Finite Group Databasebeta

← #14803911

Subgroups — #14803911

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622464C211yesmaximal, characteristic, complemented
2#13073608C211yesmaximal, characteristic
3#13073538C211yesmaximal, characteristic
4#13070049C212yesmaximal, complemented
5#13069813C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069380C211yesmaximal, characteristic, complemented
8#13069039C212yesmaximal, complemented
9#13068641C212yesmaximal, complemented
10C4×#66880C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic
12C23×C8×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66989—21no—
15C2×#66977C2212yes—
16C2×#66922C2211yescharacteristic
17C2×C4×Dic22C2211yescharacteristic
18C8×D4×C11—24no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2212yes—
21C2×C4×C8×C11C2211yescharacteristic
22#10622834—21no—
23#10622825C2212yes—
24#10622825C2212yes—
25#10622825C2212yes—
26C2×#66881C2212yes—
27C2×#66881C2212yes—
28C2×#66880C2212yes—
29C2×#66880C2211yescharacteristic
30C2×#66880C2211yescharacteristic
31#10622587—21no—
32#10622586—21no—
33#10622566—22no—
34#10622561—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37#10622464—24no—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43C22×D4×C11D411yescharacteristic
44C23×C4×C11C2312yes—
45C22×Dic22—21no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11—24no—
48C22×C8×C11—24no—
49C22×C8×C11—42no—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2312yes—
52C22×C8×C11C2311yescharacteristic
53C4×D4×C11—22no—
54C4×D4×C11—22no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4D412yes—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59C2×C22⋊Dic11—22no—
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62#66989—44no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2312yes—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71#66977—24no—
72#66977—42no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77#66922—22no—
78#66922—22no—
79C4×Dic22—22no—
80C4×Dic22—22no—
81C11×C4⋊C8D414yes—
82C11×C22⋊C8—24no—
83C4×C8×C11—22no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66881—24no—
89#66881—42no—
90#66880—22no—
91#66880—24no—
92#66880—22no—
93#25341—111nomaximal, Sylow
94C24×C11C2×D412yes—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11SD1614yes—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2411yescharacteristic
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C2×Dic22—21no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—42no—
120C2×Dic22—42no—
121C2×Dic22—42no—
122C2×Dic22#4112yes—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—21no—
130C2×C8×C11—48no—
131C2×C8×C11C2×D414yes—
132C2×C8×C11#4112yes—
133C11×C4⋊C4—22no—
134C11×C22⋊C4—24no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137C22⋊Dic11—44no—
138C22⋊Dic11—44no—
139C22⋊Dic11—44no—
140C22⋊Dic11—82no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—21no—
149C4⋊Dic11—22no—
150C4⋊Dic11—21no—
151C4⋊Dic11—42no—
152C4⋊Dic11—42no—
153C4⋊Dic11—81no—
154Dic11⋊C4—44no—
155Dic11⋊C4—42no—
156C4×Dic11—42no—
157C4×Dic11—42no—
158C2×#475—111no—
159C2×C8×D4D1111yescharacteristic
160#2547—111no—
161#2538—111no—
162#2077—112no—
163#2035—112no—
164#1990—111no—
165#1948—111no—
166#1892—112no—
167#1807—112no—
168C4×#103—111no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11—22no—
175C23×C11C2×SD1614yes—
176C23×C11C22×D411yescharacteristic
177D4×C11—28no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11#12112yes—
188C2×C4×C11#12112yes—
189C2×C4×C11C2×SD1612yes—
190C2×C4×C11#13512yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C112−1+411yescharacteristic
197C2×Dic11—22no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215Dic22—22no—
216Dic22—22no—
217Dic22—41no—
218Dic22—41no—
219Dic22—84no—
220C8×C11—22no—
221C8×C11—24no—
222C8×C11—41no—
223C23×C8C2×D1112yes—
224C2×C4⋊Q8—111no—
225C2×#124—221no—
226C2×C22⋊Q8—112no—
227C2×C4×Q8—111no—
228C2×C4×D4C2×D1111yescharacteristic
229#475—224no—
230C8×D4—24no—
231C2×#106—112no—
232C2×#106—112no—
233C2×C4⋊C8C2×D1111yescharacteristic
234C2×#103—112no—
235C2×#103—111no—
236C2×#103—111no—
237C2×C22⋊C8C2×D1112yes—
238C2×C4×C8C2×D1111yescharacteristic
239#397—222no—
240#396—222no—
241#391—221no—
242#390—221no—
243#389—221no—
244#384—111no—
245#380—112no—
246#380—112no—
247#380—112no—
248C4×C4⋊C4—111no—
249#340—111no—
250#340—112no—
251#340—111no—
252#340—112no—
253#340—112no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—24no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C2×#12111yescharacteristic
262C22×C11#54611yescharacteristic
263C22×C11#54711yescharacteristic
264C22×C11C22×SD1611yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C22×C11#57711yescharacteristic
267C22×C11#57811yescharacteristic
268C4×C11—22no—
269C4×C11—42no—
270C4×C11#46514yes—
271C4×C11#52911yescharacteristic
272C4×C11#54211yescharacteristic
273C4×C11#54611yescharacteristic
274C4×C11#54811yescharacteristic
275Dic11—42no—
276Dic11—81no—
277Dic11—81no—
278Dic11—82no—
279Dic11—82no—
280Dic11—81no—
281C22×Q8—111no—
282C22×Q8—221no—
283C22×D4D4411yescharacteristic
284C23×C4C22×D1112yes—
285C22×C8—24no—
286C22×C8—24no—
287C22×C8—42no—
288C22×C8C22×D1111yescharacteristic
289C22×C8C22×D1111yescharacteristic
290C22×C8C22×D1112yes—
291C4⋊Q8—222no—
292C4⋊Q8—222no—
293#124—444no—
294C22⋊Q8—224no—
295C22⋊Q8—442no—
296C4×Q8—222no—
297C4×Q8—222no—
298C4×D4—22no—
299C4×D4—22no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4D4411yescharacteristic
311C2×C22⋊C4—222no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4D4412yes—
316C2×C42—221no—
317C2×C42—221no—
318C2×C42C22×D1111yescharacteristic
319#106—224no—
320#106—442no—
321C4⋊C8C22⋊D1114yes—
322#103—222no—
323#103—222no—
324#103—224no—
325C22⋊C8—24no—
326C4×C8—22no—
327#95—221no—
328#95—222no—
329#95—222no—
330#95—222no—
331C2×C11—44no—
332C2×C11#242711yescharacteristic
333C2×C11C2×#46511yescharacteristic
334C2×C11#306311yescharacteristic
335C2×C11#329811yescharacteristic
336C2×C11#330411yescharacteristic
337C2×C11#333511yescharacteristic
338C2×C11#334211yescharacteristic
339C24C2×D4412yes—
340C2×Q8—112no—
341C2×Q8—221no—
342C2×Q8—221no—
343C2×Q8—221no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8—442no—
347C2×Q8—442no—
348C2×Q8—442no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4#431414yes—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4C2×D4412yes—
365C22×C4C2×D4411yescharacteristic
366C22×C4C2×D4411yescharacteristic
367C22×C4C23×D1111yescharacteristic
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—48no—
376C2×C8#434112yes—
377C2×C8C2×C22⋊D1114yes—
378C4⋊C4—22no—
379C4⋊C4—221no—
380C4⋊C4—222no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—221no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—444no—
390C4⋊C4—442no—
391C4⋊C4—442no—
392C4⋊C4—442no—
393C4⋊C4—881no—
394C22⋊C4—24no—
395C22⋊C4—444no—
396C22⋊C4—444no—
397C22⋊C4—444no—
398C22⋊C4—882no—
399C42—442no—
400C42—442no—
401C42#433912yes—
402C42C2×C22⋊D1112yes—
403C11#2534111yescharacteristic, complemented, Sylow
404C23—22no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23C2×#431414yes—
411C23C22×D4411yescharacteristic
412Q8—222no—
413Q8—222no—
414Q8—441no—
415Q8—441no—
416Q8—884no—
417D4—28no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—222no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4C2×#431412yes—
446C2×C4#6695712yes—
447C2×C4#6698312yes—
448C2×C4#6698312yes—
449C2×C4C2×#433911yescharacteristic
450C2×C4C2×#434111yescharacteristic
451C2×C4#6703711yescharacteristic
452C2×C4#41×D1111yescharacteristic
453C2×C4#6704311yescharacteristic
454C2×C4C22×C22⋊D1111yescharacteristic
455C8—22no—
456C8—24no—
457C8—41no—
458C22—24no—
459C22—24no—
460C22—24no—
461C22—42no—
462C22—42no—
463C22—42no—
464C22—42no—
465C22#1062308511yescharacteristic
466C22#1062308611yescharacteristic
467C22C22×#431411yescharacteristic
468C22C2×#6695711yescharacteristic
469C22#1062328211yescharacteristic
470C22#1062328411yescharacteristic
471C22C2×#6698311yescharacteristic
472C4—22no—
473C4—42no—
474C4—442no—
475C4—881no—
476C4—881no—
477C4—882no—
478C4—881no—
479C4—882no—
480C4#1062272714yes—
481C4#1062308811yescharacteristic
482C4#1062309211yescharacteristic
483C4#1062333711yescharacteristic
484C4#1062336211yescharacteristic
485C2—44no—
486C2#1307218711yescharacteristic
487C2C2×#1062272711yescharacteristic
488C2#1307830711yescharacteristic
489C2#1308048211yescharacteristic
490C2#1308055611yescharacteristic
491C2#1308097411yescharacteristic
492C2#1308104711yescharacteristic
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#25341
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×#10622464C2semidirect
4. #13070049C2semidirect
5. #13069813C2semidirect
6. #13069577C2semidirect
7. #13069380C2semidirect
8. #13069039C2semidirect
9. #13068641C2semidirect
10. C4×#66880C2semidirect
403. C11#25341semidirect

Maximal subgroups

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

subgroupindex
C2×#106224642
#130736082
#130735382
#130700492
#130698132
#130695772
#130693802
#130690392
#130686412
C4×#668802
C2×C8×D4×C112
#2534111