Finite Group Databasebeta

← #13082262

Subgroups — #13082262

Order 1408.

1492 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67043C211yesmaximal, characteristic, complemented
2C22×Q8×D11C211yesmaximal, characteristic, complemented
3C11×#548C211yesmaximal, characteristic, complemented
4#10623362C211yesmaximal, characteristic, complemented
5Q8×C22⋊D11C211yesmaximal, characteristic, complemented
6#10623208C213yesmaximal, complemented
7#10623206C213yesmaximal, complemented
8#10623163C213yesmaximal, complemented
9#10623159C213yesmaximal, complemented
10#10623137C213yesmaximal, complemented
11#10623129C213yesmaximal, complemented
12Q8×D44C211yesmaximal, characteristic, complemented
13#10623103C211yesmaximal, characteristic, complemented
14#10623078C213yesmaximal, complemented
15D4×Dic22C213yesmaximal, complemented
16C2×C11×#41C2211yescharacteristic, complemented
17C22×Q8×C11C2211yescharacteristic
18#67043—28no—
19C2×Q8×D11—28no—
20C2×Q8×D11C2211yescharacteristic
21C2×Q8×D11C2213yes—
22C2×Q8×D11C2213yes—
23C2×Q8×D11C2211yescharacteristic
24C2×Q8×D11C2211yescharacteristic, complemented
25C2×#4341C2213yes—
26C2×#4341C2213yescomplemented
27C2×#4339C2213yes—
28C22×C4×D11C2213yes—
29C22×Dic22C2213yes—
30C22×Dic22C2213yescomplemented
31C11×#124C2213yescomplemented
32C11×C22⋊Q8C2213yescomplemented
33C11×#121C2213yes—
34C4×Q8×C11C2211yescharacteristic, complemented
35C4×D4×C11C2213yes—
36#66999C2213yescomplemented
37Q8×Dic11C2211yescharacteristic, complemented
38#66997C2213yescomplemented
39#66992C2213yes—
40#66991C2213yes—
41#66990C2213yes—
42#66989C2213yescomplemented
43D4×Dic11C2216yes—
44C4×C22⋊D11C2213yes—
45C4×C22⋊D11C2213yes—
46#66977C2213yes—
47#66977C2213yescomplemented
48#66950C2213yes—
49#66950C2213yescomplemented
50#66949C2213yes—
51#66947C2213yes—
52#66945C2213yes—
53#66941C2216yescomplemented
54#66940C2213yescomplemented
55#66938C2216yescomplemented
56#66937C2213yes—
57#66936C2213yes—
58#66936C2216yes—
59#66935C2211yescharacteristic
60(C22⋊D11)⋊C4C2216yes—
61#66931C2213yes—
62#66931C2216yescomplemented
63#66931C2216yescomplemented
64C4×D44C2213yes—
65#66925C2213yes—
66#66922C2213yescomplemented
67C4×Dic22C2213yescomplemented
68C23×D11C2311yescharacteristic
69C11×#41—24no—
70C2×Q8×C11—24no—
71C2×Q8×C11C2313yes—
72C2×Q8×C11C2311yescharacteristic
73C2×D4×C11C2313yes—
74C2×D4×C11C2313yes—
75C22×C4×C11C2313yes—
76C22×C4×C11C2313yes—
77C2×C22⋊D11C2313yes—
78C2×C22⋊D11C2311yescharacteristic
79C2×C22⋊D11C2313yes—
80C2×C22⋊D11C2313yes—
81C22×Dic11C2313yes—
82C22×Dic11C2316yes—
83Q8×D11—212no—
84Q8×D11—212no—
85Q8×D11—24no—
86Q8×D11—24no—
87Q8×D11D418yescomplemented
88#4341—212no—
89#4341—212no—
90#4339—212no—
91C2×D44C2311yescharacteristic
92C2×D44C2311yescharacteristic
93C2×C4×D11—212no—
94C2×C4×D11C2313yes—
95C2×C4×D11C2313yes—
96C2×C4×D11C2313yes—
97C2×C4×D11C2313yes—
98C2×C4×D11C2313yes—
99C2×Dic22—212no—
100C2×Dic22—212no—
101C2×Dic22C2313yes—
102C2×Dic22C2313yes—
103C2×Dic22C2313yes—
104C2×Dic22C2316yes—
105C2×Dic22C2313yes—
106C11×C4⋊C4C2313yes—
107C11×C4⋊C4C2313yes—
108C11×C22⋊C4C2311yescharacteristic
109C11×C22⋊C4C2313yes—
110C11×C22⋊C4C2316yes—
111C42×C11C2313yes—
112C22⋊Dic11C2313yes—
113C22⋊Dic11C2313yes—
114C22⋊Dic11C2316yes—
115(C2×D11)⋊C4C2311yescharacteristic
116(C2×D11)⋊C4C2313yes—
117(C2×D11)⋊C4C2313yes—
118(C2×D11)⋊C4C2313yes—
119(C2×D11)⋊C4C2311yescharacteristic
120(C2×D11)⋊C4C2313yes—
121C4⋊Dic11C2313yes—
122C4⋊Dic11C2313yes—
123C4⋊Dic11C2316yes—
124Dic11⋊C4C2313yes—
125Dic11⋊C4C2313yes—
126Dic11⋊C4C2313yes—
127Dic11⋊C4C2313yes—
128Dic11⋊C4C2316yes—
129C4×Dic11C2316yes—
130C4×Dic11C2313yes—
131#3486—111nomaximal, Sylow
132C23×C11C2413yes—
133C23×C11C2411yescharacteristic
134C22×D11—22no—
135C22×D11—22no—
136C22×D11—22no—
137C22×D11C2411yescharacteristic
138C22×D11C2411yescharacteristic
139C22×D11C2411yescharacteristic
140Q8×C11—26no—
141Q8×C11C2×D414yes—
142D4×C11—26no—
143D4×C11—26no—
144C2×C4×C11—26no—
145C2×C4×C11—26no—
146C2×C4×C11C2413yes—
147C2×C4×C11C2411yescharacteristic
148C2×C4×C11C2413yes—
149C2×C4×C11C2411yescharacteristic
150C2×C4×C11C2413yes—
151C22⋊D11—22no—
152C22⋊D11—26no—
153C22⋊D11—26no—
154C22⋊D11—26no—
155C2×Dic11—26no—
156C2×Dic11—212no—
157C2×Dic11C2411yescharacteristic
158C2×Dic11C2413yes—
159C2×Dic11C2413yes—
160C2×Dic11C2413yes—
161C2×Dic11C2413yes—
162D44—22no—
163D44—22no—
164C4×D11—26no—
165C4×D11—26no—
166C4×D11—26no—
167C4×D11—26no—
168C4×D11C2×D4112yes—
169Dic22—26no—
170Dic22—26no—
171Dic22—26no—
172Dic22—212no—
173Dic22C2×D4112yes—
174C2×2−1+4—111no—
175C23×Q8—111no—
176D4×Q8—111no—
177D4×Q8—113no—
178D4×Q8—111no—
179D4×Q8—113no—
180#548—111no—
181#548—113no—
182#548—113no—
183#548D1111yescharacteristic, complemented
184#536—113no—
185#536—113no—
186#525—113no—
187#525—113no—
188#519—111no—
189C22×C11—21no—
190C22×C11—21no—
191C22×C11—23no—
192C22×C11—23no—
193C22×C11—23no—
194C22×C112−1+412yescomplemented
195C22×C11C2511yescharacteristic
196C2×D11—28no—
197C2×D11—21no—
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—21no—
201C2×D11—21no—
202C2×D11—21no—
203C2×D11—21no—
204C2×D11C22×D412yes—
205C2×D112−1+412yescomplemented
206C4×C11—21no—
207C4×C11—23no—
208C4×C11—23no—
209C4×C11—21no—
210C4×C11C22×D416yes—
211Dic11—23no—
212Dic11—23no—
213Dic11—21no—
214Dic11—23no—
215Dic11C22×D416yes—
2162−1+4—228no—
217C2×#41—113no—
218C2×#41—113no—
219C2×#41—113no—
220C2×#41C2×D1111yescharacteristic, complemented
221C22×Q8—111no—
222C22×Q8—113no—
223C22×Q8—113no—
224C22×Q8—111no—
225C22×Q8—111no—
226C22×Q8—113no—
227C22×Q8—113no—
228C22×Q8—228no—
229C22×Q8C2×D1111yescharacteristic
230C23×C4—113no—
231C4⋊Q8—113no—
232C4⋊Q8—116no—
233C4⋊Q8—113no—
234#124—113no—
235#124—116no—
236#124C2×D1113yescomplemented
237#123—113no—
238#123—116no—
239#123—113no—
240C22⋊Q8—113no—
241C22⋊Q8—113no—
242C22⋊Q8—113no—
243C22⋊Q8—113no—
244C22⋊Q8—113no—
245C22⋊Q8—113no—
246C22⋊Q8—113no—
247C22⋊Q8—116no—
248C22⋊Q8—116no—
249C22⋊Q8C2×D1113yescomplemented
250#121—113no—
251#121—113no—
252#121—113no—
253#121C2×D1113yes—
254#120—113no—
255#120—111no—
256C4×Q8—111no—
257C4×Q8—113no—
258C4×Q8—113no—
259C4×Q8C2×D1111yescharacteristic, complemented
260C4×D4—116no—
261C4×D4—113no—
262C4×D4—113no—
263C4×D4—116no—
264C4×D4—113no—
265C4×D4C2×D1113yes—
266#117—113no—
267#117—113no—
268C2×C11—22no—
269C2×C11—43no—
270C2×C11C23×D411yescharacteristic
271C2×C11C2×2−1+411yescharacteristic
272C2×C11C2×2−1+411yescharacteristic
273D11—22no—
274D11—22no—
275D11—41no—
276C24—111no—
277#41—24no—
278#41—2212no—
279#41—2212no—
280#41—2212no—
281C2×Q8—24no—
282C2×Q8—118no—
283C2×Q8—113no—
284C2×Q8—116no—
285C2×Q8—113no—
286C2×Q8—113no—
287C2×Q8—113no—
288C2×Q8—2212no—
289C2×Q8—2212no—
290C2×Q8—2212no—
291C2×Q8—2212no—
292C2×Q8—224no—
293C2×Q8—224no—
294C2×Q8C22×D1113yes—
295C2×Q8C22×D1111yescharacteristic
296C2×D4—113no—
297C2×D4—111no—
298C2×D4—113no—
299C2×D4—113no—
300C2×D4—111no—
301C2×D4—111no—
302C2×D4C22×D1113yes—
303C2×D4C22×D1113yes—
304C22×C4—113no—
305C22×C4—113no—
306C22×C4—116no—
307C22×C4—113no—
308C22×C4—113no—
309C22×C4—113no—
310C22×C4—113no—
311C22×C4—2212no—
312C22×C4C22×D1113yes—
313C22×C4C22×D1113yes—
314C4⋊C4—113no—
315C4⋊C4—113no—
316C4⋊C4—113no—
317C4⋊C4—113no—
318C4⋊C4—113no—
319C4⋊C4—116no—
320C4⋊C4—116no—
321C4⋊C4—113no—
322C4⋊C4C22×D1113yes—
323C4⋊C4C22×D1113yes—
324C22⋊C4—113no—
325C22⋊C4—116no—
326C22⋊C4—113no—
327C22⋊C4—113no—
328C22⋊C4—111no—
329C22⋊C4—111no—
330C22⋊C4—113no—
331C22⋊C4—113no—
332C22⋊C4—113no—
333C22⋊C4C22×D1116yes—
334C22⋊C4C22×D1111yescharacteristic
335C22⋊C4C22×D1113yes—
336C42—116no—
337C42—113no—
338C42C22×D1113yes—
339C11#348611yescharacteristic, complemented, Sylow
340C23—111no—
341C23—111no—
342C23—111no—
343C23—222no—
344C23—222no—
345C23—222no—
346C23C23×D1113yes—
347C23C23×D1111yescharacteristic
348Q8—26no—
349Q8—1112no—
350Q8—2212no—
351Q8—226no—
352Q8—226no—
353Q8—226no—
354Q8D4×D1114yes—
355D4—26no—
356D4—26no—
357D4—222no—
358D4—222no—
359D4—226no—
360D4—226no—
361D4—226no—
362D4—222no—
363C2×C4—26no—
364C2×C4—26no—
365C2×C4—113no—
366C2×C4—1112no—
367C2×C4—111no—
368C2×C4—113no—
369C2×C4—113no—
370C2×C4—113no—
371C2×C4—226no—
372C2×C4—226no—
373C2×C4—226no—
374C2×C4—2212no—
375C2×C4—226no—
376C2×C4—226no—
377C2×C4C23×D1113yes—
378C2×C4C23×D1111yescharacteristic
379C2×C4C23×D1113yes—
380C2×C4C23×D1111yescharacteristic
381C2×C4C23×D1113yes—
382C22—21no—
383C22—21no—
384C22—23no—
385C22—23no—
386C22—23no—
387C22—112no—
388C22—112no—
389C22—228no—
390C22—221no—
391C22—221no—
392C22—221no—
393C22—221no—
394C22—221no—
395C22—221no—
396C22—221no—
397C22#6704312yescomplemented
398C22C24×D1111yescharacteristic
399C4—21no—
400C4—23no—
401C4—23no—
402C4—21no—
403C4—116no—
404C4—223no—
405C4—223no—
406C4—221no—
407C4—223no—
408C4C2×D4×D1116yes—
409C2—22no—
410C2—43no—
411C2—222no—
412C2—222no—
413C2—441no—
414C2C22×D4×D1111yescharacteristic
415C2C2×#6704311yescharacteristic
416C2D11×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#548C2
hypercenter#548D11
hypocenterC11#3486
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#67043C2semidirect
2. C22×Q8×D11C2semidirect
3. C11×#548C2semidirect
4. #10623362C2semidirect
5. Q8×C22⋊D11C2semidirect
6. #10623208C2semidirect
7. #10623206C2semidirect
8. #10623163C2semidirect
9. #10623159C2semidirect
10. #10623137C2semidirect
11. #10623129C2semidirect
12. Q8×D44C2semidirect
13. #10623103C2semidirect
14. #10623078C2semidirect
15. D4×Dic22C2semidirect
16. C2×C11×#41C22semidirect
24. C2×Q8×D11C22semidirect
26. C2×#4341C22semidirect
30. C22×Dic22C22semidirect
31. C11×#124C22semidirect
32. C11×C22⋊Q8C22semidirect
34. C4×Q8×C11C22semidirect
36. #66999C22semidirect
37. Q8×Dic11C22semidirect
38. #66997C22semidirect
42. #66989C22semidirect
47. #66977C22semidirect
49. #66950C22semidirect
53. #66941C22semidirect
54. #66940C22semidirect
55. #66938C22semidirect
62. #66931C22semidirect
63. #66931C22semidirect
66. #66922C22semidirect
67. C4×Dic22C22semidirect
87. Q8×D11D4semidirect
183. #548D11semidirect
194. C22×C112−1+4semidirect
205. C2×D112−1+4semidirect
220. C2×#41C2×D11semidirect
236. #124C2×D11semidirect
249. C22⋊Q8C2×D11semidirect
259. C4×Q8C2×D11semidirect
339. C11#3486semidirect
397. C22#67043semidirect

Maximal subgroups

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

subgroupindex
C2×#670432
C22×Q8×D112
C11×#5482
#106233622
Q8×C22⋊D112
#106232082
#106232062
#106231632
#106231592
#106231372
#106231292
Q8×D442
#106231032
#106230782
D4×Dic222
#348611