Finite Group Databasebeta

← #14759447

Subgroups — #14759447

Order 2816.

1436 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
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×#10622663C211yesmaximal, characteristic
3C2×#10622643C212yesmaximal, complemented
4#13068960C212yesmaximal, complemented
5#13068924C211yesmaximal, characteristic
6#13068883C212yesmaximal, complemented
7#13068808C211yesmaximal, characteristic
8#13068550C211yesmaximal, characteristic
9#13068449C212yesmaximal, complemented
10#13068378C211yesmaximal, characteristic
11C4×C11×C22⋊Q8C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×#4326C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×Dic11⋊C4—21no—
19C22×C4×Dic11—21no—
20C2×C4×Dic22—21no—
21C2×C4×Dic22—21no—
22C2×C4×Dic22—28no—
23C2×C4×Dic22C2212yes—
24C2×C4×Dic22C2212yes—
25C11×#391C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#385—21no—
29C11×#380C2211yescharacteristic
30C4×C11×C4⋊C4—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C4×C11×C22⋊C4—21no—
33C2×#66899C2212yes—
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622663C418yescomplemented
37#10622643—28no—
38C2×#66874C2212yes—
39C2×#66874C2212yes—
40C2×#66874C2212yes—
41C2×#66872C2212yes—
42C2×#66867C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—21no—
52C22×Dic22—21no—
53C22×Dic22—22no—
54C22×Dic22—24no—
55C22×Dic22—24no—
56C22×Dic22C2×C414yes—
57C22×Dic22C2312yes—
58C11×C22⋊Q8—22no—
59C11×C22⋊Q8C2×C414yes—
60C4×Q8×C11—24no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—24no—
70C2×C42×C11—21no—
71C2×C42×C11—21no—
72C2×C42×C11D411yescharacteristic
73C2×C42×C11D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×#4326—24no—
77C2×#4326—24no—
78C2×#4326C2×C418yescomplemented
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11C2312yes—
82C2×Dic11⋊C4—28no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—22no—
85C2×C4×Dic11—28no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C22×C11⋊C8C2312yes—
89C22×C11⋊C8C2312yes—
90C4×Dic22—28no—
91C4×Dic22—28no—
92C4×Dic22—24no—
93C4×Dic22—24no—
94C4×Dic22—24no—
95C4×Dic22D418yes—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101#66899—24no—
102C22⋊(C11⋊C8)—22no—
103C22⋊(C11⋊C8)C2×C414yes—
104#66874—24no—
105#66874—24no—
106#66874C2×C418yescomplemented
107#66872—24no—
108#66867—24no—
109#21455—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C22×C412yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—41no—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—42no—
142C22×Dic11—42no—
143C2×Dic22—24no—
144C2×Dic22—24no—
145C2×Dic22—216no—
146C2×Dic22—216no—
147C2×Dic22—24no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22C22×C414yes—
152C2×Dic22C2×D414yes—
153C2×Dic22#4114yes—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C22×C412yes—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—42no—
163C42×C11—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11—42no—
167C42×C11—42no—
168C42×C11C2×D414yes—
169#4326—216no—
170C4⋊Dic11—24no—
171C4⋊Dic11—22no—
172C4⋊Dic11C2×D414yes—
173Dic11⋊C4—28no—
174Dic11⋊C4—28no—
175C4×Dic11—28no—
176C4×Dic11—28no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8C22×C414yes—
183C22×C4×Q8—111no—
184C2×#451—111no—
185C2×#441—112no—
186C4×C22⋊Q8D1111yescharacteristic
187#1878—112no—
188#1872—111no—
189#1865—112no—
190#1853—111no—
191#1787—111no—
192#1763—112no—
193#1749—111no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11C4×D412yes—
199C23×C11#13712yes—
200C23×C11#13712yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—24no—
203Q8×C11—42no—
204C2×C4×C11—28no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—44no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11C4×D412yes—
232C2×C4×C11#12012yes—
233C2×C4×C11#12012yes—
234C2×C4×C11#13712yes—
235C2×C4×C11C23×C411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4112yes—
239C2×Dic11—216no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—48no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247Dic22—216no—
248Dic22—24no—
249Dic22—24no—
250Dic22—24no—
251Dic22C4×D418yes—
252C11⋊C8—24no—
253C11⋊C8—42no—
254C23×Q8—111no—
255C22×Q16—112no—
256C2×C22⋊Q8C2×D1111yescharacteristic
257C2×C4×Q8—112no—
258C2×C4×Q8—112no—
259C2×C4×Q8—228no—
260C2×C4×Q8—221no—
261C2×C4×Q8—221no—
262C2×C4×Q8C2×D1111yescharacteristic
263C22×C4⋊C4—111no—
264C22×C4⋊C4—221no—
265C22×C42—221no—
266C22×C42C2×D1111yescharacteristic
267#451—118no—
268#441—228no—
269C2×#106—112no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103—112no—
274C2×C22⋊C8—111no—
275C2×C22⋊C8—111no—
276C2×#97—112no—
277#391C2×D1111yescharacteristic
278#389C2×D1111yescharacteristic
279#387—21no—
280#385—21no—
281#380C2×D1111yescharacteristic
282C4×C4⋊C4—21no—
283C4×C4⋊C4C2×D1111yescharacteristic
284C4×C22⋊C4—21no—
285#340—112no—
286#340—112no—
287#336—112no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11#44114yescomplemented
295C22×C11C2×C4×D411yescharacteristic
296C22×C11C2×#12011yescharacteristic
297C22×C11#52511yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11C2×#13711yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57511yescharacteristic
302C4×C11—22no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—22no—
306C4×C11—42no—
307C4×C11—41no—
308C4×C11—42no—
309C4×C11—81no—
310C4×C11—81no—
311C4×C11C2×C4×D412yes—
312C4×C11#52512yes—
313Dic11—28no—
314Dic11—44no—
315C22×Q8—114no—
316C22×Q8—112no—
317C22×Q8—224no—
318C22×Q8—224no—
319C22×Q8—222no—
320C22×Q8—221no—
321C22×Q8C22×D1111yescharacteristic
322C23×C4—221no—
323C23×C4—221no—
324C23×C4C22⋊D1111yescharacteristic
325C23×C4C22⋊D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C2×Q16—118no—
328C2×Q16—224no—
329C2×Q16—224no—
330C22×C8—112no—
331C22×C8—112no—
332C22⋊Q8—22no—
333C22⋊Q8C4×D1114yes—
334C4×Q8—24no—
335C4×Q8—118no—
336C4×Q8—224no—
337C4×Q8—224no—
338C4×Q8—228no—
339C4×Q8—228no—
340C4×Q8—224no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—112no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4C22×D1111yescharacteristic
351C2×C4⋊C4C22×D1111yescharacteristic
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C42—24no—
356C2×C42—21no—
357C2×C42—21no—
358C2×C42—228no—
359C2×C42—222no—
360C2×C42—222no—
361C2×C42C22⋊D1111yescharacteristic
362C2×C42C22⋊D1111yescharacteristic
363C2×C42C22×D1111yescharacteristic
364C2×C42C22×D1111yescharacteristic
365#106—224no—
366#103—118no—
367#103—224no—
368#103—224no—
369#103—224no—
370C22⋊C8—114no—
371C22⋊C8—222no—
372#97—224no—
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C2×C11—24no—
379C2×C11C4×#12011yescharacteristic
380C2×C11C2×#44111yescharacteristic
381C2×C11C4×#13711yescharacteristic
382C2×C11#300411yescharacteristic
383C2×C11#300711yescharacteristic
384C2×C11#311311yescharacteristic
385C2×C11#311711yescharacteristic
386C24C2×C22⋊D1111yescharacteristic
387C2×Q8—21no—
388C2×Q8—22no—
389C2×Q8—22no—
390C2×Q8—114no—
391C2×Q8—114no—
392C2×Q8—114no—
393C2×Q8—2216no—
394C2×Q8—224no—
395C2×Q8—224no—
396C2×Q8—2216no—
397C2×Q8—224no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8C2×C4×D1112yes—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—41no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4C2×C4×D1112yes—
423C22×C4#433912yes—
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C23×D1111yescharacteristic
430Q16—2216no—
431C2×C8—114no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8—222no—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—42no—
442C4⋊C4—42no—
443C4⋊C4—114no—
444C4⋊C4—228no—
445C4⋊C4—224no—
446C4⋊C4—228no—
447C4⋊C4—222no—
448C4⋊C4C2×C4×D1112yes—
449C22⋊C4—24no—
450C22⋊C4—42no—
451C42—22no—
452C42—22no—
453C42—22no—
454C42—42no—
455C42—42no—
456C42—228no—
457C42—228no—
458C42D4×D1114yes—
459C11#2145511yescharacteristic, complemented, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23C4×C22⋊D1112yes—
465C23#6699512yes—
466C23#6700412yes—
467C23C22×C22⋊D1111yescharacteristic
468Q8—24no—
469Q8—42no—
470Q8—118no—
471Q8—2216no—
472Q8—224no—
473Q8—224no—
474Q8—224no—
475C2×C4—28no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—44no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—2216no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—448no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4C4×C22⋊D1112yes—
511C2×C4#6699012yes—
512C2×C4#6699012yes—
513C2×C4#6700412yes—
514C2×C4C22×C4×D1111yescharacteristic
515C2×C4C2×#433911yescharacteristic
516C2×C4C2×D4×D1112yes—
517C2×C4#41×D1112yes—
518C8—224no—
519C8—442no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22#1062264314yescomplemented
527C22C2×C4×C22⋊D1111yescharacteristic
528C22C2×#6699011yescharacteristic
529C22C2×#6699511yescharacteristic
530C22#1062335311yescharacteristic
531C22C2×#6700411yescharacteristic
532C22C2×#6700411yescharacteristic
533C22#1062335911yescharacteristic
534C4—22no—
535C4—22no—
536C4—22no—
537C4—22no—
538C4—42no—
539C4—41no—
540C4—42no—
541C4—81no—
542C4—81no—
543C4—228no—
544C4—444no—
545C4C4×D4×D1112yes—
546C4#1062307812yes—
547C2—24no—
548C2C4×#6699011yescharacteristic
549C2C2×#1062264311yescharacteristic
550C2C4×#6700411yescharacteristic
551C2#1307784911yescharacteristic
552C2#1307787411yescharacteristic
553C2#1307874211yescharacteristic
554C2#1307878311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC4×C22⋊Q8D11
hypocenterC11#21455
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#10622643C2semidirect
4. #13068960C2semidirect
6. #13068883C2semidirect
9. #13068449C2semidirect
36. #10622663C4semidirect
78. C2×#4326C2×C4semidirect
106. #66874C2×C4semidirect
294. C22×C11#441semidirect
459. C11#21455semidirect
526. C22#10622643semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106226632
C2×#106226432
#130689602
#130689242
#130688832
#130688082
#130685502
#130684492
#130683782
C4×C11×C22⋊Q82
#2145511