Finite Group Databasebeta

← #14764323

Subgroups — #14764323

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622332C211yesmaximal, characteristic
2#13071018C211yesmaximal, characteristic
3C2×#10622590C211yesmaximal, characteristic
4#13069387C212yesmaximal, complemented
5#13069385C212yesmaximal, complemented
6#13068809C211yesmaximal, characteristic
7#13068806C211yesmaximal, characteristic
8#13068803C211yesmaximal, characteristic
9#13068781C212yesmaximal, complemented
10#13068748C212yesmaximal, complemented
11C11×#1853C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C2×#66930—21no—
16C2×C11×#106C2212yes—
17C2×C11×C22⋊C8C2211yescharacteristic
18C11×#380C2211yescharacteristic
19#10622825C2211yescharacteristic
20C2×C11⋊#95—21no—
21C2×C11⋊#95—21no—
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×#66882C2212yes—
24C2×#66879C2212yes—
25C2×Dic11⋊C8C2212yes—
26#10622590—21no—
27#10622590—21no—
28#10622590C2212yes—
29#10622590C2212yes—
30#10622589C2211yescharacteristic
31#10622589C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34C2×#66872C2212yes—
35C2×#66871C2212yes—
36#10622555—21no—
37#10622332C418yescomplemented
38#10622263—21no—
39#10622262—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11D411yescharacteristic
48C23×Dic11D411yescharacteristic
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—42no—
59C2×C4⋊Dic11C2312yes—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2311yescharacteristic
62C2×Dic11⋊C4—21no—
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11C2×C414yes—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11Q814yes—
72C2×C4×Dic11C2311yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C22×C11⋊C8C2312yes—
75#66930—44no—
76C11×#106—42no—
77C11×C22⋊C8C2×C414yes—
78C11×#95—21no—
79C11⋊#95—21no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C22⋊(C11⋊C8)C2×C414yes—
87#66882—42no—
88#66879C2×C418yescomplemented
89Dic11⋊C8C2×C418yescomplemented
90#66872—42no—
91#66871—42no—
92#21986—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11C22×C412yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×Q812yes—
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—42no—
114C22×Dic11—42no—
115C22×Dic11—42no—
116C22×Dic11C4⋊C414yes—
117C22×Dic11C4⋊C414yes—
118C22×Dic11C2×D411yescharacteristic
119C22×Dic11C2×D411yescharacteristic
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11C22×C414yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C22⋊C4—42no—
131C22⋊Dic11—42no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—42no—
137Dic11⋊C4—42no—
138Dic11⋊C4—42no—
139Dic11⋊C4—42no—
140Dic11⋊C4—42no—
141C4×Dic11—42no—
142C4×Dic11—42no—
143C4×Dic11C4⋊C414yes—
144C4×Dic11C4⋊C414yes—
145C4×Dic11C22×C412yes—
146C4×Dic11C22×C412yes—
147C4×Dic11C2×Q812yes—
148C4×Dic11C2×Q812yes—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C22×C414yes—
152C2×#432—111no—
153#2285—111no—
154C2×#382—111no—
155#1949—112no—
156#1949—112no—
157#1853—111no—
158#1853D1111yescharacteristic
159#1852—111no—
160#1852—111no—
161#1847—112no—
162#1836—112no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11C2×C4⋊C412yes—
168C23×C11AGL(1,ℤ/8)12yes—
169C23×C11#13712yes—
170C23×C11C22×D411yescharacteristic
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—84no—
185C2×C4×C11C2×C4⋊C412yes—
186C2×C4×C11C23×C411yescharacteristic
187C2×C4×C11C22×Q811yescharacteristic
188C2×C4×C11H(5,𝔽2)12yes—
189C2×C4×C112−1+412yes—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—21no—
198C2×Dic11—28no—
199C2×Dic11—44no—
200C2×Dic11—42no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—84no—
210C2×Dic11C2×C4⋊C412yes—
211C2×Dic11C2×C4⋊C412yes—
212C2×Dic11C2×C4⋊C412yes—
213C2×Dic11C2×C4⋊C412yes—
214C8×C11—24no—
215C11⋊C8—24no—
216C2×#117—221no—
217C22×C4⋊C4—111no—
218C22×C4⋊C4C2×D1111yescharacteristic
219C22×C42—111no—
220#432—118no—
221C2×#107—112no—
222C2×#107—112no—
223C2×#106—112no—
224C2×#106C2×D1112yes—
225C2×C4⋊C8—112no—
226C2×C22⋊C8—111no—
227C2×C22⋊C8C2×D1111yescharacteristic
228C2×#97—112no—
229#384—111no—
230#384—111no—
231#382—112no—
232#382—112no—
233#382—221no—
234#382—221no—
235#382—221no—
236#380—111no—
237#380—221no—
238#380C2×D1111yescharacteristic
239C4×C4⋊C4—111no—
240C4×C4⋊C4—111no—
241C4×C4⋊C4—221no—
242C2×#95—221no—
243C2×#95—221no—
244#340—112no—
245#340—112no—
246#340—112no—
247#340C2×D1112yes—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11#42814yes—
255C22×C11C22×C4⋊C411yescharacteristic
256C22×C11#53511yescharacteristic
257C22×C11#53611yescharacteristic
258C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C11C2×#13711yescharacteristic
260C22×C11#57511yescharacteristic
261C22×C11#57511yescharacteristic
262C4×C11—22no—
263C4×C11—81no—
264C4×C11—82no—
265C4×C11—81no—
266C4×C11#52012yes—
267C4×C11#54412yes—
268Dic11—22no—
269Dic11—22no—
270Dic11—22no—
271Dic11—22no—
272Dic11—81no—
273Dic11—82no—
274Dic11—81no—
275C23×C4—21no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—221no—
279C23×C4C22×D1111yescharacteristic
280C22×C8—112no—
281C22×C8C22×D1112yes—
282#117—444no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—112no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—442no—
294C2×C4⋊C4C22×D1112yes—
295C2×C4⋊C4C22×D1111yescharacteristic
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C22⋊C4—21no—
298C2×C22⋊C4—221no—
299C2×C42—114no—
300C2×C42—111no—
301C2×C42—111no—
302C2×C42—114no—
303C2×C42—111no—
304C2×C42—111no—
305C2×C42—221no—
306C2×C42—221no—
307#107—442no—
308#107—442no—
309#106—42no—
310#106—442no—
311C4⋊C8—118no—
312C22⋊C8—114no—
313C22⋊C8C4×D1114yes—
314#97—118no—
315#95—21no—
316#95—222no—
317#95—222no—
318#95—222no—
319#95—222no—
320#95—221no—
321#95—221no—
322#95—221no—
323C2×C11—24no—
324C2×C11#231711yescharacteristic
325C2×C11C2×#42811yescharacteristic
326C2×C11#291111yescharacteristic
327C2×C11#321311yescharacteristic
328C2×C11#321511yescharacteristic
329C2×C11#323411yescharacteristic
330C2×C11#323611yescharacteristic
331C24D4×D1111yescharacteristic
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—114no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—111no—
345C22×C4—114no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4—442no—
356C22×C4C2×C4×D1112yes—
357C22×C4D4×D1111yescharacteristic
358C22×C4Q8×D1112yes—
359C22×C4C23×D1111yescharacteristic
360C2×C8—22no—
361C2×C8—22no—
362C2×C8—114no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8C2×C4×D1114yes—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—42no—
371C4⋊C4—222no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—442no—
376C4⋊C4—442no—
377C4⋊C4—442no—
378C4⋊C4—442no—
379C4⋊C4—442no—
380C22⋊C4—42no—
381C22⋊C4—442no—
382C42—114no—
383C42—114no—
384C42—112no—
385C42—112no—
386C42—112no—
387C42—112no—
388C42—442no—
389C42—442no—
390C11#2198611yescharacteristic, complemented, Sylow
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23C4⋊C4×D1112yes—
396C23#6696712yes—
397C23#6696812yes—
398C23C2×D4×D1111yescharacteristic
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—84no—
413C2×C4—112no—
414C2×C4—112no—
415C2×C4—112no—
416C2×C4—112no—
417C2×C4—228no—
418C2×C4—221no—
419C2×C4—221no—
420C2×C4—221no—
421C2×C4—221no—
422C2×C4—221no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—221no—
426C2×C4—444no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—442no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—884no—
437C2×C4C4⋊C4×D1112yes—
438C2×C4C22×C4×D1111yescharacteristic
439C2×C4#6703712yes—
440C2×C4C2×Q8×D1111yescharacteristic
441C2×C4#6704312yes—
442C8—24no—
443C8—224no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22#1062247414yes—
451C22C2×C4⋊C4×D1111yescharacteristic
452C22#1062312311yescharacteristic
453C22#1062317911yescharacteristic
454C22C2×#6696711yescharacteristic
455C22C2×#6696811yescharacteristic
456C22#1062330411yescharacteristic
457C22#1062330811yescharacteristic
458C4—22no—
459C4—81no—
460C4—82no—
461C4—81no—
462C4—222no—
463C4—222no—
464C4—222no—
465C4—222no—
466C4—882no—
467C4—881no—
468C4—881no—
469C4#1062307712yes—
470C4#1062315412yes—
471C2—24no—
472C2#1307123511yescharacteristic
473C2C2×#1062247411yescharacteristic
474C2#1307720311yescharacteristic
475C2#1307960211yescharacteristic
476C2#1307961611yescharacteristic
477C2#1307980511yescharacteristic
478C2#1307981911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1853C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1853D11
hypocenterC11#21986
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #13069387C2semidirect
5. #13069385C2semidirect
9. #13068781C2semidirect
10. #13068748C2semidirect
37. #10622332C4semidirect
88. #66879C2×C4semidirect
89. Dic11⋊C8C2×C4semidirect
390. C11#21986semidirect

Maximal subgroups

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

subgroupindex
C2×#106223322
#130710182
C2×#106225902
#130693872
#130693852
#130688092
#130688062
#130688032
#130687812
#130687482
C11×#18532
#2198611