C2semidirect
30. #66992C4semidirect
61. C2×D4×C11C2×C4semidirect
74. C2×C22⋊D11C2×C4semidirect
75. C2×C22⋊D11C2×C4semidirect
84. C22×Dic11C2×C4semidirect
99. C22⋊Dic11C2×C4semidirect
100. C22⋊Dic11D4semidirect
104. (C2×D11)⋊C4C2×C4semidirect
110. Dic11⋊C4C2×C4semidirect
111. Dic11⋊C4D4semidirect
193. #386D11semidirect
211. C22×C11C4×D4semidirect
237. Dic11C4×D4semidirect
299. C2×D4C4×D11semidirect
348. C11#2361semidirect
435. C22(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C2×D4×Dic112
C2×C4×C22⋊D112
C22×Dic11⋊C42
C2×(C22⋊D11)⋊C42
C11×#3862
#106225712
#106225702
#106225592
#106225582
C22⋊C4×Dic112
#106222822
#106222812
#106222622
#106222602
#236111