Finite Group Databasebeta

← #13072197

Subgroups — #13072197

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×#66993C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic, complemented
3C2×#66992C211yesmaximal, characteristic, complemented
4C2×#66992C211yesmaximal, characteristic, complemented
5C2×#66991C211yesmaximal, characteristic, complemented
6C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
7C11×#392C211yesmaximal, characteristic, complemented
8#10622833C211yesmaximal, characteristic, complemented
9#10622574C211yesmaximal, characteristic, complemented
10#10622573C211yesmaximal, characteristic, complemented
11#10622572C211yesmaximal, characteristic, complemented
12#10622570C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
14#10622278C211yesmaximal, characteristic, complemented
15#10622260C211yesmaximal, characteristic, complemented
16C22×D4×C11C2211yescharacteristic
17C22×D4×C11C2211yescharacteristic
18C22×D4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C22×C22⋊D11C2211yescharacteristic
24C22×C22⋊D11C2211yescharacteristic
25C23×Dic11C2211yescharacteristic
26C23×Dic11C2211yescharacteristic
27C22×D44C2211yescharacteristic
28C22×C4×D11C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36#66993—24no—
37#66992—24no—
38#66992—24no—
39#66992—24no—
40#66991—24no—
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×(C2×D11)⋊C4C2211yescharacteristic
43C2×(C2×D11)⋊C4C2211yescharacteristic
44C2×(C2×D11)⋊C4C2211yescharacteristic
45C2×(C2×D11)⋊C4C2211yescharacteristic
46C2×C4⋊Dic11C2211yescharacteristic
47C2×Dic11⋊C4C2211yescharacteristic
48C2×Dic11⋊C4C2211yescharacteristic
49C2×Dic11⋊C4C2211yescharacteristic
50C2×C4×Dic11C2211yescharacteristic
51C2×C4×Dic11C2211yescharacteristic
52(C22⋊D11)⋊C4—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×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—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⋊D11D414yescomplemented
93C22×Dic11—22no—
94C22×Dic11—22no—
95C22×Dic11—22no—
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×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—41no—
114C22⋊Dic11—22no—
115C22⋊Dic11—22no—
116C22⋊Dic11—22no—
117C22⋊Dic11D414yescomplemented
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—22no—
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—21no—
179C2×C4×C11C2×D412yes—
180C2×C4×C11#4112yes—
181C22⋊D11—28no—
182C22⋊D11—44no—
183C22⋊D11—44no—
184C22⋊D11—44no—
185C22⋊D11—44no—
186C22⋊D11—44no—
187C2×Dic11—21no—
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—44no—
200C2×Dic11—44no—
201C2×Dic11C2×D412yes—
202C2×Dic11C2×D412yes—
203C2×Dic11C2×D412yes—
204C2×Dic11C2×D412yes—
205C2×Dic11C2×D412yes—
206C2×Dic11#4112yes—
207D44—44no—
208C4×D11—44no—
209C2×#127—111no—
210C2×#121—111no—
211C2×#121—111no—
212C2×#121—111no—
213C2×#121—111no—
214C2×C4×D4—111no—
215#394—111no—
216#394—111no—
217#392—111no—
218#392D1111yescharacteristic, complemented
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—41no—
269C4×C11—41no—
270Dic11—22no—
271Dic11—22no—
272Dic11—22no—
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×C4—111no—
289#127—224no—
290#121—224no—
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⋊C4—111no—
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⋊C4C2×D1111yescharacteristic
309C2×C22⋊C4C2×D1111yescharacteristic
310C2×C22⋊C4C2×D1111yescharacteristic
311C2×C42—111no—
312C2×C42—111no—
313#95—111no—
314#95—111no—
315#95—111no—
316#95C2×D1111yescharacteristic
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—111no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—111no—
369C22×C4—111no—
370C22×C4—222no—
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×C4C22×D1111yescharacteristic
380C22×C4C22×D1111yescharacteristic
381C22×C4C22×D1111yescharacteristic
382C22×C4C22×D1111yescharacteristic
383C4⋊C4—114no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—41no—
390C22⋊C4—114no—
391C22⋊C4—222no—
392C22⋊C4—222no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C22⋊C4—222no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—441no—
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—
436C23D4×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—21no—
458C2×C4—112no—
459C2×C4—112no—
460C2×C4—112no—
461C2×C4—112no—
462C2×C4—112no—
463C2×C4—112no—
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×C4—444no—
479C2×C4D4×D1112yes—
480C2×C4#434112yes—
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
518C22C2×D4×D1111yescharacteristic
519C22C2×#434111yescharacteristic
520C22#6703711yescharacteristic
521C22#6703711yescharacteristic
522C22#41×D1111yescharacteristic
523C4—22no—
524C4—22no—
525C4—41no—
526C4—41no—
527C4—114no—
528C4—222no—
529C4—222no—
530C4—222no—
531C4—441no—
532C4—441no—
533C2—42no—
534C2—42no—
535C2—81no—
536C2—442no—
537C2—881no—
538C2#1062312111yescharacteristic
539C2#1062312111yescharacteristic
540C2#1062312211yescharacteristic
541C2#1062312711yescharacteristic
542C2D11×#12111yescharacteristic
543C2#1062314611yescharacteristic
544C2#1062324911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#392C2
hypercenter#392D11
hypocenterC11#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#66993C2semidirect
2. C2×#66992C2semidirect
3. C2×#66992C2semidirect
4. C2×#66992C2semidirect
5. C2×#66991C2semidirect
6. C2×(C22⋊D11)⋊C4C2semidirect
7. C11×#392C2semidirect
8. #10622833C2semidirect
9. #10622574C2semidirect
10. #10622573C2semidirect
11. #10622572C2semidirect
12. #10622570C2semidirect
13. C22⋊C4×Dic11C2semidirect
14. #10622278C2semidirect
15. #10622260C2semidirect
92. C2×C22⋊D11D4semidirect
117. C22⋊Dic11D4semidirect
126. Dic11⋊C4D4semidirect
218. #392D11semidirect
275. Dic11#121semidirect
401. C11#2428semidirect

Maximal subgroups

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

subgroupindex
C2×#669932
C2×#669922
C2×#669912
C2×(C22⋊D11)⋊C42
C11×#3922
#106228332
#106225742
#106225732
#106225722
#106225702
C22⋊C4×Dic112
#106222782
#106222602
#242811