Finite Group Databasebeta

← #14804510

Subgroups — #14804510

Order 2816.

1018 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622729C212yesmaximal, complemented
2C2×#10622462C211yesmaximal, characteristic, complemented
3#13073569C211yesmaximal, characteristic
4#13073538C211yesmaximal, characteristic
5#13069820C212yesmaximal, complemented
6#13069626C212yesmaximal, complemented
7#13069418C211yesmaximal, characteristic, complemented
8#13069375C211yesmaximal, characteristic, complemented
9#13069039C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic
12C23×C8×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66977C2212yes—
15C2×#66977C2212yes—
16C2×#66977C2212yes—
17C22×Dic44C2212yes—
18C2×#66922C2211yescharacteristic
19C2×C4×Dic22C2211yescharacteristic
20C8×D4×C11—24no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2212yes—
23C2×C4×C8×C11C2211yescharacteristic
24#10622834—21no—
25#10622834—21no—
26#10622825C2212yes—
27#10622729—28no—
28C2×#66882C2212yes—
29C2×#66880C2212yes—
30C2×#66880C2211yescharacteristic
31C2×#66880C2212yes—
32C2×#66880C2212yes—
33C2×#66880C2211yescharacteristic
34#10622589—21no—
35#10622586—21no—
36#10622562—22no—
37#10622561—22no—
38#10622548C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622462—24no—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×Dic22C2312yes—
47C22×Dic22C2311yescharacteristic
48C22×C8×C11—24no—
49C22×C8×C11—24no—
50C22×C8×C11—42no—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2312yes—
53C22×C8×C11C2311yescharacteristic
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4D412yes—
58C2×C42×C11C2311yescharacteristic
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71#66977—24no—
72#66977—24no—
73#66977—24no—
74#66977—42no—
75#66977—42no—
76#66977—42no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×Dic44—24no—
84C2×Dic44—24no—
85C2×Dic44—42no—
86#66922—22no—
87#66922—22no—
88C4×Dic22—22no—
89C4×Dic22—22no—
90C11×C4⋊C8D414yes—
91C11×C22⋊C8—24no—
92C4×C8×C11—22no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95#66882—24no—
96#66880—24no—
97#66880—24no—
98#66880—22no—
99#66880—42no—
100#66880D414yescomplemented
101#25386—111nomaximal, Sylow
102C24×C11C2×D412yes—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11Q1614yescomplemented
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C2×Dic22—21no—
123C2×Dic22—22no—
124C2×Dic22—22no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22—22no—
132C2×Dic22—22no—
133C2×Dic22C2×D412yes—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—22no—
139C2×C8×C11—21no—
140C2×C8×C11—21no—
141C2×C8×C11—48no—
142C2×C8×C11C2×D412yes—
143C2×C8×C11C2×D414yes—
144C11×C4⋊C4—22no—
145C11×C22⋊C4—24no—
146C42×C11C2×D412yes—
147C42×C11#4112yes—
148C22⋊Dic11—44no—
149C22⋊Dic11—44no—
150C22⋊Dic11—44no—
151C22⋊Dic11—82no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11—42no—
159C4⋊Dic11—42no—
160C4⋊Dic11—42no—
161C4⋊Dic11—81no—
162C4⋊Dic11C2×D412yes—
163C4⋊Dic11#4112yes—
164Dic11⋊C4—44no—
165Dic11⋊C4—44no—
166Dic11⋊C4—44no—
167Dic11⋊C4—42no—
168C4×Dic11—42no—
169C4×Dic11—42no—
170Dic44—48no—
171C2×#467—112no—
172C2×#462—111no—
173C2×C8×D4D1111yescharacteristic
174#2542—111no—
175#2538—111no—
176#2036—112no—
177#2001—112no—
178#1956—111no—
179#1947—111no—
180#1892—112no—
181C4×#103—111no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11C2×Q1614yes—
189C23×C11C22×D411yescharacteristic
190D4×C11—28no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11#12112yes—
201C2×C4×C11#12112yes—
202C2×C4×C11C2×Q1612yes—
203C2×C4×C11#13512yes—
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228Dic22—22no—
229Dic22—22no—
230Dic22—41no—
231Dic22—41no—
232Dic22—42no—
233Dic22—42no—
234Dic22—42no—
235Dic22—42no—
236C8×C11—24no—
237C8×C11—22no—
238C8×C11—41no—
239C22×Q16—112no—
240C23×C8C2×D1112yes—
241C2×C4⋊Q8—111no—
242C2×C22⋊Q8—112no—
243C2×C22⋊Q8—112no—
244C2×C22⋊Q8—112no—
245C2×C4×Q8—111no—
246C2×C4×D4C2×D1111yescharacteristic
247#467—228no—
248#462—224no—
249C8×D4—24no—
250C2×#107—112no—
251C2×C4⋊C8C2×D1111yescharacteristic
252C2×#103—111no—
253C2×#103—112no—
254C2×#103—112no—
255C2×#103—111no—
256C2×#103—112no—
257C2×C22⋊C8C2×D1112yes—
258C2×C4×C8C2×D1111yescharacteristic
259#399—222no—
260#396—222no—
261#390—221no—
262#390—221no—
263#389—221no—
264#384—111no—
265#384—221no—
266#380—112no—
267C4×C4⋊C4—111no—
268#340—111no—
269#340—112no—
270#340—111no—
271C22×C11—24no—
272C22×C11—24no—
273C22×C11—24no—
274C22×C11—42no—
275C22×C11—42no—
276C22×C11—42no—
277C22×C11—42no—
278C22×C11C2×#12111yescharacteristic
279C22×C11D4211yescharacteristic
280C22×C11#54611yescharacteristic
281C22×C11C22×Q1611yescharacteristic
282C22×C11C2×#13511yescharacteristic
283C22×C11#57711yescharacteristic
284C22×C11#57811yescharacteristic
285C4×C11—22no—
286C4×C11—42no—
287C4×C11#46714yescomplemented
288C4×C11#53211yescharacteristic
289C4×C11#54011yescharacteristic
290C4×C11D4211yescharacteristic
291C4×C11#55011yescharacteristic
292Dic11—42no—
293Dic11—42no—
294Dic11—42no—
295Dic11—82no—
296Dic11—82no—
297Dic11—81no—
298C22×Q8—111no—
299C22×Q8—112no—
300C22×D4D4411yescharacteristic
301C23×C4C22×D1112yes—
302C2×Q16—224no—
303C2×Q16—224no—
304C2×Q16—442no—
305C22×C8—24no—
306C22×C8—24no—
307C22×C8—42no—
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1111yescharacteristic
310C22×C8C22×D1112yes—
311C4⋊Q8—222no—
312C4⋊Q8—222no—
313C22⋊Q8—224no—
314C22⋊Q8—224no—
315C22⋊Q8—224no—
316C22⋊Q8—442no—
317C22⋊Q8—442no—
318C22⋊Q8—442no—
319C4×Q8—222no—
320C4×Q8—222no—
321C4×D4—22no—
322C4×D4—22no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—111no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—222no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—221no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4D4411yescharacteristic
336C2×C22⋊C4—222no—
337C2×C22⋊C4—222no—
338C2×C22⋊C4—222no—
339C2×C22⋊C4—222no—
340C2×C22⋊C4D4412yes—
341C2×C42—221no—
342C2×C42—221no—
343C2×C42C22×D1111yescharacteristic
344#107—224no—
345C4⋊C8C22⋊D1114yes—
346#103—114no—
347#103—222no—
348#103—224no—
349#103—224no—
350#103—442no—
351C22⋊C8—24no—
352C4×C8—22no—
353#95—221no—
354#95—222no—
355C2×C11—44no—
356C2×C11#242811yescharacteristic
357C2×C11C2×#46711yescharacteristic
358C2×C11#306311yescharacteristic
359C2×C11#328411yescharacteristic
360C2×C11D4×Q1611yescharacteristic
361C2×C11#329911yescharacteristic
362C2×C11#330211yescharacteristic
363C24C2×D4412yes—
364C2×Q8—112no—
365C2×Q8—221no—
366C2×Q8—221no—
367C2×Q8—222no—
368C2×Q8—222no—
369C2×Q8—221no—
370C2×Q8—222no—
371C2×Q8—221no—
372C2×Q8—222no—
373C2×Q8—222no—
374C2×Q8—221no—
375C2×Q8—222no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4Dic4414yescomplemented
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4C2×D4412yes—
392C22×C4C2×D4411yescharacteristic
393C22×C4C2×D4411yescharacteristic
394C22×C4C23×D1111yescharacteristic
395Q16—448no—
396C2×C8—22no—
397C2×C8—21no—
398C2×C8—22no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—48no—
404C2×C8D4×D1112yes—
405C2×C8C2×C22⋊D1114yes—
406C4⋊C4—22no—
407C4⋊C4—112no—
408C4⋊C4—112no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—222no—
414C4⋊C4—221no—
415C4⋊C4—444no—
416C4⋊C4—444no—
417C4⋊C4—444no—
418C4⋊C4—442no—
419C4⋊C4—442no—
420C4⋊C4—442no—
421C4⋊C4—442no—
422C4⋊C4—881no—
423C22⋊C4—24no—
424C22⋊C4—444no—
425C22⋊C4—444no—
426C22⋊C4—444no—
427C22⋊C4—882no—
428C42—442no—
429C42—442no—
430C42#433912yes—
431C42C2×C22⋊D1112yes—
432C11#2538611yescharacteristic, complemented, Sylow
433C23—22no—
434C23—22no—
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23C2×Dic4414yes—
440C23C22×D4411yescharacteristic
441Q8—222no—
442Q8—222no—
443Q8—441no—
444Q8—441no—
445Q8—442no—
446Q8—442no—
447Q8—442no—
448Q8—442no—
449D4—28no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—222no—
460C2×C4—222no—
461C2×C4—222no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—442no—
469C2×C4—441no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—442no—
477C2×C4#6695712yes—
478C2×C4C2×Dic4412yes—
479C2×C4#6698312yes—
480C2×C4#6698312yes—
481C2×C4C2×#433911yescharacteristic
482C2×C4C2×D4×D1111yescharacteristic
483C2×C4#6703711yescharacteristic
484C2×C4#41×D1111yescharacteristic
485C2×C4#6704211yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—22no—
488C8—24no—
489C8—41no—
490C22—24no—
491C22—24no—
492C22—24no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—42no—
497C22D4×D4411yescharacteristic
498C22#1062308511yescharacteristic
499C22C2×#6695711yescharacteristic
500C22C22×Dic4411yescharacteristic
501C22#1062328211yescharacteristic
502C22#1062328411yescharacteristic
503C22C2×#6698311yescharacteristic
504C4—22no—
505C4—42no—
506C4—442no—
507C4—442no—
508C4—442no—
509C4—882no—
510C4—881no—
511C4—882no—
512C4#1062272914yescomplemented
513C4#1062307911yescharacteristic
514C4#1062309311yescharacteristic
515C4D4×C22⋊D1111yescharacteristic
516C4#1062336511yescharacteristic
517C2—44no—
518C2#1307219811yescharacteristic
519C2C2×#1062272911yescharacteristic
520C2#1307830711yescharacteristic
521C2#1308034811yescharacteristic
522C2D4×Dic4411yescharacteristic
523C2#1308049311yescharacteristic
524C2#1308053411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×C8×D4D11
hypocenterC11#25386
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622729C2semidirect
2. C2×#10622462C2semidirect
5. #13069820C2semidirect
6. #13069626C2semidirect
7. #13069418C2semidirect
8. #13069375C2semidirect
9. #13069039C2semidirect
10. C4×#66880C2semidirect
100. #66880D4semidirect
105. C2×D4×C11Q16semidirect
287. C4×C11#467semidirect
378. C2×D4Dic44semidirect
432. C11#25386semidirect
512. C4#10622729semidirect

Maximal subgroups

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

subgroupindex
C2×#106227292
C2×#106224622
#130735692
#130735382
#130698202
#130696262
#130694182
#130693752
#130690392
C4×#668802
C2×C8×D4×C112
#2538611