Finite Group Databasebeta

← #13074997

Subgroups — #13074997

Order 1408.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66935C211yesmaximal, characteristic
2C2×#66928C211yesmaximal, characteristic, complemented
3C11×#388C211yesmaximal, characteristic, complemented
4#10622606C211yesmaximal, characteristic, complemented
5#10622604C211yesmaximal, characteristic, complemented
6#10622572C211yesmaximal, characteristic, complemented
7#10622569C211yesmaximal, characteristic, complemented
8#10622568C211yesmaximal, characteristic, complemented
9#10622568C211yesmaximal, characteristic, complemented
10#10622560C211yesmaximal, characteristic, complemented
11#10622553C211yesmaximal, characteristic, complemented
12#10622288C211yesmaximal, characteristic, complemented
13#10622286C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×D44C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×C4×D11C2211yescharacteristic, complemented
21C22×Dic22C2211yescharacteristic, complemented
22C2×C11×C4⋊C4C2211yescharacteristic, complemented
23C2×C11×C22⋊C4C2211yescharacteristic
24C2×C11×C22⋊C4C2211yescharacteristic
25C2×C11×C22⋊C4C2211yescharacteristic
26C2×C42×C11C2211yescharacteristic, complemented
27C2×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊Dic11C2211yescharacteristic
29C2×(C2×D11)⋊C4C2211yescharacteristic
30C2×(C2×D11)⋊C4C2211yescharacteristic
31C2×(C2×D11)⋊C4C2211yescharacteristic
32C2×(C2×D11)⋊C4C2211yescharacteristic
33C2×(C2×D11)⋊C4C2211yescharacteristic
34C2×(C2×D11)⋊C4C2211yescharacteristic
35C2×(C2×D11)⋊C4C2211yescharacteristic
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C2×Dic11⋊C4C2211yescharacteristic, complemented
43#66935—24no—
44#66928—24no—
45C11×#95C2211yescharacteristic, complemented
46C11×#95C2211yescharacteristic, complemented
47C11⋊#95C2211yescharacteristic, complemented
48C11⋊#95C2211yescharacteristic, complemented
49C11⋊#95C2211yescharacteristic, complemented
50C11⋊#95C2211yescharacteristic, complemented
51C11⋊#95C2211yescharacteristic, complemented
52C11⋊#95C2211yescharacteristic, complemented
53C24×C11C2311yescharacteristic
54C23×D11—22no—
55C23×D11—22no—
56C23×D11—22no—
57C23×D11—41no—
58C23×D11—41no—
59C23×D11—41no—
60C23×D11—41no—
61C23×D11C2311yescharacteristic
62C23×D11C2311yescharacteristic
63C23×D11C2311yescharacteristic
64C22×C4×C11C2311yescharacteristic
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—41no—
73C22×Dic11C2311yescharacteristic
74C22×Dic11C2311yescharacteristic
75C22×Dic11C2311yescharacteristic
76C22×Dic11C2311yescharacteristic
77C22×Dic11C2311yescharacteristic
78C2×D44—22no—
79C2×D44—22no—
80C2×D44—41no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44D414yes—
84C2×C4×D11—41no—
85C2×C4×D11—41no—
86C2×C4×D11—41no—
87C2×Dic22—22no—
88C2×Dic22—41no—
89C2×Dic22—41no—
90C11×C4⋊C4—41no—
91C11×C22⋊C4—22no—
92C11×C22⋊C4—22no—
93C11×C22⋊C4—41no—
94C42×C11—22no—
95C22⋊Dic11—41no—
96C22⋊Dic11—41no—
97(C2×D11)⋊C4—22no—
98(C2×D11)⋊C4—22no—
99(C2×D11)⋊C4—22no—
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102(C2×D11)⋊C4—22no—
103(C2×D11)⋊C4—22no—
104(C2×D11)⋊C4—41no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107(C2×D11)⋊C4—41no—
108(C2×D11)⋊C4—41no—
109(C2×D11)⋊C4—41no—
110Dic11⋊C4—41no—
111#2684—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C23×C11—21no—
117C23×C11—21no—
118C23×C11#4112yes—
119C23×C11C2411yescharacteristic
120C22×D11—21no—
121C22×D11—21no—
122C22×D11—21no—
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11—21no—
135C22×D11—21no—
136C22×D11—21no—
137C22×D11—21no—
138C22×D11—44no—
139C22×D11—44no—
140C22×D11—44no—
141C22×D11—44no—
142C22×D11—44no—
143C22×D11—44no—
144C22×D11—44no—
145C22×D11C2×D412yes—
146C22×D11C2×D412yes—
147C22×D11#4112yes—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11C2×D412yes—
166C22⋊D11—44no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182D44—44no—
183D44—44no—
184C4×D11—44no—
185Dic22—44no—
186C2×#124—111no—
187C2×#120—111no—
188#397—111no—
189#397—111no—
190#394—111no—
191#394—111no—
192#393—111no—
193#393—111no—
194#388—111no—
195#388D1111yescharacteristic, complemented
196#386—111no—
197#386—111no—
198#386—111no—
199#379—111no—
200#379—111no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—41no—
205C22×C11—41no—
206C22×C11—41no—
207C22×C11—41no—
208C22×C11C22×D411yescharacteristic
209C22×C11C2×#4111yescharacteristic
210C22×C11C2×#4111yescharacteristic
211C22×C11H(5,𝔽2)11yescharacteristic
212C22×C11H(5,𝔽2)11yescharacteristic
213C22×C11H(5,𝔽2)11yescharacteristic
214C22×C11H(5,𝔽2)11yescharacteristic
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—22no—
219C2×D11—22no—
220C2×D11—22no—
221C2×D11—22no—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—416no—
225C2×D11—41no—
226C2×D11—41no—
227C2×D11—41no—
228C2×D11—41no—
229C2×D11—41no—
230C2×D11—41no—
231C2×D11—41no—
232C2×D11—41no—
233C2×D11—41no—
234C2×D11—41no—
235C2×D11—41no—
236C2×D11—41no—
237C4×C11—22no—
238C4×C11—41no—
239C4×C11—41no—
240C4×C11—41no—
241C4×C11—41no—
242C4×C11—41no—
243Dic11—41no—
244Dic11—41no—
245Dic11—41no—
246Dic11—41no—
247Dic11—41no—
248C25—111no—
249C22×Q8—111no—
250C22×D4—111no—
251C22×D4—111no—
252C22×D4—111no—
253C23×C4—111no—
254#124—224no—
255#120—224no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4C2×D1111yescharacteristic, complemented
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⋊C4—111no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4—111no—
273C2×C22⋊C4C2×D1111yescharacteristic
274C2×C22⋊C4C2×D1111yescharacteristic
275C2×C22⋊C4C2×D1111yescharacteristic
276C2×C42C2×D1111yescharacteristic, complemented
277#95—111no—
278#95—111no—
279#95—111no—
280#95—111no—
281#95—111no—
282#95—111no—
283#95C2×D1111yescharacteristic, complemented
284#95C2×D1111yescharacteristic, complemented
285C2×C11—42no—
286C2×C11#53411yescharacteristic
287C2×C11#53811yescharacteristic
288C2×C11#53811yescharacteristic
289C2×C11#54611yescharacteristic
290C2×C11#54611yescharacteristic
291C2×C11#55111yescharacteristic
292C2×C11H(3,𝔽4)11yescharacteristic
293D11—42no—
294D11—42no—
295D11—42no—
296C24—111no—
297C24—111no—
298C24—111no—
299C24—222no—
300C24—222no—
301C24—222no—
302C24—441no—
303C24—441no—
304C24—441no—
305C24—441no—
306C24C22×D1111yescharacteristic
307C2×Q8—222no—
308C2×Q8—441no—
309C2×Q8—441no—
310C2×D4—114no—
311C2×D4—222no—
312C2×D4—222no—
313C2×D4—222no—
314C2×D4—222no—
315C2×D4—441no—
316C2×D4—441no—
317C2×D4—441no—
318C2×D4—441no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4C22×D1111yescharacteristic
328C22×C4C22×D1111yescharacteristic
329C22×C4C22×D1111yescharacteristic
330C22×C4C22×D1111yescharacteristic
331C22×C4C22×D1111yescharacteristic
332C22×C4C22×D1111yescharacteristic
333C4⋊C4—41no—
334C4⋊C4—441no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—222no—
339C22⋊C4—222no—
340C22⋊C4—222no—
341C22⋊C4—222no—
342C22⋊C4—222no—
343C22⋊C4—222no—
344C22⋊C4—222no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C22⋊C4—441no—
348C22⋊C4—441no—
349C22⋊C4—441no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C22⋊C4—441no—
353C42—22no—
354C11#268411yescharacteristic, complemented, Sylow
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—112no—
362C23—112no—
363C23—112no—
364C23—221no—
365C23—221no—
366C23—221no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23—221no—
375C23—221no—
376C23—221no—
377C23—221no—
378C23—221no—
379C23—221no—
380C23—221no—
381C23—221no—
382C23—444no—
383C23—444no—
384C23—444no—
385C23—444no—
386C23—444no—
387C23—444no—
388C23—444no—
389C23#433912yes—
390C23C23×D1111yescharacteristic
391Q8—444no—
392D4—444no—
393D4—444no—
394D4—444no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—444no—
428C2×C4D4×D1112yes—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22—4416no—
446C22—441no—
447C22—441no—
448C22—441no—
449C22—441no—
450C22—441no—
451C22—441no—
452C22—441no—
453C22—441no—
454C22—441no—
455C22—441no—
456C22—441no—
457C22—441no—
458C22C2×#433911yescharacteristic
459C22C2×D4×D1111yescharacteristic
460C22#6703711yescharacteristic
461C22#41×D1111yescharacteristic
462C22#6704211yescharacteristic
463C22#6704211yescharacteristic
464C22#6704211yescharacteristic
465C4—22no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—441no—
472C4—441no—
473C4—441no—
474C4—441no—
475C4—441no—
476C2—42no—
477C2—442no—
478C2—442no—
479C2—442no—
480C2#1062305811yescharacteristic
481C2#1062308111yescharacteristic
482C2#1062309111yescharacteristic
483C2#1062314311yescharacteristic
484C2#1062318411yescharacteristic
485C2#1062321411yescharacteristic
486C2#1062323511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
prime radicalC2×#66935C2
hypercenter#388D11
hypocenterC11#2684
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×#66928C2semidirect
3. C11×#388C2semidirect
4. #10622606C2semidirect
5. #10622604C2semidirect
6. #10622572C2semidirect
7. #10622569C2semidirect
8. #10622568C2semidirect
9. #10622568C2semidirect
10. #10622560C2semidirect
11. #10622553C2semidirect
12. #10622288C2semidirect
13. #10622286C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
20. C22×C4×D11C22semidirect
21. C22×Dic22C22semidirect
22. C2×C11×C4⋊C4C22semidirect
26. C2×C42×C11C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×Dic11⋊C4C22semidirect
45. C11×#95C22semidirect
46. C11×#95C22semidirect
47. C11⋊#95C22semidirect
48. C11⋊#95C22semidirect
49. C11⋊#95C22semidirect
50. C11⋊#95C22semidirect
51. C11⋊#95C22semidirect
52. C11⋊#95C22semidirect
195. #388D11semidirect
257. C2×C4⋊C4C2×D11semidirect
276. C2×C42C2×D11semidirect
283. #95C2×D11semidirect
284. #95C2×D11semidirect
354. C11#2684semidirect

Maximal subgroups

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

subgroupindex
C2×#669352
C2×#669282
C11×#3882
#106226062
#106226042
#106225722
#106225692
#106225682
#106225602
#106225532
#106222882
#106222862
#106222782
#268411