Finite Group Databasebeta

← #14645149

Subgroups — #14645149

Order 2816.

1120 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic, complemented
2C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
3C2×Q8⋊(C11⋊C8)C212yesmaximal, complemented
4C2×D4⋊(C11⋊C8)C212yesmaximal, complemented
5C2×C4×C11×#41C211yesmaximal, characteristic
6C22×C11×#41C411yescharacteristic
7C4×C11×#41—24no—
8C4×C11×#41—24no—
9C2×C4×Q8×C11C411yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×C4×D4×C11—21no—
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11C411yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×C11×#117—21no—
16C2×C11×#117C411yescharacteristic
17C22×C42×C11—21no—
18C22×C42×C11C2211yescharacteristic
19C2×C22⋊(C11⋊C8)—21no—
20C2×C22⋊(C11⋊C8)—21no—
21C2×C4⋊(C11⋊C8)C2212yes—
22C2×C4×C11⋊C8C2212yes—
23Q8⋊(C11⋊C8)—24no—
24D4⋊(C11⋊C8)—24no—
25#10622162—21no—
26#10622162—21no—
27C2×C11×#41—22no—
28C2×C11×#41—22no—
29C2×C11×#41—22no—
30C2×C11×#41—22no—
31C2×C11×#41—22no—
32C2×C11×#41C814yescomplemented
33C22×Q8×C11C2×C411yescharacteristic
34C22×D4×C11—21no—
35C22×D4×C11C2×C411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11—21no—
38C23×C4×C11—21no—
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C4×Q8×C11—22no—
43C4×Q8×C11—22no—
44C4×Q8×C11—22no—
45C4×Q8×C11D414yes—
46C4×D4×C11—28no—
47C4×D4×C11—28no—
48C4×D4×C11—22no—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C4×D4×C11D414yes—
52C11×#117—28no—
53C11×#117—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—21no—
62C2×C42×C11—28no—
63C2×C42×C11—21no—
64C2×C42×C11—21no—
65C2×C42×C11—21no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11C2×C411yescharacteristic
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C22×C11⋊C8—22no—
73C22×C11⋊C8—22no—
74C22⋊(C11⋊C8)—24no—
75C22⋊(C11⋊C8)—42no—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)—22no—
78C4×C11⋊C8—22no—
79C4×C11⋊C8—22no—
80#8312—111nomaximal, Sylow
81C24×C11—21no—
82C24×C11C22⋊C411yescharacteristic
83C11×#41—28no—
84C11×#41—28no—
85C11×#41—28no—
86C11×#41—28no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11C22⋊C412yes—
91C2×Q8×C11C2×C812yes—
92C2×Q8×C11M1612yes—
93C2×D4×C11—24no—
94C2×D4×C11—24no—
95C2×D4×C11—24no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C22⋊C412yes—
100C2×D4×C11C2×C812yes—
101C2×D4×C11M1612yes—
102C22×C4×C11—24no—
103C22×C4×C11—24no—
104C22×C4×C11—21no—
105C22×C4×C11—24no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—24no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—41no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—42no—
124C22×C4×C11—41no—
125C22×C4×C11—41no—
126C22×C4×C11C22⋊C411yescharacteristic
127C22×C4×C11C22⋊C411yescharacteristic
128C22×C4×C11C22⋊C411yescharacteristic
129C22×C4×C11C2×C812yes—
130C22×C4×C11M1612yes—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C11×C4⋊C4—24no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—24no—
138C11×C4⋊C4C22⋊C412yes—
139C11×C4⋊C4C22⋊C412yes—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143C42×C11—24no—
144C42×C11—24no—
145C42×C11—21no—
146C42×C11—21no—
147C42×C11—22no—
148C42×C11—24no—
149C42×C11—22no—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152C2×C11⋊C8—24no—
153C2×C11⋊C8—42no—
154C2×C11⋊C8—42no—
155C2×C11⋊C8—42no—
156C2×C11⋊C8—42no—
157C2×C11⋊C8—42no—
158C2×C4×#41D1111yescharacteristic
159#1797—111no—
160C4×C22⋊C8—111no—
161C2×Q8⋊C8—112no—
162C2×D4⋊C8—112no—
163C23×C11—21no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—21no—
167C23×C11—22no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22⋊C812yes—
177C23×C11C2×C22⋊C411yescharacteristic
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—22no—
181Q8×C11C22⋊C814yescomplemented
182D4×C11—216no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11—22no—
186D4×C11C22⋊C814yescomplemented
187C2×C4×C11—216no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—44no—
207C2×C4×C11—48no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11C22⋊C812yes—
217C2×C4×C11#10412yes—
218C2×C4×C11C2×C22⋊C411yescharacteristic
219C2×C4×C11C2×C22⋊C411yescharacteristic
220C2×C4×C11#12012yes—
221C2×C4×C11#12012yes—
222C2×C4×C11C22×C811yescharacteristic
223C2×C4×C11C2×M1611yescharacteristic
224C2×C4×C11C2×M1611yescharacteristic
225C2×C4×C11C2×M1611yescharacteristic
226C2×C4×C11#13512yes—
227C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
228C2×C4×C11#13711yescharacteristic
229C11⋊C8—44no—
230C11⋊C8—82no—
231C22×#41Dic1111yescharacteristic
232C4×#41—24no—
233C4×#41—24no—
234C2×C4×Q8Dic1111yescharacteristic
235C2×C4×Q8C2×D1111yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4Dic1111yescharacteristic
239C2×C4×D4C2×D1111yescharacteristic
240C2×#117—21no—
241C2×#117Dic1111yescharacteristic
242C22×C42—21no—
243C22×C42C2×D1111yescharacteristic
244C2×C4⋊C8—112no—
245C2×C22⋊C8—221no—
246C2×C22⋊C8—221no—
247C2×C4×C8—112no—
248#336—221no—
249#336—221no—
250Q8⋊C8—224no—
251D4⋊C8—224no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—24no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—41no—
259C22×C11—42no—
260C22×C11—41no—
261C22×C11—42no—
262C22×C11—41no—
263C22×C11—42no—
264C22×C11—41no—
265C22×C11—42no—
266C22×C11#37911yescharacteristic
267C22×C11C2×C22⋊C811yescharacteristic
268C22×C11#40711yescharacteristic
269C22×C11#41611yescharacteristic
270C22×C11#41711yescharacteristic
271C22×C11C2×#10411yescharacteristic
272C22×C11#42111yescharacteristic
273C4×C11—22no—
274C4×C11—24no—
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—41no—
278C4×C11—42no—
279C4×C11—42no—
280C4×C11C2×C22⋊C811yescharacteristic
281C4×C11C2×C22⋊C811yescharacteristic
282C4×C11#40711yescharacteristic
283C4×C11#40711yescharacteristic
284C4×C11#44912yes—
285C4×C11#45212yes—
286C2×#41—22no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—22no—
290C2×#41—22no—
291C2×#41C11⋊C814yescomplemented
292C22×Q8C2×Dic1111yescharacteristic
293C22×D4—21no—
294C22×D4C2×Dic1111yescharacteristic
295C23×C4—21no—
296C23×C4—21no—
297C23×C4—21no—
298C23×C4C2×Dic1111yescharacteristic
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22⋊D1111yescharacteristic
301C22×C8—222no—
302C22×C8—222no—
303C4×Q8—22no—
304C4×Q8—22no—
305C4×Q8—22no—
306C4×Q8C22⋊D1114yes—
307C4×D4—28no—
308C4×D4—28no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4C22⋊D1114yes—
313#117—28no—
314#117—22no—
315#117—22no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4C2×Dic1111yescharacteristic
319C2×C4⋊C4C2×Dic1111yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C42—28no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42—22no—
328C2×C42—22no—
329C2×C42C2×Dic1111yescharacteristic
330C2×C42C22⋊D1111yescharacteristic
331C2×C42C22⋊D1111yescharacteristic
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—222no—
334C4⋊C8—222no—
335C22⋊C8—224no—
336C22⋊C8—442no—
337C4×C8—222no—
338C4×C8—222no—
339C2×C11—42no—
340C2×C11—44no—
341C2×C11#147611yescharacteristic
342C2×C11#147711yescharacteristic
343C2×C11#148811yescharacteristic
344C2×C11#148911yescharacteristic
345C2×C11#177911yescharacteristic
346C2×C11#178811yescharacteristic
347C2×C11#178911yescharacteristic
348C24—21no—
349C24C22⋊Dic1111yescharacteristic
350#41—28no—
351#41—28no—
352#41—28no—
353#41—28no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8C2×C11⋊C812yes—
358C2×Q8#431812yes—
359C2×Q8C22⋊Dic1112yes—
360C2×D4—24no—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4C2×C11⋊C812yes—
367C2×D4#431812yes—
368C2×D4C22⋊Dic1112yes—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—21no—
372C22×C4—24no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—24no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—22no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—24no—
387C22×C4—41no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—41no—
391C22×C4—42no—
392C22×C4—41no—
393C22×C4C2×C11⋊C812yes—
394C22×C4#431812yes—
395C22×C4C22⋊Dic1111yescharacteristic
396C22×C4C22⋊Dic1111yescharacteristic
397C22×C4C22⋊Dic1111yescharacteristic
398C22×C4C22×Dic1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C2×C8—224no—
402C2×C8—442no—
403C2×C8—442no—
404C2×C8—442no—
405C2×C8—442no—
406C2×C8—442no—
407C4⋊C4—24no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—24no—
411C4⋊C4C22⋊Dic1112yes—
412C4⋊C4C22⋊Dic1112yes—
413C22⋊C4—24no—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C42—24no—
417C42—24no—
418C42—21no—
419C42—21no—
420C42—22no—
421C42—24no—
422C42—22no—
423C42C2×C22⋊D1112yes—
424C42C2×C22⋊D1112yes—
425C11#831211yescharacteristic, complemented, Sylow
426C23—22no—
427C23—21no—
428C23—22no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23—41no—
439C23C22⋊(C11⋊C8)12yes—
440C23C2×C22⋊Dic1111yescharacteristic
441Q8—22no—
442Q8—22no—
443Q8—22no—
444Q8C22⋊(C11⋊C8)14yescomplemented
445D4—216no—
446D4—22no—
447D4—22no—
448D4—22no—
449D4C22⋊(C11⋊C8)14yescomplemented
450C2×C4—216no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—44no—
470C2×C4—48no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—44no—
479C2×C4C22⋊(C11⋊C8)12yes—
480C2×C4#6690112yes—
481C2×C4C22×C11⋊C811yescharacteristic
482C2×C4C2×#431811yescharacteristic
483C2×C4C2×#431811yescharacteristic
484C2×C4C2×#431811yescharacteristic
485C2×C4#6700211yescharacteristic
486C2×C4#6700312yes—
487C2×C4#6700411yescharacteristic
488C2×C4C2×C22⋊Dic1111yescharacteristic
489C2×C4C2×C22⋊Dic1111yescharacteristic
490C2×C4#6700612yes—
491C2×C4#6700612yes—
492C8—444no—
493C8—882no—
494C22—22no—
495C22—24no—
496C22—22no—
497C22—22no—
498C22—41no—
499C22—42no—
500C22—41no—
501C22—42no—
502C22—41no—
503C22—42no—
504C22—41no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22C2×C22⋊(C11⋊C8)11yescharacteristic
509C22#1062282011yescharacteristic
510C22#1062284511yescharacteristic
511C22#1062284611yescharacteristic
512C22C2×#6690111yescharacteristic
513C22#1062284911yescharacteristic
514C22#1062286011yescharacteristic
515C4—22no—
516C4—22no—
517C4—22no—
518C4—24no—
519C4—41no—
520C4—42no—
521C4—42no—
522C4C2×C22⋊(C11⋊C8)11yescharacteristic
523C4C2×C22⋊(C11⋊C8)11yescharacteristic
524C4#1062282011yescharacteristic
525C4#1062282011yescharacteristic
526C4#1062285112yes—
527C4#1062285212yes—
528C2—42no—
529C2—44no—
530C2#1306699811yescharacteristic
531C2#1306700311yescharacteristic
532C2#1306705011yescharacteristic
533C2#1306705511yescharacteristic
534C2#1306852611yescharacteristic
535C2#1306855611yescharacteristic
536C2#1306856011yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC2×C4×C11C22×C8
FrattiniC2×C42C22×D11
FittingC2×C4×C11×#41C2
socleC23×C11C2×C22⋊C4
prime radicalC22×C11×#41C4
cosocleC2×C42×C11C23
hypercenterC2×C4×#41D11
hypocenterC11#8312
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
2. C4×C22⋊(C11⋊C8)C2semidirect
3. C2×Q8⋊(C11⋊C8)C2semidirect
4. C2×D4⋊(C11⋊C8)C2semidirect
32. C2×C11×#41C8semidirect
181. Q8×C11C22⋊C8semidirect
186. D4×C11C22⋊C8semidirect
291. C2×#41C11⋊C8semidirect
425. C11#8312semidirect
444. Q8C22⋊(C11⋊C8)semidirect
449. D4C22⋊(C11⋊C8)semidirect

Maximal subgroups

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

subgroupindex
#130685962
C4×C22⋊(C11⋊C8)2
C2×Q8⋊(C11⋊C8)2
C2×D4⋊(C11⋊C8)2
C2×C4×C11×#412
#831211