Finite Group Databasebeta

← #13072157

Subgroups — #13072157

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×#66948C211yesmaximal, characteristic, complemented
2C2×#66937C211yesmaximal, characteristic, complemented
3C2×#66935C211yesmaximal, characteristic, complemented
4C2×#66935C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D11C211yesmaximal, characteristic, complemented
6C2×C4×D44C211yesmaximal, characteristic, complemented
7C11×#388C211yesmaximal, characteristic, complemented
8#10622607C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622574C211yesmaximal, characteristic, complemented
11#10622552C211yesmaximal, characteristic, complemented
12#10622284C211yesmaximal, characteristic, complemented
13#10622281C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622278C211yesmaximal, characteristic, complemented
16C24×D11C2211yescharacteristic
17C22×C22⋊D11C2211yescharacteristic
18C22×C22⋊D11C2211yescharacteristic
19C22×D44C2211yescharacteristic
20C22×D44C2211yescharacteristic
21C22×D44C2211yescharacteristic
22C22×D44C2211yescharacteristic
23C22×D44C2211yescharacteristic, complemented
24C22×C4×D11C2211yescharacteristic
25C22×C4×D11C2211yescharacteristic
26C22×C4×D11C2211yescharacteristic, complemented
27C2×C11×C4⋊C4C2211yescharacteristic, complemented
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C42×C11C2211yescharacteristic, complemented
32C2×C22⋊Dic11C2211yescharacteristic
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×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×C4⋊Dic11C2211yescharacteristic, complemented
45C2×C4⋊Dic11C2211yescharacteristic, complemented
46C2×Dic11⋊C4C2211yescharacteristic, complemented
47#66948—24no—
48#66937—24no—
49#66935—24no—
50#66935—24no—
51C22⋊C4×D11—24no—
52C4×D44—24no—
53C11×#95C2211yescharacteristic, complemented
54C11×#95C2211yescharacteristic, complemented
55C11⋊#95C2211yescharacteristic, complemented
56C11⋊#95C2211yescharacteristic, complemented
57C24×C11C2311yescharacteristic
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—22no—
61C23×D11—22no—
62C23×D11—22no—
63C23×D11—41no—
64C23×D11—41no—
65C23×D11C2311yescharacteristic
66C23×D11C2311yescharacteristic
67C23×D11C2311yescharacteristic
68C23×D11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×C4×C11C2311yescharacteristic
71C22×C4×C11C2311yescharacteristic
72C22×C4×C11C2311yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C2×C22⋊D11—22no—
76C2×C22⋊D11—22no—
77C2×C22⋊D11—22no—
78C2×C22⋊D11—22no—
79C2×C22⋊D11—41no—
80C2×C22⋊D11—41no—
81C22×Dic11C2311yescharacteristic
82C22×Dic11C2311yescharacteristic
83C22×Dic11C2311yescharacteristic
84C22×Dic11C2311yescharacteristic
85C2×D44—22no—
86C2×D44—22no—
87C2×D44—22no—
88C2×D44—22no—
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44—22no—
95C2×D44—22no—
96C2×D44—41no—
97C2×D44—41no—
98C2×D44—41no—
99C2×D44D414yescomplemented
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—41no—
107C2×C4×D11—41no—
108C2×C4×D11—41no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4D414yescomplemented
113C42×C11—22no—
114C22⋊Dic11—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)⋊C4—22no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4D414yescomplemented
126C4⋊Dic11—22no—
127C4⋊Dic11—41no—
128Dic11⋊C4—22no—
129#2424—111nomaximal, Sylow
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11C2×D412yes—
137C23×C11C2411yescharacteristic
138C22×D11—21no—
139C22×D11—21no—
140C22×D11—21no—
141C22×D11—21no—
142C22×D11—28no—
143C22×D11—21no—
144C22×D11—21no—
145C22×D11—21no—
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—44no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11—44no—
166C22×D11—44no—
167C22×D11—44no—
168C22×D11C2×D412yes—
169C22×D11C2×D412yes—
170C22×D11C2×D412yes—
171C22×D11#4112yes—
172C22×D11#4112yes—
173C2×C4×C11—21no—
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×C11C2×D412yes—
188C2×C4×C11C2×D412yes—
189C2×C4×C11C2×D412yes—
190C2×C4×C11C2×D412yes—
191C22⋊D11—44no—
192C22⋊D11—44no—
193C2×Dic11—21no—
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×Dic11C2×D412yes—
205D44—28no—
206D44—44no—
207D44—44no—
208D44—44no—
209D44—44no—
210C4×D11—44no—
211C4×D11—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#388D1111yescharacteristic, complemented
225#386—111no—
226#386—111no—
227#385—111no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11C22×D411yescharacteristic
236C22×C11C22×D411yescharacteristic
237C22×C11C22×D411yescharacteristic
238C22×C11C2×#4111yescharacteristic
239C22×C11C2×#4111yescharacteristic
240C22×C11H(5,𝔽2)11yescharacteristic
241C22×C11H(5,𝔽2)11yescharacteristic
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—22no—
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—416no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
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#12114yescomplemented
271C4×C11—22no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—22no—
275C4×C11—41no—
276C4×C11—41no—
277Dic11—22no—
278Dic11—41no—
279Dic11—41no—
280Dic11—41no—
281C25—111no—
282C22×D4—111no—
283C22×D4—111no—
284C22×D4—111no—
285C22×D4—111no—
286C22×D4—111no—
287C22×D4—111no—
288C22×D4—111no—
289C23×C4—111no—
290C23×C4—111no—
291C23×C4—111no—
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⋊C4C2×D1111yescharacteristic, complemented
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
316C2×C22⋊C4C2×D1111yescharacteristic
317C2×C42C2×D1111yescharacteristic, complemented
318#95—111no—
319#95—111no—
320#95C2×D1111yescharacteristic, complemented
321#95C2×D1111yescharacteristic, complemented
322C2×C11—42no—
323C2×C11C2×#12111yescharacteristic
324C2×C11#52511yescharacteristic
325C2×C11#53811yescharacteristic
326C2×C11D4211yescharacteristic
327C2×C11D4211yescharacteristic
328C2×C11#54611yescharacteristic
329C2×C11#54611yescharacteristic
330D11—24no—
331D11—42no—
332D11—42no—
333D11—81no—
334C24—111no—
335C24—111no—
336C24—111no—
337C24—111no—
338C24—222no—
339C24—222no—
340C24—222no—
341C24—222no—
342C24—222no—
343C24—441no—
344C24—441no—
345C24C22×D1111yescharacteristic
346C2×D4—114no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—222no—
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—111no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—441no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4C22×D1111yescharacteristic
381C22×C4C22×D1111yescharacteristic
382C22×C4C22×D1111yescharacteristic
383C22×C4C22×D1111yescharacteristic
384C22×C4C22×D1111yescharacteristic
385C22×C4C22×D1111yescharacteristic
386C4⋊C4—22no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—441no—
390C22⋊C4—22no—
391C22⋊C4—22no—
392C22⋊C4—114no—
393C22⋊C4—222no—
394C22⋊C4—222no—
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—441no—
404C22⋊C4D4414yescomplemented
405C42—22no—
406C11#242411yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—112no—
414C23—112no—
415C23—112no—
416C23—112no—
417C23—112no—
418C23—228no—
419C23—221no—
420C23—221no—
421C23—221no—
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—221no—
441C23—221no—
442C23—444no—
443C23—444no—
444C23—444no—
445C23—444no—
446C23—444no—
447C23—444no—
448C23C2×D4412yes—
449C23C23×D1111yescharacteristic
450D4—228no—
451D4—444no—
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—112no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—221no—
483C2×C4—444no—
484C2×C4—444no—
485C2×C4—444no—
486C2×C4C2×D4412yes—
487C2×C4C2×D4412yes—
488C2×C4D4×D1112yes—
489C2×C4D4×D1112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—114no—
498C22—222no—
499C22—222no—
500C22—222no—
501C22—222no—
502C22—222no—
503C22—222no—
504C22—222no—
505C22—222no—
506C22—222no—
507C22—222no—
508C22—222no—
509C22—222no—
510C22—4416no—
511C22—441no—
512C22—441no—
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—441no—
526C22C22×D4411yescharacteristic
527C22C2×D4×D1111yescharacteristic
528C22C2×D4×D1111yescharacteristic
529C22#41×D1111yescharacteristic
530C22#41×D1111yescharacteristic
531C22#6704211yescharacteristic
532C22#6704211yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—41no—
539C4—222no—
540C4—441no—
541C4—441no—
542C4—441no—
543C2—42no—
544C2—224no—
545C2—442no—
546C2—442no—
547C2—881no—
548C2#1062305511yescharacteristic
549C2D4×D4411yescharacteristic
550C2D4×D4411yescharacteristic
551C2D11×#12111yescharacteristic
552C2#1062318511yescharacteristic
553C2#1062320711yescharacteristic
554C2#1062323511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#388C2
hypercenter#388D11
hypocenterC11#2424
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#66948C2semidirect
2. C2×#66937C2semidirect
3. C2×#66935C2semidirect
4. C2×#66935C2semidirect
5. C2×C22⋊C4×D11C2semidirect
6. C2×C4×D44C2semidirect
7. C11×#388C2semidirect
8. #10622607C2semidirect
9. #10622574C2semidirect
10. #10622574C2semidirect
11. #10622552C2semidirect
12. #10622284C2semidirect
13. #10622281C2semidirect
14. #10622278C2semidirect
15. #10622278C2semidirect
23. C22×D44C22semidirect
26. C22×C4×D11C22semidirect
27. C2×C11×C4⋊C4C22semidirect
31. C2×C42×C11C22semidirect
39. C2×(C2×D11)⋊C4C22semidirect
40. C2×(C2×D11)⋊C4C22semidirect
41. C2×(C2×D11)⋊C4C22semidirect
42. C2×(C2×D11)⋊C4C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×C4⋊Dic11C22semidirect
45. C2×C4⋊Dic11C22semidirect
46. C2×Dic11⋊C4C22semidirect
53. C11×#95C22semidirect
54. C11×#95C22semidirect
55. C11⋊#95C22semidirect
56. C11⋊#95C22semidirect
99. C2×D44D4semidirect
112. C11×C22⋊C4D4semidirect
125. (C2×D11)⋊C4D4semidirect
224. #388D11semidirect
270. C2×D11#121semidirect
300. C2×C4⋊C4C2×D11semidirect
317. C2×C42C2×D11semidirect
320. #95C2×D11semidirect
321. #95C2×D11semidirect
404. C22⋊C4D44semidirect
406. C11#2424semidirect

Maximal subgroups

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

subgroupindex
C2×#669482
C2×#669372
C2×#669352
C2×C22⋊C4×D112
C2×C4×D442
C11×#3882
#106226072
#106225742
#106225522
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