Finite Group Databasebeta

← #14772197

Subgroups — #14772197

Order 2816.

986 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622371C212yesmaximal
2C2×C4×#4324C211yesmaximal, characteristic
3#13071533C211yesmaximal, characteristic, complemented
4#13071526C211yesmaximal, characteristic
5#13069343C212yesmaximal, complemented
6#13068871C212yesmaximal, complemented
7#13068861C212yesmaximal
8#13068778C211yesmaximal, characteristic, complemented
9#13068632C211yesmaximal, characteristic, complemented
10#13068481C211yesmaximal, characteristic, complemented
11C11×#1804C211yesmaximal, characteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C2212yes—
14C22×#4324C2211yescharacteristic
15C2×#66940C2212yes—
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102C2212yes—
19C11×#382C2211yescharacteristic
20C2×#66896C2211yescharacteristic
21#10622825—21no—
22C2×C11⋊#95—21no—
23C2×#66880C2212yes—
24C2×C8×Dic11C2212yes—
25C4×#4324C418yescomplemented
26#10622598C2212yes—
27#10622586C2212yes—
28C2×#66874C2211yescharacteristic
29C2×#66872C2212yes—
30C2×#66872C2211yescharacteristic
31C2×#66871C2212yes—
32#10622563—22no—
33#10622549C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622371—28no—
37#10622263—21no—
38#10622262—21no—
39#10622260—22no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×Dic11—22no—
46C22×Dic22C2311yescharacteristic
47C22×C8×C11C2312yes—
48C4×D4×C11—22no—
49C4×D4×C11C2×C414yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2311yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55D4×Dic11—24no—
56D4×Dic11—42no—
57C2×#4324C2×C414yes—
58C2×#4324D414yes—
59C2×#4324Q814yes—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11D412yes—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72#66940—24no—
73#66940—42no—
74C4×Dic22—22no—
75C4×Dic22C2×C414yescomplemented
76C11×C4⋊C8—22no—
77C11×#102—24no—
78C11×#95—21no—
79C11×#95—21no—
80#66896C2×C414yes—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95D411yescharacteristic
86C11⋊#95D411yescharacteristic
87#66880—24no—
88C8×Dic11—24no—
89#66874C2×C414yescomplemented
90#66872—24no—
91#66872C2×C414yescomplemented
92#66871—42no—
93C4×C11⋊C8C2×C414yescomplemented
94#22683—111nomaximal, Sylow
95C24×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11C22×C412yes—
100C2×D4×C11C2×D412yes—
101C2×D4×C11C2×Q812yes—
102C22×C4×C11—21no—
103C22×C4×C11—24no—
104C22×C4×C11—22no—
105C22×C4×C11—82no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—44no—
113C22×Dic11—44no—
114C22×Dic11—82no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22C22×C412yes—
121C2×Dic22C2×D412yes—
122C2×Dic22C2×Q812yes—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4C22×C412yes—
130C11×C22⋊C4—24no—
131C42×C11C22×C412yes—
132C42×C11#4112yes—
133C22⋊Dic11—44no—
134#4324C4⋊C4116yescomplemented
135C4⋊Dic11—24no—
136C4⋊Dic11—22no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11—82no—
140C4⋊Dic11C22×C412yes—
141Dic11⋊C4—24no—
142Dic11⋊C4—44no—
143Dic11⋊C4—44no—
144C4×Dic11—24no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—44no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C22×C412yes—
151C2×C11⋊C8C22×C412yes—
152C2×C11⋊C8C2×D412yes—
153C2×C11⋊C8C2×Q812yes—
154C2×C4×SD16—112no—
155C2×C4×SD16—111no—
156#2351—111no—
157#2349—111no—
158#1941—112no—
159#1863—112no—
160#1862—112no—
161#1846—111no—
162#1805—111no—
163#1804D1111yescharacteristic
164C8×C4⋊C4—111no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—42no—
169C23×C11—42no—
170C23×C11C22×D411yescharacteristic
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—22no—
174D4×C11C2×C4⋊C414yes—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—84no—
183C2×C4×C11C4×D412yes—
184C2×C4×C11C4×D412yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11H(5,𝔽2)11yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—88no—
205C2×Dic11#13514yes—
206Dic22—22no—
207Dic22—22no—
208Dic22—22no—
209Dic22C2×C4⋊C414yes—
210C8×C11—42no—
211C11⋊C8—22no—
212C11⋊C8C2×C4⋊C414yes—
213C22×SD16—111no—
214C2×C4×Q8—112no—
215C2×C4×Q8—111no—
216C2×C4×D4—112no—
217C2×C4×D4C2×D1111yescharacteristic
218C4×SD16—118no—
219C4×SD16—228no—
220C2×#107—112no—
221C2×#106—111no—
222C2×#106—112no—
223C2×C4⋊C8C2×D1111yescharacteristic
224C2×#103—111no—
225C2×#103—112no—
226C2×#102—111no—
227C2×#102C2×D1112yes—
228C2×C4×C8—111no—
229C2×C4×C8—112no—
230#389—112no—
231#389—112no—
232#389—222no—
233#385—222no—
234#382—111no—
235#382—221no—
236#382C2×D1111yescharacteristic
237#380—221no—
238C4×C4⋊C4—111no—
239C4×C4⋊C4—221no—
240C2×#95—221no—
241#340—112no—
242#340C2×D1112yes—
243#336—112no—
244C22×C11—24no—
245C22×C11—44no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—44no—
249C22×C11C2×C4×D411yescharacteristic
250C22×C11D4211yescharacteristic
251C22×C11D4×Q811yescharacteristic
252C22×C11C2×#13512yes—
253C22×C11#57712yes—
254C4×C11—22no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—82no—
258C4×C11C22×C4⋊C411yescharacteristic
259C4×C11#52011yescharacteristic
260C4×C11#54711yescharacteristic
261C4×C11#55411yescharacteristic
262Dic11—24no—
263Dic11—24no—
264Dic11—42no—
265Dic11—42no—
266Dic11—82no—
267C22×Q8—111no—
268C22×D4C22×D1111yescharacteristic
269C23×C4—21no—
270C23×C4—222no—
271C2×SD16—114no—
272C2×SD16—114no—
273C2×SD16—114no—
274C22×C8—111no—
275C22×C8—111no—
276C22×C8C22×D1112yes—
277C4×Q8—114no—
278C4×Q8—222no—
279C4×Q8—224no—
280C4×Q8—442no—
281C4×D4—22no—
282C4×D4—224no—
283C4×D4—442no—
284C4×D4C4×D1114yes—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—222no—
296C2×C42—112no—
297C2×C42—221no—
298C2×C42—222no—
299C2×C42C22×D1111yescharacteristic
300#107—442no—
301#106—114no—
302#106—224no—
303C4⋊C8—22no—
304#103—114no—
305#103—224no—
306#102—24no—
307#102—114no—
308C4×C8—114no—
309C4×C8—224no—
310#95—21no—
311#95—21no—
312#95—111no—
313#95—111no—
314#95—222no—
315#95—222no—
316#95—221no—
317#95—221no—
318C2×C11—44no—
319C2×C11D4×C4⋊C411yescharacteristic
320C2×C11C4×#13511yescharacteristic
321C2×C11#294911yescharacteristic
322C2×C11#328212yes—
323C2×C11#338112yes—
324C24—21no—
325C2×Q8—112no—
326C2×Q8—112no—
327C2×Q8—112no—
328C2×Q8—221no—
329C2×Q8—221no—
330C2×Q8—221no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4C2×C4×D1112yes—
335C2×D4D4×D1112yes—
336C2×D4Q8×D1112yes—
337C22×C4—21no—
338C22×C4—24no—
339C22×C4—22no—
340C22×C4—82no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4—444no—
347C22×C4—444no—
348C22×C4—882no—
349C22×C4D4×D1111yescharacteristic
350C22×C4D4×D1111yescharacteristic
351C22×C4C23×D1111yescharacteristic
352SD16—1116no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—112no—
357C2×C8—112no—
358C2×C8—112no—
359C2×C8—112no—
360C2×C8—221no—
361C2×C8—221no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—112no—
366C4⋊C4—224no—
367C4⋊C4—224no—
368C4⋊C4—221no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—444no—
372C4⋊C4—444no—
373C4⋊C4—882no—
374C4⋊C4C2×C4×D1112yes—
375C22⋊C4—24no—
376C22⋊C4—444no—
377C42—224no—
378C42—222no—
379C42—222no—
380C42—444no—
381C42C2×C4×D1112yes—
382C42#434112yes—
383C11#2268311yescharacteristic, complemented, Sylow
384C23—22no—
385C23—22no—
386C23—22no—
387C23—42no—
388C23—42no—
389C23C2×D4×D1111yescharacteristic
390Q8—114no—
391Q8—222no—
392Q8—222no—
393Q8—222no—
394D4—22no—
395D4—22no—
396D4—22no—
397D4C4⋊C4×D1114yes—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—84no—
406C2×C4—114no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—888no—
421C2×C4(C22⋊D11)⋊C412yes—
422C2×C4(C22⋊D11)⋊C412yes—
423C2×C4C22×C4×D1111yescharacteristic
424C2×C4C2×D4×D1111yescharacteristic
425C2×C4C2×#434111yescharacteristic
426C2×C4C2×Q8×D1111yescharacteristic
427C2×C4#6704211yescharacteristic
428C2×C4#6704311yescharacteristic
429C8—42no—
430C8—114no—
431C8—222no—
432C22—24no—
433C22—44no—
434C22—42no—
435C22—44no—
436C22—42no—
437C22C2×(C22⋊D11)⋊C411yescharacteristic
438C22#1062314011yescharacteristic
439C22#1062316311yescharacteristic
440C22D11×#13512yes—
441C22#1062330612yes—
442C4—22no—
443C4—22no—
444C4—42no—
445C4—82no—
446C4—224no—
447C4—224no—
448C4—442no—
449C4—442no—
450C4—882no—
451C4C2×C4⋊C4×D1111yescharacteristic
452C4#1062305411yescharacteristic
453C4#1062314211yescharacteristic
454C4#1062316611yescharacteristic
455C2—44no—
456C2#1307151211yescharacteristic
457C2#1307738411yescharacteristic
458C2#1307747811yescharacteristic
459C2#1308032912yes—
460C2#1308148612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#22683
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
3. #13071533C2semidirect
5. #13069343C2semidirect
6. #13068871C2semidirect
8. #13068778C2semidirect
9. #13068632C2semidirect
10. #13068481C2semidirect
25. C4×#4324C4semidirect
75. C4×Dic22C2×C4semidirect
89. #66874C2×C4semidirect
91. #66872C2×C4semidirect
93. C4×C11⋊C8C2×C4semidirect
134. #4324C4⋊C4semidirect
383. C11#22683semidirect

Maximal subgroups

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

subgroupindex
C2×#106223712
C2×C4×#43242
#130715332
#130715262
#130693432
#130688712
#130688612
#130687782
#130686322
#130684812
C11×#18042
#2268311