Finite Group Databasebeta

← #14781788

Subgroups — #14781788

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×#66962C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic
3C2×#10622733C211yesmaximal, characteristic, complemented
4#13071106C211yesmaximal, characteristic
5C2×#10622542C211yesmaximal, characteristic, complemented
6#13069939C214yesmaximal, complemented
7#13069934C214yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C2×C11×#423C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×M16C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C2×#66962—24no—
18C2×#66962—24no—
19C2×#66962—24no—
20C22×Dic44C2212yes—
21C22×#4314C2212yes—
22C11×#423—24no—
23C2×C11×C4⋊C8C2214yes—
24#10622826—22no—
25C2×C11⋊#95—22no—
26#10622746—24no—
27#10622733—24no—
28C2×#66885C2212yes—
29C2×#66880C2214yes—
30C2×#66880C2212yes—
31#10622552C2212yes—
32C4×(C2×D11)⋊C4—21no—
33C4×(C2×D11)⋊C4—21no—
34#10622542—21no—
35#10622542—21no—
36#10622542C2212yes—
37#10622542C2214yes—
38#10622189C2214yes—
39C23×C4×C11D412yes—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—21no—
42C23×Dic11—21no—
43C23×Dic11—21no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339D414yes—
50C22×D44C2311yescharacteristic
51C22×C4×D11—21no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×Dic22D414yes—
59C22×Dic22C2312yes—
60C22×Dic22C2311yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16D414yes—
67C22×C8×C11C2312yes—
68C22×C8×C11C2312yes—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11D411yescharacteristic
72C2×C42×C11D411yescharacteristic
73C2×C42×C11C2312yes—
74C2×C22⋊Dic11—21no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77#66979—22no—
78#66979—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2312yes—
83C2×C4⋊Dic11C2312yes—
84C2×C4×Dic11—21no—
85#66962—232no—
86C2×Dic44—24no—
87C2×Dic44—24no—
88C2×Dic44—24no—
89C2×#4314—24no—
90C2×#4314—24no—
91C2×#4314—24no—
92C11×C4⋊C8—28no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97#66885—24no—
98#66880—28no—
99#66880—24no—
100#23547—111nomaximal, Sylow
101C24×C11C2×D411yescharacteristic
102C23×D11—21no—
103C22×C4×C11—24no—
104C22×C4×C11—24no—
105C22×C4×C11—42no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4112yes—
113C22×C4×C11#4112yes—
114C22×C4×C11#4112yes—
115C22×C4×C11C2411yescharacteristic
116C2×C22⋊D11—24no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—42no—
119C22×Dic11—24no—
120C22×Dic11—22no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—44no—
125C22×Dic11—42no—
126C22×Dic11—42no—
127C22×Dic11—42no—
128#4339—28no—
129#4339—28no—
130#4339—44no—
131#4339—44no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44C2×D412yes—
138C2×C4×D11—24no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×Dic22—28no—
142C2×Dic22—24no—
143C2×Dic22—28no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—22no—
153C2×Dic22—21no—
154C2×Dic22—42no—
155C2×Dic22—42no—
156C2×Dic22—44no—
157C2×Dic22—44no—
158C2×Dic22C2×D414yes—
159C2×Dic22C2×D412yes—
160C11×M16—28no—
161C11×M16—44no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C2×C8×C11C2×D414yes—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—22no—
172C22⋊Dic11—42no—
173(C2×D11)⋊C4—44no—
174(C2×D11)⋊C4—44no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4×Dic11—42no—
181Dic44—216no—
182#4314—216no—
183C22×#137—111no—
184C2×#423D1111yescharacteristic, complemented
185C2×#417—111no—
186C2×#419—111no—
187#2297—111no—
188C2×#391—111no—
189#2056—114no—
190#2055—114no—
191#1736—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11#12112yes—
195C23×C11#12112yes—
196C23×C11#12112yes—
197C23×C11C22×D411yescharacteristic
198C22×D11—22no—
199C22×D11—41no—
200C22×D11—41no—
201C22×D11—42no—
202C22×D11—42no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—48no—
209C2×C4×C11#12014yes—
210C2×C4×C11#12112yes—
211C2×C4×C11#12112yes—
212C2×C4×C11#12112yes—
213C2×C4×C11#12314yes—
214C2×C4×C11#12314yes—
215C2×C4×C11#12414yes—
216C2×C4×C11#13714yescomplemented
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C22⋊D11—48no—
224C2×Dic11—24no—
225C2×Dic11—22no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—48no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—44no—
236C2×Dic11—84no—
237D44—22no—
238D44—22no—
239D44—41no—
240D44—41no—
241C4×D11—48no—
242Dic22—24no—
243Dic22—22no—
244Dic22—24no—
245Dic22—22no—
246Dic22—42no—
247Dic22—41no—
248Dic22—42no—
249Dic22—41no—
250Dic22—48no—
251C8×C11—24no—
252C8×C11—42no—
253C22×#41—111no—
254C23×Q8—111no—
255C2×#137—224no—
256C2×#137—224no—
257C2×#137—224no—
258C22×Q16—112no—
259C22×SD16—112no—
260C22×M16C2×D1111yescharacteristic
261C22×M16C2×D1111yescharacteristic
262C2×#117—111no—
263C22×C4⋊C4—111no—
264C22×C42C2×D1111yescharacteristic
265#423—24no—
266C2×C4⋊C8C2×D1114yes—
267#419—224no—
268#417—224no—
269C2×#103—114no—
270C2×#103—112no—
271C2×#102—112no—
272#391—114no—
273#391—112no—
274#391—221no—
275#391—221no—
276#390—112no—
277#386—222no—
278C4×C22⋊C4—221no—
279C4×C22⋊C4—221no—
280C2×#95—222no—
281#340—114no—
282C22×C11—24no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—24no—
286C22×C11#39414yes—
287C22×C11C2×#12111yescharacteristic
288C22×C11C2×#12111yescharacteristic
289C22×C11C2×#12111yescharacteristic
290C22×C11C2×#13712yes—
291C22×C11#57512yes—
292C2×D11—42no—
293C2×D11—42no—
294C2×D11—42no—
295C2×D11—82no—
296C2×D11—82no—
297C4×C11—24no—
298C4×C11—42no—
299C4×C11#39414yes—
300C4×C11C2×#12011yescharacteristic
301C4×C11C2×#12311yescharacteristic
302C4×C11C2×#12311yescharacteristic
303C4×C11C2×#12411yescharacteristic
304Dic11—44no—
305Dic11—42no—
306Dic11—82no—
307Dic11—82no—
308C2×#41—114no—
309C2×#41—222no—
310C2×#41—222no—
311C2×#41—222no—
312C2×#41—222no—
313C2×#41—222no—
314C22×Q8—114no—
315C22×Q8—112no—
316C22×Q8—111no—
317C22×Q8—221no—
318C22×Q8—222no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×D4—111no—
324C22×D4—221no—
325C23×C4—221no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4D4412yes—
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—22no—
338C2×M16—22no—
339C2×M16—22no—
340C2×M16—22no—
341C2×M16—22no—
342C2×M16C22⋊D1114yes—
343C22×C8C22×D1112yes—
344C22×C8C22×D1112yes—
345#117—222no—
346#117—222no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—221no—
358C2×C42D4411yescharacteristic
359C2×C42D4411yescharacteristic
360C2×C42C22×D1112yes—
361C4⋊C8—28no—
362#103—224no—
363#103—228no—
364#102—224no—
365#95—224no—
366#95—224no—
367#95—222no—
368#95—222no—
369C2×C11—24no—
370C2×C11C2×#39411yescharacteristic
371C2×C11#303712yes—
372C2×C11#303911yescharacteristic
373C2×C11#304011yescharacteristic
374C2×C11#305612yes—
375D11—82no—
376C24—221no—
377C24C2×D4411yescharacteristic
378#41—228no—
379#41—228no—
380#41—444no—
381#41—444no—
382C2×Q8—114no—
383C2×Q8—112no—
384C2×Q8—224no—
385C2×Q8—222no—
386C2×Q8—221no—
387C2×Q8—228no—
388C2×Q8—228no—
389C2×Q8—222no—
390C2×Q8—221no—
391C2×Q8—222no—
392C2×Q8—221no—
393C2×Q8—222no—
394C2×Q8—221no—
395C2×Q8—222no—
396C2×Q8—221no—
397C2×Q8—444no—
398C2×Q8—442no—
399C2×Q8—442no—
400C2×Q8—444no—
401C2×D4—112no—
402C2×D4—224no—
403C2×D4—221no—
404C2×D4—221no—
405C2×D4—221no—
406C2×D4—221no—
407C2×D4—221no—
408C2×D4—442no—
409C2×D4—442no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—42no—
413C22×C4—224no—
414C22×C4—221no—
415C22×C4—222no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—442no—
420C22×C4—442no—
421C22×C4—442no—
422C22×C4—442no—
423C22×C4—444no—
424C22×C4—442no—
425C22×C4C2×D4412yes—
426C22×C4C2×D4412yes—
427C22×C4C2×D4411yescharacteristic
428C22×C4#433912yes—
429C22×C4D4×D1112yes—
430C22×C4D4×D1112yes—
431C22×C4#434312yes—
432C22×C4#434312yes—
433C22×C4C2×C22⋊D1112yes—
434C22×C4C23×D1111yescharacteristic
435Q16—2216no—
436SD16—2216no—
437M16—28no—
438M16—44no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—22no—
444C2×C8C2×C22⋊D1114yes—
445C4⋊C4—222no—
446C4⋊C4—222no—
447C4⋊C4—222no—
448C4⋊C4—222no—
449C4⋊C4—442no—
450C22⋊C4—444no—
451C22⋊C4—442no—
452C22⋊C4—444no—
453C42—22no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—442no—
458C11#2354711yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—222no—
462C23—442no—
463C23—442no—
464C23—441no—
465C23—441no—
466C23#6694812yes—
467C23#6694812yes—
468C23#6698312yes—
469C23C22×D4411yescharacteristic
470Q8—224no—
471Q8—222no—
472Q8—224no—
473Q8—222no—
474Q8—442no—
475Q8—441no—
476Q8—442no—
477Q8—441no—
478Q8—448no—
479D4—222no—
480D4—222no—
481D4—448no—
482D4—441no—
483D4—441no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—48no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—441no—
493C2×C4—442no—
494C2×C4—441no—
495C2×C4—442no—
496C2×C4—448no—
497C2×C4—448no—
498C2×C4—442no—
499C2×C4—442no—
500C2×C4—444no—
501C2×C4—442no—
502C2×C4—442no—
503C2×C4—884no—
504C2×C4#6694714yes—
505C2×C4#6694714yes—
506C2×C4#6694812yes—
507C2×C4#6694812yes—
508C2×C4#6696214yescomplemented
509C2×C4#6698312yes—
510C2×C4#6699014yes—
511C2×C4#6700014yes—
512C2×C4C2×#433911yescharacteristic
513C2×C4C2×D4×D1111yescharacteristic
514C2×C4C2×D4×D1111yescharacteristic
515C2×C4C2×#434311yescharacteristic
516C2×C4C2×#434311yescharacteristic
517C2×C4C22×C22⋊D1111yescharacteristic
518C8—24no—
519C8—42no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—882no—
528C22—882no—
529C22#1062260414yes—
530C22C2×#6694811yescharacteristic
531C22C2×#6694811yescharacteristic
532C22C2×#6696212yes—
533C22#1062327912yes—
534C22C2×#6698311yescharacteristic
535C4—24no—
536C4—42no—
537C4—442no—
538C4—444no—
539C4—882no—
540C4—882no—
541C4#1062260414yes—
542C4C2×#6694711yescharacteristic
543C4C2×#6694711yescharacteristic
544C4C2×#6699011yescharacteristic
545C4C2×#6700011yescharacteristic
546C2—24no—
547C2—882no—
548C2C2×#1062260411yescharacteristic
549C2#1307809012yes—
550C2#1307810411yescharacteristic
551C2#1307811111yescharacteristic
552C2#1307824612yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#423C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenterC2×#423D11
hypocenterC11#23547
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
5. C2×#10622542C2semidirect
6. #13069939C2semidirect
7. #13069934C2semidirect
8. #13068336C2semidirect
9. C2×C11×#423C2semidirect
184. C2×#423D11semidirect
216. C2×C4×C11#137semidirect
458. C11#23547semidirect
508. C2×C4#66962semidirect

Maximal subgroups

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

subgroupindex
C22×#669622
C2×#106227462
C2×#106227332
#130711062
C2×#106225422
#130699392
#130699342
#130683362
C2×C11×#4232
#2354711