Finite Group Databasebeta

← #14805629

Subgroups — #14805629

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic
2C2×C8×Dic22C211yesmaximal, characteristic, complemented
3#13073825C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic
5#13070120C212yesmaximal, complemented
6#13069991C212yesmaximal
7#13069377C211yesmaximal, characteristic, complemented
8#13069343C212yesmaximal, complemented
9#13069297C212yesmaximal
10C4×#66885C211yesmaximal, characteristic
11C11×#1990C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×#66950—21no—
14C2×C4×D44C2211yescharacteristic
15C2×C4×Dic22C2211yescharacteristic
16C2×C4×C8×C11C2211yescharacteristic
17C11×#384C2211yescharacteristic
18#10622842—22no—
19C2×#66885C2211yescharacteristic
20C2×#66885C2211yescharacteristic
21C2×Dic11⋊C8C2212yes—
22C2×C8×Dic11C2212yes—
23#10622697—24no—
24#10622607—22no—
25#10622601C2212yes—
26#10622600—21no—
27#10622598C2212yes—
28#10622589—21no—
29#10622587—21no—
30#10622586C2212yes—
31#10622586C2212yes—
32C2×#66873C2212yes—
33C2×#66872C2212yes—
34C2×#66872C2212yes—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C8×Dic22—24no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2211yescharacteristic
41#10622189C2211yescharacteristic
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11C2311yescharacteristic
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×C4⋊Dic11C2311yescharacteristic
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4D412yes—
68C2×C4×Dic11—21no—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2312yes—
71#66950—44no—
72C4×D44—22no—
73C4×D44—22no—
74C4×Dic22—22no—
75C4×Dic22—22no—
76C4×C8×C11—22no—
77C11⋊#95—21no—
78C11⋊#95—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81#66885—22no—
82#66885Q814yescomplemented
83Dic11⋊C8—24no—
84C8×Dic11—24no—
85#66873—24no—
86#66872—24no—
87#66872—24no—
88C4⋊(C11⋊C8)D414yes—
89#25470—111nomaximal, Sylow
90C23×D11—21no—
91C2×Q8×C11—42no—
92C2×Q8×C11—81no—
93C2×Q8×C11—81no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11C2×D412yes—
103C22×Dic11C2×D412yes—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44C2×Q812yes—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22SD1614yes—
116C2×C8×C11—21no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11C2×Q812yes—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—42no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—81no—
129C42×C11C2×D412yes—
130C42×C11#4112yes—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—42no—
133(C2×D11)⋊C4—82no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—44no—
140C4⋊Dic11C2×Q812yes—
141C4⋊Dic11#4112yes—
142Dic11⋊C4—24no—
143Dic11⋊C4—82no—
144Dic11⋊C4—82no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—42no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8C2×D414yes—
151C2×#476—111no—
152C2×C8×Q8—111no—
153#2567—111no—
154#2538—111no—
155#2088—112no—
156#2065—112no—
157#1990D1111yescharacteristic, complemented
158#1948—111no—
159#1941—112no—
160#1934—112no—
161C4×#102—111no—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—41no—
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170Q8×C11—84no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11#12112yes—
180C2×C4×C11#12112yes—
181C2×C4×C11C2×SD1612yes—
182C2×C4×C11#13512yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×Q811yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C112−1+411yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11C2×SD1614yes—
204D44—22no—
205D44—22no—
206D44—41no—
207D44—41no—
208C4×D11—84no—
209Dic22—28no—
210C8×C11—22no—
211C8×C11—41no—
212C11⋊C8—24no—
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×C22⋊Q8—221no—
215C2×C4×Q8—111no—
216C2×C4×D4—111no—
217#476—224no—
218C8×Q8—224no—
219C2×#106—112no—
220C2×#106—112no—
221C2×C4⋊C8—111no—
222C2×C4⋊C8—112no—
223C2×#102—111no—
224C2×#102—111no—
225C2×#102—112no—
226C2×C4×C8—112no—
227C2×C4×C8C2×D1111yescharacteristic
228#396—222no—
229#395—222no—
230#391—221no—
231#390—112no—
232#389—112no—
233#389—112no—
234#389—112no—
235#384—221no—
236#384C2×D1111yescharacteristic
237#380—221no—
238C4×C4⋊C4—111no—
239#340—111no—
240#340—111no—
241#340—112no—
242#340C2×D1112yes—
243#340C2×D1112yes—
244C22×C11C2×#12111yescharacteristic
245C22×C11#54811yescharacteristic
246C22×C11D4×Q811yescharacteristic
247C22×C11C22×SD1611yescharacteristic
248C22×C11C2×#13511yescharacteristic
249C22×C11#57611yescharacteristic
250C22×C11#57711yescharacteristic
251C2×D11—42no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C4×C11—22no—
259C4×C11—82no—
260C4×C11—82no—
261C4×C11#46514yes—
262C4×C11#53311yescharacteristic
263C4×C11#54111yescharacteristic
264C4×C11#54711yescharacteristic
265C4×C11D4×Q811yescharacteristic
266Dic11—24no—
267Dic11—42no—
268Dic11—42no—
269Dic11—42no—
270Dic11—81no—
271C22×Q8—21no—
272C22×Q8—111no—
273C22×D4—111no—
274C23×C4—221no—
275C22×C8—112no—
276C22×C8C22×D1111yescharacteristic
277C22×C8C22×D1111yescharacteristic
278C4⋊Q8—22no—
279C4⋊Q8—22no—
280C22⋊Q8—444no—
281C4×Q8—222no—
282C4×Q8—222no—
283C4×D4—222no—
284C4×D4—222no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—111no—
290C2×C4⋊C4—111no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4C22×D1112yes—
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—221no—
300C2×C22⋊C4—222no—
301C2×C42—112no—
302C2×C42—221no—
303C2×C42C22×D1111yescharacteristic
304#106—224no—
305#106—224no—
306C4⋊C8—114no—
307C4⋊C8—224no—
308#102—114no—
309#102—224no—
310#102—222no—
311C4×C8—22no—
312C4×C8—224no—
313#95—222no—
314#95—222no—
315#95—222no—
316#95—221no—
317C2×C11#242911yescharacteristic
318C2×C11C2×#46511yescharacteristic
319C2×C11#306211yescharacteristic
320C2×C11#336011yescharacteristic
321C2×C11#336211yescharacteristic
322C2×C11Q8×SD1611yescharacteristic
323C2×C11#338011yescharacteristic
324D11—82no—
325C24—221no—
326C2×Q8—42no—
327C2×Q8—81no—
328C2×Q8—81no—
329C2×Q8—114no—
330C2×Q8—222no—
331C2×Q8—222no—
332C2×D4—112no—
333C2×D4—221no—
334C2×D4—221no—
335C2×D4—221no—
336C2×D4—221no—
337C2×D4—221no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—112no—
341C22×C4—112no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—442no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4D4×D1111yescharacteristic
349C22×C4D4×D1111yescharacteristic
350C22×C4C23×D1111yescharacteristic
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—114no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8Q8×D1112yes—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—42no—
365C4⋊C4—42no—
366C4⋊C4—81no—
367C4⋊C4—112no—
368C4⋊C4—112no—
369C4⋊C4—224no—
370C4⋊C4—222no—
371C4⋊C4—221no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4—221no—
375C4⋊C4—444no—
376C4⋊C4—882no—
377C4⋊C4—882no—
378C22⋊C4—444no—
379C22⋊C4—442no—
380C22⋊C4—882no—
381C42—222no—
382C42—222no—
383C42—442no—
384C42#433912yes—
385C42D4×D1112yes—
386C11#2547011yescharacteristic, complemented, Sylow
387C23—222no—
388C23—441no—
389C23—441no—
390C23—441no—
391C23—441no—
392C23—441no—
393C23—441no—
394C23C2×D4×D1111yescharacteristic
395Q8—84no—
396Q8—228no—
397D4—222no—
398D4—222no—
399D4—441no—
400D4—441no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—114no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—884no—
425C2×C4#6693712yes—
426C2×C4#6693712yes—
427C2×C4SD16×D1112yes—
428C2×C4#6697212yes—
429C2×C4C2×#433911yescharacteristic
430C2×C4C2×D4×D1111yescharacteristic
431C2×C4C2×Q8×D1111yescharacteristic
432C2×C4#6704011yescharacteristic
433C2×C4#41×D1111yescharacteristic
434C2×C4#6704311yescharacteristic
435C8—22no—
436C8—41no—
437C8—224no—
438C22—442no—
439C22—442no—
440C22—442no—
441C22—881no—
442C22—881no—
443C22—881no—
444C22—881no—
445C22C2×#6693711yescharacteristic
446C22#1062320811yescharacteristic
447C22#1062325811yescharacteristic
448C22#1062328811yescharacteristic
449C22C2×SD16×D1111yescharacteristic
450C22#1062329311yescharacteristic
451C22C2×#6697211yescharacteristic
452C4—22no—
453C4—82no—
454C4—82no—
455C4—224no—
456C4—442no—
457C4—442no—
458C4—442no—
459C4—881no—
460C4#1062242014yes—
461C4#1062310911yescharacteristic
462C4#1062311411yescharacteristic
463C4#1062316211yescharacteristic
464C4#1062316311yescharacteristic
465C2—882no—
466C2#1307221611yescharacteristic
467C2C2×#1062242011yescharacteristic
468C2#1307829411yescharacteristic
469C2#1308127011yescharacteristic
470C2#1308128411yescharacteristic
471C2#1308147311yescharacteristic
472C2#1308148511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1990D11
hypocenterC11#25470
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×C8×Dic22C2semidirect
3. #13073825C2semidirect
5. #13070120C2semidirect
7. #13069377C2semidirect
8. #13069343C2semidirect
11. C11×#1990C2semidirect
82. #66885Q8semidirect
157. #1990D11semidirect
386. C11#25470semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×C8×Dic222
#130738252
#130735392
#130701202
#130699912
#130693772
#130693432
#130692972
C4×#668852
C11×#19902
#2547011