Finite Group Databasebeta

← #14781789

Subgroups — #14781789

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×#10622731C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic
4C2×#10622617C211yesmaximal, characteristic, complemented
5#13071104C211yesmaximal, characteristic
6C2×#10622587C211yesmaximal, characteristic, complemented
7#13069940C214yesmaximal, complemented
8#13069935C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C4×Dic11C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C2×#66962—24no—
18C2×#66962—24no—
19C2×#66962—24no—
20C22×Dic44C2212yes—
21C22×#4314C2212yes—
22C2×C11⋊#95—22no—
23#10622731—24no—
24C2×Dic11⋊C8C2214yes—
25#10622617—24no—
26#10622601C2212yes—
27#10622587—21no—
28#10622587—21no—
29#10622587C2212yes—
30#10622587C2214yes—
31C2×#66874C2214yes—
32C2×#66874C2212yes—
33#10622579—24no—
34C2×#66873C2212yes—
35#10622571—22no—
36C4×(C2×D11)⋊C4—21no—
37C4×(C2×D11)⋊C4—21no—
38C11×#340C2214yes—
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—21no—
42C23×Dic11—21no—
43C23×Dic11D412yes—
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×M16D414yes—
64C22×C8×C11C2312yes—
65C11×#117—22no—
66C11×#117—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11C2312yes—
81C2×#4318—22no—
82C2×#4318—22no—
83C2×#4318—22no—
84C22×C11⋊C8C2312yes—
85#66962—232no—
86C2×Dic44—24no—
87C2×Dic44—24no—
88C2×Dic44—24no—
89C2×#4314—24no—
90C2×#4314—24no—
91C2×#4314—24no—
92C11⋊#95—22no—
93C11⋊#95—22no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96Dic11⋊C8—28no—
97#66874—24no—
98#66874—28no—
99#66873—24no—
100#23547—111nomaximal, Sylow
101C24×C11C2×D411yescharacteristic
102C23×D11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—44no—
106C22×C4×C11—42no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4112yes—
112C22×C4×C11#4112yes—
113C22×C4×C11#4112yes—
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—24no—
116C2×C22⋊D11—42no—
117C2×C22⋊D11—42no—
118C22×Dic11—24no—
119C22×Dic11—24no—
120C22×Dic11—24no—
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C22×Dic11C2×D412yes—
127C22×Dic11C2×D412yes—
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—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11C2×D414yes—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—42no—
169C11×C22⋊C4—42no—
170C42×C11—42no—
171(C2×D11)⋊C4—44no—
172(C2×D11)⋊C4—44no—
173C4×Dic11—22no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177#4318—44no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181Dic44—216no—
182#4314—216no—
183C22×#137—111no—
184C2×#423—111no—
185C2×#417—111no—
186C2×#419—111no—
187#2297—111no—
188C2×#391—111no—
189#2056—114no—
190#2055—114no—
191#1736D1111yescharacteristic, complemented
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—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—44no—
208C2×C4×C11—84no—
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×C11C22×D411yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4111yescharacteristic
220C2×C4×C11C2×#4111yescharacteristic
221C2×C4×C11C2×#4111yescharacteristic
222C22⋊D11—48no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—48no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—41no—
234C2×Dic11—41no—
235C2×Dic11—48no—
236C2×Dic11#13714yescomplemented
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—
252C11⋊C8—42no—
253C22×#41—111no—
254C23×Q8—111no—
255C2×#137—224no—
256C2×#137—224no—
257C2×#137—224no—
258C22×Q16—112no—
259C22×SD16—112no—
260C22×M16—111no—
261C22×M16C2×D1111yescharacteristic
262C2×#117C2×D1111yescharacteristic
263C22×C4⋊C4C2×D1111yescharacteristic
264C22×C42—111no—
265#423—224no—
266C2×C4⋊C8—114no—
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#340C2×D1114yes—
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—82no—
298C4×C11—82no—
299C4×C11#39414yes—
300C4×C11C2×#12011yescharacteristic
301C4×C11C2×#12311yescharacteristic
302C4×C11C2×#12311yescharacteristic
303C4×C11C2×#12411yescharacteristic
304Dic11—24no—
305Dic11—44no—
306Dic11—42no—
307Dic11—42no—
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—222no—
318C22×Q8—221no—
319C22×Q8—222no—
320C22×Q8—222no—
321C22×Q8—222no—
322C22×Q8—222no—
323C22×D4—111no—
324C22×D4—221no—
325C23×C4—21no—
326C23×C4—112no—
327C23×C4—221no—
328C23×C4—221no—
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—222no—
340C2×M16—222no—
341C2×M16—222no—
342C2×M16D4414yes—
343C22×C8—112no—
344C22×C8C22×D1112yes—
345#117—22no—
346#117—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4C22×D1112yes—
351C2×C4⋊C4C22×D1112yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—222no—
354C2×C22⋊C4—222no—
355C2×C42—21no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—112no—
359C2×C42—222no—
360C2×C42—222no—
361C4⋊C8—228no—
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—
377C24D4×D1111yescharacteristic
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—444no—
400C2×Q8—442no—
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—22no—
411C22×C4—22no—
412C22×C4—44no—
413C22×C4—42no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—224no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—442no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4—442no—
427C22×C4C2×D4412yes—
428C22×C4#433912yes—
429C22×C4#433912yes—
430C22×C4D4×D1112yes—
431C22×C4D4×D1112yes—
432C22×C4D4×D1111yescharacteristic
433C22×C4#434312yes—
434C22×C4C23×D1111yescharacteristic
435Q16—2216no—
436SD16—2216no—
437M16—28no—
438M16—444no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—222no—
442C2×C8—222no—
443C2×C8—222no—
444C2×C8C2×D4414yes—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C22⋊C4—42no—
451C22⋊C4—444no—
452C22⋊C4—444no—
453C42—42no—
454C42—222no—
455C42—222no—
456C42—222no—
457C42—222no—
458C11#2354711yescharacteristic, complemented, Sylow
459C23—22no—
460C23—22no—
461C23—222no—
462C23—441no—
463C23—441no—
464C23—442no—
465C23—442no—
466C23#6693712yes—
467C23#6693712yes—
468C23#6694812yes—
469C23C2×D4×D1111yescharacteristic
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—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—84no—
490C2×C4—114no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—448no—
499C2×C4—441no—
500C2×C4—442no—
501C2×C4—441no—
502C2×C4—442no—
503C2×C4—448no—
504C2×C4—448no—
505C2×C4#6692814yes—
506C2×C4#6693514yes—
507C2×C4#6693712yes—
508C2×C4#6693712yes—
509C2×C4#6694714yes—
510C2×C4#6694714yes—
511C2×C4#6694812yes—
512C2×C4C22×D4411yescharacteristic
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×#433911yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4C2×#434311yescharacteristic
518C8—24no—
519C8—442no—
520C22—24no—
521C22—22no—
522C22—22no—
523C22—24no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—882no—
528C22—882no—
529C22#1062228514yes—
530C22C2×#6693711yescharacteristic
531C22C2×#6693711yescharacteristic
532C22C2×#6694811yescharacteristic
533C22#1062330412yes—
534C22D11×#13712yes—
535C4—82no—
536C4—82no—
537C4—224no—
538C4—442no—
539C4—444no—
540C4—442no—
541C4#1062228514yes—
542C4C2×#6692811yescharacteristic
543C4C2×#6693511yescharacteristic
544C4C2×#6694711yescharacteristic
545C4C2×#6694711yescharacteristic
546C2—24no—
547C2—882no—
548C2C2×#1062228511yescharacteristic
549C2#1307808712yes—
550C2#1307810211yescharacteristic
551C2#1307810911yescharacteristic
552C2#1307824712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#1736D11
hypocenterC11#23547
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10622731C2semidirect
4. C2×#10622617C2semidirect
6. C2×#10622587C2semidirect
7. #13069940C2semidirect
8. #13069935C2semidirect
9. C11×#1736C2semidirect
191. #1736D11semidirect
236. C2×Dic11#137semidirect
458. C11#23547semidirect

Maximal subgroups

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

subgroupindex
C22×#669622
C2×#106227312
C2×#106225792
C2×#106226172
#130711042
C2×#106225872
#130699402
#130699352
C11×#17362
#2354711