Finite Group Databasebeta

← #13072201

Subgroups — #13072201

Order 1408.

832 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×#66993C211yesmaximal, characteristic, complemented
3C2×#66992C211yesmaximal, characteristic, complemented
4C2×#66992C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6C2×#66937C211yesmaximal, characteristic, complemented
7#10622836C211yesmaximal, characteristic, complemented
8#10622836C211yesmaximal, characteristic, complemented
9#10622835C211yesmaximal, characteristic, complemented
10#10622826C211yesmaximal, characteristic, complemented
11#10622604C211yesmaximal, characteristic, complemented
12#10622585C211yesmaximal, characteristic, complemented
13#10622570C211yesmaximal, characteristic, complemented
14#10622569C211yesmaximal, characteristic, complemented
15C22⋊C4×Dic11C211yesmaximal, 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#66993—24no—
39#66992—24no—
40#66992—24no—
41C4×C22⋊D11—24no—
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×(C2×D11)⋊C4C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48C2×Dic11⋊C4C2211yescharacteristic
49C2×Dic11⋊C4C2211yescharacteristic
50C2×C4×Dic11C2211yescharacteristic
51C2×C4×Dic11C2211yescharacteristic
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—22no—
89C2×C22⋊D11—22no—
90C2×C22⋊D11—22no—
91C2×C22⋊D11—41no—
92C2×C22⋊D11—41no—
93C2×C22⋊D11—41no—
94C2×C22⋊D11—41no—
95C2×C22⋊D11D414yescomplemented
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11—22no—
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—22no—
117C22⋊Dic11—22no—
118C22⋊Dic11—41no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—41no—
124Dic11⋊C4—22no—
125Dic11⋊C4—22no—
126Dic11⋊C4D414yescomplemented
127C4×Dic11—22no—
128C4×Dic11—22no—
129#2428—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—28no—
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—44no—
202C2×Dic11C2×D412yes—
203C2×Dic11C2×D412yes—
204C2×Dic11C2×D412yes—
205C2×Dic11#4112yes—
206C2×Dic11#4112yes—
207D44—44no—
208C4×D11—44no—
209C2×#127—111no—
210C2×#121—111no—
211C2×#121—111no—
212C2×#121—111no—
213C2×#121D1111yescharacteristic, complemented
214C2×C4×D4—111no—
215#394—111no—
216#394—111no—
217#392—111no—
218#392—111no—
219#390—111no—
220#389—111no—
221#386—111no—
222#386—111no—
223C4×C22⋊C4—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×C11C2×#4111yescharacteristic
249C22×C11C2×#4111yescharacteristic
250C22×C11H(5,𝔽2)11yescharacteristic
251C22×C11H(5,𝔽2)11yescharacteristic
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—41no—
273Dic11—41no—
274Dic11—41no—
275Dic11#12114yescomplemented
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#127—224no—
290#121—24no—
291#121—224no—
292#121—224no—
293#121—224no—
294C4×D4—224no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4C2×D1111yescharacteristic
299C2×C22⋊C4—111no—
300C2×C22⋊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⋊C4C2×D1111yescharacteristic
310C2×C22⋊C4C2×D1111yescharacteristic
311C2×C42—111no—
312C2×C42—111no—
313#95—111no—
314#95—111no—
315#95—111no—
316#95—111no—
317C2×C11—42no—
318C2×C11—42no—
319C2×C11—81no—
320C2×C11C2×#12111yescharacteristic
321C2×C11#53211yescharacteristic
322C2×C11#54011yescharacteristic
323C2×C11D4211yescharacteristic
324C2×C11D4211yescharacteristic
325C2×C11#54611yescharacteristic
326C2×C11#55011yescharacteristic
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—114no—
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—222no—
356C2×D4—222no—
357C2×D4—222no—
358C2×D4—222no—
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—222no—
378C22×C4—441no—
379C22×C4C22×D1111yescharacteristic
380C22×C4C22×D1111yescharacteristic
381C22×C4C22×D1111yescharacteristic
382C22×C4C22×D1111yescharacteristic
383C4⋊C4—22no—
384C4⋊C4—114no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C22⋊C4—22no—
388C22⋊C4—222no—
389C22⋊C4—222no—
390C22⋊C4—222no—
391C22⋊C4—222no—
392C22⋊C4—222no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C22⋊C4C22⋊D1114yescomplemented
399C42—222no—
400C42—222no—
401C11#242811yescharacteristic, 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—228no—
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—112no—
462C2×C4—112no—
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#41×D1111yescharacteristic
521C22#41×D1111yescharacteristic
522C22C22×C22⋊D1111yescharacteristic
523C4—22no—
524C4—22no—
525C4—22no—
526C4—41no—
527C4—114no—
528C4—222no—
529C4—222no—
530C4—441no—
531C4—441no—
532C4—441no—
533C2—42no—
534C2—42no—
535C2—81no—
536C2—442no—
537C2—881no—
538C2#1062313011yescharacteristic
539C2D11×#12111yescharacteristic
540C2#1062314111yescharacteristic
541C2#1062314611yescharacteristic
542C2D4×C22⋊D1111yescharacteristic
543C2D4×C22⋊D1111yescharacteristic
544C2#1062336311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#121C2
hypercenterC2×#121D11
hypocenterC11#2428
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×#66993C2semidirect
3. C2×#66992C2semidirect
4. C2×#66992C2semidirect
5. C2×C4×C22⋊D11C2semidirect
6. C2×#66937C2semidirect
7. #10622836C2semidirect
8. #10622836C2semidirect
9. #10622835C2semidirect
10. #10622826C2semidirect
11. #10622604C2semidirect
12. #10622585C2semidirect
13. #10622570C2semidirect
14. #10622569C2semidirect
15. C22⋊C4×Dic11C2semidirect
95. C2×C22⋊D11D4semidirect
113. C11×C22⋊C4D4semidirect
126. Dic11⋊C4D4semidirect
213. C2×#121D11semidirect
275. Dic11#121semidirect
398. C22⋊C4C22⋊D11semidirect
401. C11#2428semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×#669932
C2×#669922
C2×C4×C22⋊D112
C2×#669372
#106228362
#106228352
#106228262
#106226042
#106225852
#106225702
#106225692
C22⋊C4×Dic112
#242811