Finite Group Databasebeta

← #13074906

Subgroups — #13074906

Order 1408.

804 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#121C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×#66992C211yesmaximal, characteristic, complemented
4C2×#66991C211yesmaximal, characteristic, complemented
5C2×#66983C211yesmaximal, characteristic, complemented
6C2×#66937C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622836C211yesmaximal, characteristic, complemented
10#10622823C211yesmaximal, characteristic, complemented
11#10622607C211yesmaximal, characteristic, complemented
12#10622602C211yesmaximal, characteristic, complemented
13#10622573C211yesmaximal, characteristic, complemented
14#10622563C211yesmaximal, characteristic, complemented
15#10622561C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C22×C22⋊D11C2211yescharacteristic
26C23×Dic11C2211yescharacteristic
27C22×D44C2211yescharacteristic
28C22×C4×D11C2211yescharacteristic
29C11×#121—24no—
30C2×C11×C4⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C11×C22⋊C4C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38#66992—24no—
39#66992—24no—
40#66991—24no—
41#66983—24no—
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×(C2×D11)⋊C4C2211yescharacteristic
47C2×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊Dic11C2211yescharacteristic
49C2×Dic11⋊C4C2211yescharacteristic
50C2×Dic11⋊C4C2211yescharacteristic
51C2×Dic11⋊C4C2211yescharacteristic
52#66937—24no—
53C11⋊#95C2211yescharacteristic
54C11⋊#95C2211yescharacteristic
55C11⋊#95C2211yescharacteristic
56C11⋊#95C2211yescharacteristic
57C24×C11C2311yescharacteristic
58C24×C11C2311yescharacteristic
59C24×C11C2311yescharacteristic
60C23×D11C2311yescharacteristic
61C23×D11C2311yescharacteristic
62C2×D4×C11—22no—
63C2×D4×C11—22no—
64C2×D4×C11—22no—
65C2×D4×C11—22no—
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—41no—
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C2×C22⋊D11—22no—
79C2×C22⋊D11—22no—
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⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11—41no—
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—41no—
99C22×Dic11C2311yescharacteristic
100C22×Dic11C2311yescharacteristic
101C22×Dic11C2311yescharacteristic
102C22×Dic11C2311yescharacteristic
103C22×Dic11C2311yescharacteristic
104C22×Dic11C2311yescharacteristic
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—41no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—41no—
111C11×C4⋊C4—22no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4D414yescomplemented
114C22⋊Dic11—22no—
115C22⋊Dic11—22no—
116C22⋊Dic11—41no—
117C22⋊Dic11—41no—
118C22⋊Dic11D414yescomplemented
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4D414yescomplemented
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126Dic11⋊C4—22no—
127Dic11⋊C4—22no—
128Dic11⋊C4—22no—
129#2675—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×C11—21no—
142C23×C11—21no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11C2×D412yes—
150C23×C11C2×D412yes—
151C23×C11C2411yescharacteristic
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—21no—
165C22×D11C2×D412yes—
166D4×C11—44no—
167D4×C11—44no—
168D4×C11—44no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—44no—
179C2×C4×C11C2×D412yes—
180C2×C4×C11C2×D412yes—
181C2×C4×C11C2×D412yes—
182C22⋊D11—44no—
183C22⋊D11—44no—
184C22⋊D11—44no—
185C22⋊D11—44no—
186C22⋊D11—44no—
187C22⋊D11—44no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
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—44no—
204C2×Dic11C2×D412yes—
205C2×Dic11C2×D412yes—
206C2×Dic11C2×D412yes—
207D44—44no—
208C4×D11—44no—
209C2×#121—111no—
210C2×#121—111no—
211C2×#121—111no—
212C2×#121—111no—
213C2×#121—111no—
214C2×#121D1111yescharacteristic, complemented
215#396—111no—
216#396—111no—
217#392—111no—
218#392—111no—
219#392—111no—
220#392—111no—
221#385—111no—
222#385—111no—
223#385—111no—
224C22×C11—22no—
225C22×C11—22no—
226C22×C11—22no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—41no—
231C22×C11—41no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—41no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—41no—
243C22×C11—41no—
244C22×C11—41no—
245C22×C11C22×D411yescharacteristic
246C22×C11C22×D411yescharacteristic
247C22×C11C22×D411yescharacteristic
248C22×C11H(5,𝔽2)11yescharacteristic
249C22×C11H(5,𝔽2)11yescharacteristic
250C22×C11H(5,𝔽2)11yescharacteristic
251C22×C112−1+411yescharacteristic
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—22no—
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—
266C4×C11—22no—
267C4×C11—22no—
268C4×C11—22no—
269C4×C11—41no—
270Dic11—22no—
271Dic11—22no—
272Dic11—22no—
273Dic11—41no—
274Dic11—41no—
275Dic11—41no—
276C22×D4—111no—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4—111no—
280C22×D4—111no—
281C22×D4—111no—
282C22×D4—111no—
283C22×D4C2×D1111yescharacteristic
284C22×D4C2×D1111yescharacteristic
285C22×D4C2×D1111yescharacteristic
286C23×C4—111no—
287C23×C4—111no—
288C23×C4C2×D1111yescharacteristic
289#121—24no—
290#121—224no—
291#121—224no—
292#121—224no—
293#121—224no—
294#121—224no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
312C2×C22⋊C4C2×D1111yescharacteristic
313#95—111no—
314#95—111no—
315#95—111no—
316#95—111no—
317C2×C11—42no—
318C2×C11—42no—
319C2×C11—81no—
320C2×C11#53711yescharacteristic
321C2×C11#53711yescharacteristic
322C2×C11#53711yescharacteristic
323C2×C11D4211yescharacteristic
324C2×C11D4211yescharacteristic
325C2×C11D4211yescharacteristic
326C2×C11#56011yescharacteristic
327D11—42no—
328D11—81no—
329C24—111no—
330C24—111no—
331C24C22×D1111yescharacteristic
332C24C22×D1111yescharacteristic
333C24C22×D1111yescharacteristic
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—222no—
344C2×D4—222no—
345C2×D4—222no—
346C2×D4—222no—
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—441no—
356C2×D4—441no—
357C2×D4—441no—
358C2×D4—441no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4—441no—
362C2×D4—441no—
363C2×D4—441no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—41no—
367C22×C4—111no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—111no—
371C22×C4—111no—
372C22×C4—111no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—441no—
378C22×C4—441no—
379C22×C4C22×D1111yescharacteristic
380C22×C4C22×D1111yescharacteristic
381C22×C4C22×D1111yescharacteristic
382C22×C4C22×D1111yescharacteristic
383C4⋊C4—22no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C22⋊C4—22no—
390C22⋊C4—114no—
391C22⋊C4—114no—
392C22⋊C4—222no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C22⋊C4C22⋊D1114yescomplemented
401C11#267511yescharacteristic, complemented, Sylow
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—112no—
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—
435C23D4×D1112yes—
436C23C2×C22⋊D1112yes—
437C23C23×D1111yescharacteristic
438D4—44no—
439D4—44no—
440D4—44no—
441D4—444no—
442D4—444no—
443D4—444no—
444D4—444no—
445D4—444no—
446D4—444no—
447D4—444no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—44no—
458C2×C4—112no—
459C2×C4—112no—
460C2×C4—112no—
461C2×C4—221no—
462C2×C4—221no—
463C2×C4—221no—
464C2×C4—221no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—221no—
469C2×C4—221no—
470C2×C4—221no—
471C2×C4—221no—
472C2×C4—221no—
473C2×C4—221no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—444no—
477C2×C4—444no—
478C2×C4D4×D1112yes—
479C2×C4C2×C22⋊D1112yes—
480C2×C4C2×C22⋊D1112yes—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—22no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—222no—
503C22—222no—
504C22—222no—
505C22—441no—
506C22—441no—
507C22—441no—
508C22—441no—
509C22—441no—
510C22—441no—
511C22—441no—
512C22—441no—
513C22—441no—
514C22—441no—
515C22—441no—
516C22C2×D4×D1111yescharacteristic
517C22C2×D4×D1111yescharacteristic
518C22#6703711yescharacteristic
519C22#6703711yescharacteristic
520C22#6704211yescharacteristic
521C22#6704311yescharacteristic
522C22C22×C22⋊D1111yescharacteristic
523C4—22no—
524C4—22no—
525C4—22no—
526C4—41no—
527C4—222no—
528C4—222no—
529C4—222no—
530C4—441no—
531C4—441no—
532C4—441no—
533C2—42no—
534C2—42no—
535C2—81no—
536C2—442no—
537C2—881no—
538C2#1062312811yescharacteristic
539C2#1062313911yescharacteristic
540C2#1062314011yescharacteristic
541C2#1062315111yescharacteristic
542C2D4×C22⋊D1111yescharacteristic
543C2D4×C22⋊D1111yescharacteristic
544C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2675
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C11×#121C2semidirect
2. C2×#66992C2semidirect
3. C2×#66992C2semidirect
4. C2×#66991C2semidirect
5. C2×#66983C2semidirect
6. C2×#66937C2semidirect
7. #10622836C2semidirect
8. #10622836C2semidirect
9. #10622836C2semidirect
10. #10622823C2semidirect
11. #10622607C2semidirect
12. #10622602C2semidirect
13. #10622573C2semidirect
14. #10622563C2semidirect
15. #10622561C2semidirect
113. C11×C22⋊C4D4semidirect
118. C22⋊Dic11D4semidirect
123. (C2×D11)⋊C4D4semidirect
214. C2×#121D11semidirect
400. C22⋊C4C22⋊D11semidirect
401. C11#2675semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669922
C2×#669912
C2×#669832
C2×#669372
#106228362
#106228232
#106226072
#106226022
#106225732
#106225632
#106225612
#267511