Finite Group Databasebeta

← #13072154

Subgroups — #13072154

Order 1408.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66992C211yesmaximal, characteristic, complemented
2C2×#66990C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5C2×#66937C211yesmaximal, characteristic, complemented
6C2×#66935C211yesmaximal, characteristic, complemented
7C11×#386C211yesmaximal, characteristic, complemented
8#10622573C211yesmaximal, characteristic, complemented
9#10622572C211yesmaximal, characteristic, complemented
10#10622570C211yesmaximal, characteristic, complemented
11#10622559C211yesmaximal, characteristic, complemented
12#10622289C211yesmaximal, characteristic, complemented
13#10622285C211yesmaximal, characteristic, complemented
14#10622282C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic, complemented
23C23×Dic11C2211yescharacteristic
24C22×D44C2211yescharacteristic
25C22×D44C2211yescharacteristic
26C22×C4×D11C2211yescharacteristic, complemented
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic, complemented
29C2×C11×C22⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊Dic11C2211yescharacteristic, complemented
32#66992—24no—
33#66990—24no—
34C4×C22⋊D11—24no—
35C2×(C2×D11)⋊C4—24no—
36C2×(C2×D11)⋊C4C2211yescharacteristic
37C2×(C2×D11)⋊C4C2211yescharacteristic
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47C2×Dic11⋊C4C2211yescharacteristic, complemented
48C2×Dic11⋊C4C2211yescharacteristic, complemented
49C2×Dic11⋊C4C2211yescharacteristic, complemented
50C2×C4×Dic11C2211yescharacteristic, complemented
51#66937—24no—
52#66935—24no—
53C11×#95C2211yescharacteristic, complemented
54C11×#95C2211yescharacteristic, complemented
55C11⋊#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—22no—
63C23×D11—22no—
64C23×D11—41no—
65C23×D11—41no—
66C23×D11C2311yescharacteristic
67C23×D11C2311yescharacteristic
68C23×D11C2311yescharacteristic
69C2×D4×C11—22no—
70C2×D4×C11—22no—
71C2×D4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—41no—
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C2×C22⋊D11—22no—
81C2×C22⋊D11—22no—
82C2×C22⋊D11—22no—
83C2×C22⋊D11—22no—
84C2×C22⋊D11—22no—
85C2×C22⋊D11—22no—
86C2×C22⋊D11—22no—
87C2×C22⋊D11—22no—
88C2×C22⋊D11—41no—
89C2×C22⋊D11—41no—
90C2×C22⋊D11—41no—
91C2×C22⋊D11D414yescomplemented
92C22×Dic11—22no—
93C22×Dic11—22no—
94C22×Dic11—41no—
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C22×Dic11C2311yescharacteristic
99C22×Dic11C2311yescharacteristic
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—22no—
104C2×D44—41no—
105C2×D44—41no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—41no—
109C11×C22⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—41no—
112C22⋊Dic11—22no—
113C22⋊Dic11D414yescomplemented
114(C2×D11)⋊C4—22no—
115(C2×D11)⋊C4—22no—
116(C2×D11)⋊C4—22no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4D414yescomplemented
124Dic11⋊C4—22no—
125Dic11⋊C4—22no—
126Dic11⋊C4—22no—
127Dic11⋊C4—41no—
128C4×Dic11—22no—
129#2424—111nomaximal, Sylow
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11C2×D412yes—
142C23×C11C2×D412yes—
143C23×C11#4112yes—
144C23×C11C2411yescharacteristic
145C22×D11—28no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—21no—
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11—21no—
161C22×D11—21no—
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—44no—
165C22×D11—44no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11—44no—
169C22×D11—44no—
170C22×D11C2×D412yes—
171C22×D11C2×D412yes—
172C22×D11#4112yes—
173D4×C11—44no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—44no—
189C2×C4×C11C2×D412yes—
190C22⋊D11—28no—
191C22⋊D11—44no—
192C22⋊D11—44no—
193C22⋊D11—44no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—44no—
206C2×Dic11C2×D412yes—
207C2×Dic11C2×D412yes—
208C2×Dic11C2×D412yes—
209C2×Dic11C2×D412yes—
210D44—44no—
211D44—44no—
212C4×D11—44no—
213C2×#121—111no—
214C2×#121—111no—
215C2×#120—111no—
216C2×#120—111no—
217C2×C4×D4—111no—
218C22×C22⋊C4—111no—
219#396—111no—
220#394—111no—
221#394—111no—
222#392—111no—
223#390—111no—
224#388—111no—
225#386—111no—
226#386D1111yescharacteristic, complemented
227#385—111no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—22no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11#12114yescomplemented
242C22×C11C22×D411yescharacteristic
243C22×C11C22×D411yescharacteristic
244C22×C11C22×D411yescharacteristic
245C22×C11C2×#4111yescharacteristic
246C22×C11C2×#4111yescharacteristic
247C22×C11H(5,𝔽2)11yescharacteristic
248C22×C11H(5,𝔽2)11yescharacteristic
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
255C2×D11—22no—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—416no—
259C2×D11—41no—
260C2×D11—41no—
261C2×D11—41no—
262C2×D11—41no—
263C2×D11—41no—
264C2×D11—41no—
265C2×D11—41no—
266C2×D11—41no—
267C2×D11—41no—
268C2×D11—41no—
269C2×D11—41no—
270C2×D11—41no—
271C4×C11—22no—
272C4×C11—41no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—41no—
276Dic11—22no—
277Dic11—22no—
278Dic11—22no—
279Dic11—22no—
280Dic11—41no—
281C25—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4—111no—
287C22×D4—111no—
288C22×D4C2×D1111yescharacteristic
289C23×C4—111no—
290C23×C4—111no—
291C23×C4C2×D1111yescharacteristic
292#121—224no—
293#121—224no—
294#120—224no—
295#120—224no—
296C4×D4—224no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C22⋊C4—111no—
302C2×C22⋊C4—111no—
303C2×C22⋊C4—111no—
304C2×C22⋊C4—111no—
305C2×C22⋊C4—111no—
306C2×C22⋊C4—111no—
307C2×C22⋊C4—111no—
308C2×C22⋊C4—111no—
309C2×C22⋊C4—111no—
310C2×C22⋊C4—111no—
311C2×C22⋊C4—111no—
312C2×C22⋊C4—111no—
313C2×C22⋊C4—224no—
314C2×C22⋊C4C2×D1111yescharacteristic
315C2×C22⋊C4C2×D1111yescharacteristic, complemented
316C2×C22⋊C4C2×D1111yescharacteristic, complemented
317C2×C42—111no—
318#95—111no—
319#95—111no—
320#95C2×D1111yescharacteristic, complemented
321#95C2×D1111yescharacteristic, complemented
322C2×C11—24no—
323C2×C11—81no—
324C2×C11C2×#12111yescharacteristic
325C2×C11#52511yescharacteristic
326C2×C11#53811yescharacteristic
327C2×C11D4211yescharacteristic
328C2×C11D4211yescharacteristic
329C2×C11#54611yescharacteristic
330C2×C11#54611yescharacteristic
331D11—42no—
332D11—42no—
333D11—42no—
334C24—111no—
335C24—111no—
336C24—111no—
337C24—222no—
338C24—222no—
339C24—222no—
340C24—222no—
341C24—222no—
342C24—441no—
343C24—441no—
344C24C22×D1111yescharacteristic
345C24C22×D1111yescharacteristic
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—114no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—222no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
359C2×D4—222no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—441no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—41no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4C22×D1111yescharacteristic
382C22×C4C22×D1111yescharacteristic
383C22×C4C22×D1111yescharacteristic
384C22×C4C22×D1111yescharacteristic
385C22×C4C22×D1111yescharacteristic
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—441no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—41no—
393C22⋊C4—114no—
394C22⋊C4—114no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C22⋊C4—222no—
401C22⋊C4—222no—
402C22⋊C4—222no—
403C22⋊C4—222no—
404C22⋊C4—222no—
405C42—222no—
406C11#242411yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—112no—
419C23—112no—
420C23—112no—
421C23—228no—
422C23—221no—
423C23—221no—
424C23—221no—
425C23—221no—
426C23—221no—
427C23—221no—
428C23—221no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—221no—
433C23—221no—
434C23—221no—
435C23—221no—
436C23—221no—
437C23—221no—
438C23—221no—
439C23—221no—
440C23—444no—
441C23—444no—
442C23—444no—
443C23—444no—
444C23—444no—
445C23—444no—
446C23#433912yes—
447C23D4×D1112yes—
448C23D4×D1112yes—
449C23C23×D1111yescharacteristic
450D4—44no—
451D4—228no—
452D4—444no—
453D4—444no—
454D4—444no—
455D4—444no—
456D4—444no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—44no—
472C2×C4—112no—
473C2×C4—112no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—221no—
484C2×C4—221no—
485C2×C4—221no—
486C2×C4—221no—
487C2×C4—444no—
488C2×C4—444no—
489C2×C4D4×D1112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—222no—
504C22—222no—
505C22—222no—
506C22—222no—
507C22—222no—
508C22—222no—
509C22—222no—
510C22—222no—
511C22—222no—
512C22—4416no—
513C22—441no—
514C22—441no—
515C22—441no—
516C22—441no—
517C22—441no—
518C22—441no—
519C22—441no—
520C22—441no—
521C22—441no—
522C22—441no—
523C22—441no—
524C22—441no—
525C22#6693714yescomplemented
526C22C2×#433911yescharacteristic
527C22C2×D4×D1111yescharacteristic
528C22C2×D4×D1111yescharacteristic
529C22C2×D4×D1111yescharacteristic
530C22#6703711yescharacteristic
531C22#41×D1111yescharacteristic
532C22#6704211yescharacteristic
533C4—22no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—222no—
539C4—222no—
540C4—222no—
541C4—222no—
542C4—441no—
543C2—24no—
544C2—81no—
545C2—442no—
546C2—442no—
547C2—442no—
548C2C2×#6693711yescharacteristic
549C2#1062307811yescharacteristic
550C2#1062309111yescharacteristic
551C2#1062312111yescharacteristic
552C2#1062314011yescharacteristic
553C2#1062314111yescharacteristic
554C2#1062318511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#386C2
hypercenter#386D11
hypocenterC11#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#66992C2semidirect
2. C2×#66990C2semidirect
3. C2×C4×C22⋊D11C2semidirect
4. C22×(C2×D11)⋊C4C2semidirect
5. C2×#66937C2semidirect
6. C2×#66935C2semidirect
7. C11×#386C2semidirect
8. #10622573C2semidirect
9. #10622572C2semidirect
10. #10622570C2semidirect
11. #10622559C2semidirect
12. #10622289C2semidirect
13. #10622285C2semidirect
14. #10622282C2semidirect
15. #10622278C2semidirect
22. C22×C22⋊D11C22semidirect
26. C22×C4×D11C22semidirect
28. C2×C11×C22⋊C4C22semidirect
29. C2×C11×C22⋊C4C22semidirect
31. C2×C22⋊Dic11C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. C2×Dic11⋊C4C22semidirect
47. C2×Dic11⋊C4C22semidirect
48. C2×Dic11⋊C4C22semidirect
49. C2×Dic11⋊C4C22semidirect
50. C2×C4×Dic11C22semidirect
53. C11×#95C22semidirect
54. C11×#95C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
91. C2×C22⋊D11D4semidirect
113. C22⋊Dic11D4semidirect
123. (C2×D11)⋊C4D4semidirect
226. #386D11semidirect
241. C22×C11#121semidirect
315. C2×C22⋊C4C2×D11semidirect
316. C2×C22⋊C4C2×D11semidirect
320. #95C2×D11semidirect
321. #95C2×D11semidirect
406. C11#2424semidirect
525. C22#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#669922
C2×#669902
C2×C4×C22⋊D112
C22×(C2×D11)⋊C42
C2×#669372
C2×#669352
C11×#3862
#106225732
#106225722
#106225702
#106225592
#106222892
#106222852
#106222822
#106222782
#242411