Finite Group Databasebeta

← #14726749

Subgroups — #14726749

Order 2816.

1282 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic
2C2×#10622580C212yesmaximal, complemented
3#13067618C214yesmaximal, complemented
4#13067601C214yesmaximal, complemented
5#13067183C212yesmaximal, complemented
6#13066934C211yesmaximal, characteristic, complemented
7C11×#2486C211yesmaximal, characteristic, complemented
8C2×#67037—21no—
9C2×C11×#123—21no—
10C2×C4×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic, complemented
12C2×#66983—21no—
13C2×#66983C2212yes—
14#10623086—22no—
15#10623085—24no—
16D4×D44—22no—
17#10623041C2212yes—
18#10623024—21no—
19#10623024C2212yes—
20#10623008—21no—
21C11×#398C2212yescomplemented
22C11×#397C2212yescomplemented
23C11×#389—21no—
24C11×#381—21no—
25C11×#380—21no—
26C11×#380C2211yescharacteristic, complemented
27C2×C22⋊(C11⋊C8)C2212yescomplemented
28#10622580—24no—
29#10622580C2218yescomplemented
30C2×#66873—22no—
31C2×#66871—22no—
32#10622166C2212yescomplemented
33#10622163C2212yescomplemented
34#10622089C2218yescomplemented
35C22×D4×C11D411yescharacteristic
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C22×C22⋊D11—22no—
41#67037—44no—
42#67037—44no—
43C2×#4341—24no—
44C2×D4×D11—24no—
45C2×#4339—22no—
46C22×D44—21no—
47C22×D44D412yes—
48C11×#123—44no—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—22no—
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4D411yescharacteristic
61C2×C11×C22⋊C4C2311yescharacteristic
62C2×C42×C11D411yescharacteristic
63#66983—22no—
64#66983—22no—
65#66983—22no—
66#66983—22no—
67#66983—22no—
68#66983—22no—
69#66983D414yes—
70#66983C2314yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D412yes—
75C22×C11⋊C8—22no—
76#66950—24no—
77#66948—24no—
78#66939—24no—
79#66939—24no—
80#66935—24no—
81#66935—24no—
82#66928—22no—
83#66927—21no—
84C4×D44—22no—
85C4×D44—22no—
86#66922—21no—
87C11×#95—22no—
88C11×#95—22no—
89C11×#95C2312yes—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)C2314yes—
92#66873—28no—
93#66871—28no—
94#18202—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C24×C11C2×D411yescharacteristic
97C23×D11—22no—
98C23×D11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—22no—
101C2×D4×C11D814yes—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—24no—
119C2×C22⋊D11—24no—
120C2×C22⋊D11—24no—
121C2×C22⋊D11—44no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—44no—
124C2×C22⋊D11—44no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127#4341—416no—
128D4×D11—416no—
129#4339—44no—
130#4339—44no—
131C2×D44—22no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44—44no—
136C2×D44—82no—
137C2×D44C2×D414yes—
138C2×C4×D11—24no—
139C2×Dic22—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—44no—
146C11×C22⋊C4—22no—
147C11×C22⋊C4—22no—
148C11×C22⋊C4—42no—
149C11×C22⋊C4—44no—
150C42×C11—21no—
151C42×C11—21no—
152(C2×D11)⋊C4—24no—
153(C2×D11)⋊C4—24no—
154(C2×D11)⋊C4—24no—
155(C2×D11)⋊C4—24no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11C2×D414yes—
160C2×C11⋊C8—24no—
161C2×C11⋊C8—44no—
162#3496—111no—
163C2×#480—112no—
164#2486D1111yescharacteristic, complemented
165#1610—114no—
166#1607—114no—
167#1519—112no—
168#1459—111no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11#12012yes—
176C23×C11C2×D812yes—
177C23×C11C2×D812yes—
178C23×C11AGL(1,ℤ/8)12yes—
179C23×C11C22×D411yescharacteristic
180C22×D11—24no—
181C22×D11—44no—
182C22×D11—44no—
183C22×D11—82no—
184C22×D11—82no—
185C22×D11—82no—
186C22×D11—82no—
187D4×C11—28no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—24no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—81no—
206C2×C4×C11—84no—
207C2×C4×C11#12011yescharacteristic
208C2×C4×C11#12011yescharacteristic
209C2×C4×C11C2×D812yes—
210C2×C4×C11C22×D412yes—
211C22⋊D11—48no—
212C22⋊D11—44no—
213C22⋊D11—44no—
214C22⋊D11—48no—
215C2×Dic11—24no—
216C2×Dic11—44no—
217C2×Dic11—44no—
218D44—44no—
219D44—44no—
220D44—44no—
221D44—82no—
222D44—82no—
223C4×D11—48no—
224Dic22—44no—
225C11⋊C8—44no—
226C2×H(5,𝔽2)—221no—
227#547—222no—
228#546—224no—
229D42—222no—
230#537—112no—
231#534—112no—
232#534—221no—
233#532—221no—
234C2×#123—21no—
235C2×#121—112no—
236C2×#121—221no—
237C2×C4×D4C2×D1111yescharacteristic
238C22×C4⋊C4C2×D1111yescharacteristic, complemented
239#480—118no—
240#480—224no—
241C2×#107—222no—
242C2×#102—222no—
243C2×C22⋊C8—112no—
244#398C2×D1112yescomplemented
245#397C2×D1112yescomplemented
246#389—21no—
247#381—21no—
248#380—21no—
249#380C2×D1111yescharacteristic, complemented
250#327—118no—
251#324—112no—
252#323—112no—
253C22×C11—21no—
254C22×C11—22no—
255C22×C11—21no—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—81no—
264C22×C11#44714yes—
265C22×C11C2×#12011yescharacteristic
266C22×C11C22×D811yescharacteristic
267C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
268C2×D11—44no—
269C2×D11—44no—
270C2×D11—44no—
271C2×D11—164no—
272C2×D11—164no—
273C4×C11—22no—
274C4×C11—21no—
275C4×C11—22no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11—82no—
279C4×C11—82no—
280C4×C11#45812yes—
281Dic11—44no—
282H(5,𝔽2)—444no—
283H(5,𝔽2)—444no—
284C2×#41—224no—
285C2×#41—222no—
286C22×D4—112no—
287C22×D4—221no—
288C22×D4—224no—
289C22×D4—222no—
290C22×D4—222no—
291C22×D4C22⋊D1111yescharacteristic
292C23×C4—21no—
293C23×C4C22⋊D1111yescharacteristic
294C23×C4C22×D1111yescharacteristic
295C22×C8—222no—
296C4⋊Q8—221no—
297#127—221no—
298#124—222no—
299#123—44no—
300#123—224no—
301#123—224no—
302C22⋊Q8—224no—
303#121—114no—
304#121—114no—
305#121—224no—
306#121—222no—
307#121—222no—
308#121—222no—
309#121—222no—
310#121—222no—
311#121—222no—
312#120—224no—
313#120—224no—
314C4×D4—22no—
315C4×D4—22no—
316C4×D4—222no—
317C4×D4—222no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4C22×D1112yes—
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C22⋊C4—22no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4C22⋊D1111yescharacteristic
332C2×C22⋊C4C22×D1111yescharacteristic
333C2×C42C22⋊D1111yescharacteristic
334#107—228no—
335#102—228no—
336C22⋊C8—114no—
337C22⋊C8—222no—
338#95—22no—
339#95—22no—
340#95C22×D1112yes—
341C2×C11—21no—
342C2×C11—24no—
343C2×C11—21no—
344C2×C11—42no—
345C2×C11C2×#44711yescharacteristic
346C2×C11#302211yescharacteristic
347C2×C11C2×#45811yescharacteristic
348D11—84no—
349C24—222no—
350C24—222no—
351C24C2×C22⋊D1111yescharacteristic
352C24C2×C22⋊D1111yescharacteristic
353#41—444no—
354#41—4416no—
355#41—444no—
356C2×Q8—222no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—114no—
360C2×D4—222no—
361C2×D4—222no—
362C2×D4—222no—
363C2×D4—224no—
364C2×D4—224no—
365C2×D4—224no—
366C2×D4—222no—
367C2×D4—444no—
368C2×D4—4416no—
369C2×D4—444no—
370C2×D4—444no—
371C2×D4—444no—
372C2×D4—444no—
373C2×D4—882no—
374C2×D4#432314yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—224no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4D4×D1112yes—
388C22×C4D4×D1112yes—
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C23×D1111yescharacteristic
394C2×C8—224no—
395C2×C8—444no—
396C4⋊C4—22no—
397C4⋊C4—24no—
398C4⋊C4—42no—
399C4⋊C4—44no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—114no—
403C4⋊C4—222no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C22⋊C4—22no—
407C22⋊C4—22no—
408C22⋊C4—42no—
409C22⋊C4—44no—
410C22⋊C4—224no—
411C22⋊C4—224no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C42—21no—
415C42—21no—
416C11#1820211yescharacteristic, complemented, Sylow
417C23—21no—
418C23—21no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—224no—
424C23—444no—
425C23—444no—
426C23—882no—
427C23—882no—
428C23—882no—
429C23—882no—
430C23C2×#432312yes—
431C23C2×#432312yes—
432C23#6699012yes—
433C23#6700212yes—
434C23C22×C22⋊D1111yescharacteristic
435Q8—444no—
436D4—28no—
437D4—444no—
438D4—444no—
439D4—448no—
440D4—444no—
441D4—444no—
442D4—448no—
443D4—444no—
444D4—882no—
445D4—882no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—42no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—81no—
464C2×C4—84no—
465C2×C4—224no—
466C2×C4—448no—
467C2×C4—444no—
468C2×C4—444no—
469C2×C4C2×#432312yes—
470C2×C4#6699011yescharacteristic
471C2×C4#6699011yescharacteristic
472C2×C4C2×D4×D1112yes—
473C8—444no—
474C22—21no—
475C22—22no—
476C22—21no—
477C22—22no—
478C22—22no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—41no—
483C22—41no—
484C22—81no—
485C22—444no—
486C22—444no—
487C22—444no—
488C22—1764no—
489C22—1764no—
490C22#1062264914yes—
491C22C22×#432311yescharacteristic
492C22C2×#6699011yescharacteristic
493C22C2×#6700211yescharacteristic
494C4—22no—
495C4—22no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—82no—
500C4—82no—
501C4—444no—
502C4#1062266612yes—
503C2—21no—
504C2—21no—
505C2—24no—
506C2—42no—
507C2—884no—
508C2C2×#1062264911yescharacteristic
509C2#1307799411yescharacteristic
510C2C2×#1062266611yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2486C2
socleC22×C11C2×#120
prime radical#13082380C2
hypercenter#2486D11
hypocenterC11#18202
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2486

Complements

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

NH ≅ G/Ntype
2. C2×#10622580C2semidirect
3. #13067618C2semidirect
4. #13067601C2semidirect
5. #13067183C2semidirect
6. #13066934C2semidirect
7. C11×#2486C2semidirect
11. C22×C11×C4⋊C4C22semidirect
21. C11×#398C22semidirect
22. C11×#397C22semidirect
26. C11×#380C22semidirect
27. C2×C22⋊(C11⋊C8)C22semidirect
29. #10622580C22semidirect
32. #10622166C22semidirect
33. #10622163C22semidirect
34. #10622089C22semidirect
164. #2486D11semidirect
238. C22×C4⋊C4C2×D11semidirect
244. #398C2×D11semidirect
245. #397C2×D11semidirect
249. #380C2×D11semidirect
416. C11#18202semidirect

Maximal subgroups

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

subgroupindex
#130823802
C2×#106225802
#130676182
#130676012
#130671832
#130669342
C11×#24862
#1820211