Finite Group Databasebeta

← #14758364

Subgroups — #14758364

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×C4×#4313C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4#13069587C214yesmaximal, complemented
5#13069578C211yesmaximal, characteristic, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13068334C214yesmaximal
9C11×#1990C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13C22×#4313C2212yes—
14D11×C4⋊Q8—24no—
15D11×C4⋊Q8C418yescomplemented
16C2×#66945C2212yes—
17C2×C4⋊C4×D11—21no—
18C2×C4⋊C4×D11C2212yes—
19C2×#66941—21no—
20C2×#66941C2212yes—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C11×#384C2211yescharacteristic
25C2×#66879C2212yes—
26#10622600—21no—
27#10622600—21no—
28#10622590C2212yes—
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11—21no—
31#10622548C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33C4×#4313—24no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×Q8×D11—28no—
40C2×Q8×D11—44no—
41C2×Q8×D11—44no—
42C22×C4×D11—22no—
43C22×C4×D11D411yescharacteristic
44C22×C4×D11D411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×C8×C11C2312yes—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yes—
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
57#66997—28no—
58C2×(C2×D11)⋊C4—22no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2312yes—
63C2×C4⋊Dic11C2312yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C2×#4313—24no—
72C2×#4313—24no—
73C2×#4313Q818yescomplemented
74#66945—28no—
75C4⋊C4×D11—28no—
76C4⋊C4×D11—24no—
77C4⋊C4×D11C2×C418yes—
78#66941—28no—
79#66941—24no—
80#66941C2×C418yes—
81C42×D11C2×C414yes—
82C42×D11D414yes—
83#66922—22no—
84#66922C2×C414yes—
85C4×C8×C11—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66879—24no—
89C4×C11⋊C8—22no—
90#21324—111nomaximal, Sylow
91C23×D11C2×D411yescharacteristic
92C2×Q8×C11—24no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105Q8×D11—432no—
106C2×C4×D11—28no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—44no—
112C2×C4×D11—44no—
113C2×C4×D11C22⋊C414yes—
114C2×C4×D11C22⋊C414yes—
115C2×C4×D11C22×C412yes—
116C2×C4×D11C2×D412yes—
117C2×C4×D11C2×Q814yes—
118C2×C4×D11#4114yes—
119C2×Dic22—28no—
120C2×Dic22—24no—
121C2×Dic22—44no—
122C2×Dic22—44no—
123C2×Dic22—42no—
124C2×Dic22—42no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11C2×Q814yescomplemented
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—42no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4C22×C414yes—
134C42×C11C22×C412yes—
135C42×C11C2×D412yes—
136(C2×D11)⋊C4—44no—
137C4⋊Dic11—24no—
138C4⋊Dic11—22no—
139C4⋊Dic11—24no—
140C4⋊Dic11—42no—
141C4⋊Dic11—42no—
142C4⋊Dic11C22×C414yes—
143Dic11⋊C4—28no—
144Dic11⋊C4—28no—
145C4×Dic11—44no—
146C4×Dic11C22⋊C414yes—
147C4×Dic11C22⋊C414yes—
148C4×Dic11C22×C412yes—
149C4×Dic11C2×D412yes—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8C2×Q814yescomplemented
153#4313—216no—
154C22×C4⋊Q8—111no—
155C2×C4×M16—111no—
156#2285—111no—
157#1993—114no—
158#1990—111no—
159#1990—111no—
160#1990—111no—
161#1990D1111yescharacteristic, complemented
162#1736—114no—
163C23×C11C22×D411yescharacteristic
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11C2×C22⋊C412yes—
169C22×D11#12412yes—
170C22×D11C4⋊Q812yes—
171Q8×C11—48no—
172C2×C4×C11—24no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11C2×C22⋊C412yes—
179C2×C4×C11C2×C22⋊C412yes—
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11AGL(1,ℤ/8)12yes—
182C2×C4×C11#13712yes—
183C2×C4×C11#13712yes—
184C2×C4×C11C23×C411yescharacteristic
185C2×C4×C11C22×D411yescharacteristic
186C2×C4×C11C22×Q812yes—
187C2×C4×C11C2×#4112yes—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—24no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11C2×C22⋊C412yes—
199C2×Dic11C2×C22⋊C412yes—
200C2×Dic11C2×C22⋊C412yes—
201C2×Dic11#12412yes—
202C2×Dic11C4⋊Q812yes—
203C4×D11—28no—
204C4×D11—28no—
205C4×D11—416no—
206C4×D11C4×Q818yes—
207C4×D11C22⋊Q818yes—
208Dic22—416no—
209Dic22—48no—
210C8×C11—24no—
211C11⋊C8—24no—
212C23×Q8—221no—
213C22×M16—112no—
214C2×C4⋊Q8—118no—
215C2×C4⋊Q8—112no—
216C2×C4⋊Q8—111no—
217C2×C4⋊Q8—221no—
218C2×C4⋊Q8—224no—
219C2×C4⋊Q8—221no—
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×#117—112no—
222C22×C4⋊C4—112no—
223C22×C4⋊C4—221no—
224C22×C42—111no—
225C4×M16—224no—
226C2×#97—112no—
227C2×C4×C8—111no—
228C2×C4×C8C2×D1111yescharacteristic
229#384—111no—
230#384C2×D1111yescharacteristic
231#382—112no—
232#380—221no—
233#380—221no—
234C4×C4⋊C4—221no—
235C4×C4⋊C4—221no—
236#340—114no—
237#340—114no—
238#340—114no—
239#340C2×D1114yes—
240C22×C11C22×C22⋊C411yescharacteristic
241C22×C11C2×#12411yescharacteristic
242C22×C11C2×C4⋊Q811yescharacteristic
243C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C22×C11C2×#13711yescharacteristic
246C22×C11C2×#13711yescharacteristic
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—22no—
251C2×D11—22no—
252C2×D11—22no—
253C2×D11#39114yes—
254C4×C11—44no—
255C4×C11—82no—
256C4×C11#41814yes—
257C4×C11#41914yes—
258C4×C11C2×C4×Q812yes—
259C4×C11C2×C22⋊Q812yes—
260Dic11—22no—
261Dic11—22no—
262Dic11—44no—
263Dic11—82no—
264Dic11#39114yes—
265C22×Q8—21no—
266C22×Q8—222no—
267C22×Q8—228no—
268C22×Q8—221no—
269C22×Q8—444no—
270C22×Q8—444no—
271C23×C4—111no—
272C23×C4—111no—
273C23×C4—111no—
274C23×C4—222no—
275C2×M16—118no—
276C2×M16—224no—
277C2×M16—224no—
278C22×C8—112no—
279C22×C8C22×D1112yes—
280C4⋊Q8—22no—
281C4⋊Q8—118no—
282C4⋊Q8—114no—
283C4⋊Q8—228no—
284C4⋊Q8—224no—
285C4⋊Q8—228no—
286C4⋊Q8—222no—
287C4⋊Q8C4×D1114yes—
288#117—228no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—112no—
293C2×C4⋊C4—118no—
294C2×C4⋊C4—112no—
295C2×C4⋊C4—224no—
296C2×C4⋊C4—228no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4C22×D1112yes—
303C2×C4⋊C4C22×D1112yes—
304C2×C22⋊C4—222no—
305C2×C42—111no—
306C2×C42—111no—
307C2×C42—111no—
308C2×C42—114no—
309C2×C42—114no—
310C2×C42—222no—
311C2×C42C22×D1111yescharacteristic
312#97—224no—
313C4×C8—22no—
314C4×C8—222no—
315#95—222no—
316#95—222no—
317C2×C11C2×#39111yescharacteristic
318C2×C11C2×#41811yescharacteristic
319C2×C11C2×#41911yescharacteristic
320C2×C11#314111yescharacteristic
321C2×C11#314111yescharacteristic
322C2×C11#316511yescharacteristic
323C2×C11#316511yescharacteristic
324D11—24no—
325C24—111no—
326C2×Q8—24no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—228no—
330C2×Q8—224no—
331C2×Q8—444no—
332C2×Q8—444no—
333C2×Q8—4432no—
334C2×Q8—442no—
335C2×Q8—442no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—111no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—114no—
342C22×C4—114no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—114no—
346C22×C4—114no—
347C22×C4—228no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—444no—
355C22×C4—444no—
356C22×C4D4×D1111yescharacteristic
357C22×C4D4×D1111yescharacteristic
358C22×C4C23×D1111yescharacteristic
359M16—2216no—
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—114no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8Q8×D1114yescomplemented
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—24no—
369C4⋊C4—42no—
370C4⋊C4—42no—
371C4⋊C4—114no—
372C4⋊C4—228no—
373C4⋊C4—228no—
374C4⋊C4—224no—
375C4⋊C4—222no—
376C4⋊C4—224no—
377C4⋊C4—442no—
378C4⋊C4—442no—
379C4⋊C4C2×C4×D1114yes—
380C22⋊C4—444no—
381C42—114no—
382C42—114no—
383C42—112no—
384C42—112no—
385C42—444no—
386C42C2×C4×D1112yes—
387C42D4×D1112yes—
388C11#2132411yescharacteristic, complemented, Sylow
389C23—112no—
390C23—112no—
391C23—112no—
392C23—221no—
393C23—221no—
394C23—221no—
395C23—221no—
396C23C2×D4×D1111yescharacteristic
397Q8—48no—
398Q8—4416no—
399Q8—448no—
400C2×C4—24no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—112no—
407C2×C4—112no—
408C2×C4—112no—
409C2×C4—118no—
410C2×C4—118no—
411C2×C4—112no—
412C2×C4—112no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—221no—
417C2×C4—228no—
418C2×C4—228no—
419C2×C4—224no—
420C2×C4—4416no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4C22⋊C4×D1112yes—
427C2×C4C22⋊C4×D1112yes—
428C2×C4#6696412yes—
429C2×C4#6696712yes—
430C2×C4#6696812yes—
431C2×C4#6697112yes—
432C2×C4C22×C4×D1111yescharacteristic
433C2×C4C2×D4×D1111yescharacteristic
434C2×C4C2×Q8×D1112yes—
435C2×C4#41×D1112yes—
436C8—24no—
437C8—224no—
438C22—114no—
439C22—222no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—222no—
444C22—222no—
445C22C2×C22⋊C4×D1111yescharacteristic
446C22D11×#12411yescharacteristic
447C22D11×C4⋊Q811yescharacteristic
448C22C2×#6696411yescharacteristic
449C22C2×#6696711yescharacteristic
450C22C2×#6696811yescharacteristic
451C22C2×#6697111yescharacteristic
452C4—44no—
453C4—82no—
454C4—114no—
455C4—222no—
456C4—222no—
457C4—444no—
458C4—882no—
459C4#1062238314yes—
460C4#1062241514yes—
461C4C4×Q8×D1112yes—
462C4D11×C22⋊Q812yes—
463C2—224no—
464C2D11×#39111yescharacteristic
465C2C2×#1062238311yescharacteristic
466C2C2×#1062241511yescharacteristic
467C2#1307900611yescharacteristic
468C2#1307901111yescharacteristic
469C2#1307915711yescharacteristic
470C2#1307915911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#21324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13069587C2semidirect
5. #13069578C2semidirect
6. #13069577C2semidirect
7. #13069576C2semidirect
9. C11×#1990C2semidirect
15. D11×C4⋊Q8C4semidirect
73. C2×#4313Q8semidirect
127. C2×C8×C11C2×Q8semidirect
152. C2×C11⋊C8C2×Q8semidirect
161. #1990D11semidirect
365. C2×C8Q8×D11semidirect
388. C11#21324semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×C4×#43132
#130710212
#130695872
#130695782
#130695772
#130695762
#130683342
C11×#19902
#2132411