Finite Group Databasebeta

← #14907668

Subgroups — #14907668

Order 2816.

1132 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623279C211yesmaximal, characteristic, complemented
2#13081750C212yesmaximal, complemented
3#13070566C214yesmaximal, complemented
4#13070561C214yesmaximal, complemented
5#13070351C212yesmaximal, complemented
6C2×#10622191C211yesmaximal, characteristic, complemented
7C11×#3054C211yesmaximal, characteristic, complemented
8C22×#4339—21no—
9C2×C11×#135C2211yescharacteristic, complemented
10C22×C11×M16C2211yescharacteristic
11C11×#525—21no—
12#10623279—22no—
13#10623279—24no—
14#10623279C2214yes—
15C2×#66962—22no—
16C2×#66961—22no—
17C2×#66957—21no—
18C2×#66957C2212yes—
19C11×#470C2212yescomplemented
20C11×#469C2212yescomplemented
21C11×#468—22no—
22C11×#427C2211yescharacteristic, complemented
23C11×#416—21no—
24#10622808—22no—
25#10622807—24no—
26#10622806—22no—
27#10622792C2214yescomplemented
28#10622760C2214yescomplemented
29C2×#66876C2212yescomplemented
30#10622191C2214yescomplemented
31#10622126C2218yescomplemented
32C2×C11×#41—21no—
33C23×C4×C11D411yescharacteristic
34C22×C22⋊D11—41no—
35C2×#4339—22no—
36C2×#4339—24no—
37C2×#4339—22no—
38C2×#4339—24no—
39C2×#4339—42no—
40C2×#4339—41no—
41C2×#4339—42no—
42C2×#4339—41no—
43C22×D44—21no—
44C22×C4×D11—41no—
45C22×Dic22—21no—
46C11×#135—22no—
47C11×#135—22no—
48C2×C11×Q16C2311yescharacteristic, complemented
49C2×C11×SD16—21no—
50C2×C11×D8C2311yescharacteristic, complemented
51C2×C11×M16—22no—
52C2×C11×M16—22no—
53C2×C11×M16D412yes—
54C2×C11×M16C2312yes—
55C22×C8×C11D411yescharacteristic
56C22×C8×C11C2311yescharacteristic
57C11×#123—41no—
58C11×C22⋊Q8—22no—
59C11×#121—22no—
60C11×#120—41no—
61C4×D4×C11—42no—
62C11×#117—21no—
63#66962—28no—
64#66962—28no—
65#66961—28no—
66#66961—28no—
67C2×Dic44—21no—
68C2×Dic44D412yescomplemented
69#66957—24no—
70#66957—24no—
71#66957—22no—
72#66957—22no—
73#66957D414yescomplemented
74#66957C2314yes—
75C2×D88—21no—
76C2×D88D412yescomplemented
77C2×#4314—22no—
78C2×#4314—22no—
79C11×#107—21no—
80C11×#106C2312yescomplemented
81C11×#103—22no—
82C11×#102—22no—
83#66893—24no—
84#66892—24no—
85#66891—24no—
86#66890—24no—
87#66876—22no—
88#66876C2314yescomplemented
89C2×C11⋊C16—22no—
90#33530—111nomaximal, Sylow
91C24×C11D811yescharacteristic
92C23×D11—41no—
93C11×#41—41no—
94C11×#41—41no—
95C11×#41—41no—
96C11×#41—41no—
97C2×Q8×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—41no—
106C22×C4×C11D812yes—
107C22×C4×C11D811yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D411yescharacteristic
110C2×C22⋊D11—44no—
111C2×C22⋊D11—42no—
112C2×C22⋊D11—44no—
113C2×C22⋊D11—42no—
114C22×Dic11—41no—
115#4339—28no—
116#4339—24no—
117#4339—24no—
118#4339—44no—
119#4339—44no—
120#4339—44no—
121#4339—44no—
122#4339—44no—
123#4339—42no—
124#4339—42no—
125C2×D44—24no—
126C2×D44—22no—
127C2×D44—41no—
128C2×D44—42no—
129C2×C4×D11—42no—
130C2×C4×D11—44no—
131C2×C4×D11—44no—
132C2×C4×D11—42no—
133C2×Dic22—24no—
134C2×Dic22—22no—
135C2×Dic22—41no—
136C2×Dic22—42no—
137C11×Q16—22no—
138C11×SD16—42no—
139C11×D8—22no—
140C11×M16—24no—
141C11×M16—24no—
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11C2×D412yes—
145C2×C8×C11C2×D412yes—
146C2×C8×C11C2×D412yes—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—22no—
150C11×C4⋊C4—42no—
151C11×C22⋊C4—41no—
152C11×C22⋊C4—42no—
153C11×C22⋊C4—42no—
154C42×C11—41no—
155Dic44—24no—
156Dic44—22no—
157Dic44C2×D414yes—
158D88—24no—
159D88—22no—
160D88C2×D414yes—
161#4314—28no—
162#4314—24no—
163#4314—24no—
164C11⋊C16—24no—
165C2×#575—111no—
166#3414—112no—
167#3054D1111yescharacteristic, complemented
168#2191—114no—
169#2190—114no—
170#2145—112no—
171C2×#349—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—41no—
175C23×C11—81no—
176C23×C11C2×D812yes—
177C23×C11C2×D811yescharacteristic
178C22×D11—44no—
179C22×D11—42no—
180C22×D11—84no—
181Q8×C11—41no—
182Q8×C11—41no—
183D4×C11—41no—
184D4×C11—41no—
185D4×C11—84no—
186D4×C11—81no—
187D4×C11—81no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11C2×D812yes—
201C2×C4×C11C2×D811yescharacteristic
202C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—48no—
206C22⋊D11—44no—
207C22⋊D11—44no—
208C2×Dic11—44no—
209C2×Dic11—42no—
210D44—24no—
211D44—44no—
212D44—42no—
213C4×D11—48no—
214C4×D11—44no—
215C4×D11—44no—
216Dic22—24no—
217Dic22—44no—
218Dic22—42no—
219C8×C11—22no—
220C8×C11#12012yes—
221C8×C11C22×D412yes—
222C22×#41—221no—
223#575—114no—
224#575—224no—
225#575—222no—
226C2×#137—222no—
227C2×AGL(1,ℤ/8)—222no—
228C2×#135—112no—
229C2×#135—221no—
230C2×#135C2×D1111yescharacteristic, complemented
231C22×M16C2×D1111yescharacteristic
232#525—21no—
233#510—114no—
234#510—222no—
235#509—114no—
236#509—222no—
237#508—224no—
238C2×M32—112no—
239#470C2×D1112yescomplemented
240#469C2×D1112yescomplemented
241#468—22no—
242#427C2×D1111yescharacteristic, complemented
243#416—21no—
244#360—118no—
245#349—114no—
246C22×C11—22no—
247C22×C11—41no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—81no—
251C22×C11—82no—
252C22×C11—81no—
253C22×C11#44711yescharacteristic
254C22×C11#44711yescharacteristic
255C22×C11C22×D811yescharacteristic
256C2×D11—44no—
257C2×D11—84no—
258C2×D11—88no—
259C4×C11—22no—
260C4×C11—82no—
261C4×C11—81no—
262C4×C11#44711yescharacteristic
263C4×C11#44711yescharacteristic
264C4×C11C2×#12011yescharacteristic
265C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
266Dic11—44no—
267C2×#41—21no—
268C2×#41—222no—
269C2×#41—224no—
270C2×#41—224no—
271C2×#41—222no—
272C2×#41—441no—
273C2×#41—442no—
274C2×#41—442no—
275C2×#41—441no—
276C22×Q8—221no—
277C22×D4—221no—
278C22×D4—441no—
279C23×C4—441no—
280C23×C4C22⋊D1111yescharacteristic
281#137—228no—
282#137—228no—
283AGL(1,ℤ/8)—228no—
284AGL(1,ℤ/8)—228no—
285#135—22no—
286#135—22no—
287#135—114no—
288#135—114no—
289#135—224no—
290#135—222no—
291#135—222no—
292#135—224no—
293C2×Q16—112no—
294C2×Q16—221no—
295C2×Q16C22×D1111yescharacteristic, complemented
296C2×SD16—21no—
297C2×SD16—222no—
298C2×SD16—222no—
299C2×D8—112no—
300C2×D8—221no—
301C2×D8C22×D1111yescharacteristic, complemented
302C2×M16—22no—
303C2×M16—22no—
304C2×M16C22⋊D1112yes—
305C2×M16C22×D1112yes—
306C22×C8C22⋊D1111yescharacteristic
307C22×C8C22×D1111yescharacteristic
308#123—41no—
309C22⋊Q8—22no—
310#121—22no—
311#120—41no—
312C4×D4—42no—
313#117—21no—
314Q32—224no—
315SD32—224no—
316SD32—224no—
317D16—224no—
318M32—114no—
319M32—222no—
320C2×C16—222no—
321#107—21no—
322#106C22×D1112yescomplemented
323#103—22no—
324#102—22no—
325C2×C11—21no—
326C2×C11—21no—
327C2×C11—21no—
328C2×C11—42no—
329C2×C11—161no—
330C2×C11C2×#44711yescharacteristic
331D11—84no—
332C24—441no—
333C24#432311yescharacteristic
334#41—41no—
335#41—41no—
336#41—41no—
337#41—41no—
338#41—228no—
339#41—224no—
340#41—224no—
341#41—444no—
342#41—444no—
343#41—444no—
344#41—444no—
345#41—444no—
346#41—442no—
347#41—442no—
348C2×Q8—21no—
349C2×Q8—224no—
350C2×Q8—222no—
351C2×Q8—441no—
352C2×Q8—442no—
353C2×D4—21no—
354C2×D4—42no—
355C2×D4—41no—
356C2×D4—224no—
357C2×D4—222no—
358C2×D4—441no—
359C2×D4—442no—
360C2×D4—444no—
361C2×D4—442no—
362C2×D4—444no—
363C2×D4—442no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—442no—
370C22×C4—444no—
371C22×C4—444no—
372C22×C4—441no—
373C22×C4—442no—
374C22×C4#432312yes—
375C22×C4#432311yescharacteristic
376C22×C4C2×C22⋊D1112yes—
377C22×C4C2×C22⋊D1111yescharacteristic
378Q16—22no—
379Q16—114no—
380Q16—224no—
381Q16—222no—
382SD16—42no—
383SD16—228no—
384SD16—224no—
385SD16—224no—
386D8—22no—
387D8—114no—
388D8—224no—
389D8—222no—
390M16—24no—
391M16—24no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8D4×D1112yes—
395C2×C8D4×D1112yes—
396C2×C8C2×C22⋊D1112yes—
397C2×C8C2×C22⋊D1111yescharacteristic
398C2×C8C23×D1111yescharacteristic
399C4⋊C4—22no—
400C4⋊C4—42no—
401C22⋊C4—41no—
402C22⋊C4—42no—
403C22⋊C4—42no—
404C42—41no—
405C16—224no—
406C11#3353011yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—41no—
410C23—81no—
411C23—444no—
412C23—442no—
413C23—884no—
414C23C2×#432312yes—
415C23C2×#432311yescharacteristic
416Q8—41no—
417Q8—41no—
418Q8—224no—
419Q8—444no—
420Q8—442no—
421D4—41no—
422D4—41no—
423D4—84no—
424D4—81no—
425D4—81no—
426D4—224no—
427D4—444no—
428D4—448no—
429D4—444no—
430D4—444no—
431D4—442no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—448no—
443C2×C4—444no—
444C2×C4—442no—
445C2×C4—444no—
446C2×C4—444no—
447C2×C4C2×#432312yes—
448C2×C4C2×#432311yescharacteristic
449C2×C4#6699011yescharacteristic
450C2×C4#6699011yescharacteristic
451C2×C4#6700211yescharacteristic
452C2×C4#6700211yescharacteristic
453C2×C4C22×C22⋊D1111yescharacteristic
454C8—22no—
455C8#6699012yes—
456C8C2×D4×D1112yes—
457C22—22no—
458C22—41no—
459C22—42no—
460C22—42no—
461C22—81no—
462C22—82no—
463C22—81no—
464C22—444no—
465C22—884no—
466C22—888no—
467C22#1062264911yescharacteristic
468C22#1062264911yescharacteristic
469C22C22×#432311yescharacteristic
470C4—22no—
471C4—82no—
472C4—81no—
473C4—444no—
474C4#1062264911yescharacteristic
475C4#1062264911yescharacteristic
476C4C2×#6699011yescharacteristic
477C4C2×#6700211yescharacteristic
478C2—21no—
479C2—21no—
480C2—21no—
481C2—42no—
482C2—161no—
483C2—884no—
484C2C2×#1062264911yescharacteristic
subgroupG/H
centerC4#10622649
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3054C2
socleC2×C11C2×#447
hypercenter#3054D11
hypocenterC11#33530
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×M16 ◁ #3054

Complements

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

NH ≅ G/Ntype
1. C2×#10623279C2semidirect
2. #13081750C2semidirect
3. #13070566C2semidirect
4. #13070561C2semidirect
5. #13070351C2semidirect
6. C2×#10622191C2semidirect
7. C11×#3054C2semidirect
9. C2×C11×#135C22semidirect
19. C11×#470C22semidirect
20. C11×#469C22semidirect
22. C11×#427C22semidirect
27. #10622792C22semidirect
28. #10622760C22semidirect
29. C2×#66876C22semidirect
30. #10622191C22semidirect
31. #10622126C22semidirect
48. C2×C11×Q16C23semidirect
50. C2×C11×D8C23semidirect
68. C2×Dic44D4semidirect
73. #66957D4semidirect
76. C2×D88D4semidirect
80. C11×#106C23semidirect
88. #66876C23semidirect
167. #3054D11semidirect
230. C2×#135C2×D11semidirect
239. #470C2×D11semidirect
240. #469C2×D11semidirect
242. #427C2×D11semidirect
295. C2×Q16C22×D11semidirect
301. C2×D8C22×D11semidirect
322. #106C22×D11semidirect
406. C11#33530semidirect

Maximal subgroups

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

subgroupindex
C2×#106232792
#130817502
#130705662
#130705612
#130703512
C2×#106221912
C11×#30542
#3353011