Finite Group Databasebeta

← #14781784

Subgroups — #14781784

Order 2816.

1458 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C2×#10622537C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic
4C2×#10622617C211yesmaximal, characteristic, complemented
5C2×#10622542C211yesmaximal, characteristic, complemented
6#13069938C214yesmaximal, complemented
7#13069933C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C11×#2297C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C2×#67004—24no—
15C2×#67004—24no—
16C2×#67004—24no—
17C22×#4326C2212yes—
18C22×#4324C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C11×#391C2212yes—
23C11×#390C2212yes—
24C11×#386—22no—
25C4×C11×C22⋊C4—21no—
26C4×C11×C22⋊C4—21no—
27#10622845—24no—
28C2×#66899C2212yes—
29C2×#66896C2212yes—
30C2×C11⋊#95—22no—
31#10622617—24no—
32C2×#66874C2214yes—
33#10622542—21no—
34#10622542—21no—
35#10622542C2214yes—
36#10622537—24no—
37C2×C4⋊(C11⋊C8)C2214yes—
38#10622167C2214yes—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41D414yes—
45C22×Q8×C11C2311yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11D412yes—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C23×Dic11—21no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—21no—
58C22×Dic22—22no—
59C22×Dic22D414yes—
60C22×Dic22C2312yes—
61C11×#117—22no—
62C11×#117—22no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—21no—
70C2×C42×C11D411yescharacteristic
71C2×C42×C11D411yescharacteristic
72C2×C42×C11C2312yes—
73#67004—232no—
74C2×#4326—24no—
75C2×#4326—24no—
76C2×#4326—24no—
77C2×#4324—24no—
78C2×#4324—24no—
79C2×#4324—24no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2312yes—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318D414yes—
90C22×C11⋊C8C2312yes—
91C22×C11⋊C8C2312yes—
92C11×#95—22no—
93C11×#95—22no—
94#66899—24no—
95#66896—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98#66874—28no—
99C4⋊(C11⋊C8)—28no—
100#23547—111nomaximal, Sylow
101C24×C11—21no—
102C24×C11C2×D411yescharacteristic
103C11×#41—28no—
104C11×#41—28no—
105C11×#41—44no—
106C11×#41—44no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—21no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11C2×D412yes—
113C2×D4×C11—24no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11C2×D412yes—
122C22×C4×C11—24no—
123C22×C4×C11—21no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—42no—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—44no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C2×Dic22—28no—
148C2×Dic22—24no—
149C2×Dic22—28no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—42no—
156C2×Dic22—42no—
157C2×Dic22—44no—
158C2×Dic22—44no—
159C2×Dic22C2×D414yes—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—42no—
164C11×C22⋊C4—44no—
165C42×C11—22no—
166C42×C11—22no—
167C42×C11—22no—
168C42×C11—22no—
169C42×C11—42no—
170#4326—216no—
171#4324—216no—
172C4⋊Dic11—22no—
173C4⋊Dic11—22no—
174C4⋊Dic11—42no—
175#4318—28no—
176#4318—44no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8C2×D414yes—
183C22×#137—111no—
184C2×#423—111no—
185C2×#417—111no—
186C2×#419—111no—
187#2297D1111yescharacteristic
188C2×#391—111no—
189#2056—114no—
190#2055—114no—
191#1736—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11—42no—
198C23×C11—42no—
199C23×C11#12112yes—
200C23×C11#12112yes—
201C23×C11#12112yes—
202C23×C11C22×D411yescharacteristic
203Q8×C11—22no—
204Q8×C11—22no—
205Q8×C11—41no—
206Q8×C11—41no—
207D4×C11—22no—
208D4×C11—22no—
209D4×C11—48no—
210D4×C11—41no—
211D4×C11—41no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—48no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—48no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11#12014yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12314yes—
230C2×C4×C11#12314yes—
231C2×C4×C11#12414yes—
232C2×C4×C11#13714yescomplemented
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×Dic11—24no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—48no—
243C2×Dic11—42no—
244C2×Dic11—44no—
245C2×Dic11—84no—
246Dic22—24no—
247Dic22—24no—
248Dic22—42no—
249Dic22—42no—
250Dic22—48no—
251C11⋊C8—24no—
252C11⋊C8—42no—
253C22×#41C2×D1111yescharacteristic
254C23×Q8—111no—
255C2×#137—224no—
256C2×#137—224no—
257C2×#137—224no—
258C22×Q16—112no—
259C22×SD16—112no—
260C22×M16—111no—
261C22×M16—111no—
262C2×#117C2×D1111yescharacteristic
263C22×C4⋊C4—111no—
264C22×C42C2×D1111yescharacteristic
265#423—224no—
266C2×C4⋊C8—114no—
267#419—224no—
268#417—224no—
269C2×#103—112no—
270C2×#103—114no—
271C2×#102—112no—
272#391—114no—
273#391—221no—
274#391—221no—
275#391C2×D1112yes—
276#390C2×D1112yes—
277#386—22no—
278C4×C22⋊C4—21no—
279C4×C22⋊C4—21no—
280C2×#95—222no—
281#340—114no—
282C22×C11—24no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—42no—
289C22×C11—82no—
290C22×C11—82no—
291C22×C11#39414yes—
292C22×C11C2×#12111yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C2×#12111yescharacteristic
295C22×C11C2×#13712yes—
296C22×C11#57512yes—
297C4×C11—24no—
298C4×C11—42no—
299C4×C11—42no—
300C4×C11—82no—
301C4×C11#39414yes—
302C4×C11C2×#12011yescharacteristic
303C4×C11C2×#12311yescharacteristic
304C4×C11C2×#12311yescharacteristic
305C4×C11C2×#12411yescharacteristic
306Dic11—44no—
307Dic11—82no—
308C2×#41—22no—
309C2×#41—22no—
310C2×#41—22no—
311C2×#41—22no—
312C2×#41—22no—
313C2×#41D4414yes—
314C22×Q8—114no—
315C22×Q8—112no—
316C22×Q8—222no—
317C22×Q8—221no—
318C22×Q8—222no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8C22×D1111yescharacteristic
323C22×D4—21no—
324C22×D4C22×D1111yescharacteristic
325C23×C4—21no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4C22⋊D1112yes—
329C23×C4C22×D1111yescharacteristic
330#137—2232no—
331C2×Q16—224no—
332C2×Q16—224no—
333C2×Q16—224no—
334C2×SD16—224no—
335C2×SD16—224no—
336C2×SD16—224no—
337C2×M16—114no—
338C2×M16—222no—
339C2×M16—222no—
340C2×M16—222no—
341C2×M16—222no—
342C2×M16—222no—
343C22×C8—112no—
344C22×C8—112no—
345#117—22no—
346#117—22no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—21no—
358C2×C42C22⋊D1111yescharacteristic
359C2×C42C22⋊D1111yescharacteristic
360C2×C42C22×D1112yes—
361C4⋊C8—228no—
362#103—228no—
363#103—224no—
364#102—224no—
365#95—22no—
366#95—22no—
367#95—224no—
368#95—224no—
369C2×C11—24no—
370C2×C11—82no—
371C2×C11C2×#39411yescharacteristic
372C2×C11#303712yes—
373C2×C11#303911yescharacteristic
374C2×C11#304011yescharacteristic
375C2×C11#305612yes—
376C24—21no—
377C24C2×C22⋊D1111yescharacteristic
378#41—28no—
379#41—28no—
380#41—44no—
381#41—44no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—21no—
385C2×Q8—21no—
386C2×Q8—21no—
387C2×Q8—114no—
388C2×Q8—224no—
389C2×Q8—222no—
390C2×Q8—228no—
391C2×Q8—228no—
392C2×Q8—222no—
393C2×Q8—222no—
394C2×Q8—222no—
395C2×Q8—222no—
396C2×Q8—444no—
397C2×Q8—444no—
398C2×Q8—442no—
399C2×Q8—442no—
400C2×Q8C2×D4412yes—
401C2×D4—24no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—42no—
409C2×D4C2×D4412yes—
410C22×C4—24no—
411C22×C4—21no—
412C22×C4—24no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—444no—
424C22×C4—442no—
425C22×C4C2×D4412yes—
426C22×C4#433912yes—
427C22×C4D4×D1112yes—
428C22×C4D4×D1112yes—
429C22×C4#434112yes—
430C22×C4#434112yes—
431C22×C4C2×C22⋊D1112yes—
432C22×C4C2×C22⋊D1112yes—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435Q16—2216no—
436SD16—2216no—
437M16—228no—
438M16—444no—
439C2×C8—114no—
440C2×C8—222no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8—222no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—442no—
450C22⋊C4—44no—
451C22⋊C4—42no—
452C22⋊C4—44no—
453C42—22no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—42no—
458C11#2354711yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23#6698312yes—
467C23#6699112yes—
468C23#6699212yes—
469C23C22×C22⋊D1111yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—41no—
473Q8—41no—
474Q8—224no—
475Q8—224no—
476Q8—442no—
477Q8—442no—
478Q8—448no—
479D4—22no—
480D4—22no—
481D4—48no—
482D4—41no—
483D4—41no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—48no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—48no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—224no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—448no—
501C2×C4—442no—
502C2×C4—444no—
503C2×C4—884no—
504C2×C4#6693514yes—
505C2×C4#6693614yes—
506C2×C4#6693814yes—
507C2×C4#6693914yes—
508C2×C4#6698312yes—
509C2×C4#6699112yes—
510C2×C4#6699212yes—
511C2×C4#6700414yescomplemented
512C2×C4C22×D4411yescharacteristic
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4C2×#434111yescharacteristic
518C8—224no—
519C8—442no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—82no—
528C22—82no—
529C22#1062257414yes—
530C22C2×#6698311yescharacteristic
531C22C2×#6699111yescharacteristic
532C22C2×#6699211yescharacteristic
533C22#1062335312yes—
534C22C2×#6700412yes—
535C4—24no—
536C4—42no—
537C4—42no—
538C4—82no—
539C4—444no—
540C4—882no—
541C4#1062257414yes—
542C4C2×#6693511yescharacteristic
543C4C2×#6693611yescharacteristic
544C4C2×#6693811yescharacteristic
545C4C2×#6693911yescharacteristic
546C2—24no—
547C2—82no—
548C2C2×#1062257411yescharacteristic
549C2#1307808412yes—
550C2#1307810311yescharacteristic
551C2#1307811011yescharacteristic
552C2#1307824812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2297C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
hypercenter#2297D11
hypocenterC11#23547
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. C2×#10622537C2semidirect
4. C2×#10622617C2semidirect
5. C2×#10622542C2semidirect
6. #13069938C2semidirect
7. #13069933C2semidirect
8. #13068337C2semidirect
232. C2×C4×C11#137semidirect
458. C11#23547semidirect
511. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106225372
C2×#106228452
C2×#106226172
C2×#106225422
#130699382
#130699332
#130683372
C11×#22972
#2354711